pg-i symbolic logic by lewis carroll pg-ii pg-iii pg-iv a syllogism worked out. that story of yours, about your once meeting the sea-serpent, always sets me off yawning; i never yawn, unless when i'm listening to something totally devoid of interest. the premisses, separately. ·---------------· ·---------------· |( ) | ( )| | | | | ·---|---· | | ·---|---· | | | (#) | | | | |( )| | |---|---|---|---| |---|---|---|---| | | | | | | | |( )| | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· the premisses, combined. ·---------------· |( ) | ( )| | ·---|---· | | |(#)|( )| | |---|---|---|---| | | |( )| | | ·---|---· | | | | ·---------------· the conclusion. ·-------· |(#)|( )| |---|---| | | | ·-------· that story of yours, about your once meeting the sea-serpent, is totally devoid of interest. pg-v symbolic logic _part i_ elementary by lewis carroll second thousand fourth edition _price two shillings_ london macmillan and co., limited new york: the macmillan company _all rights reserved_ pg-vi richard clay and sons, limited, london and bungay pg-vii advertisement. an envelope, containing two blank diagrams (biliteral and triliteral) and counters ( red and grey), may be had, from messrs. macmillan, for _d._, by post _d._ * * * * * i shall be grateful to any reader of this book who will point out any mistakes or misprints he may happen to notice in it, or any passage which he thinks is not clearly expressed. * * * * * i have a quantity of ms. in hand for parts ii and iii, and hope to be able----should life, and health, and opportunity, be granted to me, to publish them in the course of the next few years. their contents will be as follows:-- _part ii. advanced._ further investigations in the subjects of part i. propositions of other forms (such as "not-all x are y"). triliteral and multiliteral propositions (such as "all abc are de"). hypotheticals. dilemmas. &c. &c. _part iii. transcendental._ analysis of a proposition into its elements. numerical and geometrical problems. the theory of inference. the construction of problems. and many other _curiosa logica_. pg-viii preface to the fourth edition. the chief alterations, since the first edition, have been made in the chapter on 'classification' (pp. , ) and the book on 'propositions' (pp. to ). the chief additions have been the questions on words and phrases, added to the examination-papers at p. , and the notes inserted at pp. , . in book i, chapter ii, i have adopted a new definition of 'classification', which enables me to regard the whole universe as a 'class,' and thus to dispense with the very awkward phrase 'a set of things.' in the chapter on 'propositions of existence' i have adopted a new 'normal form,' in which the class, whose existence is affirmed or denied, is regarded as the _predicate_, instead of the _subject_, of the proposition, thus evading a very subtle difficulty which besets the other form. these subtle difficulties seem to lie at the root of every tree of knowledge, and they are _far_ more hopeless to grapple with than any that occur in its higher branches. for example, the difficulties of the forty-seventh proposition of euclid are mere child's play compared with the mental torture endured in the effort to think out the essential nature of a straight line. and, in the present work, the difficulties of the " liars" problem, at p. , are "trifles, light as air," compared with the bewildering question "what is a thing?" in the chapter on 'propositions of relation' i have inserted a new section, containing the proof that a proposition, beginning with "all," is a _double_ proposition (a fact that is quite independent of the arbitrary rule, laid down in the next section, that such a proposition is to be understood as implying the actual _existence_ of its subject). this proof was given, in the earlier editions, incidentally, in the course of the discussion of the biliteral diagram: but its _proper_ place, in this treatise, is where i have now introduced it. pg-ix in the sorites-examples, i have made a good many verbal alterations, in order to evade a difficulty, which i fear will have perplexed some of the readers of the first three editions. some of the premisses were so worded that their terms were not specieses of the univ. named in the dictionary, but of a larger class, of which the univ. was only a portion. in all such cases, it was intended that the reader should perceive that what was asserted of the larger class was thereby asserted of the univ., and should ignore, as superfluous, all that it asserted of its _other_ portion. thus, in ex. , the univ. was stated to be "ducks in this village," and the third premiss was "mrs. bond has no gray ducks," i.e. "no gray ducks are ducks belonging to mrs. bond." here the terms are _not_ specieses of the univ., but of the larger class "ducks," of which the univ. is only a portion: and it was intended that the reader should perceive that what is here asserted of "ducks" is thereby asserted of "ducks in this village." and should treat this premiss as if it were "mrs. bond has no gray ducks in this village," and should ignore, as superfluous, what it asserts as to the _other_ portion of the class "ducks," viz. "mrs. bond has no gray ducks _out of_ this village". in the appendix i have given a new version of the problem of the "five liars." my object, in doing so, is to escape the subtle and mysterious difficulties which beset all attempts at regarding a proposition as being its own subject, or a set of propositions as being subjects for one another. it is certainly, a most bewildering and unsatisfactory theory: one cannot help feeling that there is a great lack of _substance_ in all this shadowy host----that, as the procession of phantoms glides before us, there is not _one_ that we can pounce upon, and say "_here_ is a proposition that _must_ be either true or false!"----that it is but a barmecide feast, to which we have been bidden----and that its prototype is to be found in that mythical island, whose inhabitants "earned a precarious living by taking in each others' washing"! by simply translating "telling truths" into "taking _both_ of condiments (salt and mustard)," "telling lies" into "taking _neither_ of them" and "telling a truth and a lie (order not specified)" into "taking only _one_ condiment (it is not specified _which_)," i have escaped all those metaphysical puzzles, and have produced a problem which, when translated into a set of symbolized premisses, furnishes the very same _data_ as were furnished by the problem of the "five liars." pg-x the coined words, introduced in previous editions, such as "eliminands" and "retinends", perhaps hardly need any apology: they were indispensable to my system: but the new plural, here used for the first time, viz. "soriteses", will, i fear, be condemned as "bad english", unless i say a word in its defence. we have _three_ singular nouns, in english, of plural _form_, "series", "species", and "sorites": in all three, the awkwardness, of using the same word for both singular and plural, must often have been felt: this has been remedied, in the case of "series" by coining the plural "serieses", which has already found its way into the dictionaries: so i am no rash innovator, but am merely "following suit", in using the new plural "soriteses". in conclusion, let me point out that even those, who are obliged to study _formal_ logic, with a view to being able to answer examination-papers in that subject, will find the study of _symbolic_ logic most helpful for this purpose, in throwing light upon many of the obscurities with which formal logic abounds, and in furnishing a delightfully easy method of _testing_ the results arrived at by the cumbrous processes which formal logic enforces upon its votaries. this is, i believe, the very first attempt (with the exception of my own little book, _the game of logic_, published in , a very incomplete performance) that has been made to _popularise_ this fascinating subject. it has cost me _years_ of hard work: but if it should prove, as i hope it may, to be of _real_ service to the young, and to be taken up, in high schools and in private families, as a valuable addition to their stock of healthful mental recreations, such a result would more than repay ten times the labour that i have expended on it. l. c. , bedford street, strand. _christmas, ._ pg-xi introduction. _to learners._ [n.b. some remarks, addressed to _teachers_, will be found in the appendix, at p. .] the learner, who wishes to try the question _fairly_, whether this little book does, or does not, supply the materials for a most interesting mental recreation, is _earnestly_ advised to adopt the following rules:-- ( ) begin at the _beginning_, and do not allow yourself to gratify a mere idle curiosity by dipping into the book, here and there. this would very likely lead to your throwing it aside, with the remark "this is _much_ too hard for me!", and thus losing the chance of adding a very _large_ item to your stock of mental delights. this rule (of not _dipping_) is very _desirable_ with _other_ kinds of books----such as novels, for instance, where you may easily spoil much of the enjoyment you would otherwise get from the story, by dipping into it further on, so that what the author meant to be a pleasant surprise comes to you as a matter of course. some people, i know, make a practice of looking into vol. iii first, just to see how the story ends: and perhaps it _is_ as well just to know that all ends _happily_----that the much-persecuted lovers _do_ marry after all, that he is proved to be quite innocent of the murder, that the wicked cousin is completely foiled in his plot and gets the punishment he deserves, and that the rich uncle in india (_qu._ why in _india_? _ans._ because, somehow, uncles never _can_ get rich anywhere else) dies at exactly the right moment----before taking the trouble to read vol. i. this, i say, is _just_ permissible with a _novel_, where vol. iii has a _meaning_, even for those who have not read the earlier part of the story; but, with a _scientific_ book, it is sheer insanity: you will find the latter part _hopelessly_ unintelligible, if you read it before reaching it in regular course. pg-xii ( ) don't begin any fresh chapter, or section, until you are certain that you _thoroughly_ understand the whole book _up to that point_, and that you have worked, correctly, most if not all of the examples which have been set. so long as you are conscious that all the land you have passed through is absolutely _conquered_, and that you are leaving no unsolved difficulties _behind_ you, which will be sure to turn up again later on, your triumphal progress will be easy and delightful. otherwise, you will find your state of puzzlement get worse and worse as you proceed, till you give up the whole thing in utter disgust. ( ) when you come to any passage you don't understand, _read it again_: if you _still_ don't understand it, _read it again_: if you fail, even after _three_ readings, very likely your brain is getting a little tired. in that case, put the book away, and take to other occupations, and next day, when you come to it fresh, you will very likely find that it is _quite_ easy. ( ) if possible, find some genial friend, who will read the book along with you, and will talk over the difficulties with you. _talking_ is a wonderful smoother-over of difficulties. when _i_ come upon anything----in logic or in any other hard subject----that entirely puzzles me, i find it a capital plan to talk it over, _aloud_, even when i am all alone. one can explain things so _clearly_ to one's self! and then, you know, one is so _patient_ with one's self: one _never_ gets irritated at one's own stupidity! if, dear reader, you will faithfully observe these rules, and so give my little book a really _fair_ trial, i promise you, most confidently, that you will find symbolic logic to be one of the most, if not _the_ most, fascinating of mental recreations! in this first part, i have carefully avoided all difficulties which seemed to me to be beyond the grasp of an intelligent child of (say) twelve or fourteen years of age. i have myself taught most of its contents, _vivâ voce_, to _many_ children, and have found them take a real intelligent interest in the subject. for those, who succeed in mastering part i, and who begin, like oliver, "asking for more," i hope to provide, in part ii, some _tolerably_ hard nuts to crack----nuts that will require all the nut-crackers they happen to possess! pg-xiii mental recreation is a thing that we all of us need for our mental health; and you may get much healthy enjoyment, no doubt, from games, such as back-gammon, chess, and the new game "halma". but, after all, when you have made yourself a first-rate player at any one of these games, you have nothing real to _show_ for it, as a _result!_ you enjoyed the game, and the victory, no doubt, _at the time_: but you have no _result_ that you can treasure up and get real _good_ out of. and, all the while, you have been leaving unexplored a perfect _mine_ of wealth. once master the machinery of symbolic logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real _use_ to you in _any_ subject you may take up. it will give you clearness of thought----the ability to _see your way_ through a puzzle----the habit of arranging your ideas in an orderly and get-at-able form----and, more valuable than all, the power to detect _fallacies_, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating art. _try it._ that is all i ask of you! l. c. , bedford street, strand. _february , ._ pg-xiv pg-xv contents. =book i.= =things and their attributes.= chapter i. _introductory._ page '=things=' '=attributes=' " '=adjuncts=' " chapter ii. _classification._ '=classification=' ½ '=class=' " '=peculiar=' attributes " '=genus=' " '=species=' " '=differentia=' " '=real=' and '=unreal=', or '=imaginary=', classes '=individual=' " a class regarded as a single thing ½ pg-xvi chapter iii. _division._ § . _introductory._ '=division=' '=codivisional=' classes " § . _dichotomy._ '=dichotomy=' ½ arbitrary limits of classes " subdivision of classes chapter iv. _names._ '=name=' ½ '=real=' and '=unreal=' names " three ways of expressing a name " two senses in which a plural name may be used chapter v. _definitions._ '=definition=' examples worked as models " pg-xvii =book ii.= =propositions.= chapter i. _propositions generally._ § . _introductory._ technical meaning of "some" '=proposition=' " '=normal form=' of a proposition " '=subject=', '=predicate=', and '=terms=' § . _normal form of a proposition._ its four parts:-- ( ) '=sign of quantity=' ( ) name of subject " ( ) '=copula=' " ( ) name of predicate " § . _various kinds of propositions._ three kinds of propositions:-- ( ) begins with "some". called a '=particular=' proposition: also a proposition '=in i=' ( ) begins with "no". called a '=universal negative=' proposition: also a proposition '=in e=' " ( ) begins with "all". called a '=universal affirmative=' proposition: also a proposition '=in a=' " pg-xviii a proposition, whose subject is an individual, is to be regarded as universal " two kinds of propositions, 'propositions of existence', and 'propositions of relation' " chapter ii. _propositions of existence._ '=proposition of existence =' chapter iii. _propositions of relation._ § . _introductory._ '=proposition of relation=' '=universe of discourse=,' or '=univ.=' " § . _reduction of a proposition of relation to normal form._ rules examples worked " § . _a proposition of relation, beginning with "all", is a double proposition._ its equivalence to _two_ propositions pg-xix § . _what is implied, in a proposition of relation, as to the reality of its terms?_ propositions beginning with "some" " " "no" " " " "all" " § . _translation of a proposition of relation into one or more propositions of existence._ rules examples worked " =book iii.= =the biliteral diagram.= chapter i. _symbols and cells._ the diagram assigned to a certain set of things, viz. our univ. univ. divided into 'the x-class' and 'the x'-class' the north and south halves assigned to these two classes " the x-class subdivided into 'the xy-class' and 'the xy'-class' " the north-west and north-east cells assigned to these two classes " the x'-class similarly divided " the south-west and south-east cells similarly assigned " the west and east halves have thus been assigned to 'the y-class' and 'the y'-class' =table i.= attributes of classes, and compartments, or cells, assigned to them pg-xx chapter ii. _counters._ meaning of a red counter placed in a cell " " " " on a partition " american phrase "=sitting on the fence=" " meaning of a grey counter placed in a cell " chapter iii. _representation of propositions._ § . _introductory._ the word "things" to be henceforwards omitted '=uniliteral=' proposition " '=biliteral=' do. " proposition '=in terms of=' certain letters " § . _representation of propositions of existence._ the proposition "some x exist" three other similar propositions " the proposition "no x exist" " three other similar propositions the proposition "some xy exist" " three other similar propositions " the proposition "no xy exist" " three other similar propositions " the proposition "no x exist" is _double_, and is equivalent to the two propositions "no xy exist" and "no xy' exist" pg-xxi § . _representation of propositions of relations._ the proposition "some x are y" " three other similar propositions " the proposition "some y are x" three other similar propositions " trio of equivalent propositions, viz. "some xy exist" = "some x are y" = "some y are x" " '=converse=' propositions, and '=conversion=' " three other similar trios the proposition "no x are y" " three other similar propositions " the proposition "no y are x" " three other similar propositions " trio of equivalent propositions, viz. "no xy exist" = "no x are y" = "no y are x" three other similar trios " the proposition "all x are y" is _double_, and is equivalent to the two propositions "some x are y" and "no x are _y'_" " seven other similar propositions =tables ii, iii.= representation of propositions of existence and relation , chapter iv. _interpretation of biliteral diagram, when marked with counters._ ·-------· |(.)| | interpretation of |---|---| | | | ·-------· and of three other similar arrangements " pg-xxii ·-------· |( )| | interpretation of |---|---| " | | | ·-------· and of three other similar arrangements " ·-------· | (.) | interpretation of |---|---| | | | ·-------· and of three other similar arrangements " ·-------· |(.)|(.)| interpretation of |---|---| " | | | ·-------· and of three other similar arrangements " ·-------· |( )|( )| interpretation of |---|---| " | | | ·-------· and of three other similar arrangements " ·-------· |(.)|( )| interpretation of |---|---| " | | | ·-------· and of seven other similar arrangements =book iv.= =the triliteral diagram.= chapter i. _symbols and cells._ change of biliteral into triliteral diagram the xy-class subdivided into 'the xym-class' and 'the xym'-class' pg-xxiii the inner and outer cells of the north-west quarter assigned to these classes " the xy'-class, the x'y-class, and the x'y'-class similarly subdivided " the inner and outer cells of the north-east, the south-west, and the south-east quarter similarly assigned " the inner square and the outer border have thus been assigned to 'the m-class' and 'the _m'_-class' " rules for finding readily the compartment, or cell, assigned to any given attribute or attributes " =table iv.= attributes of classes, and compartments, or cells, assigned to them chapter ii. _representation of propositions in terms of x and m, or of y and m._ § . _representation of propositions of existence in terms of x and m, or of y and m._ the proposition "some xm exist" seven other similar propositions " the proposition "no xm exist" seven other similar propositions " § . _representation of propositions of relation in terms of x and m, or of y and m._ the pair of converse propositions "some x are m" = "some m are x" " seven other similar pairs " the pair of converse propositions "no x are m" = "no m are x" " seven other similar pairs " the proposition "all x are m" fifteen other similar propositions " =tables v, vi, vii, viii.= representations of propositions in terms of x and m, or of y and m to pg-xxiv chapter iii. _representation of two propositions of relation, one in terms of x and m, and the other in terms of y and m, on the same diagram._ the digits "i" and "o" to be used instead of red and grey counters rules " examples worked " chapter iv. _interpretation, in terms of x and y, of triliteral diagram, when marked with counters or digits._ rules examples worked =book v.= =syllogisms.= chapter i. _introductory._ '=syllogism=' '=premisses=' " '=conclusion=' " '=eliminands=' '=retinends=' " '=consequent=' " the symbol ".'." " specimen-syllogisms " pg-xxv chapter ii. _problems in syllogisms._ § . _introductory._ '=concrete=' and '=abstract=' propositions method of translating a proposition from concrete into abstract form " two forms of problems " § . _given a pair of propositions of relation, which contain between them a pair of codivisional classes, and which are proposed as premisses: to ascertain what conclusion, if any, is consequent from them._ rules examples worked fully " the same worked briefly, as models § . _given a trio of propositions of relation, of which every two contain a pair of codivisional classes, and which are proposed as a syllogism: to ascertain whether the proposed conclusion is consequent from the proposed premisses, and, if so, whether it is complete._ rules examples worked briefly, as models " pg-xxvi =book vi.= =the method of subscripts.= chapter i. _introductory._ meaning of x_{ }, xy_{ }, &c. '=entity=' " meaning of x_{ }, xy_{ }, &c. " '=nullity=' " the symbols "+" and "¶" " '=like=' and '=unlike=' signs " chapter ii. _representation of propositions of relation._ the pair of converse propositions "some x are y" = "some y are x" three other similar pairs " the pair of converse propositions "no x are y" = "no y are x" " three other similar pairs " the proposition "all x are y" the proposition "all x are y" is _double_, and is equivalent to the two propositions "some x exist" and "no x and y'" " seven other similar propositions " rule for translating "all x are y" from abstract into subscript form, and _vice versâ_ " pg-xxvii chapter iii. _syllogisms._ § . _representation of syllogisms._ rules § . _formulæ for syllogisms._ three formulæ worked out:-- fig. i. xm_{ } + ym'_{ } ¶ xy_{ } its two variants (a) and (b) " fig. ii. xm_{ } + ym_{ } ¶ x'y_{ } fig. iii. xm_{ } + ym_{ } + m_{ } ¶ x'y'_{ } =table ix.= formulæ and rules examples worked briefly, as models " § . _fallacies._ '=fallacy=' method of finding forms of fallacies forms best stated in _words_ " three forms of fallacies:-- ( ) fallacy of like eliminands not asserted to exist " ( ) fallacy of unlike eliminands with an entity-premiss ( ) fallacy of two entity-premisses " § . _method of proceeding with a given pair of propositions._ rules pg-xxviii =book vii.= =soriteses.= chapter i. _introductory._ '=sorites=' '=premisses=' " '=partial conclusion=' " '=complete conclusion=' (or '=conclusion=') " '=eliminands=' " '=retinends=' " '=consequent=' " the symbol ".'." " specimen-soriteses chapter ii. _problems in soriteses._ § . _introductory._ form of problem two methods of solution " § . _solution by method of separate syllogisms._ rules example worked " pg-xxix § . _solution by method of underscoring._ '=underscoring=' subscripts to be omitted " example worked fully example worked briefly, as model seventeen examination-papers =book viii.= =examples, with answers and solutions.= chapter i. _examples._ § . _propositions of relation, to be reduced to normal form_ § . _pairs of abstract propositions, one in terms of x and m, and the other in terms of y and m, to be represented on the same triliteral diagram_ § . _marked triliteral diagrams, to be interpreted in terms of x and y_ § . _pairs of abstract propositions, proposed as premisses: conclusions to be found_ pg-xxx § . _pairs of concrete propositions, proposed as premisses: conclusions to be found_ § . _trios of abstract propositions, proposed as syllogisms: to be examined_ § . _trios of concrete propositions, proposed as syllogisms: to be examined_ § . _sets of abstract propositions, proposed as premisses for soriteses: conclusions to be found_ § . _sets of concrete propositions, proposed as premisses for soriteses: conclusions to be found_ chapter ii. _answers._ answers to § § §§ , § § § §§ , pg-xxxi chapter iii. _solutions._ § . _propositions of relation reduced to normal form._ solutions for § § . _method of diagrams._ solutions for § nos. to § " to § " to § " to § . _method of subscripts._ solutions for § § nos. to §§ , , , to =notes= =appendix, addressed to teachers= =notes to appendix= =index.= § . tables § . words &c. explained " pg-xxxii pg book i. things and their attributes. chapter i. _introductory._ the universe contains '=things=.' [for example, "i," "london," "roses," "redness," "old english books," "the letter which i received yesterday."] things have '=attributes=.' [for example, "large," "red," "old," "which i received yesterday."] one thing may have many attributes; and one attribute may belong to many things. [thus, the thing "a rose" may have the attributes "red," "scented," "full-blown," &c.; and the attribute "red" may belong to the things "a rose," "a brick," "a ribbon," &c.] any attribute, or any set of attributes, may be called an '=adjunct=.' [this word is introduced in order to avoid the constant repetition of the phrase "attribute or set of attributes." thus, we may say that a rose has the attribute "red" (or the adjunct "red," whichever we prefer); or we may say that it has the adjunct "red, scented and full-blown."] pg ½ chapter ii. _classification._ 'classification,' or the formation of classes, is a mental process, in which we imagine that we have put together, in a group, certain things. such a group is called a '=class=.' this process may be performed in three different ways, as follows:-- ( ) we may imagine that we have put together all things. the class so formed (i.e. the class "things") contains the whole universe. ( ) we may think of the class "things," and may imagine that we have picked out from it all the things which possess a certain adjunct _not_ possessed by the whole class. this adjunct is said to be '=peculiar=' to the class so formed. in this case, the class "things" is called a '=genus=' with regard to the class so formed: the class, so formed, is called a '=species=' of the class "things": and its peculiar adjunct is called its '=differentia='. pg as this process is entirely _mental_, we can perform it whether there _is_, or _is not_, an _existing_ thing which possesses that adjunct. if there _is_, the class is said to be '=real='; if not, it is said to be '=unreal=', or '=imaginary=.' [for example, we may imagine that we have picked out, from the class "things," all the things which possess the adjunct "material, artificial, consisting of houses and streets"; and we may thus form the real class "towns." here we may regard "things" as a _genus_, "towns" as a _species_ of things, and "material, artificial, consisting of houses and streets" as its _differentia_. again, we may imagine that we have picked out all the things which possess the adjunct "weighing a ton, easily lifted by a baby"; and we may thus form the _imaginary_ class "things that weigh a ton and are easily lifted by a baby."] ( ) we may think of a certain class, _not_ the class "things," and may imagine that we have picked out from it all the members of it which possess a certain adjunct _not_ possessed by the whole class. this adjunct is said to be '=peculiar=' to the smaller class so formed. in this case, the class thought of is called a '=genus=' with regard to the smaller class picked out from it: the smaller class is called a '=species=' of the larger: and its peculiar adjunct is called its '=differentia='. [for example, we may think of the class "towns," and imagine that we have picked out from it all the towns which possess the attribute "lit with gas"; and we may thus form the real class "towns lit with gas." here we may regard "towns" as a _genus_, "towns lit with gas" as a _species_ of towns, and "lit with gas" as its _differentia_. if, in the above example, we were to alter "lit with gas" into "paved with gold," we should get the _imaginary_ class "towns paved with gold."] a class, containing only _one_ member is called an '=individual=.' [for example, the class "towns having four million inhabitants," which class contains only _one_ member, viz. "london."] pg ½ hence, any single thing, which we can name so as to distinguish it from all other things, may be regarded as a one-member class. [thus "london" may be regarded as the one-member class, picked out from the class "towns," which has, as its differentia, "having four million inhabitants."] a class, containing two or more members, is sometimes regarded as _one single thing_. when so regarded, it may possess an adjunct which is _not_ possessed by any member of it taken separately. [thus, the class "the soldiers of the tenth regiment," when regarded as _one single thing_, may possess the attribute "formed in square," which is _not_ possessed by any member of it taken separately.] pg chapter iii. _division._ § . _introductory._ 'division' is a mental process, in which we think of a certain class of things, and imagine that we have divided it into two or more smaller classes. [thus, we might think of the class "books," and imagine that we had divided it into the two smaller classes "bound books" and "unbound books," or into the three classes, "books priced at less than a shilling," "shilling-books," "books priced at more than a shilling," or into the twenty-six classes, "books whose names begin with _a_," "books whose names begin with _b_," &c.] a class, that has been obtained by a certain division, is said to be 'codivisional' with every class obtained by that division. [thus, the class "bound books" is codivisional with each of the two classes, "bound books" and "unbound books." similarly, the battle of waterloo may be said to have been "contemporary" with every event that happened in .] hence a class, obtained by division, is codivisional with itself. [thus, the class "bound books" is codivisional with itself. similarly, the battle of waterloo may be said to have been "contemporary" with itself.] pg ½ § . _dichotomy._ if we think of a certain class, and imagine that we have picked out from it a certain smaller class, it is evident that the _remainder_ of the large class does _not_ possess the differentia of that smaller class. hence it may be regarded as _another_ smaller class, whose differentia may be formed, from that of the class first picked out, by prefixing the word "not"; and we may imagine that we have _divided_ the class first thought of into _two_ smaller classes, whose differentiæ are _contradictory_. this kind of division is called '=dichotomy='. [for example, we may divide "books" into the two classes whose differentiæ are "old" and "not-old."] in performing this process, we may sometimes find that the attributes we have chosen are used so loosely, in ordinary conversation, that it is not easy to decide _which_ of the things belong to the one class and _which_ to the other. in such a case, it would be necessary to lay down some arbitrary _rule_, as to _where_ the one class should end and the other begin. [thus, in dividing "books" into "old" and "not-old," we may say "let all books printed before a.d. , be regarded as 'old,' and all others as 'not-old'."] henceforwards let it be understood that, if a class of things be divided into two classes, whose differentiæ have contrary meanings, each differentia is to be regarded as equivalent to the other with the word "not" prefixed. [thus, if "books" be divided into "old" and "new" the attribute "old" is to be regarded as equivalent to "not-new," and the attribute "new" as equivalent to "not-old."] pg after dividing a class, by the process of _dichotomy_, into two smaller classes, we may sub-divide each of these into two still smaller classes; and this process may be repeated over and over again, the number of classes being doubled at each repetition. [for example, we may divide "books" into "old" and "new" (i.e. "_not_-old"): we may then sub-divide each of these into "english" and "foreign" (i.e. "_not_-english"), thus getting _four_ classes, viz. ( ) old english; ( ) old foreign; ( ) new english; ( ) new foreign. if we had begun by dividing into "english" and "foreign," and had then sub-divided into "old" and "new," the four classes would have been ( ) english old; ( ) english new; ( ) foreign old; ( ) foreign new. the reader will easily see that these are the very same four classes which we had before.] pg ½ chapter iv. _names._ the word "thing", which conveys the idea of a thing, _without_ any idea of an adjunct, represents _any_ single thing. any other word (or phrase), which conveys the idea of a thing, _with_ the idea of an adjunct represents _any_ thing which possesses that adjunct; i.e., it represents any member of the class to which that adjunct is _peculiar_. such a word (or phrase) is called a '=name='; and, if there be an existing thing which it represents, it is said to be a name of that thing. [for example, the words "thing," "treasure," "town," and the phrases "valuable thing," "material artificial thing consisting of houses and streets," "town lit with gas," "town paved with gold," "old english book."] just as a class is said to be _real_, or _unreal_, according as there _is_, or _is not_, an existing thing in it, so also a name is said to be _real_, or _unreal_, according as there _is_, or _is not_, an existing thing represented by it. [thus, "town lit with gas" is a _real_ name: "town paved with gold" is an _unreal_ name.] every name is either a substantive only, or else a phrase consisting of a substantive and one or more adjectives (or phrases used as adjectives). every name, except "thing", may usually be expressed in three different forms:-- (_a_) the substantive "thing", and one or more adjectives (or phrases used as adjectives) conveying the ideas of the attributes; pg (_b_) a substantive, conveying the idea of a thing with the ideas of _some_ of the attributes, and one or more adjectives (or phrases used as adjectives) conveying the ideas of the _other_ attributes; (_c_) a substantive conveying the idea of a thing with the ideas of _all_ the attributes. [thus, the phrase "material living thing, belonging to the animal kingdom, having two hands and two feet" is a name expressed in form (_a_). if we choose to roll up together the substantive "thing" and the adjectives "material, living, belonging to the animal kingdom," so as to make the new substantive "animal," we get the phrase "animal having two hands and two feet," which is a name (representing the same thing as before) expressed in form (_b_). and, if we choose to roll up the whole phrase into one word, so as to make the new substantive "man," we get a name (still representing the very same thing) expressed in form (_c_).] a name, whose substantive is in the _plural_ number, may be used to represent either ( ) members of a class, _regarded as separate things_; or ( ) a whole class, _regarded as one single thing_. [thus, when i say "some soldiers of the tenth regiment are tall," or "the soldiers of the tenth regiment are brave," i am using the name "soldiers of the tenth regiment" in the _first_ sense; and it is just the same as if i were to point to each of them _separately_, and to say "_this_ soldier of the tenth regiment is tall," "_that_ soldier of the tenth regiment is tall," and so on. but, when i say "the soldiers of the tenth regiment are formed in square," i am using the phrase in the _second_ sense; and it is just the same as if i were to say "the _tenth regiment_ is formed in square."] pg chapter v. _definitions._ it is evident that every member of a _species_ is _also_ a member of the _genus_ out of which that species has been picked, and that it possesses the _differentia_ of that species. hence it may be represented by a name consisting of two parts, one being a name representing any member of the _genus_, and the other being the _differentia_ of that species. such a name is called a '=definition=' of any member of that species, and to give it such a name is to '=define=' it. [thus, we may define a "treasure" as a "valuable thing." in this case we regard "things" as the _genus_, and "valuable" as the _differentia_.] the following examples, of this process, may be taken as models for working others. [note that, in each definition, the substantive, representing a member (or members) of the _genus_, is printed in capitals.] . define "a treasure." _ans._ "a valuable thing." . define "treasures." _ans._ "valuable things." . define "a town." _ans._ "a material artificial thing, consisting of houses and streets." pg . define "men." _ans._ "material, living things, belonging to the animal kingdom, having two hands and two feet"; or else "animals having two hands and two feet." . define "london." _ans._ "the material artificial thing, which consists of houses and streets, and has four million inhabitants"; or else "the town which has four million inhabitants." [note that we here use the article "the" instead of "a", because we happen to know that there is only _one_ such thing. the reader can set himself any number of examples of this process, by simply choosing the name of any common thing (such as "house," "tree," "knife"), making a definition for it, and then testing his answer by referring to any english dictionary.] pg book ii. propositions. chapter i. _propositions generally._ § . _introductory._ note that the word "some" is to be regarded, henceforward, as meaning "one or more." the word 'proposition,' as used in ordinary conversation, may be applied to _any_ word, or phrase, which conveys any information whatever. [thus the words "yes" and "no" are propositions in the ordinary sense of the word; and so are the phrases "you owe me five farthings" and "i don't!" such words as "oh!" or "never!", and such phrases as "fetch me that book!" "which book do you mean?" do not seem, at first sight, to convey any _information_; but they can easily be turned into equivalent forms which do so, viz. "i am surprised," "i will never consent to it," "i order you to fetch me that book," "i want to know which book you mean."] but a '=proposition=,' as used in this first part of "symbolic logic," has a peculiar form, which may be called its '=normal form='; and if any proposition, which we wish to use in an argument, is not in normal form, we must reduce it to such a form, before we can use it. pg a '=proposition=,' when in normal form, asserts, as to certain two classes, which are called its '=subject=' and '=predicate=,' either ( ) that _some_ members of its subject are members of its predicate; or ( ) that _no_ members of its subject are members of its predicate; or ( ) that _all_ members of its subject are members of its predicate. the subject and the predicate of a proposition are called its '=terms=.' two propositions, which convey the _same_ information, are said to be '=equivalent='. [thus, the two propositions, "i see john" and "john is seen by me," are equivalent.] § . _normal form of a proposition._ a proposition, in normal form, consists of four parts, viz.-- ( ) the word "some," or "no," or "all." (this word, which tells us _how many_ members of the subject are also members of the predicate, is called the '=sign of quantity=.') ( ) name of subject. ( ) the verb "are" (or "is"). (this is called the '=copula=.') ( ) name of predicate. pg § . _various kinds of propositions._ a proposition, that begins with "some", is said to be '=particular=.' it is also called 'a proposition =in i=.' [note, that it is called 'particular,' because it refers to a _part_ only of the subject.] a proposition, that begins with "no", is said to be '=universal negative=.' it is also called 'a proposition =in e=.' a proposition, that begins with "all", is said to be '=universal affirmative=.' it is also called 'a proposition =in a=.' [note, that they are called 'universal', because they refer to the _whole_ of the subject.] a proposition, whose subject is an _individual_, is to be regarded as _universal_. [let us take, as an example, the proposition "john is not well". this of course implies that there is an _individual_, to whom the speaker refers when he mentions "john", and whom the listener _knows_ to be referred to. hence the class "men referred to by the speaker when he mentions 'john'" is a one-member class, and the proposition is equivalent to "_all_ the men, who are referred to by the speaker when he mentions 'john', are not well."] propositions are of two kinds, 'propositions of existence' and 'propositions of relation.' these shall be discussed separately. pg chapter ii. _propositions of existence._ a '=proposition of existence=', when in normal form, has, for its _subject_, the class "existing things". its sign of quantity is "some" or "no". [note that, though its sign of quantity tells us _how many_ existing things are members of its predicate, it does _not_ tell us the _exact_ number: in fact, it only deals with _two_ numbers, which are, in ascending order, " " and " or more."] it is called "a proposition of existence" because its effect is to assert the _reality_ (i.e. the real _existence_), or else the _imaginariness_, of its predicate. [thus, the proposition "some existing things are honest men" asserts that the class "honest men" is _real_. this is the _normal_ form; but it may also be expressed in any one of the following forms:-- ( ) "honest men exist"; ( ) "some honest men exist"; ( ) "the class 'honest men' exists"; ( ) "there are honest men"; ( ) "there are some honest men". similarly, the proposition "no existing things are men fifty feet high" asserts that the class "men feet high" is _imaginary_. this is the _normal_ form; but it may also be expressed in any one of the following forms:-- ( ) "men feet high do not exist"; ( ) "no men feet high exist"; ( ) "the class 'men feet high' does not exist"; ( ) "there are not any men feet high"; ( ) "there are no men feet high."] pg chapter iii. _propositions of relation._ § . _introductory._ a =proposition of relation=, of the kind to be here discussed, has, for its terms, two specieses of the same genus, such that each of the two names conveys the idea of some attribute _not_ conveyed by the other. [thus, the proposition "some merchants are misers" is of the right kind, since "merchants" and "misers" are specieses of the same genus "men"; and since the name "merchants" conveys the idea of the attribute "mercantile", and the name "misers" the idea of the attribute "miserly", each of which ideas is _not_ conveyed by the other name. but the proposition "some dogs are setters" is _not_ of the right kind, since, although it is true that "dogs" and "setters" are specieses of the same genus "animals", it is _not_ true that the name "dogs" conveys the idea of any attribute not conveyed by the name "setters". such propositions will be discussed in part ii.] the genus, of which the two terms are specieses, is called the '=universe of discourse=,' or (more briefly) the '=univ.=' the sign of quantity is "some" or "no" or "all". [note that, though its sign of quantity tells us _how many_ members of its subject are _also_ members of its predicate, it does not tell us the _exact_ number: in fact, it only deals with _three_ numbers, which are, in ascending order, " ", " or more", "the total number of members of the subject".] it is called "a proposition of relation" because its effect is to assert that a certain _relationship_ exists between its terms. pg § . _reduction of a proposition of relation to normal form._ the rules, for doing this, are as follows:-- ( ) ascertain what is the _subject_ (i.e., ascertain what class we are _talking about_); ( ) if the verb, governed by the subject, is _not_ the verb "are" (or "is"), substitute for it a phrase beginning with "are" (or "is"); ( ) ascertain what is the _predicate_ (i.e., ascertain what class it is, which is asserted to contain _some_, or _none_, or _all_, of the members of the subject); ( ) if the name of each term is _completely expressed_ (i.e. if it contains a substantive), there is no need to determine the 'univ.'; but, if either name is _incompletely expressed_, and contains _attributes_ only, it is then necessary to determine a 'univ.', in order to insert its name as the substantive. ( ) ascertain the _sign of quantity_; ( ) arrange in the following order:-- sign of quantity, subject, copula, predicate. [let us work a few examples, to illustrate these rules. ( ) "some apples are not ripe." ( ) the subject is "apples." ( ) the verb is "are." ( ) the predicate is "not-ripe * * *." (as no substantive is expressed, and we have not yet settled what the univ. is to be, we are forced to leave a blank.) ( ) let univ. be "fruit." ( ) the sign of quantity is "some." ( ) the proposition now becomes "some | apples | are | not-ripe fruit." pg ( ) "none of my speculations have brought me as much as per cent." ( ) the subject is "my speculations." ( ) the verb is "have brought," for which we substitute the phrase "are * * * that have brought". ( ) the predicate is "* * * that have brought &c." ( ) let univ. be "transactions." ( ) the sign of quantity is "none of." ( ) the proposition now becomes "none of | my speculations | are | transactions that have brought me as much as per cent." ( ) "none but the brave deserve the fair." to begin with, we note that the phrase "none but the brave" is equivalent to "no _not_-brave." ( ) the subject has for its _attribute_ "not-brave." but no _substantive_ is supplied. so we express the subject as "not-brave * * *." ( ) the verb is "deserve," for which we substitute the phrase "are deserving of". ( ) the predicate is "* * * deserving of the fair." ( ) let univ. be "persons." ( ) the sign of quantity is "no." ( ) the proposition now becomes "no | not-brave persons | are | persons deserving of the fair." ( ) "a lame puppy would not say "thank you" if you offered to lend it a skipping-rope." ( ) the subject is evidently "lame puppies," and all the rest of the sentence must somehow be packed into the predicate. ( ) the verb is "would not say," &c., for which we may substitute the phrase "are not grateful for." ( ) the predicate may be expressed as "* * * not grateful for the loan of a skipping-rope." ( ) let univ. be "puppies." ( ) the sign of quantity is "all." ( ) the proposition now becomes "all | lame puppies | are | puppies not grateful for the loan of a skipping-rope." pg ( ) "no one takes in the _times_, unless he is well-educated." ( ) the subject is evidently persons who are not well-educated ("no _one_" evidently means "no _person_"). ( ) the verb is "takes in," for which we may substitute the phrase "are persons taking in." ( ) the predicate is "persons taking in the _times_." ( ) let univ. be "persons." ( ) the sign of quantity is "no." ( ) the proposition now becomes "no | persons who are not well-educated | are | persons taking in the _times_." ( ) "my carriage will meet you at the station." ( ) the subject is "my carriage." this, being an 'individual,' is equivalent to the class "my carriages." (note that this class contains only _one_ member.) ( ) the verb is "will meet", for which we may substitute the phrase "are * * * that will meet." ( ) the predicate is "* * * that will meet you at the station." ( ) let univ. be "things." ( ) the sign of quantity is "all." ( ) the proposition now becomes "all | my carriages | are | things that will meet you at the station." ( ) "happy is the man who does not know what 'toothache' means!" ( ) the subject is evidently "the man &c." (note that in this sentence, the _predicate_ comes first.) at first sight, the subject seems to be an '_individual_'; but on further consideration, we see that the article "the" does _not_ imply that there is only _one_ such man. hence the phrase "the man who" is equivalent to "all men who". ( ) the verb is "are." ( ) the predicate is "happy * * *." ( ) let univ. be "men." ( ) the sign of quantity is "all." ( ) the proposition now becomes "all | men who do not know what 'toothache' means | are | happy men." pg ( ) "some farmers always grumble at the weather, whatever it may be." ( ) the subject is "farmers." ( ) the verb is "grumble," for which we substitute the phrase "are * * * who grumble." ( ) the predicate is "* * * who always grumble &c." ( ) let univ. be "persons." ( ) the sign of quantity is "some." ( ) the proposition now becomes "some | farmers | are | persons who always grumble at the weather, whatever it may be." ( ) "no lambs are accustomed to smoke cigars." ( ) the subject is "lambs." ( ) the verb is "are." ( ) the predicate is "* * * accustomed &c." ( ) let univ. be "animals." ( ) the sign of quantity is "no." ( ) the proposition now becomes "no | lambs | are | animals accustomed to smoke cigars." ( ) "i ca'n't understand examples that are not arranged in regular order, like those i am used to." ( ) the subject is "examples that," &c. ( ) the verb is "i ca'n't understand," which we must alter, so as to have "examples," instead of "i," as the nominative case. it may be expressed as "are not understood by me." ( ) the predicate is "* * * not understood by me." ( ) let univ. be "examples." ( ) the sign of quantity is "all." ( ) the proposition now becomes "all | examples that are not arranged in regular order like those i am used to | are | examples not understood by me."] pg § . _a proposition of relation, beginning with "all", is a double proposition._ a proposition of relation, beginning with "all", asserts (as we already know) that "_all_ members of the subject are members of the predicate". this evidently contains, as a _part_ of what it tells us, the smaller proposition "_some_ members of the subject are members of the predicate". [thus, the proposition "_all_ bankers are rich men" evidently contains the smaller proposition "_some_ bankers are rich men".] the question now arises "what is the _rest_ of the information which this proposition gives us?" in order to answer this question, let us begin with the smaller proposition, "_some_ members of the subject are members of the predicate," and suppose that this is _all_ we have been told; and let us proceed to inquire what _else_ we need to be told, in order to know that "_all_ members of the subject are members of the predicate". [thus, we may suppose that the proposition "_some_ bankers are rich men" is all the information we possess; and we may proceed to inquire what _other_ proposition needs to be added to it, in order to make up the entire proposition "_all_ bankers are rich men".] let us also suppose that the 'univ.' (i.e. the genus, of which both the subject and the predicate are specieses) has been divided (by the process of _dichotomy_) into two smaller classes, viz. ( ) the predicate; ( ) the class whose differentia is _contradictory_ to that of the predicate. [thus, we may suppose that the genus "men," (of which both "bankers" and "rich men" are specieses) has been divided into the two smaller classes, "rich men", "poor men".] pg now we know that _every_ member of the subject is (as shown at p. ) a member of the univ. hence _every_ member of the subject is either in class ( ) or else in class ( ). [thus, we know that _every_ banker is a member of the genus "men". hence, _every_ banker is either in the class "rich men", or else in the class "poor men".] also we have been told that, in the case we are discussing, _some_ members of the subject are in class ( ). what _else_ do we need to be told, in order to know that _all_ of them are there? evidently we need to be told that _none_ of them are in class ( ); i.e. that _none_ of them are members of the class whose differentia is _contradictory_ to that of the predicate. [thus, we may suppose we have been told that _some_ bankers are in the class "rich men". what _else_ do we need to be told, in order to know that _all_ of them are there? evidently we need to be told that _none_ of them are in the class "_poor_ men".] hence a proposition of relation, beginning with "all", is a _double_ proposition, and is '=equivalent=' to (i.e. gives the same information as) the _two_ propositions ( ) "_some_ members of the subject are members of the predicate"; ( ) "_no_ members of the subject are members of the class whose differentia is _contradictory_ to that of the predicate". [thus, the proposition "_all_ bankers are rich men" is a _double_ proposition, and is equivalent to the _two_ propositions ( ) "_some_ bankers are rich men"; ( ) "_no_ bankers are _poor_ men".] pg § . _what is implied, in a proposition of relation, as to the reality of its terms?_ note that the rules, here laid down, are _arbitrary_, and only apply to part i of my "symbolic logic." a proposition of relation, beginning with "some", is henceforward to be understood as asserting that there are _some existing things_, which, being members of the subject, are also members of the predicate; i.e. that _some existing things_ are members of _both_ terms at once. hence it is to be understood as implying that _each_ term, taken by itself, is _real_. [thus, the proposition "some rich men are invalids" is to be understood as asserting that _some existing things_ are "rich invalids". hence it implies that _each_ of the two classes, "rich men" and "invalids", taken by itself, is _real_.] a proposition of relation, beginning with "no", is henceforward to be understood as asserting that there are _no existing things_ which, being members of the subject, are also members of the predicate; i.e. that _no existing things_ are members of _both_ terms at once. but this implies nothing as to the _reality_ of either term taken by itself. [thus, the proposition "no mermaids are milliners" is to be understood as asserting that _no existing things_ are "mermaid-milliners". but this implies nothing as to the _reality_, or the _unreality_, of either of the two classes, "mermaids" and "milliners", taken by itself. in this case as it happens, the subject is _imaginary_, and the predicate _real_.] a proposition of relation, beginning with "all", contains (see § ) a similar proposition beginning with "some". hence it is to be understood as implying that _each_ term, taken by itself, is _real_. [thus, the proposition "all hyænas are savage animals" contains the proposition "some hyænas are savage animals". hence it implies that _each_ of the two classes, "hyænas" and "savage animals", taken by itself, is _real_.] pg § . _translation of a proposition of relation into one or more propositions of existence._ we have seen that a proposition of relation, beginning with "some," asserts that _some existing things_, being members of its subject, are _also_ members of its predicate. hence, it asserts that some existing things are members of _both_; i.e. it asserts that some existing things are members of the class of things which have _all_ the attributes of the subject and the predicate. hence, to translate it into a proposition of existence, we take "existing things" as the new _subject_, and things, which have _all_ the attributes of the subject and the predicate, as the new predicate. similarly for a proposition of relation beginning with "no". a proposition of relation, beginning with "all", is (as shown in § ) equivalent to _two_ propositions, one beginning with "some" and the other with "no", each of which we now know how to translate. [let us work a few examples, to illustrate these rules. ( ) "some apples are not ripe." here we arrange thus:-- "some" _sign of quantity_. "existing things" _subject_. "are" _copula_. "not-ripe apples" _predicate_. or thus:-- "some | existing things | are | not-ripe apples." pg ( ) "some farmers always grumble at the weather, whatever it may be." here we arrange thus:-- "some | existing things | are | farmers who always grumble at the weather, whatever it may be." ( ) "no lambs are accustomed to smoke cigars." here we arrange thus:-- "no | existing things |are | lambs accustomed to smoke cigars." ( ) "none of my speculations have brought me as much as per cent." here we arrange thus:-- "no | existing things | are | speculations of mine, which have brought me as much as per cent." ( ) "none but the brave deserve the fair." here we note, to begin with, that the phrase "none but the brave" is equivalent to "no not-brave men." we then arrange thus:-- "no | existing things | are | not-brave men deserving of the fair." ( ) "all bankers are rich men." this is equivalent to the two propositions "some bankers are rich men" and "no bankers are poor men." here we arrange thus:-- "some | existing things | are | rich bankers"; and "no | existing things | are | poor bankers."] [work examples § = =, - (p. ).] pg book iii. the biliteral diagram. ·-------------· | | | | xy | xy' | | | | |------|------| | | | | x'y | x'y' | | | | ·-------------· chapter i. _symbols and cells._ first, let us suppose that the above diagram is an enclosure assigned to a certain class of things, which we have selected as our 'universe of discourse.' or, more briefly, as our 'univ'. [for example, we might say "let univ. be 'books'"; and we might imagine the diagram to be a large table, assigned to all "books."] [the reader is strongly advised, in reading this chapter, _not_ to refer to the above diagram, but to draw a large one for himself, _without any letters_, and to have it by him while he reads, and keep his finger on that particular _part_ of it, about which he is reading.] pg secondly, let us suppose that we have selected a certain adjunct, which we may call "x," and have divided the large class, to which we have assigned the whole diagram, into the two smaller classes whose differentiæ are "x" and "not-x" (which we may call "x'"), and that we have assigned the _north_ half of the diagram to the one (which we may call "the class of x-things," or "the x-class"), and the _south_ half to the other (which we may call "the class of x'-things," or "the x'-class"). [for example, we might say "let x mean 'old,' so that x' will mean 'new'," and we might suppose that we had divided books into the two classes whose differentiæ are "old" and "new," and had assigned the _north_ half of the table to "_old_ books" and the _south_ half to "_new_ books."] thirdly, let us suppose that we have selected another adjunct, which we may call "y", and have subdivided the x-class into the two classes whose differentiæ are "y" and "y'", and that we have assigned the north-_west_ cell to the one (which we may call "the xy-class"), and the north-_east_ cell to the other (which we may call "the xy'-class"). [for example, we might say "let y mean 'english,' so that y' will mean 'foreign'", and we might suppose that we had subdivided "old books" into the two classes whose differentiæ are "english" and "foreign", and had assigned the north-_west_ cell to "old _english_ books", and the north-_east_ cell to "old _foreign_ books."] fourthly, let us suppose that we have subdivided the x'-class in the same manner, and have assigned the south-_west_ cell to the x'y-class, and the south-_east_ cell to the x'y'-class. [for example, we might suppose that we had subdivided "new books" into the two classes "new _english_ books" and "new _foreign_ books", and had assigned the south-_west_ cell to the one, and the south-_east_ cell to the other.] it is evident that, if we had begun by dividing for y and y', and had then subdivided for x and x', we should have got the _same_ four classes. hence we see that we have assigned the _west_ half to the y-class, and the _east_ half to the y'-class. pg [thus, in the above example, we should find that we had assigned the _west_ half of the table to "_english_ books" and the _east_ half to "_foreign_ books." ·-------------------· | old | old | | english | foreign | | books | books | |---------|---------| | new | new | | english | foreign | | books | books | ·-------------------· we have, in fact, assigned the four quarters of the table to four different classes of books, as here shown.] the reader should carefully remember that, in such a phrase as "the x-things," the word "things" means that particular _kind_ of things, to which the whole diagram has been assigned. [thus, if we say "let univ. be 'books'," we mean that we have assigned the whole diagram to "books." in that case, if we took "x" to mean "old", the phrase "the x-things" would mean "the old books."] the reader should not go on to the next chapter until he is _quite familiar_ with the _blank_ diagram i have advised him to draw. he ought to be able to name, _instantly_, the _adjunct_ assigned to any compartment named in the right-hand column of the following table. also he ought to be able to name, _instantly_, the _compartment_ assigned to any adjunct named in the left-hand column. to make sure of this, he had better put the book into the hands of some genial friend, while he himself has nothing but the blank diagram, and get that genial friend to question him on this table, _dodging_ about as much as possible. the questions and answers should be something like this:-- pg table i. ·----------------------------------------· | _adjuncts_ | _compartments, or cells,_ | | _of_ | _assigned to them._ | | _classes._ | | |------------|---------------------------| | x | north half. | | x' | south " | | y | west " | | y' | east " | |------------|---------------------------| | xy | north-west cell. | | xy' | " east " | | x'y | south-west " | | x'y' | " east " | ·----------------------------------------· q. "adjunct for west half?" a. "y." q. "compartment for xy'?" a. "north-east cell." q. "adjunct for south-west cell?" a. "x'y." &c., &c. after a little practice, he will find himself able to do without the blank diagram, and will be able to see it _mentally_ ("in my mind's eye, horatio!") while answering the questions of his genial friend. when _this_ result has been reached, he may safely go on to the next chapter. pg chapter ii. _counters._ let us agree that a _red_ counter, placed within a cell, shall mean "this cell is _occupied_" (i.e. "there is at least _one_ thing in it"). let us also agree that a _red_ counter, placed on the partition between two cells, shall mean "the compartment, made up of these two cells, is _occupied_; but it is not known _whereabouts_, in it, its occupants are." hence it may be understood to mean "at least _one_ of these two cells is occupied: possibly _both_ are." our ingenious american cousins have invented a phrase to describe the condition of a man who has not yet made up his mind _which_ of two political parties he will join: such a man is said to be "=sitting on the fence=." this phrase exactly describes the condition of the red counter. let us also agree that a _grey_ counter, placed within a cell, shall mean "this cell is _empty_" (i.e. "there is _nothing_ in it"). [the reader had better provide himself with red counters and grey ones.] pg chapter iii. _representation of propositions._ § . _introductory._ henceforwards, in stating such propositions as "some x-things exist" or "no x-things are y-things", i shall omit the word "things", which the reader can supply for himself, and shall write them as "some x exist" or "no x are y". [note that the word "things" is here used with a special meaning, as explained at p. .] a proposition, containing only _one_ of the letters used as symbols for attributes, is said to be '=uniliteral='. [for example, "some x exist", "no y' exist", &c.] a proposition, containing _two_ letters, is said to be ='biliteral'=. [for example, "some xy' exist", "no x' are y", &c.] a proposition is said to be '=in terms of=' the letters it contains, whether with or without accents. [thus, "some xy' exist", "no x' are y", &c., are said to be _in terms of_ x and y.] pg § . _representation of propositions of existence._ let us take, first, the proposition "some x exist". [note that this proposition is (as explained at p. ) equivalent to "some existing things are x-things."] this tells us that there is at least _one_ thing in the north half; that is, that the north half is _occupied_. and this we can evidently represent by placing a _red_ counter (here represented by a _dotted_ circle) on the partition which divides the north half. ·-------· | (.) | |---|---| | | | ·-------· [in the "books" example, this proposition would be "some old books exist".] similarly we may represent the three similar propositions "some x' exist", "some y exist", and "some y' exist". [the reader should make out all these for himself. in the "books" example, these propositions would be "some new books exist", &c.] let us take, next, the proposition "no x exist". this tells us that there is _nothing_ in the north half; that is, that the north half is _empty_; that is, that the north-west cell and the north-east cell are both of them _empty_. and this we can represent by placing _two grey_ counters in the north half, one in each cell. ·-------· |( )|( )| |---|---| | | | ·-------· [the reader may perhaps think that it would be enough to place a _grey_ counter on the partition in the north half, and that, just as a _red_ counter, so placed, would mean "this half is _occupied_", so a _grey_ one would mean "this half is _empty_". this, however, would be a mistake. we have seen that a _red_ counter, so placed, would mean "at least _one_ of these two cells is occupied: possibly _both_ are." hence a _grey_ one would merely mean "at least _one_ of these two cells is empty: possibly _both_ are". but what we have to represent is, that both cells are _certainly_ empty: and this can only be done by placing a _grey_ counter in _each_ of them. in the "books" example, this proposition would be "no old books exist".] pg similarly we may represent the three similar propositions "no x' exist", "no y exist", and "no y' exist". [the reader should make out all these for himself. in the "books" example, these three propositions would be "no new books exist", &c.] let us take, next, the proposition "some xy exist". this tells us that there is at least _one_ thing in the north-west cell; that is, that the north-west cell is _occupied_. and this we can represent by placing a _red_ counter in it. ·-------· |(.)| | |---|---| | | | ·-------· [in the "books" example, this proposition would be "some old english books exist".] similarly we may represent the three similar propositions "some xy' exist", "some x'y exist", and "some x'y' exist". [the reader should make out all these for himself. in the "books" example, these three propositions would be "some old foreign books exist", &c.] let us take, next, the proposition "no xy exist". this tells us that there is _nothing_ in the north-west cell; that is, that the north-west cell is _empty_. and this we can represent by placing a _grey_ counter in it. ·-------· |( )| | |---|---| | | | ·-------· [in the "books" example, this proposition would be "no old english books exist".] similarly we may represent the three similar propositions "no xy' exist", "no x'y exist", and "no x'y' exist". [the reader should make out all these for himself. in the "books" example, these three propositions would be "no old foreign books exist", &c.] pg we have seen that the proposition "no x exist" may be represented by placing _two grey_ counters in the north half, one in each cell. ·-------· |( )|( )| |---|---| | | | ·-------· we have also seen that these two _grey_ counters, taken _separately_, represent the two propositions "no xy exist" and "no xy' exist". hence we see that the proposition "no x exist" is a _double_ proposition, and is equivalent to the _two_ propositions "no xy exist" and "no xy' exist". [in the "books" example, this proposition would be "no old books exist". hence this is a _double_ proposition, and is equivalent to the _two_ propositions "no old _english_ books exist" and "no old _foreign_ books exist".] § . _representation of propositions of relation._ let us take, first, the proposition "some x are y". this tells us that at least _one_ thing, in the _north_ half, is also in the _west_ half. hence it must be in the space _common_ to them, that is, in the _north-west cell_. hence the north-west cell is _occupied_. and this we can represent by placing a _red_ counter in it. ·-------· |(.)| | |---|---| | | | ·-------· [note that the _subject_ of the proposition settles which _half_ we are to use; and that the _predicate_ settles in which _portion_ of it we are to place the red counter. in the "books" example, this proposition would be "some old books are english".] similarly we may represent the three similar propositions "some x are y'", "some x' are y", and "some x' are y'". [the reader should make out all these for himself. in the "books" example, these three propositions would be "some old books are foreign", &c.] pg let us take, next, the proposition "some y are x". this tells us that at least _one_ thing, in the _west_ half, is also in the _north_ half. hence it must be in the space _common_ to them, that is, in the _north-west cell_. hence the north-west cell is _occupied_. and this we can represent by placing a _red_ counter in it. ·-------· |(.)| | |---|---| | | | ·-------· [in the "books" example, this proposition would be "some english books are old".] similarly we may represent the three similar propositions "some y are x'", "some y' are x", and "some y' are x'". [the reader should make out all these for himself. in the "books" example, these three propositions would be "some english books are new", &c.] we see that this _one_ diagram has now served to represent no less than _three_ propositions, viz. ( ) "some xy exist; ( ) some x are y; ( ) some y are x". ·-------· |(.)| | |---|---| | | | ·-------· hence these three propositions are equivalent. [in the "books" example, these propositions would be ( ) "some old english books exist; ( ) some old books are english; ( ) some english books are old".] the two equivalent propositions, "some x are y" and "some y are x", are said to be '=converse=' to each other; and the process, of changing one into the other, is called '=converting=', or '=conversion='. [for example, if we were told to convert the proposition "some apples are not ripe," we should first choose our univ. (say "fruit"), and then complete the proposition, by supplying the substantive "fruit" in the predicate, so that it would be "some apples are not-ripe fruit"; and we should then convert it by interchanging its terms, so that it would be "some not-ripe fruit are apples".] pg similarly we may represent the three similar trios of equivalent propositions; the whole set of _four_ trios being as follows:-- ( ) "some xy exist" = "some x are y" = "some y are x". ( ) "some xy' exist" = "some x are y'" = "some y' are x". ( ) "some x'y exist" = "some x' are y" = "some y are x'". ( ) "some x'y' exist" = "some x' are y'" = "some y' are x'". let us take, next, the proposition "no x are y". this tell us that no thing, in the _north_ half, is also in the _west_ half. hence there is _nothing_ in the space _common_ to them, that is, in the _north-west cell_. hence the north-west cell is _empty_. and this we can represent by placing a _grey_ counter in it. ·-------· |( )| | |---|---| | | | ·-------· [in the "books" example, this proposition would be "no old books are english".] similarly we may represent the three similar propositions "no x are y'", and "no x' are y", and "no x' are y'". [the reader should make out all these for himself. in the "books" example, these three propositions would be "no old books are foreign", &c.] let us take, next, the proposition "no y are x". this tells us that no thing, in the _west_ half, is also in the _north_ half. hence there is _nothing_ in the space _common_ to them, that is, in the _north-west cell_. that is, the north-west cell is _empty_. and this we can represent by placing a _grey_ counter in it. ·-------· |( )| | |---|---| | | | ·-------· [in the "books" example, this proposition would be "no english books are old".] similarly we may represent the three similar propositions "no y are x'", "no y' are x", and "no y' are x'". [the reader should make out all these for himself. in the "books" example, these three propositions would be "no english books are new", &c.] pg ·-------· |( )| | |---|---| | | | ·-------· we see that this _one_ diagram has now served to present no less than _three_ propositions, viz. ( ) "no xy exist; ( ) no x are y; ( ) no y are x." hence these three propositions are equivalent. [in the "books" example, these propositions would be ( ) "no old english books exist; ( ) no old books are english; ( ) no english books are old".] the two equivalent propositions, "no x are y" and "no y are x", are said to be 'converse' to each other. [for example, if we were told to convert the proposition "no porcupines are talkative", we should first choose our univ. (say "animals"), and then complete the proposition, by supplying the substantive "animals" in the predicate, so that it would be "no porcupines are talkative animals", and we should then convert it, by interchanging its terms, so that it would be "no talkative animals are porcupines".] similarly we may represent the three similar trios of equivalent propositions; the whole set of _four_ trios being as follows:-- ( ) "no xy exist" = "no x are y" = "no y are x". ( ) "no xy' exist" = "no x are y'" = "no y' are x". ( ) "no x'y exist" = "no x' are y" = "no y are x'". ( ) "no x'y' exist" = "no x' are y'" = "no y' are x'". let us take, next, the proposition "all x are y". we know (see p. ) that this is a _double_ proposition, and equivalent to the _two_ propositions "some x are y" and "no x are y'", each of which we already know how to represent. ·-------· |(.)|( )| |---|---| | | | ·-------· [note that the _subject_ of the given proposition settles which _half_ we are to use; and that its _predicate_ settles in which _portion_ of that half we are to place the red counter.] pg table ii. ·-----------------------------------------------------· | | ·-------· | | ·-------· | | | | (.) | | | |( )|( )| | | some x exist | |---|---| | no x exist | |---|---| | | | | | | | | | | | | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | | | | | | some x' exist | |---|---| | no x' exist | |---|---| | | | | (.) | | | |( )|( )| | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | |( )| | | | some y exist | |(.)|---| | no y exist | |---|---| | | | | | | | | |( )| | | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | | |( )| | | some y' exist | |---|(.)| | no y' exist | |---|---| | | | | | | | | | |( )| | | | ·-------· | | ·-------· | ·-----------------------------------------------------· similarly we may represent the seven similar propositions "all x are y'", "all x' are y", "all x' are y'", "all y are x", "all y are x'", "all y' are x", and "all y' are x'". let us take, lastly, the double proposition "some x are y and some are y'", each part of which we already know how to represent. ·-------· |(.)|(.)| |---|---| | | | ·-------· similarly we may represent the three similar propositions, "some x' are y and some are y'", "some y are x and some are x'", "some y' are x and some are x'". the reader should now get his genial friend to question him, severely, on these two tables. the _inquisitor_ should have the tables before him: but the _victim_ should have nothing but a blank diagram, and the counters with which he is to represent the various propositions named by his friend, e.g. "some y exist", "no y' are x", "all x are y", &c. &c. pg table iii. ·-------------------------------------------------------------· | | ·-------· | | ·-------· | | some xy exist | |(.)| | | | |(.)|( )| | |  = some x are y | |---|---| | all x are y | |---|---| | |  = some y are x | | | | | | | | | | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | some xy' exist | | |(.)| | | |( )|(.)| | |  = some x are y' | |---|---| | all x are y' | |---|---| | |  = some y' are x | | | | | | | | | | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | some x'y exist | | | | | | | | | | |  = some x' are y | |---|---| | all x' are y | |---|---| | |  = some y are x' | |(.)| | | | |(.)|( )| | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | some x'y' exist | | | | | | | | | | |  = some x' are y'| |---|---| | all x' are y' | |---|---| | |  = some y' are x'| | |(.)| | | |( )|(.)| | | | ·-------· | | ·-------· | ·-------------------------------------------------------------· ·-------------------------------------------------------------· | | ·-------· | | ·-------· | | no xy exist | |( )| | | | |(.)| | | |  = no x are y | |---|---| | all y are x | |---|---| | |  = no y are x | | | | | | |( )| | | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | no xy' exist | | |( )| | | |( )| | | |  = no x are y' | |---|---| | all y are x' | |---|---| | |  = no y' are x | | | | | | |(.)| | | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | no x'y exist | | | | | | | |(.)| | |  = no x' are y | |---|---| | all y' are x | |---|---| | |  = no y are x' | |( )| | | | | |( )| | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | no x'y' exist | | | | | | | |( )| | |  = no x' are y' | |---|---| | all y' are x' | |---|---| | |  = no y' are x' | | |( )| | | | |(.)| | | | ·-------· | | ·-------· | ·-------------------------------------------------------------· ·-------------------------------------------------------------· | | ·-------· | | ·-------· | | | |(.)|(.)| | | |(.)| | | | some x are y, | |---|---| | some y are x | |---|---| | | and some are y' | | | | | and some are x' | |(.)| | | | | ·-------· | | ·-------· | |------------------|-----------|------------------|-----------| | | ·-------· | | ·-------· | | | | | | | | | |(.)| | | some x' are y, | |---|---| | some y' are x | |---|---| | | and some are y' | |(.)|(.)| | and some are x' | | |(.)| | | | ·-------· | | ·-------· | ·-------------------------------------------------------------· pg chapter iv. _interpretation of biliteral diagram when marked with counters._ the diagram is supposed to be set before us, with certain counters placed upon it; and the problem is to find out what proposition, or propositions, the counters represent. as the process is simply the reverse of that discussed in the previous chapter, we can avail ourselves of the results there obtained, as far as they go. first, let us suppose that we find a _red_ counter placed in the north-west cell. ·-------· |(.)| | |---|---| | | | ·-------· we know that this represents each of the trio of equivalent propositions "some xy exist" = "some x are y" = "some y are x". similarly we may interpret a _red_ counter, when placed in the north-east, or south-west, or south-east cell. next, let us suppose that we find a _grey_ counter placed in the north-west cell. ·-------· |( )| | |---|---| | | | ·-------· we know that this represents each of the trio of equivalent propositions "no xy exist" = "no x are y" = "no y are x". similarly we may interpret a _grey_ counter, when placed in the north-east, or south-west, or south-east cell. pg next, let us suppose that we find a _red_ counter placed on the partition which divides the north half. ·-------· | (.) | |---|---| | | | ·-------· we know that this represents the proposition "some x exist." similarly we may interpret a _red_ counter, when placed on the partition which divides the south, or west, or east half. * * * * * next, let us suppose that we find _two red_ counters placed in the north half, one in each cell. ·-------· |(.)|(.)| |---|---| | | | ·-------· we know that this represents the _double_ proposition "some x are y and some are y'". similarly we may interpret _two red_ counters, when placed in the south, or west, or east half. * * * * * next, let us suppose that we find _two grey_ counters placed in the north half, one in each cell. ·-------· |( )|( )| |---|---| | | | ·-------· we know that this represents the proposition "no x exist". similarly we may interpret _two grey_ counters, when placed in the south, or west, or east half. * * * * * lastly, let us suppose that we find a _red_ and a _grey_ counter placed in the north half, the _red_ in the north-_west_ cell, and the _grey_ in the north-_east_ cell. ·-------· |(.)|( )| |---|---| | | | ·-------· we know that this represents the proposition, "all x are y". [note that the _half_, occupied by the two counters, settles what is to be the _subject_ of the proposition, and that the _cell_, occupied by the _red_ counter, settles what is to be its _predicate_.] pg similarly we may interpret a _red_ and a _grey_ counter, when placed in any one of the seven similar positions red in north-east, grey in north-west; red in south-west, grey in south-east; red in south-east, grey in south-west; red in north-west, grey in south-west; red in south-west, grey in north-west; red in north-east, grey in south-east; red in south-east, grey in north-east. once more the genial friend must be appealed to, and requested to examine the reader on tables ii and iii, and to make him not only _represent_ propositions, but also _interpret_ diagrams when marked with counters. the questions and answers should be like this:-- q. represent "no x' are y'." a. grey counter in s.e. cell. q. interpret red counter on e. partition. a. "some y' exist." q. represent "all y' are x." a. red in n.e. cell; grey in s.e. q. interpret grey counter in s.w. cell. a. "no x'y exist" = "no x' are y" = "no y are x'". &c., &c. at first the examinee will need to have the board and counters before him; but he will soon learn to dispense with these, and to answer with his eyes shut or gazing into vacancy. [work examples § = =, - (p. ).] pg book iv. the triliteral diagram. ·-----------------· ·-----------------· | | | | xy | xy' | | | | | m' | m' | | xy | xy' | | ·----|----· | | | | | | xy | xy'| | | | | | | m | m | | |--------|--------| |---|----|----|---| | | | | |x'y |x'y'| | | | | | | m | m | | | x'y | x'y' | | ·----|----· | | | | | x'y | x'y' | | | | | m' | m' | ·-----------------· ·-----------------· chapter i. _symbols and cells._ first, let us suppose that the above _left_-hand diagram is the biliteral diagram that we have been using in book iii., and that we change it into a _triliteral_ diagram by drawing an _inner square_, so as to divide each of its cells into portions, thus making cells altogether. the _right_-hand diagram shows the result. [the reader is strongly advised, in reading this chapter, _not_ to refer to the above diagrams, but to make a large copy of the right-hand one for himself, _without any letters_, and to have it by him while he reads, and keep his finger on that particular _part_ of it, about which he is reading.] pg secondly, let us suppose that we have selected a certain adjunct, which we may call "m", and have subdivided the xy-class into the two classes whose differentiæ are m and m', and that we have assigned the n.w. _inner_ cell to the one (which we may call "the class of xym-things", or "the xym-class"), and the n.w. _outer_ cell to the other (which we may call "the class of xym'-things", or "the xym'-class"). [thus, in the "books" example, we might say "let m mean 'bound', so that m' will mean 'unbound'", and we might suppose that we had subdivided the class "old english books" into the two classes, "old english bound books" and "old english unbound books", and had assigned the n.w. _inner_ cell to the one, and the n.w. _outer_ cell to the other.] thirdly, let us suppose that we have subdivided the xy'-class, the x'y-class, and the x'y'-class in the same manner, and have, in each case, assigned the _inner_ cell to the class possessing the attribute m, and the _outer_ cell to the class possessing the attribute m'. [thus, in the "books" example, we might suppose that we had subdivided the "new english books" into the two classes, "new english bound books" and "new english unbound books", and had assigned the s.w. _inner_ cell to the one, and the s.w. _outer_ cell to the other.] it is evident that we have now assigned the _inner square_ to the m-class, and the _outer border_ to the m'-class. [thus, in the "books" example, we have assigned the _inner square_ to "bound books" and the _outer border_ to "unbound books".] when the reader has made himself familiar with this diagram, he ought to be able to find, in a moment, the compartment assigned to a particular _pair_ of attributes, or the cell assigned to a particular _trio_ of attributes. the following rules will help him in doing this:-- ( ) arrange the attributes in the order x, y, m. pg ( ) take the _first_ of them and find the compartment assigned to it. ( ) then take the _second_, and find what _portion_ of that compartment is assigned to it. ( ) treat the _third_, if there is one, in the same way. [for example, suppose we have to find the compartment assigned to ym. we say to ourselves "y has the _west_ half; and m has the _inner_ portion of that west half." again, suppose we have to find the cell assigned to x'ym'. we say to ourselves "x' has the _south_ half; y has the _west_ portion of that south half, i.e. has the _south-west quarter_; and m' has the _outer_ portion of that south-west quarter."] the reader should now get his genial friend to question him on the table given on the next page, in the style of the following specimen-dialogue. q. adjunct for south half, inner portion? a. x'm. q. compartment for m'? a. the outer border. q. adjunct for north-east quarter, outer portion? a. xy'm'. q. compartment for ym? a. west half, inner portion. q. adjunct for south half? a. x'. q. compartment for x'y'm? a. south-east quarter, inner portion. &c. &c. pg table iv. ·-----------------------------------------------· | adjunct | | | of | compartments, or cells, assigned | | classes. | to them. | |----------|------------------------------------| | x | north half. | | x' | south " | | y | west " | | y' | east " | | m | inner square. | | m' | outer border. | |----------|------------------------------------| | xy | north-west quarter. | | xy' | " east " | | x'y | south-west " | | x'y' | " east " | | xm | north half, inner portion. | | xm' | " " outer " | | x'm | south " inner " | | x'm' | " " outer " | | ym | west " inner " | | ym' | " " outer " | | y'm | east " inner " | | y'm' | " " outer " | |----------|------------------------------------| | xym | north-west quarter, inner portion. | | xym' | " " " outer " | | xy'm | " east " inner " | | xy'm' | " " " outer " | | x'ym | south-west " inner " | | x'ym' | " " " outer " | | x'y'm | " east " inner " | | x'y'm' | " " " outer " | ·-----------------------------------------------· pg chapter ii. _representation of propositions in terms of x and m, or of y and m._ § . _representation of propositions of existence in terms of x and m, or of y and m._ let us take, first, the proposition "some xm exist". [note that the _full_ meaning of this proposition is (as explained at p. ) "some existing things are xm-things".] this tells us that there is at least _one_ thing in the inner portion of the north half; that is, that this compartment is _occupied_. and this we can evidently represent by placing a _red_ counter on the partition which divides it. ·---------------· | | | | ·---|---· | | | (.) | | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· [in the "books" example, this proposition would mean "some old bound books exist" (or "there are some old bound books").] similarly we may represent the seven similar propositions, "some xm' exist", "some x'm exist", "some x'm' exist", "some ym exist", "some ym' exist", "some y'm exist", and "some y'm' exist". pg let us take, next, the proposition "no xm exist". this tells us that there is _nothing_ in the inner portion of the north half; that is, that this compartment is _empty_. and this we can represent by placing _two grey_ counters in it, one in each cell. ·---------------· | | | | ·---|---· | | |( )|( )| | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· similarly we may represent the seven similar propositions, in terms of x and m, or of y and m, viz. "no xm' exist", "no x'm exist", &c. * * * * * these sixteen propositions of existence are the only ones that we shall have to represent on this diagram. § . _representation of propositions of relation in terms of x and m, or of y and m._ let us take, first, the pair of converse propositions "some x are m" = "some m are x." we know that each of these is equivalent to the proposition of existence "some xm exist", which we already know how to represent. ·---------------· | | | | ·---|---· | | | (.) | | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· similarly for the seven similar pairs, in terms of x and m, or of y and m. let us take, next, the pair of converse propositions "no x are m" = "no m are x." we know that each of these is equivalent to the proposition of existence "no xm exist", which we already know how to represent. ·---------------· | | | | ·---|---· | | |( )|( )| | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· similarly for the seven similar pairs, in terms of x and m, or of y and m. pg let us take, next, the proposition "all x are m." ·---------------· |( ) | ( )| | ·---|---· | | | (.) | | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· we know (see p. ) that this is a _double_ proposition, and equivalent to the _two_ propositions "some x are m" and "no x are m' ", each of which we already know how to represent. similarly for the fifteen similar propositions, in terms of x and m, or of y and m. these thirty-two propositions of relation are the only ones that we shall have to represent on this diagram. the reader should now get his genial friend to question him on the following four tables. the victim should have nothing before him but a blank triliteral diagram, a red counter, and grey ones, with which he is to represent the various propositions named by the inquisitor, _e.g._ "no y' are m", "some xm' exist", &c., &c. pg table v. ·---------------------------------------------------------· | ·---------------· some xm exist | ·---------------· | | | | |  = some x are m | | | | | | | ·---|---· |  = some m are x | | ·---|---· | | | | | (.) | | | | |( )|( )| | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | no xm exist | | | | | | | | ·---|---· | |  = no x are m | ·---|---· | | | | | | |  = no m are x | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some xm' exist | ·---------------· | | | (.) |  = some x are m' | |( ) | ( )| | | | ·---|---· |  = some m' are x | | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | no xm' exist | | | | | | | | ·---|---· | |  = no x are m' | ·---|---· | | | | | | |  = no m' are x | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some x'm exist | ·---------------· | | | | |  = some x' are m | | | | | | | ·---|---· |  = some m are x' | | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | (.) | | | no x'm exist | |( )|( )| | | | | ·---|---· | |  = no x' are m | ·---|---· | | | | | | |  = no m are x' | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some x'm' exist | ·---------------· | | | | |  = some x' are m'| | | | | | | ·---|---· |  = some m' are x'| | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | no x'm' exist | | | | | | | | ·---|---· | |  = no x' are m' | ·---|---· | | | | (.) | |  = no m' are x' |( ) | ( )| | | ·---------------· | ·---------------· | ·---------------------------------------------------------· pg table vi. ·---------------------------------------------------------· | ·---------------· some ym exist | ·---------------· | | | | |  = some y are m | | | | | | | ·---|---· |  = some m are y | | ·---|---· | | | | | | | | | | |( )| | | | | |---|(.)|---|---| ·-----------------· |---|---|---|---| | | | | | | | | no ym exist | |( )| | | | | | ·---|---· | |  = no y are m | ·---|---· | | | | | | |  = no m are y | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some ym' exist | ·---------------· | | | | |  = some y are m' | |( ) | | | | | ·---|---· |  = some m' are y | | ·---|---· | | | | | | | | | | | | | | | | |(.)|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | no ym' exist | | | | | | | | ·---|---· | |  = no y are m' | ·---|---· | | | | | | |  = no m' are y |( ) | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some y'm exist | ·---------------· | | | | |  = some y' are m | | | | | | | ·---|---· |  = some m are y' | | ·---|---· | | | | | | | | | | | |( )| | | | |---|---|(.)|---| ·-----------------· |---|---|---|---| | | | | | | | | no y'm exist | | |( )| | | | | ·---|---· | |  = no y' are m | ·---|---· | | | | | | |  = no m are y' | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· some y'm' exist | ·---------------· | | | | |  = some y' are m'| | | ( )| | | | ·---|---· |  = some m' are y'| | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|(.)| ·-----------------· |---|---|---|---| | | | | | | | | no y'm' exist | | | | | | | | ·---|---· | |  = no y' are m' | ·---|---· | | | | | | |  = no m' are y' | | ( )| | | ·---------------· | ·---------------· | ·---------------------------------------------------------· pg table vii. ·---------------------------------------------------------· | ·---------------· | ·---------------· | | |( ) | ( )| all x are m | | (.) | | | | ·---|---· | | | ·---|---· | | | | | (.) | | | | |( )|( )| | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | | | | | | | | | ·---|---· | | all x are m' | ·---|---· | | | | | | | | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | | | all x' are m | | | | | | | ·---|---· | | | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | (.) | | | | |( )|( )| | | | | ·---|---· | | all x' are m' | ·---|---· | | | |( ) | ( )| | | (.) | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | | | all m are x | | | | | | | ·---|---· | | | ·---|---· | | | | | (.) | | | | |( )|( )| | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | |( )|( )| | | | | (.) | | | | | ·---|---· | | all m are x' | ·---|---· | | | | | | | | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | (.) | all m' are x | |( ) | ( )| | | | ·---|---· | | | ·---|---· | | | | | | | | | | | | | | | | |---|---|---|---| ·-----------------· |---|---|---|---| | | | | | | | | | | | | | | | | ·---|---· | | all m' are x' | ·---|---· | | | |( ) | ( )| | | (.) | | | ·---------------· | ·---------------· | ·---------------------------------------------------------· pg table viii. ·---------------------------------------------------------· | ·---------------· | ·---------------· | | |( ) | | all y are m | | | | | | | ·---|---· | | | ·---|---· | | | | | | | | | | |( )| | | | | |---|(.)|---|---| ·-----------------· |(.)|---|---|---| | | | | | | | | | |( )| | | | | | ·---|---· | | all y are m' | ·---|---· | | | |( ) | | | | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | | ( )| all y' are m | | | | | | | ·---|---· | | | ·---|---· | | | | | | | | | | | |( )| | | | |---|---|(.)|---| ·-----------------· |---|---|---|(.)| | | | | | | | | | | |( )| | | | | ·---|---· | | all y' are m' | ·---|---· | | | | | ( )| | | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | | | all m are y | | | | | | | ·---|---· | | | ·---|---· | | | | | |( )| | | | |( )| | | | | |---|(.)|---|---| ·-----------------· |---|---|(.)|---| | | | | |( )| | | | |( )| | | | | | ·---|---· | | all m are y' | ·---|---· | | | | | | | | | | | | ·---------------· | ·---------------· | |---------------------------------------------------------| | ·---------------· | ·---------------· | | | | ( )| all m' are y | |( ) | | | | | ·---|---· | | | ·---|---· | | | | | | | | | | | | | | | | |(.)|---|---|---| ·-----------------· |---|---|---|(.)| | | | | | | | | | | | | | | | | ·---|---· | | all m' are y' | ·---|---· | | | | | ( )| | |( ) | | | | ·---------------· | ·---------------· | ·---------------------------------------------------------· pg chapter iii. _representation of two propositions of relation, one in terms of x and m, and the other in terms of y and m, on the same diagram._ the reader had better now begin to draw little diagrams for himself, and to mark them with the digits "i" and "o", instead of using the board and counters: he may put a "i" to represent a _red_ counter (this may be interpreted to mean "there is at least _one_ thing here"), and a "o" to represent a _grey_ counter (this may be interpreted to mean "there is _nothing_ here"). the pair of propositions, that we shall have to represent, will always be, one in terms of x and m, and the other in terms of y and m. when we have to represent a proposition beginning with "all", we break it up into the _two_ propositions to which it is equivalent. when we have to represent, on the same diagram, propositions, of which some begin with "some" and others with "no", we represent the _negative_ ones _first_. this will sometimes save us from having to put a "i" "on a fence" and afterwards having to shift it into a cell. [let us work a few examples. ( ) "no x are m'; no y' are m". let us first represent "no x are m'". this gives us diagram a. then, representing "no y' are m" on the same diagram, we get diagram b. pg a b ·---------------· ·---------------· |(o) | (o)| |(o) | (o)| | ·---|---· | | ·---|---· | | | | | | | | |(o)| | |---|---|---|---| |---|---|---|---| | | | | | | | |(o)| | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· ( ) "some m are x; no m are y". if, neglecting the rule, we were begin with "some m are x", we should get diagram a. and if we were then to take "no m are y", which tells us that the inner n.w. cell is _empty_, we should be obliged to take the "i" off the fence (as it no longer has the choice of _two_ cells), and to put it into the inner n.e. cell, as in diagram c. this trouble may be saved by beginning with "no m are y", as in diagram b. and _now_, when we take "some m are x", there is no fence to sit on! the "i" has to go, at once, into the n.e. cell, as in diagram c. a b c ·---------------· ·---------------· ·---------------· | | | | | | | | | | ·---|---· | | ·---|---· | | ·---|---· | | | (i) | | | |(o)| | | | |(o)|(i)| | |---|---|---|---| |---|---|---|---| |---|---|---|---| | | | | | | |(o)| | | | |(o)| | | | ·---|---· | | ·---|---· | | ·---|---· | | | | | | | | | | ·---------------· ·---------------· ·---------------· ( ) "no x' are m'; all m are y". here we begin by breaking up the second into the two propositions to which it is equivalent. thus we have _three_ propositions to represent, viz.-- ( ) "no x' are m'; ( ) some m are y; ( ) no m are y'". these we will take in the order , , . first we take no. ( ), viz. "no x' are m'". this gives us diagram a. pg adding to this, no. ( ), viz. "no m are y'", we get diagram b. this time the "i", representing no. ( ), viz. "some m are y," has to sit on the fence, as there is no "o" to order it off! this gives us diagram c. a b c ·---------------· ·---------------· ·---------------· | | | | | | | | | | ·---|---· | | ·---|---· | | ·---|---· | | | | | | | | |(o)| | | | |(o)| | |---|---|---|---| |---|---|---|---| |---|(i)|---|---| | | | | | | | |(o)| | | | |(o)| | | ·---|---· | | ·---|---· | | ·---|---· | |(o) | (o)| |(o) | (o)| |(o) | (o)| ·---------------· ·---------------· ·---------------· ( ) "all m are x; all y are m". here we break up _both_ propositions, and thus get _four_ to represent, viz.-- ( ) "some m are x; ( ) no m are x'; ( ) some y are m; ( ) no y are m'". these we will take in the order , , , . first we take no. ( ), viz. "no m are x'". this gives us diagram a. to this we add no. ( ), viz. "no y are m'", and thus get diagram b. if we were to add to this no. ( ), viz. "some m are x", we should have to put the "i" on a fence: so let us try no. ( ) instead, viz. "some y are m". this gives us diagram c. and now there is no need to trouble about no. ( ), as it would not add anything to our information to put a "i" on the fence. the diagram _already_ tells us that "some m are x".] a b c ·---------------· ·---------------· ·---------------· | | | |(o) | | |(o) | | | ·---|---· | | ·---|---· | | ·---|---· | | | | | | | | | | | | |(i)| | | |---|---|---|---| |---|---|---|---| |---|---|---|---| | |(o)|(o)| | | |(o)|(o)| | | |(o)|(o)| | | ·---|---· | | ·---|---· | | ·---|---· | | | | |(o) | | |(o) | | ·---------------· ·---------------· ·---------------· [work examples § = =, - (p. ); § = =, - (p. ).] pg chapter iv. _interpretation, in terms of x and y, of triliteral diagram, when marked with counters or digits._ the problem before us is, given a marked triliteral diagram, to ascertain _what_ propositions of relation, in terms of x and y, are represented on it. the best plan, for a _beginner_, is to draw a _biliteral_ diagram alongside of it, and to transfer, from the one to the other, all the information he can. he can then read off, from the biliteral diagram, the required propositions. after a little practice, he will be able to dispense with the biliteral diagram, and to read off the result from the triliteral diagram itself. to _transfer_ the information, observe the following rules:-- ( ) examine the n.w. quarter of the triliteral diagram. ( ) if it contains a "i", in _either_ cell, it is certainly _occupied_, and you may mark the n.w. quarter of the biliteral diagram with a "i". ( ) if it contains _two_ "o"s, one in _each_ cell, it is certainly _empty_, and you may mark the n.w. quarter of the biliteral diagram with a "o". pg ( ) deal in the same way with the n.e., the s.w., and the s.e. quarter. [let us take, as examples, the results of the four examples worked in the previous chapters. ( ) ·---------------· |(o) | (o)| | ·---|---· | | | |(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | | | ·---------------· in the n.w. quarter, only _one_ of the two cells is marked as _empty_: so we do not know whether the n.w. quarter of the biliteral diagram is _occupied_ or _empty_: so we cannot mark it. ·-------· | |(o)| |---|---| | | | ·-------· in the n.e. quarter, we find _two_ "o"s: so _this_ quarter is certainly _empty_; and we mark it so on the biliteral diagram. in the s.w. quarter, we have no information _at all_. in the s.e. quarter, we have not enough to use. we may read off the result as "no x are y'", or "no y' are x," whichever we prefer. ( ) ·---------------· | | | | ·---|---· | | |(o)|(i)| | |---|---|---|---| | |(o)| | | | ·---|---· | | | | ·---------------· in the n.w. quarter, we have not enough information to use. in the n.e. quarter, we find a "i". this shows us that it is _occupied_: so we may mark the n.e. quarter on the biliteral diagram with a "i". ·-------· | |(i)| |---|---| | | | ·-------· in the s.w. quarter, we have not enough information to use. in the s.e. quarter, we have none at all. we may read off the result as "some x are y'", or "some y' are x", whichever we prefer. pg ( ) ·---------------· | | | | ·---|---· | | | |(o)| | |---|(i)|---|---| | | |(o)| | | ·---|---· | |(o) | (o)| ·---------------· in the n.w. quarter, we have _no_ information. (the "i", sitting on the fence, is of no use to us until we know on _which_ side he means to jump down!) in the n.e. quarter, we have not enough information to use. neither have we in the s.w. quarter. ·-------· | | | |---|---| | |(o)| ·-------· the s.e. quarter is the only one that yields enough information to use. it is certainly _empty_: so we mark it as such on the biliteral diagram. we may read off the results as "no x' are y'", or "no y' are x'", whichever we prefer. ( ) ·---------------· |(o) | | | ·---|---· | | |(i)| | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | |(o) | | ·---------------· the n.w. quarter is _occupied_, in spite of the "o" in the outer cell. so we mark it with a "i" on the biliteral diagram. the n.e. quarter yields no information. ·-------· |(i)| | |---|---| | | | ·-------· the s.w. quarter is certainly _empty_. so we mark it as such on the biliteral diagram. ·-------· |(i)| | |---|---| |(o)| | ·-------· the s.e. quarter does not yield enough information to use. we read off the result as "all y are x."] [review tables v, vi (pp. , ). work examples § = =, - (p. ); § = =, - (p. ); § = =, - (p. ).] pg book v. syllogisms. chapter i. _introductory_ when a trio of biliteral propositions of relation is such that ( ) all their six terms are species of the same genus, ( ) every two of them contain between them a pair of codivisional classes, ( ) the three propositions are so related that, if the first two were true, the third would be true, the trio is called a '=syllogism='; the genus, of which each of the six terms is a species, is called its ='universe of discourse=', or, more briefly, its '=univ.='; the first two propositions are called its '=premisses=', and the third its '=conclusion='; also the pair of codivisional terms in the premisses are called its '=eliminands=', and the other two its '=retinends='. the conclusion of a syllogism is said to be '=consequent=' from its premisses: hence it is usual to prefix to it the word "therefore" (or the symbol ".'."). pg [note that the 'eliminands' are so called because they are _eliminated_, and do not appear in the conclusion; and that the 'retinends' are so called because they are _retained_, and _do_ appear in the conclusion. note also that the question, whether the conclusion is or is not _consequent_ from the premisses, is not affected by the _actual_ truth or falsity of any of the trio, but depends entirely on their _relationship to each other_. as a specimen-syllogism, let us take the trio "no x-things are m-things; no y-things are m'-things. no x-things are y-things." which we may write, as explained at p. , thus:-- "no x are m; no y are m'. no x are y". here the first and second contain the pair of codivisional classes m and m'; the first and third contain the pair x and x; and the second and third contain the pair y and y. also the three propositions are (as we shall see hereafter) so related that, if the first two were true, the third would also be true. hence the trio is a _syllogism_; the two propositions, "no x are m" and "no y are m'", are its _premisses_; the proposition "no x are y" is its _conclusion_; the terms m and m' are its _eliminands_; and the terms x and y are its _retinends_. hence we may write it thus:-- "no x are m; no y are m'. .'. no x are y". as a second specimen, let us take the trio "all cats understand french; some chickens are cats. some chickens understand french". these, put into normal form, are "all cats are creatures understanding french; some chickens are cats. some chickens are creatures understanding french". here all the six terms are species of the genus "creatures." also the first and second propositions contain the pair of codivisional classes "cats" and "cats"; the first and third contain the pair "creatures understanding french" and "creatures understanding french"; and the second and third contain the pair "chickens" and "chickens". pg also the three propositions are (as we shall see at p. ) so related that, if the first two were true, the third would be true. (the first two are, as it happens, _not_ strictly true in _our_ planet. but there is nothing to hinder them from being true in some _other_ planet, say _mars_ or _jupiter_--in which case the third would _also_ be true in that planet, and its inhabitants would probably engage chickens as nursery-governesses. they would thus secure a singular _contingent_ privilege, unknown in england, namely, that they would be able, at any time when provisions ran short, to utilise the nursery-governess for the nursery-dinner!) hence the trio is a _syllogism_; the genus "creatures" is its 'univ.'; the two propositions, "all cats understand french" and "some chickens are cats", are its _premisses_, the proposition "some chickens understand french" is its _conclusion_; the terms "cats" and "cats" are its _eliminands_; and the terms, "creatures understanding french" and "chickens", are its _retinends_. hence we may write it thus:-- "all cats understand french; some chickens are cats; .'. some chickens understand french".] pg chapter ii. _problems in syllogisms._ § . _introductory._ when the terms of a proposition are represented by _words_, it is said to be '=concrete='; when by _letters_, '=abstract=.' to translate a proposition from concrete into abstract form, we fix on a univ., and regard each term as a _species_ of it, and we choose a letter to represent its _differentia_. [for example, suppose we wish to translate "some soldiers are brave" into abstract form. we may take "men" as univ., and regard "soldiers" and "brave men" as _species_ of the _genus_ "men"; and we may choose x to represent the peculiar attribute (say "military") of "soldiers," and y to represent "brave." then the proposition may be written "some military men are brave men"; _i.e._ "some x-men are y-men"; _i.e._ (omitting "men," as explained at p. ) "some x are y." in practice, we should merely say "let univ. be "men", x = soldiers, y = brave", and at once translate "some soldiers are brave" into "some x are y."] the problems we shall have to solve are of two kinds, viz. ( ) "given a pair of propositions of relation, which contain between them a pair of codivisional classes, and which are proposed as premisses: to ascertain what conclusion, if any, is consequent from them." ( ) "given a trio of propositions of relation, of which every two contain a pair of codivisional classes, and which are proposed as a syllogism: to ascertain whether the proposed conclusion is consequent from the proposed premisses, and, if so, whether it is _complete_." these problems we will discuss separately. pg § . _given a pair of propositions of relation, which contain between them a pair of codivisional classes, and which are proposed as premisses: to ascertain what conclusion, if any, is consequent from them._ the rules, for doing this, are as follows:-- ( ) determine the 'universe of discourse'. ( ) construct a dictionary, making m and m (or m and m') represent the pair of codivisional classes, and x (or x') and y (or y') the other two. ( ) translate the proposed premisses into abstract form. ( ) represent them, together, on a triliteral diagram. ( ) ascertain what proposition, if any, in terms of x and y, is _also_ represented on it. ( ) translate this into concrete form. it is evident that, if the proposed premisses were true, this other proposition would _also_ be true. hence it is a _conclusion_ consequent from the proposed premisses. [let us work some examples. ( ) "no son of mine is dishonest; people always treat an honest man with respect". taking "men" as univ., we may write these as follows:-- "no sons of mine are dishonest men; all honest men are men treated with respect". we can now construct our dictionary, viz. m = honest; x = sons of mine; y = treated with respect. (note that the expression "x = sons of mine" is an abbreviated form of "x = the differentia of 'sons of mine', when regarded as a species of 'men'".) the next thing is to translate the proposed premisses into abstract form, as follows:-- "no x are m'; all m are y". pg next, by the process described at p. , we represent these on a triliteral diagram, thus:-- ·---------------· |(o) | (o)| | ·---|---· | | | |(o)| | |---|(i)|---|---| | | |(o)| | | ·---|---· | | | | ·---------------· next, by the process described at p. , we transfer to a biliteral diagram all the information we can. ·-------· | |(o)| |---|---| | | | ·-------· the result we read as "no x are y'" or as "no y' are x," whichever we prefer. so we refer to our dictionary, to see which will look best; and we choose "no x are y'", which, translated into concrete form, is "no son of mine fails to be treated with respect". ( ) "all cats understand french; some chickens are cats". taking "creatures" as univ., we write these as follows:-- "all cats are creatures understanding french; some chickens are cats". we can now construct our dictionary, viz. m = cats; x = understanding french; y = chickens. the proposed premisses, translated into abstract form, are "all m are x; some y are m". in order to represent these on a triliteral diagram, we break up the first into the two propositions to which it is equivalent, and thus get the _three_ propositions ( ) "some m are x; ( ) no m are x'; ( ) some y are m". the rule, given at p. , would make us take these in the order , , . this, however, would produce the result ·-----------------· | | | | ·----|----· | | |(i)(i) | | | |----|----| | | |(o) | (o)| | | ·----|----· | | | | ·-----------------· pg so it would be better to take them in the order , , . nos. ( ) and ( ) give us the result here shown; and now we need not trouble about no. ( ), as the proposition "some m are x" is _already_ represented on the diagram. ·---------------· | | | | ·---|---· | | |(i)| | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | | ·---------------· transferring our information to a biliteral diagram, we get ·-------· |(i)| | |---|---| | | | ·-------· this result we can read either as "some x are y" or "some y are x". after consulting our dictionary, we choose "some y are x", which, translated into concrete form, is "some chickens understand french." ( ) "all diligent students are successful; all ignorant students are unsuccessful". let univ. be "students"; m = successful; x = diligent; y = ignorant. these premisses, in abstract form, are "all x are m; all y are m'". these, broken up, give us the four propositions ( ) "some x are m; ( ) no x are m'; ( ) some y are m'; ( ) no y are m". which we will take in the order , , , . representing these on a triliteral diagram, we get ·---------------· |(o) | (o)| | ·---|---· | | |(o)|(i)| | |---|---|---|---| | |(o)| | | | ·---|---· | |(i) | | ·---------------· and this information, transferred to a biliteral diagram, is ·-------· |(o)|(i)| |---|---| |(i)| | ·-------· here we get _two_ conclusions, viz. "all x are y'; all y are x'." pg and these, translated into concrete form, are "all diligent students are (not-ignorant, i.e.) learned; all ignorant students are (not-diligent, i.e.) idle". (see p. .) ( ) "of the prisoners who were put on their trial at the last assizes, all, against whom the verdict 'guilty' was returned, were sentenced to imprisonment; some, who were sentenced to imprisonment, were also sentenced to hard labour". let univ. be "the prisoners who were put on their trial at the last assizes"; m = who were sentenced to imprisonment; x = against whom the verdict 'guilty' was returned; y = who were sentenced to hard labour. the premisses, translated into abstract form, are "all x are m; some m are y". breaking up the first, we get the three ( ) "some x are m; ( ) no x are m'; ( ) some m are y". representing these, in the order , , , on a triliteral diagram, we get ·---------------· |(o) | (o)| | ·---|---· | | | (i) | | |---|(i)|---|---| | | | | | | ·---|---· | | | | ·---------------· here we get no conclusion at all. you would very likely have guessed, if you had seen _only_ the premisses, that the conclusion would be "some, against whom the verdict 'guilty' was returned, were sentenced to hard labour". but this conclusion is not even _true_, with regard to the assizes i have here invented. "not _true!_" you exclaim. "then who _were_ they, who were sentenced to imprisonment and were also sentenced to hard labour? they _must_ have had the verdict 'guilty' returned against them, or how could they be sentenced?" well, it happened like _this_, you see. they were three ruffians, who had committed highway-robbery. when they were put on their trial, they _pleaded_ 'guilty'. so no _verdict_ was returned at all; and they were sentenced at once.] i will now work out, in their briefest form, as models for the reader to imitate in working examples, the above four concrete problems. pg ( ) [see p. ] "no son of mine is dishonest; people always treat an honest man with respect." univ. "men"; m = honest; x = my sons; y = treated with respect. ·---------------· ·-------· "no x are m'; |(o) | (o)| | |(o)| all m are y." | ·---|---· | |---|---| | | |(o)| | | | | |---|(i)|---|---| ·-------· | | |(o)| | | ·---|---· | .'. "no x are y'." | | | ·---------------· i.e. "no son of mine ever fails to be treated with respect." ( ) [see p. ] "all cats understand french; some chickens are cats". univ. "creatures"; m = cats; x = understanding french; y = chickens. ·---------------· ·-------· "all m are x; | | | |(i)| | some y are m." | ·---|---· | |---|---| | |(i)| | | | | | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. "some y are x." | | | ·---------------· i.e. "some chickens understand french." ( ) [see p. ] "all diligent students are successful; all ignorant students are unsuccessful". univ. "students"; m = successful; x = diligent; y = ignorant. ·---------------· ·-------· "all x are m; |(o) | (o)| |(o)|(i)| all y are m'." | ·---|---· | |---|---| | |(o)|(i)| | |(i)| | |---|---|---|---| ·-------· | |(o)| | | | ·---|---· | .'. "all x are y'; |(i) | | all y are x'." ·---------------· i.e. "all diligent students are learned; and all ignorant students are idle". pg ( ) [see p. ] "of the prisoners who were put on their trial at the last assizes, all, against whom the verdict 'guilty' was returned, were sentenced to imprisonment; some, who were sentenced to imprisonment, were also sentenced to hard labour". univ. "prisoners who were put on their trial at the last assizes", m = sentenced to imprisonment; x = against whom the verdict 'guilty' was returned; y = sentenced to hard labour. ·---------------· "all x are m; |(o) | (o)| some m are y." | ·---|---· | | | (i) | | |---|(i)|---|---| | | | | | | ·---|---· | there is no | | | conclusion. ·---------------· [review tables vii, viii (pp. , ). work examples § = =, - (p. ); § = =, - (p. ); § = =, - (p. ).] pg § . _given a trio of propositions of relation, of which every two contain a pair of codivisional classes, and which are proposed as a syllogism; to ascertain whether the proposed conclusion is consequent from the proposed premisses, and, if so, whether it is complete._ the rules, for doing this, are as follows:-- ( ) take the proposed premisses, and ascertain, by the process described at p. , what conclusion, if any, is consequent from them. ( ) if there be _no_ conclusion, say so. ( ) if there _be_ a conclusion, compare it with the proposed conclusion, and pronounce accordingly. i will now work out, in their briefest form, as models for the reader to imitate in working examples, six problems. ( ) "all soldiers are strong; all soldiers are brave. some strong men are brave." univ. "men"; m = soldiers; x = strong; y = brave. pg ·---------------· ·-------· "all m are x; | | | |(i)| | all m are y. | ·---|---· | |---|---| some x are y." | |(i)|(o)| | | | | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. "some x are y." | | | ·---------------· hence proposed conclusion is right. ( ) "i admire these pictures; when i admire anything i wish to examine it thoroughly. i wish to examine some of these pictures thoroughly." univ. "things"; m = admired by me; x = these pictures; y = things which i wish to examine thoroughly. ·---------------· ·-------· "all x are m; |(o) | (o)| |(i)|(o)| all m are y. | ·---|---· | |---|---| some x are y." | |(i)|(o)| | | | | |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | .'. "all x are y." | | | ·---------------· hence proposed conclusion is _incomplete_, the _complete_ one being "i wish to examine _all_ these pictures thoroughly". ( ) "none but the brave deserve the fair; some braggarts are cowards. some braggarts do not deserve the fair." univ. "persons"; m = brave; x = deserving of the fair; y = braggarts. ·---------------· ·-------· "no m' are x; |(o) | (o)| | | | some y are m'. | ·---|---· | |---|---| some y are x'." | | | | | |(i)| | |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. "some y are x'." |(i) | | ·---------------· hence proposed conclusion is right. pg ( ) "all soldiers can march; some babies are not soldiers. some babies cannot march". univ. "persons"; m = soldiers; x = able to march; y = babies. ·---------------· "all m are x; | | | some y are m'. | ·---|---· | some y are x'." | | (i) | | |(i)|---|---|---| | |(o)|(o)| | | ·---|---· | there is no | | | conclusion. ·---------------· ( ) "all selfish men are unpopular; all obliging men are popular. all obliging men are unselfish". univ. "men"; m = popular; x = selfish; y = obliging. ·---------------· ·-------· "all x are m'; |(o) | (i)| |(o)|(i)| all y are m. | ·---|---· | |---|---| all y are x'." | |(o)|(o)| | |(i)| | |---|---|---|---| ·-------· | |(i)| | | | ·---|---· | .'. "all x are y'; |(o) | | all y are x'." ·---------------· hence proposed conclusion is _incomplete_, the _complete_ one containing, in addition, "all selfish men are disobliging". ( ) "no one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running; this party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station. this party of tourists need not run." univ. "persons meaning to go by the train, and unable to get a conveyance"; m = having enough time to walk to the station; x = needing to run; y = these tourists. pg ·---------------· "no m' are x'; |(o) | | all y are m. | ·---|---· | all y are x'." | | | | | |---|(i)|---|---| | | | | | | ·---|---· | there is no |(o) | (o)| conclusion. ·---------------· [here is _another_ opportunity, gentle reader, for playing a trick on your innocent friend. put the proposed syllogism before him, and ask him what he thinks of the conclusion. he will reply "why, it's perfectly correct, of course! and if your precious logic-book tells you it _isn't_, don't believe it! you don't mean to tell me those tourists _need_ to run? if _i_ were one of them, and knew the _premisses_ to be true, i should be _quite_ clear that i _needn't_ run--and i _should walk!_" and _you_ will reply "but suppose there was a mad bull behind you?" and then your innocent friend will say "hum! ha! i must think that over a bit!" you may then explain to him, as a convenient _test_ of the soundness of a syllogism, that, if circumstances can be invented which, without interfering with the truth of the _premisses_, would make the _conclusion_ false, the syllogism _must_ be unsound.] [review tables v-viii (pp. - ). work examples § = =, - (p. ); § = =, - (p. ); § = =, - (p. ); § = =, - (pp. , ).] pg book vi. the method of subscripts. chapter i. _introductory._ let us agree that "x_{ }" shall mean "some existing things have the attribute x", i.e. (more briefly) "some x exist"; also that "xy_{ }" shall mean "some xy exist", and so on. such a proposition may be called an '=entity=.' [note that, when there are _two_ letters in the expression, it does not in the least matter which stands _first_: "xy_{ }" and "yx_{ }" mean exactly the same.] also that "x_{ }" shall mean "no existing things have the attribute x", i.e. (more briefly) "no x exist"; also that "xy_{ }" shall mean "no xy exist", and so on. such a proposition may be called a '=nullity='. also that "+" shall mean "and". [thus "ab_{ } + cd_{ }" means "some ab exist and no cd exist".] also that "¶" shall mean "would, if true, prove". [thus, "x_{ } ¶ xy_{ }" means "the proposition 'no x exist' would, if true, prove the proposition 'no xy exist'".] when two letters are both of them accented, or both _not_ accented, they are said to have '=like signs=', or to be '=like=': when one is accented, and the other not, they are said to have '=unlike signs=', or to be '=unlike='. pg chapter ii. _representation of propositions of relation._ let us take, first, the proposition "some x are y". this, we know, is equivalent to the proposition of existence "some xy exist". (see p. .) hence it may be represented by the expression "xy_{ }". the converse proposition "some y are x" may of course be represented by the _same_ expression, viz. "xy_{ }". similarly we may represent the three similar pairs of converse propositions, viz.-- "some x are y'"  = "some y' are x", "some x' are y"  = "some y are x'", "some x' are y'" = "some y' are x'". let us take, next, the proposition "no x are y". this, we know, is equivalent to the proposition of existence "no xy exist". (see p. .) hence it may be represented by the expression "xy_{ }". the converse proposition "no y are x" may of course be represented by the _same_ expression, viz. "xy_{ }". similarly we may represent the three similar pairs of converse propositions, viz.-- "no x are y'"  = "no y' are x", "no x' are y"  = "no y are x'", "no x' are y'" = "no y' are x'". pg let us take, next, the proposition "all x are y". now it is evident that the double proposition of existence "some x exist and no xy' exist" tells us that _some_ x-things exist, but that _none_ of them have the attribute y': that is, it tells us that _all_ of them have the attribute y: that is, it tells us that "all x are y". also it is evident that the expression "x_{ } + xy'_{ }" represents this double proposition. hence it also represents the proposition "all x are y". [the reader will perhaps be puzzled by the statement that the proposition "all x are y" is equivalent to the double proposition "some x exist and no xy' exist," remembering that it was stated, at p. , to be equivalent to the double proposition "some x are y and no x are y'" (i.e. "some xy exist and no xy' exist"). the explanation is that the proposition "some xy exist" contains _superfluous information_. "some x exist" is enough for our purpose.] this expression may be written in a shorter form, viz. "x_{ }y'_{ }", since _each_ subscript takes effect back to the _beginning_ of the expression. similarly we may represent the seven similar propositions "all x are y'", "all x' are y", "all x' are y'", "all y are x", "all y are x'", "all y' are x", and "all y' are x'". [the reader should make out all these for himself.] it will be convenient to remember that, in translating a proposition, beginning with "all", from abstract form into subscript form, or _vice versâ_, the predicate _changes sign_ (that is, changes from positive to negative, or else from negative to positive). [thus, the proposition "all y are x'" becomes "y_{ }x_{ }", where the predicate changes from x' to x. again, the expression "x'_{ }y'_{ }" becomes "all x' are y", where the predicate changes for y' to y.] pg chapter iii. _syllogisms._ § . _representation of syllogisms._ we already know how to represent each of the three propositions of a syllogism in subscript form. when that is done, all we need, besides, is to write the three expressions in a row, with "+" between the premisses, and "¶" before the conclusion. [thus the syllogism "no x are m'; all m are y. .'. no x are y'." may be represented thus:-- xm'_{ } + m_{ }y'_{ } ¶ xy'_{ } when a proposition has to be translated from concrete form into subscript form, the reader will find it convenient, just at first, to translate it into _abstract_ form, and _thence_ into subscript form. but, after a little practice, he will find it quite easy to go straight from concrete form to subscript form.] pg § . _formulæ for solving problems in syllogisms._ when once we have found, by diagrams, the conclusion to a given pair of premisses, and have represented the syllogism in subscript form, we have a _formula_, by which we can at once find, without having to use diagrams again, the conclusion to any _other_ pair of premisses having the _same_ subscript forms. [thus, the expression xm_{ } + ym'_{ } ¶ xy_{ } is a formula, by which we can find the conclusion to any pair of premisses whose subscript forms are xm_{ } + ym'_{ } for example, suppose we had the pair of propositions "no gluttons are healthy; no unhealthy men are strong". proposed as premisses. taking "men" as our 'universe', and making m = healthy; x = gluttons; y = strong; we might translate the pair into abstract form, thus:-- "no x are m; no m' are y". these, in subscript form, would be xm_{ } + m'y_{ } which are identical with those in our _formula_. hence we at once know the conclusion to be xy_{ } that is, in abstract form, "no x are y"; that is, in concrete form, "no gluttons are strong".] i shall now take three different forms of pairs of premisses, and work out their conclusions, once for all, by diagrams; and thus obtain some useful formulæ. i shall call them "fig. i", "fig. ii", and "fig. iii". pg fig. i. this includes any pair of premisses which are both of them nullities, and which contain unlike eliminands. the simplest case is ·---------------· ·-------· xm_{ } + ym'_{ } |(o) | | |(o)| | | ·---|---· | |---|---| | |(o)|(o)| | | | | |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. xy_{ } |(o) | | ·---------------· in this case we see that the conclusion is a nullity, and that the retinends have kept their signs. and we should find this rule to hold good with _any_ pair of premisses which fulfil the given conditions. [the reader had better satisfy himself of this, by working out, on diagrams, several varieties, such as m_{ }x_{ } + ym'_{ } (which ¶ xy_{ }) xm'_{ } + m_{ }y_{ } (which ¶ xy_{ }) x'm_{ } + ym'_{ } (which ¶ x'y_{ }) m'_{ }x'_{ } + m_{ }y'_{ } (which ¶ x'y'_{ }).] if either retinend is asserted in the _premisses_ to exist, of course it may be so asserted in the _conclusion_. hence we get two _variants_ of fig. i, viz. (a) where _one_ retinend is so asserted; (b) where _both_ are so asserted. [the reader had better work out, on diagrams, examples of these two variants, such as m_{ }x_{ } + y_{ }m'_{ } (which proves y_{ }x_{ }) x_{ }m'_{ } + m_{ }y_{ } (which proves x_{ }y_{ }) x'_{ }m_{ } + y_{ }m'_{ } (which proves x'_{ }y_{ } + y_{ }x'_{ }).] the formula, to be remembered, is xm_{ } + ym'_{ } ¶ xy_{ } with the following two rules:-- ( ) _two nullities, with unlike eliminands, yield a nullity, in which both retinends keep their signs._ pg ( ) _a retinend, asserted in the premisses to exist, may be so asserted in the conclusion._ [note that rule ( ) is merely the formula expressed in words.] fig. ii. this includes any pair of premisses, of which one is a nullity and the other an entity, and which contain like eliminands. the simplest case is xm_{ } + ym_{ } ·---------------· ·-------· | | | | | | | ·---|---· | |---|---| | |(o)|(o)| | |(i)| | |---|---|---|---| ·-------· | |(i)| | | | ·---|---· | .'. x'y_{ } | | | ·---------------· in this case we see that the conclusion is an entity, and that the nullity-retinend has changed its sign. and we should find this rule to hold good with _any_ pair of premisses which fulfil the given conditions. [the reader had better satisfy himself of this, by working out, on diagrams, several varieties, such as x'm_{ } + ym_{ } (which ¶ xy_{ }) x_{ }m'_{ } + y'm'_{ } (which ¶ x'y'_{ }) m_{ }x_{ } + y'm_{ } (which ¶ x'y'_{ }).] the formula, to be remembered, is, xm_{ } + ym_{ } ¶ x'y_{ } with the following rule:-- _a nullity and an entity, with like eliminands, yield an entity, in which the nullity-retinend changes its sign._ [note that this rule is merely the formula expressed in words.] pg fig. iii. this includes any pair of premisses which are both of them nullities, and which contain like eliminands asserted to exist. the simplest case is xm_{ } + ym_{ } + m_{ } [note that "m_{ }" is here stated _separately_, because it does not matter in which of the two premisses it occurs: so that this includes the _three_ forms "m_{ }x_{ } + ym_{ }", "xm_{ } + m_{ }y_{ }", and "m_{ }x_{ } + m_{ }y_{ }".] ·---------------· ·-------· | | | | | | | ·---|---· | |---|---| | |(o)|(o)| | | |(i)| |---|---|---|---| ·-------· | |(o)|(i)| | | ·---|---· | .'. x'y'_{ } | | | ·---------------· in this case we see that the conclusion is an entity, and that _both_ retinends have changed their signs. and we should find this rule to hold good with _any_ pair of premisses which fulfil the given conditions. [the reader had better satisfy himself of this, by working out, on diagrams, several varieties, such as x'm_{ } + m_{ }y_{ } (which ¶ xy'_{ }) m'_{ }x_{ } + m'y'_{ } (which ¶ x'y_{ }) m_{ }x'_{ } + m_{ }y'_{ } (which ¶ xy_{ }).] the formula, to be remembered, is xm_{ } + ym_{ } + m_{ } ¶ x'y'_{ } with the following rule (which is merely the formula expressed in words):-- _two nullities, with like eliminands asserted to exist, yield an entity, in which both retinends change their signs._ * * * * * in order to help the reader to remember the peculiarities and formulæ of these three figures, i will put them all together in one table. pg table ix. _______________________________________________________ | | | fig. i. | | | | xm_{ } + ym'_{ } ¶ xy_{ } | | | | two nullities, with unlike eliminands, yield a | | nullity, in which both retinends keep their signs. | | | | a retinend, asserted in the premisses to exist, may | | be so asserted in the conclusion. | |_______________________________________________________| | | | fig. ii. | | | | xm_{ } + ym_{ } ¶ x'y_{ } | | | | a nullity and an entity, with like eliminands, | | yield an entity, in which the nullity-retinend | | changes its sign. | |_______________________________________________________| | | | fig. iii. | | | | xm_{ } + ym_{ } + m_{ } ¶ x'y'_{ } | | | | two nullities, with like eliminands asserted | | to exist, yield an entity, in which both retinends | | change their signs. | |_______________________________________________________| i will now work out, by these formulæ, as models for the reader to imitate, some problems in syllogisms which have been already worked, by diagrams, in book v., chap. ii. ( ) [see p. ] "no son of mine is dishonest; people always treat an honest man with respect." univ. "men"; m = honest; x = my sons; y = treated with respect. xm'_{ } + m_{ }y'_{ } ¶ xy'_{ } [fig. i. _i.e._ "no son of mine ever fails to be treated with respect." pg ( ) [see p. ] "all cats understand french; some chickens are cats." univ. "creatures"; m = cats; x = understanding french; y = chickens. m_{ }x'_{ } + ym_{ } ¶ xy_{ } [fig. ii. _i.e._ "some chickens understand french." ( ) [see p. ] "all diligent students are successful; all ignorant students are unsuccessful." univ. "students"; m = successful; x = diligent; y = ignorant. x_{ }m'_{ } + y_{ }m_{ } ¶ x_{ }y_{ } + y_{ }x_{ } [fig. i (b). _i.e._ "all diligent students are learned; and all ignorant students are idle." ( ) [see p. ] "all soldiers are strong; all soldiers are brave. some strong men are brave." univ. "men"; m = soldiers; x = strong; y = brave. m_{ }x'_{ } + m_{ }y'_{ } ¶ xy_{ } [fig. iii. hence proposed conclusion is right. ( ) [see p. ] "i admire these pictures; when i admire anything, i wish to examine it thoroughly. i wish to examine some of these pictures thoroughly." univ. "things"; m = admired by me; x = these; y = things which i wish to examine thoroughly. x_{ }m'_{ } + m_{ }y'_{ } ¶ x_{ }y'_{ } [fig. i (a). hence proposed conclusion, xy_{ }, is _incomplete_, the _complete_ one being "i wish to examine _all_ these pictures thoroughly." pg ( ) [see p. ] "none but the brave deserve the fair; some braggarts are cowards. some braggarts do not deserve the fair." univ. "persons"; m = brave; x = deserving of the fair; y = braggarts. m'x_{ } + ym'_{ } ¶ x'y_{ } [fig. ii. hence proposed conclusion is right. ( ) [see p. ] "no one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running; this party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station. this party of tourists need not run." univ. "persons meaning to go by the train, and unable to get a conveyance"; m = having enough time to walk to the station; x = needing to run; y = these tourists. m'x'_{ } + y_{ }m'_{ } do not come under any of the three figures. hence it is necessary to return to the method of diagrams, as shown at p. . hence there is no conclusion. [work examples § = =, - (p. ); § = =, - (pp. , ); § = =, - (p. ); § = =, - (pp. , ). also read note (a), at p. .] pg § . _fallacies._ any argument which _deceives_ us, by seeming to prove what it does not really prove, may be called a '=fallacy=' (derived from the latin verb _fallo_ "i deceive"): but the particular kind, to be now discussed, consists of a pair of propositions, which are proposed as the premisses of a syllogism, but yield no conclusion. when each of the proposed premisses is a proposition in _i_, or _e_, or _a_, (the only kinds with which we are now concerned,) the fallacy may be detected by the 'method of diagrams,' by simply setting them out on a triliteral diagram, and observing that they yield no information which can be transferred to the biliteral diagram. but suppose we were working by the 'method of _subscripts_,' and had to deal with a pair of proposed premisses, which happened to be a 'fallacy,' how could we be certain that they would not yield any conclusion? our best plan is, i think, to deal with _fallacies_ in the same was as we have already dealt with _syllogisms_: that is, to take certain forms of pairs of propositions, and to work them out, once for all, on the triliteral diagram, and ascertain that they yield _no_ conclusion; and then to record them, for future use, as _formulæ for fallacies_, just as we have already recorded our three _formulæ for syllogisms_. pg now, if we were to record the two sets of formulæ in the _same_ shape, viz. by the method of subscripts, there would be considerable risk of confusing the two kinds. hence, in order to keep them distinct, i propose to record the formulæ for _fallacies_ in _words_, and to call them "forms" instead of "formulæ." let us now proceed to find, by the method of diagrams, three "forms of fallacies," which we will then put on record for future use. they are as follows:-- ( ) fallacy of like eliminands not asserted to exist. ( ) fallacy of unlike eliminands with an entity-premiss. ( ) fallacy of two entity-premisses. these shall be discussed separately, and it will be seen that each fails to yield a conclusion. ( ) _fallacy of like eliminands not asserted to exist._ it is evident that neither of the given propositions can be an _entity_, since that kind asserts the _existence_ of both of its terms (see p. ). hence they must both be _nullities_. hence the given pair may be represented by (xm_{ } + ym_{ }), with or without x_{ }, y_{ }. these, set out on triliteral diagrams, are xm_{ } + ym_{ } x_{ }m_{ } + ym_{ } ·---------------· ·---------------· | | | | (i) | | ·---|---· | | ·---|---· | | |(o)|(o)| | | |(o)|(o)| | |---|---|---|---| |---|---|---|---| | |(o)| | | | |(o)| | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· xm_{ } + y_{ }m_{ } x_{ }m_{ } + y_{ }m_{ } ·---------------· ·---------------· | | | | (i) | | ·---|---· | | ·---|---· | | |(o)|(o)| | | |(o)|(o)| | |(i)|---|---|---| |(i)|---|---|---| | |(o)| | | | |(o)| | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· pg ( ) _fallacy of unlike eliminands with an entity-premiss._ here the given pair may be represented by (xm_{ } + ym'_{ }) with or without x_{ } or m_{ }. these, set out on triliteral diagrams, are xm_{ } + ym'_{ } x_{ }m_{ } + ym'_{ } m_{ }x_{ } + ym'_{ } ·---------------· ·---------------· ·---------------· | | | | (i) | | | | | ·---|---· | | ·---|---· | | ·---|---· | | |(o)|(o)| | | |(o)|(o)| | | |(o)|(o)| | |(i)|---|---|---| |(i)|---|---|---| |(i)|---|---|---| | | | | | | | | | | | | (i) | | | ·---|---· | | ·---|---· | | ·---|---· | | | | | | | | | | ·---------------· ·---------------· ·---------------· ( ) _fallacy of two entity-premisses._ here the given pair may be represented by either (xm_{ } + ym_{ }) or (xm_{ } + ym'_{ }). these, set out on triliteral diagrams, are xm_{ } + ym_{ } xm_{ } + ym'_{ } ·---------------· ·---------------· | | | | | | | ·---|---· | | ·---|---· | | | (i) | | | | (i) | | |---|(i)|---|---| |(i)|---|---|---| | | | | | | | | | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------· pg § . _method of proceeding with a given pair of propositions._ let us suppose that we have before us a pair of propositions of relation, which contain between them a pair of codivisional classes, and that we wish to ascertain what conclusion, if any, is consequent from them. we translate them, if necessary, into subscript-form, and then proceed as follows:-- ( ) we examine their subscripts, in order to see whether they are (a) a pair of nullities; or (b) a nullity and an entity; or (c) a pair of entities. ( ) if they are a pair of nullities, we examine their eliminands, in order to see whether they are unlike or like. if their eliminands are _unlike_, it is a case of fig. i. we then examine their retinends, to see whether one or both of them are asserted to _exist_. if one retinend is so asserted, it is a case of fig. i (a); if both, it is a case of fig. i (b). if their eliminands are like, we examine them, in order to see whether either of them is asserted to exist. if so, it is a case of fig. iii.; if not, it is a case of "fallacy of like eliminands not asserted to exist." ( ) if they are a nullity and an entity, we examine their eliminands, in order to see whether they are like or unlike. if their eliminands are like, it is a case of fig. ii.; if _unlike_, it is a case of "fallacy of unlike eliminands with an entity-premiss." ( ) if they are a pair of entities, it is a case of "fallacy of two entity-premisses." [work examples § = =, - (p. ); § = =, - (p. ); § = =, - (p. ); § = =, - (p. ).] pg book vii. soriteses. chapter i. _introductory._ when a set of three or more biliteral propositions are such that all their terms are species of the same genus, and are also so related that two of them, taken together, yield a conclusion, which, taken with another of them, yields another conclusion, and so on, until all have been taken, it is evident that, if the original set were true, the last conclusion would _also_ be true. such a set, with the last conclusion tacked on, is called a '=sorites='; the original set of propositions is called its '=premisses='; each of the intermediate conclusions is called a '=partial conclusion=' of the sorites; the last conclusion is called its '=complete conclusion=,' or, more briefly, its '=conclusion='; the genus, of which all the terms are species, is called its '=universe of discourse=', or, more briefly, its '=univ.='; the terms, used as eliminands in the syllogisms, are called its '=eliminands='; and the two terms, which are retained, and therefore appear in the conclusion, are called its '=retinends='. [note that each _partial_ conclusion contains one or two _eliminands_; but that the _complete_ conclusion contains _retinends_ only.] the conclusion is said to be '=consequent=' from the premisses; for which reason it is usual to prefix to it the word "therefore" (or the symbol ".'."). [note that the question, whether the conclusion is or is not _consequent_ from the premisses, is not affected by the _actual_ truth or falsity of any one of the propositions which make up the sorites, by depends entirely on their _relationship to one another_. pg as a specimen-sorites, let us take the following set of propositions:-- ( ) "no a are b'; ( ) all b are c; ( ) all c are d; ( ) no e' are a'; ( ) all h are e'". here the first and second, taken together, yield "no a are c'". this, taken along with the third, yields "no a are d'". this, taken along with the fourth, yields "no d' are e'". and this, taken along with the fifth, yields "all h are d". hence, if the original set were true, this would _also_ be true. hence the original set, with this tacked on, is a _sorites_; the original set is its _premisses_; the proposition "all h are d" is its _conclusion_; the terms a, b, c, e are its _eliminands_; and the terms d and h are its _retinends_. hence we may write the whole sorites thus:-- "no a are b'; all b are c; all c are d; no e' are a'; all h are e'. .'. all h are d". in the above sorites, the partial conclusions are the positions "no a are e'", "no a are d'", "no d' are e'"; but, if the premisses were arranged in other ways, other partial conclusions might be obtained. thus, the order yields the partial conclusions "no c' are b'", "all h are b", "all h are c". there are altogether _nine_ partial conclusions to this sorites, which the reader will find it an interesting task to make out for himself.] pg chapter ii. _problems in soriteses._ § . _introductory._ the problems we shall have to solve are of the following form:-- "given three or more propositions of relation, which are proposed as premisses: to ascertain what conclusion, if any, is consequent from them." we will limit ourselves, at present, to problems which can be worked by the formulæ of fig. i. (see p. .) those, that require _other_ formulæ, are rather too hard for beginners. such problems may be solved by either of two methods, viz. ( ) the method of separate syllogisms; ( ) the method of underscoring. these shall be discussed separately. pg § . _solution by method of separate syllogisms._ the rules, for doing this, are as follows:-- ( ) name the 'universe of discourse'. ( ) construct a dictionary, making a, b, c, &c. represent the terms. ( ) put the proposed premisses into subscript form. ( ) select two which, containing between them a pair of codivisional classes, can be used as the premisses of a syllogism. ( ) find their conclusion by formula. ( ) find a third premiss which, along with this conclusion, can be used as the premisses of a second syllogism. ( ) find a second conclusion by formula. ( ) proceed thus, until all the proposed premisses have been used. ( ) put the last conclusion, which is the complete conclusion of the sorites, into concrete form. [as an example of this process, let us take, as the proposed set of premisses, ( ) "all the policemen on this beat sup with our cook; ( ) no man with long hair can fail to be a poet; ( ) amos judd has never been in prison; ( ) our cook's 'cousins' all love cold mutton; ( ) none but policemen on this beat are poets; ( ) none but her 'cousins' ever sup with our cook; ( ) men with short hair have all been in prison." univ. "men"; a = amos judd; b = cousins of our cook; c = having been in prison; d = long-haired; e = loving cold mutton; h = poets; k = policemen on this beat; l = supping with our cook pg we now have to put the proposed premisses into _subscript_ form. let us begin by putting them into _abstract_ form. the result is ( ) "all k are l; ( ) no d are h'; ( ) all a are c'; ( ) all b are e; ( ) no k' are h; ( ) no b' are l; ( ) all d' are c." and it is now easy to put them into _subscript_ form, as follows:-- ( ) k_{ }l'_{ } ( ) dh'_{ } ( ) a_{ }c_{ } ( ) b_{ }e'_{ } ( ) k'h_{ } ( ) b'l_{ } ( ) d'_{ }c'_{ } we now have to find a pair of premisses which will yield a conclusion. let us begin with no. ( ), and look down the list, till we come to one which we can take along with it, so as to form premisses belonging to fig. i. we find that no. ( ) will do, since we can take k as our eliminand. so our first syllogism is ( ) k_{ }l'_{ } ( ) k'h_{ } .'. l'h_{ } ... ( ) we must now begin again with l'h_{ } and find a premiss to go along with it. we find that no. ( ) will do, h being our eliminand. so our next syllogism is ( ) l'h_{ } ( ) dh'_{ } .'. l'd_{ } ... ( ) we have now used up nos. ( ), ( ), and ( ), and must search among the others for a partner for l'd_{ }. we find that no. ( ) will do. so we write ( ) l'd_{ } ( ) b'l_{ } .'. db'_{ } ... ( ) now what can we take along with db'_{ }? no. ( ) will do. ( ) db'_{ } ( ) b_{ }e'_{ } .'. de'_{ } ... ( ) pg along with this we may take no. ( ). ( ) de'_{ } ( ) d'_{ }c'_{ } .'. c'e'_{ } ... ( ) and along with this we may take no. ( ). ( ) c'e'_{ } ( ) a_{ }c_{ } .'. a_{ }e'_{ } this complete conclusion, translated into _abstract_ form, is "all a are e"; and this, translated into _concrete_ form, is "amos judd loves cold mutton." in actually _working_ this problem, the above explanations would, of course, be omitted, and all, that would appear on paper, would be as follows:-- ( ) k_{ }l'_{ } ( ) dh'_{ } ( ) a_{ }c_{ } ( ) b_{ }e'_{ } ( ) k'h_{ } ( ) b'l_{ } ( ) d'_{ }c'_{ } ( ) k_{ }l'_{ } ( ) k'h_{ } .'. l'h_{ } ... ( ) ( ) l'h_{ } ( ) dh'_{ } .'. l'd_{ } ... ( ) ( ) l'd_{ } ( ) b'l_{ } .'. db'_{ } ... ( ) ( ) db'_{ } ( ) b_{ }e'_{ } .'. de'_{ } ... ( ) ( ) de'_{ } ( ) d'_{ }c'_{ } .'. c'e'_{ } ... ( ) ( ) c'e'_{ } ( ) a_{ }c_{ } .'. a_{ }e'_{ } note that, in working a sorites by this process, we may begin with _any_ premiss we choose.] pg § . _solution by method of underscoring._ consider the pair of premisses xm_{ } + ym'_{ } which yield the conclusion xy_{ } we see that, in order to get this conclusion, we must eliminate m and m', and write x and y together in one expression. now, if we agree to _mark_ m and m' as eliminated, and to read the two expressions together, as if they were written in one, the two premisses will then exactly represent the _conclusion_, and we need not write it out separately. let us agree to mark the eliminated letters by _underscoring_ them, putting a _single_ score under the _first_, and a _double_ one under the _second_. the two premisses now become xm_{ } + ym'_{ } - = which we read as "xy_{ }". in copying out the premisses for underscoring, it will be convenient to _omit all subscripts_. as to the " 's" we may always _suppose_ them written, and, as to the " 's", we are not concerned to know _which_ terms are asserted to _exist_, except those which appear in the _complete_ conclusion; and for _them_ it will be easy enough to refer to the original list. pg [i will now go through the process of solving, by this method, the example worked in § . the data are k_{ }l'_{ } + dh'_{ } + a_{ }c_{ } + b_{ }e'_{ } + k'h_{ } + b'l_{ } + d'_{ }c'_{ } the reader should take a piece of paper, and write out this solution for himself. the first line will consist of the above data; the second must be composed, bit by bit, according to the following directions. we begin by writing down the first premiss, with its numeral over it, but omitting the subscripts. we have now to find a premiss which can be combined with this, _i.e._, a premiss containing either k' or l. the first we find is no. ; and this we tack on, with a +. to get the _conclusion_ from these, k and k' must be eliminated, and what remains must be taken as one expression. so we _underscore_ them, putting a _single_ score under k, and a _double_ one under k'. the result we read as l'h. we must now find a premiss containing either l or h'. looking along the row, we fix on no. , and tack it on. now these nullities are really equivalent to (l'h + dh'), in which h and h' must be eliminated, and what remains taken as one expression. so we _underscore_ them. the result reads as l'd. we now want a premiss containing l or d'. no. will do. these nullities are really equivalent to (l'd + b'l). so we underscore l' and l. the result reads as db'. we now want a premiss containing d' or b. no. will do. here we underscore b' and b. the result reads as de'. we now want a premiss containing d' or e. no. will do. here we underscore d and d'. the result reads as c'e'. we now want a premiss containing c or e. no. will do--in fact _must_ do, as it is the only one left. here we underscore c' and c; and, as the whole thing now reads as e'a, we tack on e'a_{ } as the _conclusion_, with a ¶. we now look along the row of data, to see whether e' or a has been given as _existent_. we find that a has been so given in no. . so we add this fact to the conclusion, which now stands as ¶ e'a_{ } + a_{ }, _i.e._ ¶ a_{ }e'_{ }; i.e. "all a are e." if the reader has faithfully obeyed the above directions, his written solution will now stand as follows:-- k_{ }l'_{ } + dh'_{ } + a_{ }c_{ } + b_{ }e'_{ } + k'h_{ } + b'l_{ } + d'_{ }c'_{ } kl' + k'h + dh' + b'l + be' + d'c' + ac -- = - -= - = = = - = ¶ e'a_{ } + a_{ } _i.e._ ¶ a_{ }e'_{ }; _i.e._ "all a are e." pg the reader should now take a second piece of paper, and copy the data only, and try to work out the solution for himself, beginning with some other premiss. if he fails to bring out the conclusion a_{ }e'_{ }, i would advise him to take a third piece of paper, and _begin again_!] i will now work out, in its briefest form, a sorites of premisses, to serve as a model for the reader to imitate in working examples. ( ) "i greatly value everything that john gives me; ( ) nothing but this bone will satisfy my dog; ( ) i take particular care of everything that i greatly value; ( ) this bone was a present from john; ( ) the things, of which i take particular care, are things i do _not_ give to my dog". univ. "things"; a = given by john to me; b = given by me to my dog; c = greatly valued by me; d = satisfactory to my dog; e = taken particular care of by me; h = this bone. a_{ }c'_{ } + h'd_{ } + c_{ }e'_{ } + h_{ }a'_{ } + e_{ }b_{ } ac' + ce' + ha' + h'd + eb ¶ db_{ } -- =- -= = = i.e. "nothing, that i give my dog, satisfies him," or, "my dog is not satisfied with _anything_ that i give him!" [note that, in working a sorites by this process, we may begin with _any_ premiss we choose. for instance, we might begin with no. , and the result would then be eb + ce' + ac' + ha' + h'd ¶ bd_{ }] - -= -= -= = [work examples § = =, - (p. ); § = =, - (p. ); § = =, - (p. ); § = =, - (p. ); § = =, - , , , , (pp. , ); § = =, - , , , , (pp. , , , ).] pg the reader, who has successfully grappled with all the examples hitherto set, and who thirsts, like alexander the great, for "more worlds to conquer," may employ his spare energies on the following examination-papers. he is recommended not to attempt more than _one_ paper on any one day. the answers to the questions about words and phrases may be found by referring to the index at p. . i. § = =, (p. ); § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, , (p. ); § = =, , , (pp. , , ). what is 'classification'? and what is a 'class'? ii. § = =, (p. ); § = =, - (pp. , ); § = =, (p. ); § = =, , (p. ); § = =, , (p. ); § = =, , , (pp. , , ). what are 'genus', 'species', and 'differentia'? iii. § = =, (p. ); § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, , (p. ); § = =, , , (pp. , , ). what are 'real' and 'imaginary' classes? iv. § = =, (p. ); § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, , (p. ); § = =, , , (pp. , , ). what is 'division'? when are classes said to be 'codivisional'? v. § = =, (p. ); § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, , (p. ); § = =, , , (pp. , , ). what is 'dichotomy'? what arbitrary rule does it sometimes require? pg vi. § = =, (p. ); § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is a 'definition'? vii. § = =, (p. ); § = =, - (pp. , ); § = =, , (p. ); § = =, (p. ); § = =, (p. ); § = =, , , (pp. , , ). what are the 'subject' and the 'predicate' of a proposition? what is its 'normal' form? viii. § = =, (p. ); § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is a proposition 'in _i_'? 'in _e_'? and 'in _a_'? ix. § = =, (p. ); § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is the 'normal' form of a proposition of existence? x. § = =, (p. ); § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is the 'universe of discourse'? xi. § = =, (p. ); § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is implied, in a proposition of relation, as to the reality of its terms? xii. § = =, (p. ); § = =, - (p. ); § = =, (p. ); § = =, , (pp. , ); § = =, (p. ); § = =, , , (pp. , , ). explain the phrase "sitting on the fence". xiii. § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, (p. ); § = =, , , (pp. , , ). what are 'converse' propositions? xiv. § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, (p. ); § = =, , , (pp. , , ). what are 'concrete' and 'abstract' propositions? pg xv. § = =, - (p. ); § = =, , (p. ); § = =, (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is a 'syllogism'? and what are its 'premisses' and its 'conclusion'? xvi. § = =, - (p. ); § = =, (p. ); § = =, , (p. ); § = =, (p. ); § = =, , , (pp. , , ). what is a 'sorites'? and what are its 'premisses', its 'partial conclusions', and its 'complete conclusion'? xvii. § = =, - (p. ); § = =, (p. ); § = =, (p. ); § = =, (p. ); § = =, , , , (pp. , , ). what are the 'universe of discourse', the 'eliminands', and the 'retinends', of a syllogism? and of a sorites? pg book viii. examples, answers, and solutions. [n.b. reference tags for examples, answers & solutions will be found in the right margin.] chapter i. _examples._ § . ex _propositions of relation, to be reduced to normal form._ . i have been out for a walk. . i am feeling better. . no one has read the letter but john. . neither you nor i are old. . no fat creatures run well. . none but the brave deserve the fair. . no one looks poetical unless he is pale. . some judges lose their tempers. . i never neglect important business. . what is difficult needs attention. . what is unwholesome should be avoided. . all the laws passed last week relate to excise. . logic puzzles me. . there are no jews in the house. . some dishes are unwholesome if not well-cooked. . unexciting books make one drowsy. . when a man knows what he's about, he can detect a sharper. . you and i know what we're about. . some bald people wear wigs. . those who are fully occupied never talk about their grievances. . no riddles interest me if they can be solved. pg § . ex _pairs of abstract propositions, one in terms of x and m, and the other in terms of y and m, to be represented on the same triliteral diagram._ . no x are m; no m' are y. . no x' are m'; all m' are y. . some x' are m; no m are y. . all m are x; all m' are y'. . all m' are x; all m' are y'. . all x' are m'; no y' are m. . all x are m; all y' are m'. . some m' are x'; no m are y. . all m are x'; no m are y. . no m are x'; no y are m'. . no x' are m'; no m are y. . some x are m; all y' are m. . all x' are m; no m are y. . some x are m'; all m are y. . no m' are x'; all y are m. . all x are m'; no y are m. . some m' are x; no m' are y'. . all x are m'; some m' are y'. . all m are x; some m are y'. . no x' are m; some y are m. . some x' are m'; all y' are m. . no m are x; some m are y. . no m' are x; all y are m'. . all m are x; no y' are m'. . some m are x; no y' are m. . all m' are x'; some y are m'. . some m are x'; no y' are m'. . no x are m'; all m are y'. . no x' are m; no m are y'. . no x are m; some y' are m'. . some m' are x; all y' are m; . all x are m'; all y are m. pg § . ex _marked triliteral diagrams, to be interpreted in terms of x and y._ ·---------------· |(o) | | | ·---|---· | | |(i)|(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | |(o) | | ·---------------· ·---------------· |(o) | | | ·---|---· | | | |(o)| | |---|---|---|(i)| | | |(o)| | | ·---|---· | |(o) | | ·---------------· ·---------------· | | (o)| | ·---|---· | | |(o)|(o)| | |---|---|---|---| | | |(i)| | | ·---|---· | | | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(o)| | | |---|---|(i)|---| | |(o)| | | | ·---|---· | | | | ·---------------· ·---------------· | | (i)| | ·---|---· | | | |(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | | | | | |---|---|---|---| | | |(o)| | | ·---|---· | |(i) | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(i)|(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | | | ·---------------· ·---------------· |(i) | | | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)|(i)| | | ·---|---· | |(o) | | ·---------------· ·---------------· | | | | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)|(i)| | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(o)|(i)| | |---|---|---|---| | |(o)| | | | ·---|---· | | | | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | | (i) | | |---|---|---|---| | |(o)| | | | ·---|---· | | | (o)| ·---------------· ·---------------· |(o) | | | ·---|---· | | | | | | |---|(i)|---|---| | | | | | | ·---|---· | |(o) | (i)| ·---------------· ·---------------· |(o) | (i)| | ·---|---· | | | |(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | |(o) | | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | | |(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | (i) | ·---------------· ·---------------· | | | | ·---|---· | | |(i)| | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | | ·---------------· ·---------------· |(i) | | | ·---|---· | | | | | | |---|---|---|---| | |(o)| | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | | (o)| | ·---|---· | | | |(i)| | |---|---|---|---| | |(o)|(o)| | | ·---|---· | |(i) | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(o)|(i)| | |---|---|---|---| | |(o)| | | | ·---|---· | |(i) | | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(i)|(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | | (i)| ·---------------· ·---------------· |(o) | | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | |(i)| | | | ·---|---· | |(o) | | ·---------------· pg § . ex _pairs of abstract propositions, proposed as premisses: conclusions to be found._ . no m are x'; all m' are y. . no m' are x; some m' are y'. . all m' are x; all m' are y'. . no x' are m'; all y' are m. . some m are x'; no y are m. . no x' are m; no m are y. . no m are x'; some y' are m. . all m' are x'; no m' are y. . some x' are m'; no m are y'. . all x are m; all y' are m'. . no m are x; all y' are m'. . no x are m; all y are m. . all m' are x; no y are m. . all m are x; all m' are y. . no x are m; no m' are y. . all x are m'; all y are m. . no x are m; all m' are y. . no x are m'; no m are y. . all m are x; all m are y'. . no m are x; all m' are y. . all x are m; some m' are y. . some x are m; all y are m. . all m are x; some y are m. . no x are m; all y are m. . some m are x'; all y' are m'. . no m are x'; all y are m. . all x are m'; all y' are m. . all m are x'; some m are y. . no m are x; all y are m'. . all x are m'; some y are m. . all x are m; all y are m. . no x are m'; all m are y. . no m are x; no m are y. . no m are x'; some y are m. . no m are x; all y are m. . all m are x'; some y are m. . all m are x; no y are m. . no m are x; no m' are y. . some m are x'; no m are y. . no x' are m; all y' are m. . all x are m'; no y are m'. . no m' are x; no y are m. pg § . ex _pairs of concrete propositions, proposed as premisses: conclusions to be found._ . i have been out for a walk; i am feeling better. . no one has read the letter but john; no one, who has _not_ read it, knows what it is about. . those who are not old like walking; you and i are young. . your course is always honest; your course is always the best policy. . no fat creatures run well; some greyhounds run well. . some, who deserve the fair, get their deserts; none but the brave deserve the fair. . some jews are rich; all esquimaux are gentiles. . sugar-plums are sweet; some sweet things are liked by children. . john is in the house; everybody in the house is ill. . umbrellas are useful on a journey; what is useless on a journey should be left behind. . audible music causes vibration in the air; inaudible music is not worth paying for. . some holidays are rainy; rainy days are tiresome. . no frenchmen like plumpudding; all englishmen like plumpudding. . no portrait of a lady, that makes her simper or scowl, is satisfactory; no photograph of a lady ever fails to make her simper or scowl. . all pale people are phlegmatic; no one looks poetical unless he is pale. . no old misers are cheerful; some old misers are thin. . no one, who exercises self-control, fails to keep his temper; some judges lose their tempers. pg . all pigs are fat; nothing that is fed on barley-water is fat. . all rabbits, that are not greedy, are black; no old rabbits are free from greediness. . some pictures are not first attempts; no first attempts are really good. . i never neglect important business; your business is unimportant. . some lessons are difficult; what is difficult needs attention. . all clever people are popular; all obliging people are popular. . thoughtless people do mischief; no thoughtful person forgets a promise. . pigs cannot fly; pigs are greedy. . all soldiers march well; some babies are not soldiers. . no bride-cakes are wholesome; what is unwholesome should be avoided. . john is industrious; no industrious people are unhappy. . no philosophers are conceited; some conceited persons are not gamblers. . some excise laws are unjust; all the laws passed last week relate to excise. . no military men write poetry; none of my lodgers are civilians. . no medicine is nice; senna is a medicine. . some circulars are not read with pleasure; no begging-letters are read with pleasure. . all britons are brave; no sailors are cowards. . nothing intelligible ever puzzles _me_; logic puzzles me. . some pigs are wild; all pigs are fat. pg . all wasps are unfriendly; all unfriendly creatures are unwelcome. . no old rabbits are greedy; all black rabbits are greedy. . some eggs are hard-boiled; no eggs are uncrackable. . no antelope is ungraceful; graceful creatures delight the eye. . all well-fed canaries sing loud; no canary is melancholy if it sings loud. . some poetry is original; no original work is producible at will. . no country, that has been explored, is infested by dragons; unexplored countries are fascinating. . no coals are white; no niggers are white. . no bridges are made of sugar; some bridges are picturesque. . no children are patient; no impatient person can sit still. . no quadrupeds can whistle; some cats are quadrupeds. . bores are terrible; you are a bore. . some oysters are silent; no silent creatures are amusing. . there are no jews in the house; no gentiles have beards a yard long. . canaries, that do not sing loud, are unhappy; no well-fed canaries fail to sing loud. . all my sisters have colds; no one can sing who has a cold. . all that is made of gold is precious; some caskets are precious. . some buns are rich; all buns are nice. . all my cousins are unjust; all judges are just. pg . pain is wearisome; no pain is eagerly wished for. . all medicine is nasty; senna is a medicine. . some unkind remarks are annoying; no critical remarks are kind. . no tall men have woolly hair; niggers have woolly hair. . all philosophers are logical; an illogical man is always obstinate. . john is industrious; all industrious people are happy. . these dishes are all well-cooked; some dishes are unwholesome if not well-cooked. . no exciting books suit feverish patients; unexciting books make one drowsy. . no pigs can fly; all pigs are greedy. . when a man knows what he's about, he can detect a sharper; you and i know what we're about. . some dreams are terrible; no lambs are terrible. . no bald creature needs a hairbrush; no lizards have hair. . all battles are noisy; what makes no noise may escape notice. . all my cousins are unjust; no judges are unjust. . all eggs can be cracked; some eggs are hard-boiled. . prejudiced persons are untrustworthy; some unprejudiced persons are disliked. . no dictatorial person is popular; she is dictatorial. . some bald people wear wigs; all your children have hair. . no lobsters are unreasonable; no reasonable creatures expect impossibilities. pg . no nightmare is pleasant; unpleasant experiences are not eagerly desired. . no plumcakes are wholesome; some wholesome things are nice. . nothing that is nice need be shunned; some kinds of jam are nice. . all ducks waddle; nothing that waddles is graceful. . sandwiches are satisfying; nothing in this dish is unsatisfying. . no rich man begs in the street; those who are not rich should keep accounts. . spiders spin webs; some creatures, that do not spin webs, are savage. . some of these shops are not crowded; no crowded shops are comfortable. . prudent travelers carry plenty of small change; imprudent travelers lose their luggage. . some geraniums are red; all these flowers are red. . none of my cousins are just; all judges are just. . no jews are mad; all my lodgers are jews. . busy folk are not always talking about their grievances; discontented folk are always talking about their grievances. . none of my cousins are just; no judges are unjust. . all teetotalers like sugar; no nightingale drinks wine. . no riddles interest me if they can be solved; all these riddles are insoluble. . all clear explanations are satisfactory; some excuses are unsatisfactory. . all elderly ladies are talkative; all good-tempered ladies are talkative. . no kind deed is unlawful; what is lawful may be done without scruple. pg . no babies are studious; no babies are good violinists. . all shillings are round; all these coins are round. . no honest men cheat; no dishonest men are trustworthy. . none of my boys are clever; none of my girls are greedy. . all jokes are meant to amuse; no act of parliament is a joke. . no eventful tour is ever forgotten; uneventful tours are not worth writing a book about. . all my boys are disobedient; all my girls are discontented. . no unexpected pleasure annoys me; your visit is an unexpected pleasure. § . ex _trios of abstract propositions, proposed as syllogisms: to be examined._ . some x are m; no m are y'. some x are y. . all x are m; no y are m'. no y are x'. . some x are m'; all y' are m. some x are y. . all x are m; no y are m. all x are y'. . some m' are x'; no m' are y. some x' are y'. . no x' are m; all y are m'. all y are x'. . some m' are x'; all y' are m'. some x' are y'. . no m' are x'; all y' are m'. all y' are x. . some m are x'; no m are y. some x' are y'. . all m' are x'; all m' are y. some y are x'. . all x are m'; some y are m. some y are x'. . no x are m; no m' are y'. no x are y'. . no x are m; all y' are m. all y' are x'. . all m' are x'; all m' are y. some y are x'. . some m are x'; all y are m'. some x' are y'. . no x' are m; all y' are m'. some y' are x. . no m' are x; all m' are y'. some x' are y'. pg . no x' are m; some m are y. some x are y. . some m are x; all m are y. some y are x'. . no x' are m'; some m' are y'. some x are y'. . no m are x; all m are y'. some x' are y'. . all x' are m; some y are m'. all x' are y'. . all m are x; no m' are y'. no x' are y'. . all x are m'; all m' are y. all x are y. . no x are m'; all m are y. no x are y'. . all m are x'; all y are m. all y are x'. . all x are m; no m are y'. all x are y. . all x are m; no y' are m'. all x are y. . no x' are m; no m' are y'. no x' are y'. . all x are m; all m are y'. all x are y'. . all x' are m'; no y' are m'. all x' are y. . no x are m; no y' are m'. no x are y'. . all m are x'; all y' are m. all y' are x'. . all x are m'; some y are m'. some y are x. . some x are m; all m are y. some x are y. . all m are x'; all y are m. all y are x'. . no m are x'; all m are y'. some x are y'. . no x are m; no m are y'. no x are y'. . no m are x; some m are y'. some x' are y'. . no m are x'; some y are m. some x are y. § . ex _trios of concrete propositions, proposed as syllogisms: to be examined._ . no doctors are enthusiastic; you are enthusiastic. you are not a doctor. . dictionaries are useful; useful books are valuable. dictionaries are valuable. . no misers are unselfish; none but misers save egg-shells. no unselfish people save egg-shells. . some epicures are ungenerous; all my uncles are generous. my uncles are not epicures. pg . gold is heavy; nothing but gold will silence him. nothing light will silence him. . some healthy people are fat; no unhealthy people are strong. some fat people are not strong. . "i saw it in a newspaper." "all newspapers tell lies." it was a lie. . some cravats are not artistic; i admire anything artistic. there are some cravats that i do not admire. . his songs never last an hour; a song, that lasts an hour, is tedious. his songs are never tedious. . some candles give very little light; candles are _meant_ to give light. some things, that are meant to give light, give very little. . all, who are anxious to learn, work hard; some of these boys work hard. some of these boys are anxious to learn. . all lions are fierce; some lions do not drink coffee. some creatures that drink coffee are not fierce. . no misers are generous; some old men are ungenerous. some old men are misers. . no fossil can be crossed in love; an oyster may be crossed in love. oysters are not fossils. . all uneducated people are shallow; students are all educated. no students are shallow. . all young lambs jump; no young animals are healthy, unless they jump. all young lambs are healthy. . ill-managed business is unprofitable; railways are never ill-managed. all railways are profitable. . no professors are ignorant; all ignorant people are vain. no professors are vain. pg . a prudent man shuns hyænas; no banker is imprudent. no banker fails to shun hyænas. . all wasps are unfriendly; no puppies are unfriendly. puppies are not wasps. . no jews are honest; some gentiles are rich. some rich people are dishonest. . no idlers win fame; some painters are not idle. some painters win fame. . no monkeys are soldiers; all monkeys are mischievous. some mischievous creatures are not soldiers. . all these bonbons are chocolate-creams; all these bonbons are delicious. chocolate-creams are delicious. . no muffins are wholesome; all buns are unwholesome. buns are not muffins. . some unauthorised reports are false; all authorised reports are trustworthy. some false reports are not trustworthy. . some pillows are soft; no pokers are soft. some pokers are not pillows. . improbable stories are not easily believed; none of his stories are probable. none of his stories are easily believed. . no thieves are honest; some dishonest people are found out. some thieves are found out. . no muffins are wholesome; all puffy food is unwholesome. all muffins are puffy. . no birds, except peacocks, are proud of their tails; some birds, that are proud of their tails, cannot sing. some peacocks cannot sing. . warmth relieves pain; nothing, that does not relieve pain, is useful in toothache. warmth is useful in toothache. pg . no bankrupts are rich; some merchants are not bankrupts. some merchants are rich. . bores are dreaded; no bore is ever begged to prolong his visit. no one, who is dreaded, is ever begged to prolong his visit. . all wise men walk on their feet; all unwise men walk on their hands. no man walks on both. . no wheelbarrows are comfortable; no uncomfortable vehicles are popular. no wheelbarrows are popular. . no frogs are poetical; some ducks are unpoetical. some ducks are not frogs. . no emperors are dentists; all dentists are dreaded by children. no emperors are dreaded by children. . sugar is sweet; salt is not sweet. salt is not sugar. . every eagle can fly; some pigs cannot fly. some pigs are not eagles. § . ex _sets of abstract propositions, proposed as premisses for soriteses: conclusions to be found._ [n.b. at the end of this section instructions are given for varying these examples.] . . no c are d; . all a are d; . all b are c. . . all d are b; . no a are c'; . no b are c. . . no b are a; . no c are d'; . all d are b. . . no b are c; . all a are b; . no c' are d. . . all b' are a'; . no b are c; . no a' are d. . . all a are b'; . no b' are c; . all d are a. . . no d are b'; . all b are a; . no c are d'. . . no b' are d; . no a' are b; . all c are d. pg . . all b' are a; . no a are d; . all b are c. . . no c are d; . all b are c; . no a are d'. . . no b are c; . all d are a; . all c' are a'. . . no c are b'; . all c' are d'; . all b are a. . . all d are e; . all c are a; . no b are d'; . all e are a'. . . all e are b; . all a are e; . all d are b'; . all a' are c; . . no b' are d; . all e are c; . all b are a; . all d' are c'. . . no a' are e; . all d are c'; . all a are b; . all e' are d. . . all d are c; . all a are e; . no b are d'; . all c are e'. . . all a are b; . all d are e; . all a' are c'; . no b are e. . . no b are c; . all e are h; . all a are b; . no d are h; . all e' are c. . . no d are h'; . no c are e; . all h are b; . no a are d'; . no b are e'. . . all b are a; . no d are h; . no c are e; . no a are h'; . all c' are b. . . all e are d'; . no b' are h'; . all c' are d; . all a are e; . no c are h. . . all b' are a'; . no d are e'; . all h are b'; . no c are e; . all d' are a. . . all h' are k'; . no b' are a; . all c are d; . all e are h'; . no d are k'; . no b are c'. . . all a are d; . all k are b; . all e are h; . no a' are b; . all d are c; . all h are k. . . all a' are h; . no d' are k'; . all e are b'; . no h are k; . all a are e; . no b' are d. . . all c are d'; . no h are b; . all a' are k; . no c are e'; . all b' are d; . no a are c'. . . no a' are k; . all e are b; . no h are k'; . no d' are c; . no a are b; . all c' are h. . . no e are k; . no b' are m; . no a are c'; . all h' are e; . all d are k; . no c are b; . all d' are l; . no h are m'. . . all n are m; . all a' are e; . no c' are l; . all k are r'; . no a are h'; . no d are l'; . no c are n'; . all e are b; . all m are r; . all h are d. [n.b. in each example, in sections and , it is possible to begin with _any_ premiss, at pleasure, and thus to get as many different solutions (all of course yielding the _same_ complete conclusion) as there are premisses in the example. hence § really contains different examples, and § contains .] pg § . ex _sets of concrete propositions, proposed as premisses for soriteses: conclusions to be found._ = .= ( ) babies are illogical; ( ) nobody is despised who can manage a crocodile; ( ) illogical persons are despised. univ. "persons"; a = able to manage a crocodile; b = babies; c = despised; d = logical. = .= ( ) my saucepans are the only things i have that are made of tin; ( ) i find all _your_ presents very useful; ( ) none of my saucepans are of the slightest use. univ. "things of mine"; a = made of tin; b = my saucepans; c = useful; d = your presents. = .= ( ) no potatoes of mine, that are new, have been boiled; ( ) all my potatoes in this dish are fit to eat; ( ) no unboiled potatoes of mine are fit to eat. univ. "my potatoes"; a = boiled; b = eatable; c = in this dish; d = new. = .= ( ) there are no jews in the kitchen; ( ) no gentiles say "shpoonj"; ( ) my servants are all in the kitchen. univ. "persons"; a = in the kitchen; b = jews; c = my servants; d = saying "shpoonj." = .= ( ) no ducks waltz; ( ) no officers ever decline to waltz; ( ) all my poultry are ducks. univ. "creatures"; a = ducks; b = my poultry; c = officers; d = willing to waltz. = .= ( ) every one who is sane can do logic; ( ) no lunatics are fit to serve on a jury; ( ) none of _your_ sons can do logic. univ. "persons"; a = able to do logic; b = fit to serve on a jury; c = sane; d = your sons. pg = .= ( ) there are no pencils of mine in this box; ( ) no sugar-plums of mine are cigars; ( ) the whole of my property, that is not in this box, consists of cigars. univ. "things of mine"; a = cigars; b = in this box; c = pencils; d = sugar-plums. = .= ( ) no experienced person is incompetent; ( ) jenkins is always blundering; ( ) no competent person is always blundering. univ. "persons"; a = always blundering; b = competent; c = experienced; d = jenkins. = .= ( ) no terriers wander among the signs of the zodiac; ( ) nothing, that does not wander among the signs of the zodiac, is a comet; ( ) nothing but a terrier has a curly tail. univ. "things"; a = comets; b = curly-tailed; c = terriers; d = wandering among the signs of the zodiac. = .= ( ) no one takes in the _times_, unless he is well-educated; ( ) no hedge-hogs can read; ( ) those who cannot read are not well-educated. univ. "creatures"; a = able to read; b = hedge-hogs; c = taking in the times; d = well-educated. = .= ( ) all puddings are nice; ( ) this dish is a pudding; ( ) no nice things are wholesome. univ. "things"; a = nice; b = puddings; c = this dish; d = wholesome. = .= ( ) my gardener is well worth listening to on military subjects; ( ) no one can remember the battle of waterloo, unless he is very old; ( ) nobody is really worth listening to on military subjects, unless he can remember the battle of waterloo. univ. "persons"; a = able to remember the battle of waterloo; b = my gardener; c = well worth listening to on military subjects; d = very old. pg = .= ( ) all humming-birds are richly coloured; ( ) no large birds live on honey; ( ) birds that do not live on honey are dull in colour. univ. "birds"; a = humming-birds; b = large; c = living on honey; d = richly coloured. = .= ( ) no gentiles have hooked noses; ( ) a man who is a good hand at a bargain always makes money; ( ) no jew is ever a bad hand at a bargain. univ. "persons"; a = good hands at a bargain; b = hook-nosed; c = jews; d = making money. = .= ( ) all ducks in this village, that are branded 'b,' belong to mrs. bond; ( ) ducks in this village never wear lace collars, unless they are branded 'b'; ( ) mrs. bond has no gray ducks in this village. univ. "ducks in this village"; a = belonging to mrs. bond; b = branded 'b'; c = gray; d = wearing lace-collars. = .= ( ) all the old articles in this cupboard are cracked; ( ) no jug in this cupboard is new; ( ) nothing in this cupboard, that is cracked, will hold water. univ. "things in this cupboard"; a = able to hold water; b = cracked; c = jugs; d = old. = .= ( ) all unripe fruit is unwholesome; ( ) all these apples are wholesome; ( ) no fruit, grown in the shade, is ripe. univ. "fruit"; a = grown in the shade; b = ripe; c = these apples; d = wholesome. = .= ( ) puppies, that will not lie still, are always grateful for the loan of a skipping-rope; ( ) a lame puppy would not say "thank you" if you offered to lend it a skipping-rope. ( ) none but lame puppies ever care to do worsted-work. univ. "puppies"; a = caring to do worsted-work; b = grateful for the loan of a skipping-rope; c = lame; d = willing to lie still. pg = .= ( ) no name in this list is unsuitable for the hero of a romance; ( ) names beginning with a vowel are always melodious; ( ) no name is suitable for the hero of a romance, if it begins with a consonant. univ. "names"; a = beginning with a vowel; b = in this list; c = melodious; d = suitable for the hero of a romance. = .= ( ) all members of the house of commons have perfect self-command; ( ) no m.p., who wears a coronet, should ride in a donkey-race; ( ) all members of the house of lords wear coronets. univ. "m.p.'s"; a = belonging to the house of commons; b = having perfect self-command; c = one who may ride in a donkey-race; d = wearing a coronet. = .= ( ) no goods in this shop, that have been bought and paid for, are still on sale; ( ) none of the goods may be carried away, unless labeled "sold"; ( ) none of the goods are labeled "sold," unless they have been bought and paid for. univ. "goods in this shop"; a = allowed to be carried away; b = bought and paid for; c = labeled "sold"; d = on sale. = .= ( ) no acrobatic feats, that are not announced in the bills of a circus, are ever attempted there; ( ) no acrobatic feat is possible, if it involves turning a quadruple somersault; ( ) no impossible acrobatic feat is ever announced in a circus bill. univ. "acrobatic feats"; a = announced in the bills of a circus; b = attempted in a circus; c = involving the turning of a quadruple somersault; d = possible. = .= ( ) nobody, who really appreciates beethoven, fails to keep silence while the moonlight-sonata is being played; ( ) guinea-pigs are hopelessly ignorant of music; ( ) no one, who is hopelessly ignorant of music, ever keeps silence while the moonlight-sonata is being played. univ. "creatures"; a = guinea-pigs; b = hopelessly ignorant of music; c = keeping silence while the moonlight-sonata is being played; d = really appreciating beethoven. pg = .= ( ) coloured flowers are always scented; ( ) i dislike flowers that are not grown in the open air; ( ) no flowers grown in the open air are colourless. univ. "flowers"; a = coloured; b = grown in the open air; c = liked by me; d = scented. = .= ( ) showy talkers think too much of themselves; ( ) no really well-informed people are bad company; ( ) people who think too much of themselves are not good company. univ. "persons"; a = good company; b = really well-informed; c = showy talkers; d = thinking too much of one's self. = .= ( ) no boys under are admitted to this school as boarders; ( ) all the industrious boys have red hair; ( ) none of the day-boys learn greek; ( ) none but those under are idle. univ. "boys in this school"; a = boarders; b = industrious; c = learning greek; d = red-haired; e = under . = .= ( ) the only articles of food, that my doctor allows me, are such as are not very rich; ( ) nothing that agrees with me is unsuitable for supper; ( ) wedding-cake is always very rich; ( ) my doctor allows me all articles of food that are suitable for supper. univ. "articles of food"; a = agreeing with me; b = allowed by my doctor; c = suitable for supper; d = very rich; e = wedding-cake. = .= ( ) no discussions in our debating-club are likely to rouse the british lion, so long as they are checked when they become too noisy; ( ) discussions, unwisely conducted, endanger the peacefulness of our debating-club; ( ) discussions, that go on while tomkins is in the chair, are likely to rouse the british lion; ( ) discussions in our debating-club, when wisely conducted, are always checked when they become too noisy. univ. "discussions in our debating-club"; a = checked when too noisy; b = dangerous to the peacefulness of our debating-club; c = going on while tomkins is in the chair; d = likely to rouse the british lion; e = wisely conducted. pg = .= ( ) all my sons are slim; ( ) no child of mine is healthy who takes no exercise; ( ) all gluttons, who are children of mine, are fat; ( ) no daughter of mine takes any exercise. univ. "my children"; a = fat; b = gluttons; c = healthy; d = sons; e = taking exercise. = .= ( ) things sold in the street are of no great value; ( ) nothing but rubbish can be had for a song; ( ) eggs of the great auk are very valuable; ( ) it is only what is sold in the street that is really _rubbish_. univ. "things"; a = able to be had for a song; b = eggs of the great auk; c = rubbish; d = sold in the street; e = very valuable. = .= ( ) no books sold here have gilt edges, except what are in the front shop; ( ) all the _authorised_ editions have red labels; ( ) all the books with red labels are priced at s. and upwards; ( ) none but _authorised_ editions are ever placed in the front shop. univ. "books sold here"; a = authorised editions; b = gilt-edged; c = having red labels; d = in the front shop; e = priced at s. and upwards. = .= ( ) remedies for bleeding, which fail to check it, are a mockery; ( ) tincture of calendula is not to be despised; ( ) remedies, which will check the bleeding when you cut your finger, are useful; ( ) all mock remedies for bleeding are despicable. univ. "remedies for bleeding"; a = able to check bleeding; b = despicable; c = mockeries; d = tincture of calendula; e = useful when you cut your finger. = .= ( ) none of the unnoticed things, met with at sea, are mermaids; ( ) things entered in the log, as met with at sea, are sure to be worth remembering; ( ) i have never met with anything worth remembering, when on a voyage; ( ) things met with at sea, that are noticed, are sure to be recorded in the log; univ. "things met with at sea"; a = entered in log; b = mermaids; c = met with by me; d = noticed; e = worth remembering. pg = .= ( ) the only books in this library, that i do _not_ recommend for reading, are unhealthy in tone; ( ) the bound books are all well-written; ( ) all the romances are healthy in tone; ( ) i do not recommend you to read any of the unbound books. univ. "books in this library"; a = bound; b = healthy in tone; c = recommended by me; d = romances; e = well-written. = .= ( ) no birds, except ostriches, are feet high; ( ) there are no birds in this aviary that belong to any one but _me_; ( ) no ostrich lives on mince-pies; ( ) i have no birds less than feet high. univ. "birds"; a = in this aviary; b = living on mince-pies; c = my; d =  feet high; e = ostriches. = .= ( ) a plum-pudding, that is not really solid, is mere porridge; ( ) every plum-pudding, served at my table, has been boiled in a cloth; ( ) a plum-pudding that is mere porridge is indistinguishable from soup; ( ) no plum-puddings are really solid, except what are served at _my_ table. univ. "plum-puddings"; a = boiled in a cloth; b = distinguishable from soup; c = mere porridge; d = really solid; e = served at my table. = .= ( ) no interesting poems are unpopular among people of real taste; ( ) no modern poetry is free from affectation; ( ) all _your_ poems are on the subject of soap-bubbles; ( ) no affected poetry is popular among people of real taste; ( ) no ancient poem is on the subject of soap-bubbles. univ. "poems"; a = affected; b = ancient; c = interesting; d = on the subject of soap-bubbles; e = popular among people of real taste; h = written by you. = .= ( ) all the fruit at this show, that fails to get a prize, is the property of the committee; ( ) none of my peaches have got prizes; ( ) none of the fruit, sold off in the evening, is unripe; ( ) none of the ripe fruit has been grown in a hot-house; ( ) all fruit, that belongs to the committee, is sold off in the evening. univ. "fruit at this show"; a = belonging to the committee; b = getting prizes; c = grown in a hot-house; d = my peaches; e = ripe; h = sold off in the evening. pg = .= ( ) promise-breakers are untrustworthy; ( ) wine-drinkers are very communicative; ( ) a man who keeps his promises is honest; ( ) no teetotalers are pawnbrokers; ( ) one can always trust a very communicative person. univ. "persons"; a = honest; b = pawnbrokers; c = promise-breakers; d = trustworthy; e = very communicative; h = wine-drinkers. = .= ( ) no kitten, that loves fish, is unteachable; ( ) no kitten without a tail will play with a gorilla; ( ) kittens with whiskers always love fish; ( ) no teachable kitten has green eyes; ( ) no kittens have tails unless they have whiskers. univ. "kittens"; a = green-eyed; b = loving fish; c = tailed; d = teachable; e = whiskered; h = willing to play with a gorilla. = .= ( ) all the eton men in this college play cricket; ( ) none but the scholars dine at the higher table; ( ) none of the cricketers row; ( ) _my_ friends in this college all come from eton; ( ) all the scholars are rowing-men. univ. "men in this college"; a = cricketers; b = dining at the higher table; c = etonians; d = my friends; e = rowing-men; h = scholars. = .= ( ) there is no box of mine here that i dare open; ( ) my writing-desk is made of rose-wood; ( ) all my boxes are painted, except what are here; ( ) there is no box of mine that i dare not open, unless it is full of live scorpions; ( ) all my rose-wood boxes are unpainted. univ. "my boxes"; a = boxes that i dare open; b = full of live scorpions; c = here; d = made of rose-wood; e = painted; h = writing-desks. = .= ( ) gentiles have no objection to pork; ( ) nobody who admires pigsties ever reads hogg's poems; ( ) no mandarin knows hebrew; ( ) every one, who does not object to pork, admires pigsties; ( ) no jew is ignorant of hebrew. univ. "persons"; a = admiring pigsties; b = jews; c = knowing hebrew; d = mandarins; e = objecting to pork; h = reading hogg's poems. pg = .= ( ) all writers, who understand human nature, are clever; ( ) no one is a true poet unless he can stir the hearts of men; ( ) shakespeare wrote "hamlet"; ( ) no writer, who does not understand human nature, can stir the hearts of men; ( ) none but a true poet could have written "hamlet."; univ. "writers"; a = able to stir the hearts of men; b = clever; c = shakespeare; d = true poets; e = understanding human nature; h = writer of 'hamlet.' = .= ( ) i despise anything that cannot be used as a bridge; ( ) everything, that is worth writing an ode to, would be a welcome gift to me; ( ) a rainbow will not bear the weight of a wheel-barrow; ( ) whatever can be used as a bridge will bear the weight of a wheel-barrow; ( ) i would not take, as a gift, a thing that i despise. univ. "things"; a = able to bear the weight of a wheel-barrow; b = acceptable to me; c = despised by me; d = rainbows; e = useful as a bridge; h = worth writing an ode to. = .= ( ) when i work a logic-example without grumbling, you may be sure it is one that i can understand; ( ) these soriteses are not arranged in regular order, like the examples i am used to; ( ) no easy example ever make my head ache; ( ) i ca'n't understand examples that are not arranged in regular order, like those i am used to; ( ) i never grumble at an example, unless it gives me a headache. univ. "logic-examples worked by me"; a = arranged in regular order, like the examples i am used to; b = easy; c = grumbled at by me; d = making my head ache; e = these soriteses; h = understood by me. = .= ( ) every idea of mine, that cannot be expressed as a syllogism, is really ridiculous; ( ) none of my ideas about bath-buns are worth writing down; ( ) no idea of mine, that fails to come true, can be expressed as a syllogism; ( ) i never have any really ridiculous idea, that i do not at once refer to my solicitor; ( ) my dreams are all about bath-buns; ( ) i never refer any idea of mine to my solicitor, unless it is worth writing down. univ. "my ideas"; a = able to be expressed as a syllogism; b = about bath-buns; c = coming true; d = dreams; e = really ridiculous h = referred to my solicitor; k = worth writing down. pg = .= ( ) none of the pictures here, except the battle-pieces, are valuable; ( ) none of the unframed ones are varnished; ( ) all the battle-pieces are painted in oils; ( ) all those that have been sold are valuable; ( ) all the english ones are varnished; ( ) all those in frames have been sold. univ. "the pictures here"; a = battle-pieces; b = english; c = framed; d = oil-paintings; e = sold; h = valuable; k = varnished. = .= ( ) animals, that do not kick, are always unexcitable; ( ) donkeys have no horns; ( ) a buffalo can always toss one over a gate; ( ) no animals that kick are easy to swallow; ( ) no hornless animal can toss one over a gate; ( ) all animals are excitable, except buffaloes. univ. "animals"; a = able to toss one over a gate; b = buffaloes; c = donkeys; d = easy to swallow; e = excitable; h = horned; k = kicking. = .= ( ) no one, who is going to a party, ever fails to brush his hair; ( ) no one looks fascinating, if he is untidy; ( ) opium-eaters have no self-command; ( ) every one, who has brushed his hair, looks fascinating; ( ) no one wears white kid gloves, unless he is going to a party; ( ) a man is always untidy, if he has no self-command. univ. "persons"; a = going to a party; b = having brushed one's hair; c = having self-command; d = looking fascinating; e = opium-eaters; h = tidy; k = wearing white kid gloves. = .= ( ) no husband, who is always giving his wife new dresses, can be a cross-grained man; ( ) a methodical husband always comes home for his tea; ( ) no one, who hangs up his hat on the gas-jet, can be a man that is kept in proper order by his wife; ( ) a good husband is always giving his wife new dresses; ( ) no husband can fail to be cross-grained, if his wife does not keep him in proper order; ( ) an unmethodical husband always hangs up his hat on the gas-jet. univ. "husbands"; a = always coming home for his tea; b = always giving his wife new dresses; c = cross-grained; d = good; e = hanging up his hat on the gas-jet; h = kept in proper order; k = methodical. pg = .= ( ) everything, not absolutely ugly, may be kept in a drawing-room; ( ) nothing, that is encrusted with salt, is ever quite dry; ( ) nothing should be kept in a drawing-room, unless it is free from damp; ( ) bathing-machines are always kept near the sea; ( ) nothing, that is made of mother-of-pearl, can be absolutely ugly; ( ) whatever is kept near the sea gets encrusted with salt. univ. "things"; a = absolutely ugly; b = bathing-machines; c = encrusted with salt; d = kept near the sea; e = made of mother-of-pearl; h = quite dry; k = things that may be kept in a drawing-room. = .= ( ) i call no day "unlucky," when robinson is civil to me; ( ) wednesdays are always cloudy; ( ) when people take umbrellas, the day never turns out fine; ( ) the only days when robinson is uncivil to me are wednesdays; ( ) everybody takes his umbrella with him when it is raining; ( ) my "lucky" days always turn out fine. univ. "days"; a = called by me 'lucky'; b = cloudy; c = days when people take umbrellas; d = days when robinson is civil to me; e = rainy; h = turning out fine; k = wednesdays. = .= ( ) no shark ever doubts that it is well fitted out; ( ) a fish, that cannot dance a minuet, is contemptible; ( ) no fish is quite certain that it is well fitted out, unless it has three rows of teeth; ( ) all fishes, except sharks, are kind to children; ( ) no heavy fish can dance a minuet; ( ) a fish with three rows of teeth is not to be despised. univ. "fishes"; a = able to dance a minuet; b = certain that he is well fitted out; c = contemptible; d = having rows of teeth; e = heavy; h = kind to children; k = sharks. = .= ( ) all the human race, except my footmen, have a certain amount of common-sense; ( ) no one, who lives on barley-sugar, can be anything but a mere baby; ( ) none but a hop-scotch player knows what real happiness is; ( ) no mere baby has a grain of common sense; ( ) no engine-driver ever plays hop-scotch; ( ) no footman of mine is ignorant of what true happiness is. univ. "human beings"; a = engine-drivers; b = having common sense; c = hop-scotch players; d = knowing what real happiness is; e = living on barley-sugar; h = mere babies; k = my footmen. pg = .= ( ) i trust every animal that belongs to me; ( ) dogs gnaw bones; ( ) i admit no animals into my study, unless they will beg when told to do so; ( ) all the animals in the yard are mine; ( ) i admit every animal, that i trust, into my study; ( ) the only animals, that are really willing to beg when told to do so, are dogs. univ. "animals"; a = admitted to my study; b = animals that i trust; c = dogs; d = gnawing bones; e = in the yard; h = my; k = willing to beg when told. = .= ( ) animals are always mortally offended if i fail to notice them; ( ) the only animals that belong to _me_ are in that field; ( ) no animal can guess a conundrum, unless it has been properly trained in a board-school; ( ) none of the animals in that field are badgers; ( ) when an animal is mortally offended, it always rushes about wildly and howls; ( ) i never notice any animal, unless it belongs to me; ( ) no animal, that has been properly trained in a board-school, ever rushes about wildly and howls. univ. "animals"; a = able to guess a conundrum; b = badgers; c = in that field; d = mortally offended; e = my; h = noticed by me; k = properly trained in a board-school; l = rushing about wildly and howling. = .= ( ) i never put a cheque, received by me, on that file, unless i am anxious about it; ( ) all the cheques received by me, that are not marked with a cross, are payable to bearer; ( ) none of them are ever brought back to me, unless they have been dishonoured at the bank; ( ) all of them, that are marked with a cross, are for amounts of over £ ; ( ) all of them, that are not on that file, are marked "not negotiable"; ( ) no cheque of yours, received by me, has ever been dishonoured; ( ) i am never anxious about a cheque, received by me, unless it should happen to be brought back to me; ( ) none of the cheques received by me, that are marked "not negotiable," are for amounts of over £ . univ. "cheques received by me"; a = brought back to me; b = cheques that i am anxious about; c = honoured; d = marked with a cross; e = marked 'not negotiable'; h = on that file; k = over £ ; l = payable to bearer; m = your. pg = .= ( ) all the dated letters in this room are written on blue paper; ( ) none of them are in black ink, except those that are written in the third person; ( ) i have not filed any of them that i can read; ( ) none of them, that are written on one sheet, are undated; ( ) all of them, that are not crossed, are in black ink; ( ) all of them, written by brown, begin with "dear sir"; ( ) all of them, written on blue paper, are filed; ( ) none of them, written on more than one sheet, are crossed; ( ) none of them, that begin with "dear sir," are written in the third person. univ. "letters in this room"; a = beginning with "dear sir"; b = crossed; c = dated; d = filed; e = in black ink; h = in third person; k = letters that i can read; l = on blue paper; m = on one sheet; n = written by brown. = .= ( ) the only animals in this house are cats; ( ) every animal is suitable for a pet, that loves to gaze at the moon; ( ) when i detest an animal, i avoid it; ( ) no animals are carnivorous, unless they prowl at night; ( ) no cats fails to kill mice; ( ) no animals ever take to me, except what are in this house; ( ) kangaroos are not suitable for pets; ( ) none but carnivora kill mice; ( ) i detest animals that do not take to me; ( ) animals, that prowl at night, always love to gaze at the moon. univ. "animals"; a = avoided by me; b = carnivora; c = cats; d = detested by me; e = in this house; h = kangaroos; k = killing mice; l = loving to gaze at the moon; m = prowling at night; n = suitable for pets; r = taking to me. pg chapter ii. _answers._ _answers to § ._ an . "all" _sign of quantity._ "persons represented by the name 'i'" (or "i's") _subject._ "are" _copula._ "persons who have been out for a walk" _predicate._ or, more briefly, "all | 'i's | are | persons who have been out for a walk". . "all | 'i's | are | persons who feel better". . "no | persons who are not 'john' | are | persons who have read the letter". . "no | members of the class 'you and i' | are | old persons". . "no | fat creatures | are | creatures that run well". . "no | not-brave persons | are | persons deserving of the fair". . "no | not-pale persons | are | persons who look poetical". . "some | judges | are | persons who lose their tempers". . "all | 'i's | are | persons who do not neglect important business". . "all | difficult things | are | things that need attention". . "all | unwholesome things | are | things that should be avoided". . "all | laws passed last week | are | laws relating to excise". . "all | logical studies | are | things that puzzle me". . "no | persons in the house | are | jews". . "some | not well-cooked dishes | are | unwholesome dishes". . "all | unexciting books | are | books that make one drowsy". . "all | men who know what they're about | are | men who can detect a sharper". . "all | members of the class 'you and i' | are | persons who know what they're about". . "some | bald persons | are | persons accustomed to wear wigs". . "all | fully occupied persons | are | persons who do not talk about their grievances". . "no | riddles that can be solved | are | riddles that interest me". pg _answers to § ._ an ·---------------· |(o) | | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | | | | | | ·---|---· | |(o) | | ·---------------· ·---------------· |(i) | (o)| | ·---|---· | | | | | | |---|---|---|---| | | | | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | | | | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)|(i)| | | ·---|---· | | | | ·---------------· ·---------------· |(o) | | | ·---|---· | | | (i) | | |---|---|---|(i)| | |(o)|(o)| | | ·---|---· | |(o) | | ·---------------· ·---------------· |(o) | (i)| | ·---|---· | | | | | | |---|---|---|---| | | | | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | | | | ·---|---· | | | |(o)| | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | (i) | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(i)|(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | | (i)| ·---------------· ·---------------· | | | | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)| | | | ·---|---· | | (i) | ·---------------· ·---------------· | | | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | |(o)|(i)| | | ·---|---· | | | | ·---------------· ·---------------· |(o) | | | ·---|---· | | | | | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | |(o) | | ·---------------· ·---------------· | | | | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)| | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | | (o)| | ·---|---· | | | (i) | | |---|---|(i)|---| | | | | | | ·---|---· | | | (o)| ·---------------· ·---------------· | | | | ·---|---· | | | |(o)| | |---|---|---|---| | |(i)|(o)| | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | (i) | | ·---|---· | | | |(o)| | |---|(i)|---|---| | | |(o)| | | ·---|---· | | | | ·---------------· ·---------------· |(o) | | | ·---|---· | | | | | | |---|(i)|---|---| | | | | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· | (i) | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | |(o)| | | | ·---|---· | | | | ·---------------· ·---------------· |(i) | (o)| | ·---|---· | | | | | | |---|---|---|---| | | | | | | ·---|---· | | | (o)| ·---------------· ·---------------· | (i) | | ·---|---· | | |(o)|(o)| | |---|---|---|(i)| | | | | | | ·---|---· | | | | ·---------------· ·---------------· | | | | ·---|---· | | | |(i)| | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | | ·---------------· ·---------------· | | | | ·---|---· | | |(i)| | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | | ·---------------· ·---------------· | | (o)| | ·---|---· | | | | | | |---|---|(i)|---| | | | | | | ·---|---· | |(i) | (o)| ·---------------· ·---------------· | | | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | |(i)| | | | ·---|---· | | | | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(o)| | | |---|---|---|---| | |(o)| | | | ·---|---· | |(i) | | ·---------------· ·---------------· | | (o)| | ·---|---· | | | (i) | | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | (o)| ·---------------· pg ·---------------· | | | | ·---|---· | | |(i)|(o)| | |---|---|---|---| | | |(o)| | | ·---|---· | | | | ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | | | | | |---|---|---|---| | | | | | | ·---|---· | |(i) | | ·---------------· ·---------------· | | (o)| | ·---|---· | | | | | | |---|---|---|---| | | (i) | | | ·---|---· | | | (o)| ·---------------· ·---------------· |(o) | (o)| | ·---|---· | | |(o)| | | |---|---|(i)|---| | |(o)| | | | ·---|---· | | | | ·---------------· ·---------------· | | | | ·---|---· | | | |(o)| | |---|---|---|---| | |(o)|(o)| | | ·---|---· | | | | ·---------------· ·---------------· | | | | ·---|---· | | |(o)|(o)| | |---|---|---|(i)| | | | | | | ·---|---· | | | | ·---------------· ·---------------· |(i) | (o)| | ·---|---· | | | | | | |---|---|(i)|---| | | | | | | ·---|---· | | | (o)| ·---------------· ·---------------· |(o) | (i)| | ·---|---· | | |(o)|(o)| | |---|---|---|---| | |(i)| | | | ·---|---· | |(o) | | ·---------------· _answers to § ._ an . some xy exist, or some x are y, or some y are x. . no information. . all y' are x'. . no xy exist, &c. . all y' are x. . all x' are y. . all x are y. . all x' are y', and all y are x. . all x' are y'. . all x are y'. . no information. . some x'y' exist, &c. . some xy' exist, &c. . no xy' exist, &c. . some xy exist, &c. . all y are x. . all x' are y, and all y' are x. . all x are y', and all y are x'. . all x are y, and all y' are x'. . all y are x'. _answers to § ._ an . no x' are y'. . some x' are y'. . some x are y'. . [no concl. fallacy of like eliminands not asserted to exist.] . some x' are y'. . [no concl. fallacy of like eliminands not asserted to exist.] . some x are y'. . some x' are y'. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . all x are y, and all y' are x'. . [no concl. fallacy of like eliminands not asserted to exist.] . all y are x'. . no x' are y. . no x' are y'. . no x are y. . all x are y', and all y are x'. pg . no x are y'. . no x are y. . some x are y'. . no x are y'. . some y are x'. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . some x are y. . all y are x'. . some y are x'. . all y are x. . all x are y, and all y' are x'. . some y are x'. . [no concl. fallacy of like eliminands not asserted to exist.] . some y are x'. . [no concl. fallacy of like eliminands not asserted to exist.] . no x are y'. . [no concl. fallacy of like eliminands not asserted to exist.] . some x are y. . all y are x'. . some y are x'. . some x are y'. . no x are y. . some x' are y'. . all y' are x. . all x are y'. . no x are y. _answers to § ._ an . somebody who has been out for a walk is feeling better. . no one but john knows what the letter is about. . you and i like walking. . honesty is sometimes the best policy. . some greyhounds are not fat. . some brave persons get their deserts. . some rich persons are not esquimaux. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . john is ill. . some things, that are not umbrellas, should be left behind on a journey. . no music is worth paying for, unless it causes vibration in the air. . some holidays are tiresome. . englishmen are not frenchmen. . no photograph of a lady is satisfactory. . no one looks poetical unless he is phlegmatic. . some thin persons are not cheerful. . some judges do not exercise self-control. . pigs are not fed on barley-water. . some black rabbits are not old. pg . [no concl. fallacy of unlike eliminands with an entity-premiss.] . [no concl. fallacy of like eliminands not asserted to exist.] . some lessons need attention. . [no concl. fallacy of like eliminands not asserted to exist.] . no one, who forgets a promise, fails to do mischief. . some greedy creatures cannot fly. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . no bride-cakes are things that need not be avoided. . john is happy. . some people, who are not gamblers, are not philosophers. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . none of my lodgers write poetry. . senna is not nice. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . [no concl. fallacy of like eliminands not asserted to exist.] . logic is unintelligible. . some wild creatures are fat. . all wasps are unwelcome. . all black rabbits are young. . some hard-boiled things can be cracked. . no antelopes fail to delight the eye. . all well-fed canaries are cheerful. . some poetry is not producible at will. . no country infested by dragons fails to be fascinating. . [no concl. fallacy of like eliminands not asserted to exist.] . some picturesque things are not made of sugar. . no children can sit still. . some cats cannot whistle. . you are terrible. . some oysters are not amusing. . nobody in the house has a beard a yard long. . some ill-fed canaries are unhappy. . my sisters cannot sing. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . some rich things are nice. . my cousins are none of them judges, and judges are none of them cousins of mine. . something wearisome is not eagerly wished for. . senna is nasty. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . niggers are not any of them tall. . some obstinate persons are not philosophers. . john is happy. . some unwholesome dishes are not present here (i.e. cannot be spoken of as "these"). . no books suit feverish patients unless they make one drowsy. . some greedy creatures cannot fly. . you and i can detect a sharper. . some dreams are not lambs. pg . no lizard needs a hairbrush. . some things, that may escape notice, are not battles. . my cousins are not any of them judges. . some hard-boiled things can be cracked. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . she is unpopular. . some people, who wear wigs, are not children of yours. . no lobsters expect impossibilities. . no nightmare is eagerly desired. . some nice things are not plumcakes. . some kinds of jam need not be shunned. . all ducks are ungraceful. . [no concl. fallacy of like eliminands not asserted to exist.] . no man, who begs in the street, should fail to keep accounts. . some savage creatures are not spiders. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . no travelers, who do not carry plenty of small change, fail to lose their luggage. . [no concl. fallacy of unlike eliminands with an entity-premiss.] . judges are none of them cousins of mine. . all my lodgers are sane. . those who are busy are contented, and discontented people are not busy. . none of my cousins are judges. . no nightingale dislikes sugar. . [no concl. fallacy of like eliminands not asserted to exist.] . some excuses are not clear explanations. . [no concl. fallacy of like eliminands not asserted to exist.] . no kind deed need cause scruple. . [no concl. fallacy of like eliminands not asserted to exist.] . [no concl. fallacy of like eliminands not asserted to exist.] . no cheats are trustworthy. . no clever child of mine is greedy. . some things, that are meant to amuse, are not acts of parliament. . no tour, that is ever forgotten, is worth writing a book about. . no obedient child of mine is contented. . your visit does not annoy me. _answers to § ._ an . conclusion right. . no concl. fallacy of like eliminands not asserted to exist. . concl. right. . concl. right. . concl. right. . no concl. fallacy of like eliminands not asserted to exist. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. pg . no concl. fallacy of like eliminands not asserted to exist. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . concl. wrong: the right one is "some x are y." . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . no concl. fallacy of like eliminands not asserted to exist. . concl. right. . concl. right. . concl. right. . concl. right. . concl. right. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. right. . concl. right. . concl. right. . no concl. fallacy of like eliminands not asserted to exist. . concl. right. . concl. right. _answers to § ._ an . concl. right. . concl. right. . concl. right. . concl. wrong: right one is "some epicures are not uncles of mine." . concl. right. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. wrong: right one is "the publication, in which i saw it, tells lies." . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. wrong: right one is "some tedious songs are not his." . concl. right. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. wrong: right one is "some fierce creatures do not drink coffee." . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. right. . concl. wrong: right one is "some shallow persons are not students." . no concl. fallacy of like eliminands not asserted to exist. . concl. wrong: right one is "some business, other than railways, is unprofitable." . concl. wrong: right one is "some vain persons are not professors." . concl. right. . concl. wrong: right one is "wasps are not puppies." . no concl. fallacy of unlike eliminands with an entity-premiss. . no concl. same fallacy. . concl. right. . concl. wrong: right one is "some chocolate-creams are delicious." . no concl. fallacy of like eliminands not asserted to exist. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. wrong: right one is "some pillows are not pokers." . concl. right. . no concl. fallacy of unlike eliminands with an entity-premiss. . no concl. fallacy of like eliminands not asserted to exist. . concl. right. . no concl. fallacy of like eliminands not asserted to exist. . no concl. fallacy of unlike eliminands with an entity-premiss. pg . concl. wrong: right one is "some dreaded persons are not begged to prolong their visits." . concl. wrong: right one is "no man walks on neither." . concl. right. . no concl. fallacy of unlike eliminands with an entity-premiss. . concl. wrong: right one is "some persons, dreaded by children, are not emperors." . concl. incomplete: the omitted portion is "sugar is not salt." . concl. right. _answers to § ._ an . a_{ }b_{ } + b_{ }a_{ }. . d_{ }a_{ }. . ac_{ }. . a_{ }d_{ }. . cd_{ }. . d_{ }c_{ }. . a'c_{ }. . c_{ }a'_{ }. . c'd_{ }. . b_{ }a_{ }. . d_{ }b_{ }. . a'd_{ }. . e_{ }b_{ }. . d_{ }e'_{ }. . e_{ }a'_{ }. . b'c_{ }. . a_{ }b_{ }. . d_{ }c_{ }. . a_{ }d_{ }. . ac_{ }. . de_{ }. . a_{ }b'_{ }. . h_{ }c_{ }. . e_{ }a_{ }. . e_{ }c'_{ }. . e_{ }c'_{ }. . hk'_{ }. . e_{ }d'_{ }. . l'a_{ }. . k_{ }b'_{ }. _answers to § ._ an . babies cannot manage crocodiles. . _your_ presents to me are not made of tin. . all my potatoes in this dish are old ones. . my servants never say "shpoonj." . my poultry are not officers. . none of _your_ sons are fit to serve on a jury. . no pencils of mine are sugar-plums. . jenkins is inexperienced. . no comet has a curly tail. . no hedge-hog takes in the _times_. . this dish is unwholesome. . my gardener is very old. . all humming-birds are small. . no one with a hooked nose ever fails to make money. . no gray ducks in this village wear lace collars. . no jug in this cupboard will hold water. . these apples were grown in the sun. . puppies, that will not lie still, never care to do worsted work. . no name in this list is unmelodious. . no m.p. should ride in a donkey-race, unless he has perfect self-command. . no goods in this shop, that are still on sale, may be carried away. pg . no acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus. . guinea-pigs never really appreciate beethoven. . no scentless flowers please me. . showy talkers are not really well-informed. . none but red-haired boys learn greek in this school. . wedding-cake always disagrees with me. . discussions, that go on while tomkins is in the chair, endanger the peacefulness of our debating-club. . all gluttons, who are children of mine, are unhealthy. . an egg of the great auk is not to be had for a song. . no books sold here have gilt edges, unless they are priced at s. and upwards. . when you cut your finger, you will find tincture of calendula useful. . _i_ have never come across a mermaid at sea. . all the romances in this library are well-written. . no bird in this aviary lives on mince-pies. . no plum-pudding, that has not been boiled in a cloth, can be distinguished from soup. . all _your_ poems are uninteresting. . none of my peaches have been grown in a hot-house. . no pawnbroker is dishonest. . no kitten with green eyes will play with a gorilla. . all _my_ friends dine at the lower table. . my writing-desk is full of live scorpions. . no mandarin ever reads hogg's poems. . shakespeare was clever. . rainbows are not worth writing odes to. . these sorites-examples are difficult. . all my dreams come true. . all the english pictures here are painted in oils. . donkeys are not easy to swallow. . opium-eaters never wear white kid gloves. . a good husband always comes home for his tea. . bathing-machines are never made of mother-of-pearl. . rainy days are always cloudy. . no heavy fish is unkind to children. . no engine-driver lives on barley-sugar. . all the animals in the yard gnaw bones. . no badger can guess a conundrum. . no cheque of yours, received by me, is payable to order. . i cannot read any of brown's letters. . i always avoid a kangaroo. pg chapter iii. _solutions._ § . _propositions of relation reduced to normal form._ _solutions for § ._ sl . the univ. is "persons." the individual "i" may be regarded as a class, of persons, whose peculiar attribute is "represented by the name 'i'", and may be called the class of "i's". it is evident that this class cannot possibly contain more than one member: hence the sign of quantity is "all". the verb "have been" may be replaced by the phrase "are persons who have been". the proposition may be written thus:-- "all" _sign of quantity_. "i's" _subject_. "are" _copula_. "persons who have been out for a walk" _predicate_. or, more briefly, "all | i's | are | persons who have been out for a walk". . the univ. and the subject are the same as in ex. . the proposition may be written "all | i's | are | persons who feel better". . univ. is "persons". the subject is evidently the class of persons from which john is _excluded_; _i.e._ it is the class containing all persons who are _not_ "john". the sign of quantity is "no". the verb "has read" may be replaced by the phrase "are persons who have read". the proposition may be written "no | persons who are not 'john' | are | persons who have read the letter". . univ. is "persons". the subject is evidently the class of persons whose only two members are "you and i". hence the sign of quantity is "no". the proposition may be written "no | members of the class 'you and i' | are | old persons". pg . univ. is "creatures". the verb "run well" may be replaced by the phrase "are creatures that run well". the proposition may be written "no | fat creatures | are | creatures that run well". . univ. is "persons". the subject is evidently the class of persons who are _not_ brave. the verb "deserve" may be replaced by the phrase "are deserving of". the proposition may be written "no | not-brave persons | are | persons deserving of the fair". . univ. is "persons". the phrase "looks poetical" evidently belongs to the _predicate_; and the _subject_ is the class, of persons, whose peculiar attribute is "_not_-pale". the proposition may be written "no | not-pale persons | are | persons who look poetical". . univ. is "persons". the proposition may be written "some | judges | are | persons who lose their tempers". . univ. is "persons". the phrase "never neglect" is merely a stronger form of the phrase "am a person who does not neglect". the proposition may be written "all | 'i's' | are | persons who do not neglect important business". . univ. is "things". the phrase "what is difficult" (_i.e._ "that which is difficult") is equivalent to the phrase "all difficult things". the proposition may be written "all | difficult things | are | things that need attention". . univ. is "things". the phrase "what is unwholesome" may be interpreted as in ex. . the proposition may be written "all | unwholesome things | are | things that should be avoided". . univ. is "laws". the predicate is evidently a class whose peculiar attribute is "relating to excise". the proposition may be written "all | laws passed last week | are | laws relating to excise". . univ. is "things". the subject is evidently the class, of studies, whose peculiar attribute is "logical"; hence the sign of quantity is "all". the proposition may be written "all | logical studies | are | things that puzzle me". . univ. is "persons". the subject is evidently "persons in the house". the proposition may be written "no | persons in the house | are | jews". . univ. is "dishes". the phrase "if not well-cooked" is equivalent to the attribute "not well-cooked". the proposition may be written "some | not well-cooked dishes | are | unwholesome dishes". pg . univ. is "books". the phrase "make one drowsy" may be replaced by the phrase "are books that make one drowsy". the sign of quantity is evidently "all". the proposition may be written "all | unexciting books | are | books that make one drowsy". . univ. is "men". the subject is evidently "a man who knows what he's about"; and the word "when" shows that the proposition is asserted of _every_ such man, _i.e._ of _all_ such men. the verb "can" may be replaced by "are men who can". the proposition may be written "all | men who know what they're about | are | men who can detect a sharper". . the univ. and the subject are the same as in ex. . the proposition may be written "all | members of the class 'you and i' | are | persons who know what they're about". . univ. is "persons". the verb "wear" may be replaced by the phrase "are accustomed to wear". the proposition may be written "some | bald persons | are | persons accustomed to wear wigs". . univ. is "persons". the phrase "never talk" is merely a stronger form of "are persons who do not talk". the proposition may be written "all | fully occupied persons | are | persons who do not talk about their grievances". . univ. is "riddles". the phrase "if they can be solved" is equivalent to the attribute "that can be solved". the proposition may be written "no | riddles that can be solved | are | riddles that interest me". § . _method of diagrams._ _solutions for § , nos. - ._ sl -a ·---------------· ·-------· . no m are x'; | | (o)| | | | all m' are y. | ·---|---· | |---|---| | | | | | | |(o)| |(i)|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. no x' are y'. | | (o)| ·---------------· pg ·---------------· ·-------· . no m' are x; |(o) | (o)| | | | some m' are y'. | ·---|---· | |---|---| | | | | | | |(i)| |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. some x are y'. | | (i)| ·---------------· ·---------------· ·-------· . all m' are x; |(o) | (i)| | |(i)| all m' are y'. | ·---|---· | |---|---| | | | | | | | | |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. some x are y'. |(o) | (o)| ·---------------· ·---------------· . no x' are m'; | | (o)| all y' are m. | ·---|---· | | | | | | |---|---|(i)|---| there is no conclusion. | | | | | | ·---|---· | |(o) | (o)| ·---------------· ·---------------· ·-------· . some m are x'; | | | | | | no y are m. | ·---|---· | |---|---| | |(o)| | | | |(i)| |---|---|---|---| ·-------· | |(o)|(i)| | | ·---|---· | .'. some x' are y'. | | | ·---------------· ·---------------· . no x' are m; | | | no m are y. | ·---|---· | | |(o)| | | |---|---|---|---| there is no conclusion. | |(o)|(o)| | | ·---|---· | | | | ·---------------· ·---------------· ·-------· . no m are x'; | | | | |(i)| some y' are m. | ·---|---· | |---|---| | | |(i)| | | | | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. some x are y'. | | | ·---------------· ·---------------· ·-------· . all m' are x'; |(o) | (o)| | | | no m' are y. | ·---|---· | |---|---| | | | | | | |(i)| |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. some x' are y'. |(o) | (i)| ·---------------· pg ·---------------· . some x' are m'; | | | no m are y'. | ·---|---· | | | |(o)| | |---|---|---|---| there is no conclusion. | | |(o)| | | ·---|---· | | (i) | ·---------------· ·---------------· ·-------· . all x are m; |(o) | (o)| |(i)|(o)| all y' are m'. | ·---|---· | |---|---| | |(i)|(o)| | | |(i)| |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | .'. all x are y; | | (i)| all y' are x'. ·---------------· ·---------------· . no m are x; | | | all y' are m'. | ·---|---· | | |(o)|(o)| | |---|---|---|(i)| there is no conclusion. | | |(o)| | | ·---|---· | | | | ·---------------· ·---------------· ·-------· . no x are m; |(o) | | |(o)| | all y are m. | ·---|---· | |---|---| | |(o)|(o)| | |(i)| | |---|---|---|---| ·-------· | |(i)| | | | ·---|---· | .'. all y are x'. |(o) | | ·---------------· _solutions for § , nos. - ._ sl -a . i have been out for a walk; i am feeling better. univ. is "persons"; m = the class of i's; x = persons who have been out for a walk; y = persons who are feeling better. ·---------------· ·-------· all m are x; | | | |(i)| | all m are y. | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. some x are y. | | | ·---------------· i.e. somebody, who has been out for a walk, is feeling better. pg . no one has read the letter but john; no one, who has _not_ read it, knows what it is about. univ. is "persons"; m = persons who have read the letter; x = the class of johns; y = persons who know what the letter is about. ·---------------· ·-------· no x' are m; |(o) | | | | | no m' are y. | ·---|---· | |---|---| | | | | | |(o)| | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. no x' are y. |(o) | | ·---------------· i.e. no one, but john, knows what the letter is about. . those who are not old like walking; you and i are young. univ. is "persons"; m = old; x = persons who like walking; y = you and i. ·---------------· ·-------· all m' are x; |(i) | | |(i)| | all y are m'. | ·---|---· | |---|---| | |(o)| | | |(o)| | |---|---|---|---| ·-------· | |(o)| | | | ·---|---· | .'. all y are x. |(o) | (o)| ·---------------· i.e. you and i like walking. . your course is always honest; your course is always the best policy. univ. is "courses"; m = your; x = honest; y = courses which are the best policy. ·---------------· ·-------· all m are x; | | | |(i)| | all m are y. | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | |(o)|(o)| | | ·---|---· | .'. some x are y. | | | ·---------------· i.e. honesty is sometimes the best policy. . no fat creatures run well; some greyhounds run well. univ. is "creatures"; m = creatures that run well; x = fat; y = greyhounds. ·---------------· ·-------· no x are m; | | | | | | some y are m. | ·---|---· | |---|---| | |(o)|(o)| | |(i)| | |---|---|---|---| ·-------· | |(i)| | | | ·---|---· | .'. some y are x'. | | | ·---------------· i.e. some greyhounds are not fat. pg . some, who deserve the fair, get their deserts; none but the brave deserve the fair. univ. is "persons"; m = persons who deserve the fair; x = persons who get their deserts; y = brave. ·---------------· ·-------· some m are x; | | | |(i)| | no y' are m. | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | .'. some y are x. | | | ·---------------· i.e. some brave persons get their deserts. . some jews are rich; all esquimaux are gentiles. univ. is "persons"; m = jews; x = rich; y = esquimaux. ·---------------· ·-------· some m are x; | | | | |(i)| all y are m'. | ·---|---· | |---|---| | |(o)|(i)| | | | | |(i)|---|---|---| ·-------· | |(o)| | | | ·---|---· | .'. some x are y'. | | | ·---------------· i.e. some rich persons are not esquimaux. . sugar-plums are sweet; some sweet things are liked by children. univ. is "things"; m = sweet; x = sugar-plums; y = things that are liked by children. ·---------------· all x are m; |(o) | (o)| some m are y. | ·---|---· | | | (i) | | |---|(i)|---|---| | | | | | | ·---|---· | | | | ·---------------· there is no conclusion. . john is in the house; everybody in the house is ill. univ. is "persons"; m = persons in the house; x = the class of johns; y = ill. ·---------------· ·-------· all x are m; |(o) | (o)| |(i)|(o)| all m are y. | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | .'. all x are y. | | | ·---------------· i.e. john is ill. pg . umbrellas are useful on a journey; what is useless on a journey should be left behind. univ. is "things"; m = useful on a journey; x = umbrellas; y = things that should be left behind. ·---------------· ·-------· all x are m; |(o) | (o)| | | | all m' are y. | ·---|---· | |---|---| | | (i) | | |(i)| | |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. some x' are y. |(i) | (o)| ·---------------· i.e. some things, that are not umbrellas, should be left behind on a journey. . audible music causes vibration in the air; inaudible music is not worth paying for. univ. is "music"; m = audible; x = music that causes vibration in the air; y = worth paying for. ·---------------· ·-------· all m are x; |(o) | | | | | all m' are y'. | ·---|---· | |---|---| | | (i) | | |(o)| | |---|---|---|(i)| ·-------· | |(o)|(o)| | | ·---|---· | .'. no x' are y. |(o) | | ·---------------· i.e. no music is worth paying for, unless it causes vibration in the air. . some holidays are rainy; rainy days are tiresome. univ. is "days"; m = rainy; x = holidays; y = tiresome. ·---------------· ·-------· some x are m; | | | |(i)| | all m are y. | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | .'. some x are y. | | | ·---------------· i.e. some holidays are tiresome. _solutions for § , nos. - ._ sl -a . some x are m; no m are y'. some x are y. ·---------------· ·-------· | | | |(i)| | | ·---|---· | |---|---| | |(i)|(o)| | | | | |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | hence proposed conclusion is right. | | | ·---------------· pg . all x are m; no y are m'. no y are x'. ·---------------· |(o) | (o)| | ·---|---· | | | (i) | | |---|---|---|---| there is no conclusion. | | | | | | ·---|---· | |(o) | | ·---------------· . some x are m'; all y' are m. some x are y. ·---------------· ·-------· |(i) | (o)| |(i)| | | ·---|---· | |---|---| | | | | | | | | |---|---|(i)|---| ·-------· | | | | | | ·---|---· | hence proposed conclusion is right. | | (o)| ·---------------· . all x are m; no y are m. all x are y'. ·---------------· ·-------· |(o) | (o)| |(o)|(i)| | ·---|---· | |---|---| | |(o)|(i)| | | | | |---|---|---|---| ·-------· | |(o)| | | | ·---|---· | hence proposed conclusion is right. | | | ·---------------· . some m' are x'; no m' are y. some x' are y'. ·---------------· ·-------· |(o) | | | | | | ·---|---· | |---|---| | | | | | | |(i)| |---|---|---|---| ·-------· | | | | | | ·---|---· | hence proposed conclusion is right. |(o) | (i)| ·---------------· . no x' are m; all y are m'. all y are x. ·---------------· | | | | ·---|---· | | |(o)| | | |(i)|---|---|---| there is no conclusion. | |(o)|(o)| | | ·---|---· | | | | ·---------------· pg . some m' are x'; all y' are m'. some x' are y'. ·---------------· | | | | ·---|---· | | | |(o)| | |---|---|---|(i)| there is no conclusion. | | |(o)| | | ·---|---· | | (i) | ·---------------· . no m' are x'; all y' are m'. all y' are x. ·---------------· ·-------· | | (i)| | |(i)| | ·---|---· | |---|---| | | |(o)| | | |(o)| |---|---|---|---| ·-------· | | |(o)| | | ·---|---· | hence proposed conclusion is right. |(o) | (o)| ·---------------· . some m are x'; no m are y. some x' are y'. ·---------------· ·-------· | | | | | | | ·---|---· | |---|---| | |(o)| | | | |(i)| |---|---|---|---| ·-------· | |(o)|(i)| | | ·---|---· | hence proposed conclusion is right. | | | ·---------------· . all m' are x'; all m are y. some y are x'. ·---------------· ·-------· |(o) | (o)| | | | | ·---|---· | |---|---| | | | | | |(i)| | |---|---|---|---| ·-------· | | | | | | ·---|---· | hence proposed conclusion is right. |(i) | (o)| ·---------------· pg _solutions for § , nos. - ._ sl -a . no doctors are enthusiastic; you are enthusiastic. you are not a doctor. univ. "persons"; m = enthusiastic; x = doctors; y = you. ·---------------· ·-------· |(o) | | |(o)| | | ·---|---· | |---|---| no x are m; | |(o)|(o)| | |(i)| | all y are m. |---|---|---|---| ·-------· all y are x'. | |(i)| | | | ·---|---· | .'. all y are x'. |(o) | | ·---------------· hence proposed conclusion is right. . all dictionaries are useful; useful books are valuable. dictionaries are valuable. univ. "books"; m = useful; x = dictionaries; y = valuable. ·---------------· ·-------· |(o) | (o)| |(i)|(o)| | ·---|---· | |---|---| all x are m; | |(i)|(o)| | | | | all m are y. |---|---|---|---| ·-------· all x are y. | | |(o)| | | ·---|---· | .'. all x are y. | | | ·---------------· hence proposed conclusion is right. . no misers are unselfish; none but misers save egg-shells. no unselfish people save egg-shells. univ. "people"; m = misers; x = selfish; y = people who save egg-shells. ·---------------· ·-------· |(o) | | | | | | ·---|---· | |---|---| no m are x'; | | | | | |(o)| | no m' are y. |---|---|---|---| ·-------· no x' are y. | |(o)|(o)| | | ·---|---· | .'. no x' are y. |(o) | | ·---------------· hence proposed conclusion is right. pg . some epicures are ungenerous; all my uncles are generous. my uncles are not epicures. univ. "persons"; m = generous; x = epicures; y = my uncles. ·---------------· ·-------· |(o) | (i)| | |(i)| | ·---|---· | |---|---| some x are m'. | | | | | | | | all y are m. |---|(i)|---|---| ·-------· all y are x'. | | | | | | ·---|---· | .'. some x are y'. |(o) | | ·---------------· hence proposed conclusion is wrong, the right one being "some epicures are not uncles of mine." . gold is heavy; nothing but gold will silence him. nothing light will silence him. univ. "things"; m = gold; x = heavy; y = able to silence him. ·---------------· ·-------· |(o) | | | | | | ·---|---· | |---|---| all m are x; | | (i) | | |(o)| | no m' are y. |---|---|---|---| ·-------· no x' are y. | |(o)|(o)| | | ·---|---· | .'. no x' are y. |(o) | | ·---------------· hence proposed conclusion is right. . some healthy people are fat; no unhealthy people are strong. some fat people are not strong. univ. "persons"; m = healthy; x = fat; y = strong. ·---------------· |(o) | | | ·---|---· | some m are x; | | (i) | | no m' are y. |---|---|---|---| there is no conclusion. some x are y'.| | | | | | ·---|---· | |(o) | | ·---------------· pg § . _method of subscripts._ _solutions for § ._ sl -b . mx'_{ } + m'_{ }y'_{ } ¶ x'y'_{ } [fig. i. i.e. "no x' are y'." . m'x_{ } + m'y'_{ } ¶ x'y'_{ } [fig. ii. i.e. "some x' are y'." . m'_{ }x'_{ } + m'_{ }y_{ } ¶ xy'_{ } [fig. iii. i.e. "some x are y'." . x'm'_{ } + y'_{ }m'_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . mx'_{ } + ym_{ } ¶ x'y'_{ } [fig. ii. i.e. "some x' are y'." . x'm_{ } + my_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . mx'_{ } + y'm_{ } ¶ xy'_{ } [fig. ii. i.e. "some x are y'." . m'_{ }x_{ } + m'y_{ } ¶ x'y'_{ } [fig. iii. i.e. "some x' are y'." . x'm'_{ } + my_{ } ¶ nothing. [fallacy of unlike eliminands with an entity-premiss.] . x_{ }m'_{ } + y'_{ }m_{ } ¶ x_{ }y'_{ } + y'_{ }x_{ } [fig. i (b). i.e. "all x are y, and all y' are x'." . mx_{ } + y'_{ }m_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . xm_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). i.e. "all y are x'." . m'_{ }x'_{ } + ym_{ } ¶ x'y_{ } [fig. i. i.e. "no x' are y." . m_{ }x'_{ } + m'_{ }y'_{ } ¶ x'y'_{ } [fig. i. i.e. "no x' are y'." . xm_{ } + m'y_{ } ¶ xy_{ } [fig. i. i.e. "no x are y." . x_{ }m_{ } + y_{ }m'_{ } ¶ (x_{ }y_{ } + y_{ }x_{ }) [fig. i (b). i.e. "all x are y' and all y are x'." . xm_{ } + m'_{ }y'_{ } ¶ xy'_{ } [fig. i. i.e. "no x are y'." . xm'_{ } + my_{ } ¶ xy_{ } [fig. i. i.e. "no x are y." . m_{ }x'_{ } + m_{ }y_{ } ¶ xy'_{ } [fig. iii. i.e. "some x are y'." . mx_{ } + m'_{ }y'_{ } ¶ xy'_{ } [fig. i. i.e. "no x are y'." . x_{ }m'_{ } + m'y_{ } ¶ x'y_{ } [fig. ii. i.e. "some x' are y." . xm_{ } + y_{ }m'_{ } ¶ nothing. [fallacy of unlike eliminands with an entity-premiss.] . m_{ }x'_{ } + ym_{ } ¶ xy_{ } [fig. ii. i.e. "some x are y." . xm_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). i.e. "all y are x'." . mx'_{ } + my'_{ } ¶ x'y_{ } [fig. ii. i.e. "some x' are y." . mx'_{ } + y_{ }m'_{ } ¶ y_{ }x'_{ } [fig. i (a). i.e. "all y are x." . x_{ }m_{ } + y'_{ }m'_{ } ¶ (x_{ }y'_{ } + y'_{ }x_{ }) [fig. i (b). i.e. "all x are y, and all y' are x'." . m_{ }x_{ } + my_{ } ¶ x'y_{ } [fig. ii. i.e. "some x' are y." . mx_{ } + y_{ }m_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . x_{ }m_{ } + ym_{ } ¶ x'y_{ } [fig. ii. i.e. "some y are x'." . x_{ }m'_{ } + y_{ }m'_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] pg . xm'_{ } + m_{ }y'_{ } ¶ xy'_{ } [fig. i. i.e. "no x are y'." . mx_{ } + my_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . mx'_{ } + ym_{ } ¶ xy_{ } [fig. ii. i.e. "some x are y." . mx_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). i.e. "all y are x'." . m_{ }x_{ } + ym_{ } ¶ x'y_{ } [fig. ii. i.e. "some x' are y." . m_{ }x'_{ } + ym_{ } ¶ xy'_{ } [fig. iii. i.e. "some x are y'." . mx_{ } + m'y_{ } ¶ xy_{ } [fig. i. i.e. "no x are y." . mx'_{ } + my_{ } ¶ x'y'_{ } [fig. ii. i.e. "some x' are y'." . x'm_{ } + y'_{ }m'_{ } ¶ y'_{ }x'_{ } [fig. i (a). i.e. "all y' are x." . x_{ }m_{ } + ym'_{ } ¶ x_{ }y_{ } [fig. i (a). i.e. "all x are y'." . m'x_{ } + ym_{ } ¶ xy_{ } [fig. i. i.e. "no x are y." _solutions for § , nos. - ._ sl -b . no frenchmen like plumpudding; all englishmen like plumpudding. univ. "men"; m = liking plumpudding; x = french; y = english. xm_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). i.e. englishmen are not frenchmen. . no portrait of a lady, that makes her simper or scowl, is satisfactory; no photograph of a lady ever fails to make her simper or scowl. univ. "portraits of ladies"; m = making the subject simper or scowl; x = satisfactory; y = photographic. mx_{ } + ym'_{ } ¶ xy_{ } [fig. i. i.e. no photograph of a lady is satisfactory. . all pale people are phlegmatic; no one looks poetical unless he is pale. univ. "people"; m = pale; x = phlegmatic; y = looking poetical. m_{ }x'_{ } + m'y_{ } ¶ x'y_{ } [fig. i. i.e. no one looks poetical unless he is phlegmatic. . no old misers are cheerful; some old misers are thin. univ. "persons"; m = old misers; x = cheerful; y = thin. mx_{ } + my_{ } ¶ x'y_{ } [fig. ii. i.e. some thin persons are not cheerful. . no one, who exercises self-control, fails to keep his temper; some judges lose their tempers. univ. "persons"; m = keeping their tempers; x = exercising self-control; y = judges. xm'_{ } + ym'_{ } ¶ x'y_{ } [fig. ii. i.e. some judges do not exercise self-control. pg . all pigs are fat; nothing that is fed on barley-water is fat. univ. is "things"; m = fat; x = pigs; y = fed on barley-water. x_{ }m'_{ } + ym_{ } ¶ x_{ }y_{ } [fig. i (a). i.e. pigs are not fed on barley-water. . all rabbits, that are not greedy, are black; no old rabbits are free from greediness. univ. is "rabbits"; m = greedy; x = black; y = old. m'_{ }x'_{ } + ym'_{ } ¶ xy'_{ } [fig. iii. i.e. some black rabbits are not old. . some pictures are not first attempts; no first attempts are really good. univ. is "things"; m = first attempts; x = pictures; y = really good. xm'_{ } + my_{ } ¶ nothing. [fallacy of unlike eliminands with an entity-premiss.] . i never neglect important business; your business is unimportant. univ. is "business"; m = important; x = neglected by me; y = your. mx_{ } + y_{ }m_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . some lessons are difficult; what is difficult needs attention. univ. is "things"; m = difficult; x = lessons; y = needing attention. xm_{ } + m_{ }y'_{ } ¶ xy_{ } [fig. ii. i.e. some lessons need attention. . all clever people are popular; all obliging people are popular. univ. is "people"; m = popular; x = clever; y = obliging. x_{ }m'_{ } + y_{ }m'_{ } ¶ nothing. [fallacy of like eliminands not asserted to exist.] . thoughtless people do mischief; no thoughtful person forgets a promise. univ. is "persons"; m = thoughtful; x = mischievous; y = forgetful of promises. m'_{ }x'_{ } + my_{ } ¶ x'y_{ } i.e. no one, who forgets a promise, fails to do mischief. _solutions for § ._ sl -b . xm_{ } + my'_{ } ¶ xy_{ } [fig. ii.] concl. right. . x_{ }m'_{ } + ym'_{ } fallacy of like eliminands not asserted to exist. . xm'_{ } + y'_{ }m'_{ } ¶ xy_{ } [fig. ii.] concl. right. pg . x_{ }m'_{ } + ym_{ } ¶ x_{ }y_{ } [fig. i (a).] concl. right. . m'x'_{ } + m'y_{ } ¶ x'y'_{ } [fig. ii.] " . x'm_{ } + y_{ }m_{ } fallacy of like eliminands not asserted to exist. . m'x'_{ } + y'_{ }m_{ } fallacy of unlike eliminands with an entity-premiss. . m'x'_{ } + y'_{ }m_{ } ¶ y'_{ }x'_{ } [fig. i (a).] concl. right. . mx'_{ } + my_{ } ¶ x'y'_{ } [fig. ii.] " . m'_{ }x_{ } + m'_{ }y'_{ } ¶ x'y_{ } [fig. iii.] " . x_{ }m_{ } + ym_{ } ¶ x'y_{ } [fig. ii.] " . xm_{ } + m'y'_{ } ¶ xy'_{ } [fig. i.] " . xm_{ } + y'_{ }m'_{ } ¶ y'_{ }x_{ } [fig. i (a).] " . m'_{ }x_{ } + m'_{ }y'_{ } ¶ x'y_{ } [fig. iii.] " . mx'_{ } + y_{ }m_{ } ¶ x'y'_{ } [fig. ii.] " . x'm_{ } + y'_{ }m_{ } fallacy of like eliminands not asserted to exist. . m'x_{ } + m'_{ }y_{ } ¶ x'y'_{ } [fig. iii.] concl. right. . x'm_{ } + my_{ } ¶ xy_{ } [fig. ii.] " . mx'_{ } + m_{ }y'_{ } ¶ x'y_{ } [ " ] " . x'm'_{ } + m'y'_{ } ¶ xy'_{ } [ " ] " . mx_{ } + m_{ }y_{ } ¶ x'y'_{ } [fig. iii.] " . x'_{ }m'_{ } + ym'_{ } ¶ xy_{ } [fig. ii.] concl. wrong: the right one is "some x are y." . m_{ }x'_{ } + m'y'_{ } ¶ x'y'_{ } [fig. i.] concl. right. . x_{ }m_{ } + m'_{ }y'_{ } ¶ x_{ }y'_{ } [fig. i (a).] " . xm'_{ } + m_{ }y'_{ } ¶ xy'_{ } [fig. i.] " . m_{ }x_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a).] " . x_{ }m'_{ } + my'_{ } ¶ x_{ }y'_{ } [ " ] " . x_{ }m'_{ } + y'm'_{ } fallacy of like eliminands not asserted to exist. . x'm_{ } + m'y'_{ } ¶ x'y'_{ } [fig. i.] concl. right. . x_{ }m'_{ } + m_{ }y_{ } ¶ x_{ }y_{ } [fig. i (a).] " . x'_{ }m_{ } + y'm'_{ } ¶ x'_{ }y'_{ } [ " ] " . xm_{ } + y'm'_{ } ¶ xy'_{ } [fig. i.] " . m_{ }x_{ } + y'_{ }m'_{ } ¶ y'_{ }x_{ } [fig. i (a).] " . x_{ }m_{ } + ym'_{ } fallacy of unlike eliminands with an entity-premiss. . xm_{ } + m_{ }y'_{ } ¶ xy_{ } [fig. ii.] concl. right. . m_{ }x_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a).] " . mx'_{ } + m_{ }y_{ } ¶ xy'_{ } [fig. iii.] " . xm_{ } + my'_{ } fallacy of like eliminands not asserted to exist. . mx_{ } + my'_{ } ¶ x'y'_{ } [fig. ii.] concl. right. . mx'_{ } + ym_{ } ¶ xy_{ } [fig. ii.] " pg _solutions for § ._ sl -b . no doctors are enthusiastic; you are enthusiastic. you are not a doctor. univ. "persons"; m = enthusiastic; x = doctors; y = you. xm_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). conclusion right. . dictionaries are useful; useful books are valuable. dictionaries are valuable. univ. "books"; m = useful; x = dictionaries; y = valuable. x_{ }m'_{ } + m_{ }y'_{ } ¶ x_{ }y'_{ } [fig. i (a). conclusion right. . no misers are unselfish; none but misers save egg-shells. no unselfish people save egg-shells. univ. "people"; m = misers; x = selfish; y = people who save egg-shells. mx'_{ } + m'y_{ } ¶ x'y_{ } [fig. i. conclusion right. . some epicures are ungenerous; all my uncles are generous. my uncles are not epicures. univ. "persons"; m = generous; x = epicures; y = my uncles. xm'_{ } + y_{ }m'_{ } ¶ xy'_{ } [fig. ii. conclusion wrong: right one is "some epicures are not uncles of mine." . gold is heavy; nothing but gold will silence him. nothing light will silence him. univ. "things"; m = gold; x = heavy; y = able to silence him. m_{ }x'_{ } + m'y_{ } ¶ x'y_{ } [fig. i. conclusion right. . some healthy people are fat; no unhealthy people are strong. some fat people are not strong. univ. "people"; m = healthy; x = fat; y = strong. mx_{ } + m'y_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . i saw it in a newspaper; all newspapers tell lies. it was a lie. univ. "publications"; m = newspapers; x = publications in which i saw it; y = telling lies. x_{ }m'_{ } + m_{ }y'_{ } ¶ x_{ }y'_{ } [fig. i (a). conclusion wrong: right one is "the publication, in which i saw it, tells lies." pg . some cravats are not artistic; i admire anything artistic. there are some cravats that i do not admire. univ. "things"; m = artistic; x = cravats; y = things that i admire. xm_{ } + m_{ }y_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . his songs never last an hour. a song, that lasts an hour, is tedious. his songs are never tedious. univ. "songs"; m = lasting an hour; x = his; y = tedious. x_{ }m_{ } + m_{ }y'_{ } ¶ x'y_{ } [fig. iii. conclusion wrong: right one is "some tedious songs are not his." . some candles give very little light; candles are meant to give light. some things, that are meant to give light, give very little. univ. "things"; m = candles; x = giving &c.; y = meant &c. mx_{ } + m_{ }y'_{ } ¶ xy_{ } [fig. ii. conclusion right. . all, who are anxious to learn, work hard. some of these boys work hard. some of these boys are anxious to learn. univ. "persons"; m = hard-working; x = anxious to learn; y = these boys. x_{ }m'_{ } + ym_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . all lions are fierce; some lions do not drink coffee. some creatures that drink coffee are not fierce. univ. "creatures"; m = lions; x = fierce; y = creatures that drink coffee. m_{ }x'_{ } + my'_{ } ¶ xy'_{ } [fig. ii. conclusion wrong: right one is "some fierce creatures do not drink coffee." . no misers are generous; some old men are ungenerous. some old men are misers. univ. "persons"; m = generous; x = misers; y = old men. xm_{ } + ym'_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . no fossil can be crossed in love; an oyster may be crossed in love. oysters are not fossils. univ. "things"; m = things that can be crossed in love; x = fossils; y = oysters. xm_{ } + y_{ }m'_{ } ¶ y_{ }x_{ } [fig. i (a). conclusion right. pg . all uneducated people are shallow; students are all educated. no students are shallow. univ. "people"; m = educated; x = shallow; y = students. m'_{ }x'_{ } + y_{ }m'_{ } ¶ xy'_{ } [fig. iii. conclusion wrong: right one is "some shallow people are not students." . all young lambs jump; no young animals are healthy, unless they jump. all young lambs are healthy. univ. "young animals"; m = young animals that jump; x = lambs; y = healthy. x_{ }m'_{ } + m'y_{ } no conclusion. [fallacy of like eliminands not asserted to exist.] . ill-managed business is unprofitable; railways are never ill-managed. all railways are profitable. univ. "business"; m = ill-managed; x = profitable; y = railways. m_{ }x_{ } + y_{ }m_{ } ¶ x'y'_{ } [fig. iii. conclusion wrong: right one is "some business, other than railways, is profitable." . no professors are ignorant; all ignorant people are vain. no professors are vain. univ. "people"; m = ignorant; x = professors; y = vain. xm_{ } + m_{ }y'_{ } ¶ x'y_{ } [fig. iii. conclusion wrong: right one is "some vain persons are not professors." . a prudent man shuns hyænas. no banker is imprudent. no banker fails to shun hyænas. univ. "men"; m = prudent; x = shunning hyænas; y = bankers. m_{ }x'_{ } + ym'_{ } ¶ x'y_{ } [fig. i. conclusion right. . all wasps are unfriendly; no puppies are unfriendly. no puppies are wasps. univ. "creatures"; m = friendly; x = wasps; y = puppies. x_{ }m_{ } + ym'_{ } ¶ x_{ }y_{ } [fig. i (a). conclusion incomplete: complete one is "wasps are not puppies". . no jews are honest; some gentiles are rich. some rich people are dishonest. univ. "persons"; m = jews; x = honest; y = rich. mx_{ } + m'y_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] pg . no idlers win fame; some painters are not idle. some painters win fame. univ. "persons"; m = idlers; x = persons who win fame; y = painters. mx_{ } + ym'_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . no monkeys are soldiers; all monkeys are mischievous. some mischievous creatures are not soldiers. univ. "creatures"; m = monkeys; x = soldiers; y = mischievous. mx_{ } + m_{ }y'_{ } ¶ x'y_{ } [fig. iii. conclusion right. . all these bonbons are chocolate-creams; all these bonbons are delicious. chocolate-creams are delicious. univ. "food"; m = these bonbons; x = chocolate-creams; y = delicious. m_{ }x'_{ } + m_{ }y'_{ } ¶ xy_{ } [fig. iii. conclusion wrong, being in excess of the right one, which is "some chocolate-creams are delicious." . no muffins are wholesome; all buns are unwholesome. buns are not muffins. univ. "food"; m = wholesome; x = muffins; y = buns. xm_{ } + y_{ }m_{ } no conclusion. [fallacy of like eliminands not asserted to exist.] . some unauthorised reports are false; all authorised reports are trustworthy. some false reports are not trustworthy. univ. "reports"; m = authorised; x = true; y = trustworthy. m'x'_{ } + m_{ }y'_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . some pillows are soft; no pokers are soft. some pokers are not pillows. univ. "things"; m = soft; x = pillows; y = pokers. xm_{ } + ym_{ } ¶ xy'_{ } [fig. ii. conclusion wrong: right one is "some pillows are not pokers." . improbable stories are not easily believed; none of his stories are probable. none of his stories are easily believed. univ. "stories"; m = probable; x = easily believed; y = his. m'_{ }x_{ } + ym_{ } ¶ xy_{ } [fig. i. conclusion right. pg . no thieves are honest; some dishonest people are found out. some thieves are found out. univ. "people"; m = honest; x = thieves; y = found out. xm_{ } + m'y_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . no muffins are wholesome; all puffy food is unwholesome. all muffins are puffy. univ. is "food"; m = wholesome; x = muffins; y = puffy. xm_{ } + y_{ }m_{ } no conclusion. [fallacy of like eliminands not asserted to exist.] . no birds, except peacocks, are proud of their tails; some birds, that are proud of their tails, cannot sing. some peacocks cannot sing. univ. "birds"; m = proud of their tails; x = peacocks; y = birds that cannot sing. x'm_{ } + my'_{ } ¶ xy'_{ } [fig. ii. conclusion right. . warmth relieves pain; nothing, that does not relieve pain, is useful in toothache. warmth is useful in toothache. univ. "applications"; m = relieving pain; x = warmth; y = useful in toothache. x_{ }m'_{ } + m'y_{ } no conclusion. [fallacy of like eliminands not asserted to exist.] . no bankrupts are rich; some merchants are not bankrupts. some merchants are rich. univ. "persons"; m = bankrupts; x = rich; y = merchants. mx_{ } + ym'_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . bores are dreaded; no bore is ever begged to prolong his visit. no one, who is dreaded, is ever begged to prolong his visit. univ. "persons"; m = bores; x = dreaded; y = begged to prolong their visits. m_{ }x'_{ } + my_{ } ¶ xy'_{ } [fig. iii. conclusion wrong: the right one is "some dreaded persons are not begged to prolong their visits." . all wise men walk on their feet; all unwise men walk on their hands. no man walks on both. univ. "men"; m = wise; x = walking on their feet; y = walking on their hands. m_{ }x'_{ } + m'_{ }y'_{ } ¶ x'y'_{ } [fig. i. conclusion wrong: right one is "no man walks on neither." pg . no wheelbarrows are comfortable; no uncomfortable vehicles are popular. no wheelbarrows are popular. univ. "vehicles"; m = comfortable; x = wheelbarrows; y = popular. xm_{ } + m'x_{ } ¶ xy_{ } [fig. i. conclusion right. . no frogs are poetical; some ducks are unpoetical. some ducks are not frogs. univ. "creatures"; m = poetical; x = frogs; y = ducks. xm_{ } + ym'_{ } no conclusion. [fallacy of unlike eliminands with an entity-premiss.] . no emperors are dentists; all dentists are dreaded by children. no emperors are dreaded by children. univ. "persons"; m = dentists; x = emperors; y = dreaded by children. xm_{ } + m_{ }y'_{ } ¶ x'y_{ } [fig. iii. conclusion wrong: right one is "some persons, dreaded by children, are not emperors." . sugar is sweet; salt is not sweet. salt is not sugar. univ. "things"; m = sweet; x = sugar; y = salt. x_{ }m'_{ } + y_{ }m_{ } ¶ (x_{ }y_{ } + y_{ }x_{ }) [fig. i (b). conclusion incomplete: omitted portion is "sugar is not salt." . every eagle can fly; some pigs cannot fly. some pigs are not eagles. univ. "creatures"; m = creatures that can fly; x = eagles; y = pigs. x_{ }m'_{ } + ym'_{ } ¶ x'y_{ } [fig. ii. conclusion right. _solutions for § ._ sl . cd_{ } + a_{ }d'_{ } + b_{ }c'_{ }; cd + ad' + bc' ¶ ab_{ } + a_{ } + b_{ } -- = = i.e. ¶ a_{ }b_{ } + b_{ }a_{ } . d_{ }b'_{ } + ac'_{ } + bc_{ }; db' + bc + ac' ¶ da_{ } + d_{ } i.e. ¶ d_{ }a_{ } - =- = . ba_{ } + cd'_{ } + d_{ }b'_{ }; ba + db' + cd' ¶ ac_{ } - -= = . bc_{ } + a_{ }b'_{ } + c'd_{ }; bc + ab' + c'd ¶ ad_{ } + a_{ } i.e. ¶ a_{ }d_{ } -- = = pg . b'_{ }a_{ } + bc_{ } + a'd_{ }; b'a + bc + a'd ¶ cd_{ } - - = = . a_{ }b_{ } + b'c_{ } + d_{ }a'_{ }; ab + b'c + da' ¶ cd_{ } + d_{ } i.e. ¶ d_{ }c_{ } -- = = . db'_{ } + b_{ }a'_{ } + cd'_{ }; db' + ba' + cd' ¶ a'c_{ } -- = = . b'd_{ } + a'b_{ } + c_{ }d'_{ }; b'd + a'b + cd' ¶ a'c_{ } + c_{ } i.e. ¶ c_{ }a'_{ } - - = = . b'_{ }a'_{ } + ad_{ } + b_{ }c'_{ }; b'a' + ad + bc' ¶ dc'_{ } - - = = . cd_{ } + b_{ }c'_{ } + ad'_{ }; cd + bc' + ad' ¶ ba_{ } + b_{ } i.e. ¶ b_{ }a_{ } -- = = . bc_{ } + d_{ }a'_{ } + c'_{ }a_{ }; bc + c'a + da' ¶ bd_{ } + d_{ } i.e. ¶ d_{ }b_{ } - = - = . cb'_{ } + c'_{ }d_{ } + b_{ }a'_{ }; cb' + c'd + ba' ¶ da'_{ } -- = = . d_{ }e'_{ } + c_{ }a'_{ } + bd'_{ } + e_{ }a_{ }; de' + bd' + ea + ca' ¶ bc_{ } + c_{ } i.e. ¶ c_{ }b_{ } -- = =- = . c_{ }b'_{ } + a_{ }e'_{ } + d_{ }b_{ } + a'_{ }c'_{ }; cb' + db + a'c' + ae' ¶ de'_{ } + d_{ } i.e. ¶ d_{ }e'_{ } -- = - = = . b'd_{ } + e_{ }c'_{ } + b_{ }a'_{ } + d'_{ }c_{ }; b'd + ba' + d'c + ec' ¶ a'e_{ } + e_{ } i.e. ¶ e_{ }a'_{ } - - = = - = . a'e_{ } + d_{ }c_{ } + a_{ }b'_{ } + e'_{ }d'_{ }; a'e + ab' + e'd' + dc ¶ b'c_{ } - - = = - = . d_{ }c'_{ } + a_{ }e'_{ } + bd'_{ } + c_{ }e_{ }; dc' + bd' + ce + ae' ¶ ba_{ } + a_{ } i.e. ¶ a_{ }b_{ } -- = =- = . a_{ }b'_{ } + d_{ }e'_{ } + a'_{ }c_{ } + be_{ }; ab' + a'c + be + de' ¶ cd_{ } + d_{ } i.e. ¶ d_{ }c_{ } -- = =- = . bc_{ } + e_{ }h'_{ } + a_{ }b'_{ } + dh_{ } + e'_{ }c'_{ }; bc + ab' + e'c' + eh' + dh ¶ ad_{ } + a_{ } -- = - = =- = i.e. ¶ a_{ }d_{ } . dh'_{ } + ce_{ } + h_{ }b'_{ } + ad'_{ } + be'_{ }; dh' + hb' + ad' + be' + ce ¶ ac_{ } -- =- = =- = . b_{ }a'_{ } + dh_{ } + ce_{ } + ah'_{ } + c'_{ }b'_{ }; ba' + ah' + dh + c'b' + ce ¶ de_{ } -- =- = - = = . e_{ }d_{ } + b'h'_{ } + c'_{ }d'_{ } + a_{ }e'_{ } + ch_{ }; ed + c'd' + ae' + ch + b'h' ¶ ab'_{ } + a_{ } -- - = = =- = i.e. ¶ a_{ }b_{ } pg . b'_{ }a_{ } + de'_{ } + h_{ }b_{ } + ce_{ } + d'_{ }a'_{ }; b'a + hb + d'a' + de' + ce - - = - = =- = ¶ hc_{ } + h_{ } i.e. ¶ h_{ }c_{ } . h'_{ }k_{ } + b'a_{ } + c_{ }d'_{ } + e_{ }h_{ } + dk'_{ } + bc'_{ }; h'k + eh + dk' + cd' + bc' + b'a ¶ ea_{ } + e_{ } - - = -= -= -= = i.e. ¶ e_{ }a_{ } . a_{ }d'_{ } + k_{ }b'_{ } + e_{ }h'_{ } + a'b_{ } + d_{ }c'_{ } + h_{ }k'_{ }; ad' + a'b + kb' + dc' + hk' + eh' ¶ c'e_{ } + e_{ } -- = - -= = -= = i.e. ¶ e_{ }c'_{ } . a'_{ }h'_{ } + d'k'_{ } + e_{ }b_{ } + hk_{ } + a_{ }c'_{ } + b'd_{ }; a'h' + hk + d'k' + ac' + b'd + eb ¶ c'e_{ } + e_{ } - - =- - = = - = = i.e. ¶ e_{ }c'_{ } . e_{ }d_{ } + hb_{ } + a'_{ }k'_{ } + ce'_{ } + b'_{ }d'_{ } + ac'_{ }; ed + ce' + b'd' + hb + ac' + a'k' ¶ hk'_{ } -- -= - = = -= = . a'k_{ } + e_{ }b'_{ } + hk'_{ } + d'c_{ } + ab_{ } + c'_{ }h'_{ }; a'k + hk' + ab + eb' + c'h' + d'c ¶ ed'_{ } + e_{ } - - -= =- = - = = i.e. ¶ e_{ }d'_{ } . ek_{ } + b'm_{ } + ac'_{ } + h'_{ }e'_{ } + d_{ }k'_{ } + cb_{ } + d'_{ }l'_{ } + hm'_{ }; ek + h'e' + dk' + d'l' + hm' + b'm + cb + ac' -- - = -= = =- - = -= = ¶ l'a_{ } . n_{ }m'_{ } + a'_{ }e'_{ } + c'l_{ } + k_{ }r_{ } + ah'_{ } + dl'_{ } + cn'_{ } + e_{ }b'_{ } + m_{ }r'_{ } + h_{ }d'_{ }; nm' + cn' + c'l + dl' + mr' + kr + hd' + ah' + a'e' + eb' -- -= = - -= =- = -= -= = - = ¶ kb'_{ } + k_{ } i.e. ¶ k_{ }b'_{ } _solutions for § ._ sl . b_{ }d_{ } + ac_{ } + d'_{ }c'_{ }; bd + d'c' + ac ¶ ba_{ } + b_{ }, i.e. ¶ b_{ }a_{ } - = - = i.e. babies cannot manage crocodiles. . a_{ }b'_{ } + d_{ }c'_{ } + bc_{ }; ab' + bc + dc' ¶ ad_{ } + d_{ }, i.e. ¶ d_{ }a_{ } - =- = i.e. _your_ presents to me are not made of tin. pg . da_{ } + c_{ }b'_{ } + a'b_{ }; da + a'b + cb' ¶ dc_{ } + c_{ }, i.e. ¶ c_{ }d_{ } - = - = i.e. all my potatoes in this dish are old ones. . ba_{ } + b'd_{ } + c_{ }a'_{ }; ba + b'd + ca' ¶ dc_{ } + c_{ }, i.e. ¶ c_{ }d_{ } -- = = i.e. my servants never say "shpoonj." . ad_{ } + cd'_{ } + b_{ }a'_{ }; ad + cd' + ba' ¶ cb_{ } + b_{ }, i.e. ¶ b_{ }c_{ } -- = = i.e. my poultry are not officers. . c_{ }a'_{ } + c'b_{ } + da_{ }; ca' + c'b + da ¶ bd_{ } -- = = i.e. none of your sons are fit to serve on a jury. . cb_{ } + da_{ } + b'_{ }a'_{ }; cb + b'a' + da ¶ cd_{ } - = - = i.e. no pencils of mine are sugarplums. . cb'_{ } + d_{ }a'_{ } + ba_{ }; cb' + ba + da' ¶ cd_{ } + d_{ }, i.e. ¶ d_{ }c_{ } - =- = i.e. jenkins is inexperienced. . cd_{ } + d'a_{ } + c'b_{ }; cd + d'a + c'b ¶ ab_{ } -- = = i.e. no comet has a curly tail. . d'c_{ } + ba_{ } + a'_{ }d_{ }; d'c + a'd + ba ¶ cb_{ } - - = = i.e. no hedgehog takes in the _times_. . b_{ }a'_{ } + c_{ }b'_{ } + ad_{ }; ba' + cb' + ad ¶ cd_{ } + c_{ }, i.e. ¶ c_{ }d_{ } -- = = i.e. this dish is unwholesome. . b_{ }c'_{ } + d'a_{ } + a'c_{ }; bc' + a'c + d'a ¶ bd'_{ } + b_{ }, i.e. ¶ b_{ }d'_{ } - - = = i.e. my gardener is very old. . a_{ }d'_{ } + bc_{ } + c'_{ }d_{ }; ad' + c'd + bc ¶ ab_{ } + a_{ }, i.e. ¶ a_{ }b_{ } - - = = i.e. all humming-birds are small. pg . c'b_{ } + a_{ }d'_{ } + ca'_{ }; c'b + ca' + ad' ¶ bd'_{ } - =- = i.e. no one with a hooked nose ever fails to make money. . b_{ }a'_{ } + b'_{ }d_{ } + ca_{ }; ba' + b'd + ca ¶ dc_{ } -- = = i.e. no gray ducks in this village wear lace collars. . d_{ }b'_{ } + cd'_{ } + ba_{ }; db' + cd' + ba ¶ ca_{ } -- = = i.e. no jug in this cupboard will hold water. . b'_{ }d_{ } + c_{ }d'_{ } + ab_{ }; b'd + cd' + ab ¶ ca_{ } + c_{ }, i.e. ¶ c_{ }a_{ } - - = = i.e. these apples were grown in the sun. . d'_{ }b'_{ } + c_{ }b_{ } + c'a_{ }; d'b' + cb + c'a ¶ d'a_{ } + d'_{ }, i.e. ¶ d'_{ }a_{ } - -= = i.e. puppies, that will not lie still, never care to do worsted-work. . bd'_{ } + a_{ }c'_{ } + a'd_{ }; bd' + a'd + ac' ¶ bc'_{ } - - = = i.e. no name in this list is unmelodious. . a_{ }b'_{ } + dc_{ } + a'_{ }d'_{ }; ab' + a'd' + dc ¶ b'c_{ } - = - = i.e. no m.p. should ride in a donkey-race, unless he has perfect self-command. . bd_{ } + c'a_{ } + b'c_{ }; bd + b'c + c'a ¶ da_{ } - = - = i.e. no goods in this shop, that are still on sale, may be carried away. . a'b_{ } + cd_{ } + d'a_{ }; a'b + d'a + cd ¶ bc_{ } - - = = i.e. no acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus. . dc'_{ } + a_{ }b'_{ } + bc_{ }; dc' + bc + ab' ¶ da_{ } + a_{ }, i.e. ¶ a_{ }d_{ } - -= = i.e. guinea-pigs never really appreciate beethoven. pg . a_{ }d'_{ } + b'_{ }c_{ } + ba'_{ }; ad' + ba' + b'c ¶ d'c_{ } - -= = i.e. no scentless flowers please me. . c_{ }d'_{ } + ba'_{ } + d_{ }a_{ }; cd' + da + ba' ¶ cb_{ } + c_{ }, i.e. ¶ c_{ }b_{ } - =- = i.e. showy talkers are not really well-informed. . ea_{ } + b_{ }d'_{ } + a'_{ }c_{ } + e'b'_{ }; ea + a'c + e'b' + bd' ¶ cd'_{ } -- = = - = i.e. none but red-haired boys learn greek in this school. . b_{ }d_{ } + ac'_{ } + e_{ }d'_{ } + c_{ }b'_{ }; bd + ed' + cb' + ac' ¶ ea_{ } + e_{ }, i.e. ¶ e_{ }a_{ } -- = -= = i.e. wedding-cake always disagrees with me. . ad_{ } + e'_{ }b'_{ } + c_{ }d'_{ } + e_{ }a'_{ }; ad + cd' + ea' + e'b' ¶ cb'_{ } + c_{ }, i.e. ¶ c_{ }b'_{ } -- = -= = i.e. discussions, that go on while tomkins is in the chair, endanger the peacefulness of our debating-club. . d_{ }a_{ } + e'c_{ } + b_{ }a'_{ } + d'e_{ }; da + ba' + d'e + e'c ¶ bc_{ } + b_{ }, i.e. ¶ b_{ }c_{ } -- = = - = i.e. all gluttons in my family are unhealthy. . d_{ }e_{ } + c'a_{ } + b_{ }e'_{ } + c_{ }d'_{ }; de + be' + cd' + c'a ¶ ba_{ } + b_{ }, i.e. ¶ b_{ }a_{ } -- = -= = i.e. an egg of the great auk is not to be had for a song. . d'b_{ } + a_{ }c'_{ } + c_{ }e'_{ } + a'd_{ }; d'b + a'd + ac' + ce' ¶ be'_{ } - - = =- = i.e. no books sold here have gilt edges unless they are priced at s. and upwards. . a'_{ }c'_{ } + d_{ }b_{ } + a_{ }e'_{ } + c_{ }b'_{ }; a'c' + ae' + cb' + db ¶ e'd_{ } + d_{ }, i.e. ¶ d_{ }e'_{ } - - = =- = i.e. when you cut your finger, you will find tincture of calendula useful. . d'b_{ } + a_{ }e'_{ } + ec_{ } + d_{ }a'_{ }; d'b + da' + ae' + ec ¶ bc_{ } - =- =- = i.e. _i_ have never come across a mermaid at sea. pg . c'_{ }b_{ } + a_{ }e'_{ } + d_{ }b'_{ } + a'_{ }c_{ }; c'b + db' + a'c + ae' ¶ de'_{ } + d_{ }, i.e. ¶ d_{ }e'_{ } - - = - = = i.e. all the romances in this library are well-written. . e'd_{ } + c'a_{ } + eb_{ } + d'c_{ }; e'd + eb + d'c + c'a ¶ ba_{ } - - = = - = i.e. no bird in this aviary lives on mince-pies. . d'_{ }c'_{ } + e_{ }a'_{ } + c_{ }b_{ } + e'd_{ }; d'c' + cb + e'd + ea' ¶ ba'_{ } - - = - = = i.e. no plum-pudding, that has not been boiled in a cloth, can be distinguished from soup. . ce'_{ } + b'a'_{ } + h_{ }d'_{ } + ae_{ } + bd_{ }; ce' + ae + b'a' + bd + hd' ¶ ch_{ } + h_{ }, i.e. ¶ h_{ }c_{ } - -= - = =- = i.e. all _your_ poems are uninteresting. . b'_{ }a'_{ } + db_{ } + he'_{ } + ec_{ } + a_{ }h'_{ }; b'a' + db + ah' + he' + ec ¶ dc_{ } - - = =- =- = i.e. none of my peaches have been grown in a hothouse. . c_{ }d_{ } + h_{ }e'_{ } + c'_{ }a'_{ } + h'b_{ } + e_{ }d'_{ }; cd + c'a' + ed' + he' + h'b ¶ a'b_{ } -- = -= -= = i.e. no pawnbroker is dishonest. . bd'_{ } + c'h_{ } + e_{ }b'_{ } + da_{ } + e'c_{ }; bd' + eb' + da + e'c + c'h ¶ ah_{ } -- -= = = - = i.e. no kitten with green eyes will play with a gorilla. . c_{ }a'_{ } + h'b_{ } + ae_{ } + d_{ }c'_{ } + h_{ }e'_{ }; ca' + ae + dc' + he' + h'b ¶ db_{ } + d_{ }, i.e. ¶ d_{ }b_{ } -- =- = -= = i.e. all _my_ friends in this college dine at the lower table. . ca_{ } + h_{ }d'_{ } + c'_{ }e'_{ } + b'a'_{ } + d_{ }e_{ }; ca + c'e' + b'a' + de + hd' ¶ b'h_{ } + h_{ }, -- = - = -= = i.e. ¶ h_{ }b'_{ } i.e. my writing-desk is full of live scorpions. . b'_{ }e_{ } + ah_{ } + dc_{ } + e'_{ }a'_{ } + bc'_{ } b'e + e'a' + ah + bc' + dc ¶ hd_{ } - - = - = =- = i.e. no mandarin ever reads hogg's poems. pg . e_{ }b'_{ } + a'd_{ } + c_{ }h'_{ } + e'a_{ } + d'h_{ }; eb' + e'a + a'd + d'h + ch' ¶ b'c_{ } + c_{ }, - = - = - = - = i.e. ¶ c_{ }b'_{ } i.e. shakespeare was clever. . e'_{ }c'_{ } + hb'_{ } + d_{ }a_{ } + e_{ }a'_{ } + c_{ }b_{ }; e'c' + ea' + da + cb + hb' ¶ dh_{ } + d_{ }, i.e. ¶ d_{ }h_{ } - - =- = =- = i.e. rainbows are not worth writing odes to. . c'_{ }h'_{ } + e_{ }a_{ } + bd_{ } + a'_{ }h_{ } + d'c_{ }; c'h' + a'h + ea + d'c + bd ¶ eb_{ } + e_{ }, i.e. ¶ e_{ }b_{ } - - - = = - = = i.e. these sorites-examples are difficult. . a'_{ }e'_{ } + bk_{ } + c'a_{ } + eh'_{ } + d_{ }b'_{ } + k'h_{ }; a'e' + c'a + eh' + k'h + bk + db' ¶ c'd_{ } + d_{ }, - - = =- - = -= = i.e. ¶ d_{ }c'_{ } i.e. all my dreams come true. . a'h_{ } + c'k_{ } + a_{ }d'_{ } + e_{ }h'_{ } + b_{ }k'_{ } + c_{ }e'_{ }; a'h + ad' + eh' + ce' + c'k + bk' ¶ d'b_{ } + b_{ }, - - = -= -= = - = i.e. ¶ b_{ }d'_{ } i.e. all the english pictures here are painted in oils. . k'_{ }e_{ } + c_{ }h_{ } + b_{ }a'_{ } + kd_{ } + h'a_{ } + b'_{ }e'_{ }; k'e + kd + b'e' + ba' + h'a + ch ¶ dc_{ } + c_{ }, - - = - = =- - = = i.e. ¶ c_{ }d_{ } i.e. donkeys are not easy to swallow. . ab'_{ } + h'd_{ } + e_{ }c_{ } + b_{ }d'_{ } + a'k_{ } + c'_{ }h_{ }; ab' + bd' + h'd + a'k + c'h + ec ¶ ke_{ } + e_{ }, -- =- - = = - = = i.e. ¶ e_{ }k_{ } i.e. opium-eaters never wear white kid gloves. . bc_{ } + k_{ }a'_{ } + eh_{ } + d_{ }b'_{ } + h'c'_{ } + k'_{ }e'_{ }; bc + db' + h'c' + eh + k'e' + ka' ¶ da'_{ } + d_{ }, -- = - = -= - = = i.e. ¶ d_{ }a'_{ } i.e. a good husband always comes home for his tea. . a'_{ }k'_{ } + ch_{ } + h'k_{ } + b_{ }d'_{ } + ea_{ } + d_{ }c'_{ } a'k' + h'k + ch + dc' + bd' + ea ¶ be_{ } + b_{ }, - - - = -= -= = = i.e. ¶ b_{ }e_{ } i.e. bathing-machines are never made of mother-of-pearl. pg . da'_{ } + k_{ }b'_{ } + c_{ }h_{ } + d'_{ }k'_{ } + e_{ }c'_{ } + a_{ }h'_{ }; da' + d'k' + kb' + ah' + ch + ec' -- = - = =- -= = ¶ b'e_{ } + e_{ }, i.e. ¶ e_{ }b'_{ } i.e. rainy days are always cloudy. . kb'_{ } + a'_{ }c'_{ } + d'b_{ } + k'_{ }h'_{ } + ea_{ } + d_{ }c_{ }; kb' + d'b + k'h' + dc + a'c' + ea -- - = = =- - = = ¶ h'e_{ } i.e. no heavy fish is unkind to children. . k'_{ }b'_{ } + eh'_{ } + c'd_{ } + hb_{ } + ac_{ } + kd'_{ }; k'b' + hb + eh' + kd' + c'd + ac ¶ ea_{ } - - -= = =- - = = i.e. no engine-driver lives on barley-sugar. . h_{ }b'_{ } + c_{ }d'_{ } + k'a_{ } + e_{ }h'_{ } + b_{ }a'_{ } + k_{ }c'_{ }; hb' + eh' + ba' + k'a + kc' + cd' -- = =- - = =- = ¶ ed'_{ } + e_{ }, i.e. ¶ e_{ }d'_{ } i.e. all the animals in the yard gnaw bones. . h'_{ }d'_{ } + e_{ }c'_{ } + k'a_{ } + cb_{ } + d_{ }l'_{ } + e'h_{ } + kl_{ }; h'd' + dl' + kl + k'a + e'h + ec' + cb ¶ ab_{ } - - =- -= = - = =- = i.e. no badger can guess a conundrum. . b'h_{ } + d'_{ }l'_{ } + ca_{ } + d_{ }k'_{ } + h'_{ }e'_{ } + mc'_{ } + a'b_{ } + ek_{ }; b'h + h'e' + a'b + ca + mc' + ek + dk' + d'l' ¶ ml'_{ } - - = - - = -= = =- -= = i.e. no cheque of yours, received by me, is payable to order. . c_{ }l'_{ } + h'e_{ } + kd_{ } + mc'_{ } + b'_{ }e'_{ } + n_{ }a'_{ } + l_{ }d'_{ } + m'b_{ } + ah_{ }; cl' + mc' + ld' + kd + m'b + b'e' + h'e + ah + na' -- -= =- = = - = - - = -= = ¶ kn_{ } i.e. i cannot read any of brown's letters. . e_{ }c'_{ } + l_{ }n'_{ } + d_{ }a'_{ } + m'b_{ } + ck'_{ } + e'r_{ } + h_{ }n_{ } + b'k_{ } + r'_{ }d'_{ } + m_{ }l'_{ }; ec' + ck' + e'r + b'k + m'b + r'd' + da' + ml' + ln' + hn -- =- = - - = - = = - = =- =- = ¶ a'h_{ } + h_{ }, i.e. ¶ h_{ }a'_{ } i.e. i always avoid a kangaroo. pg notes. (a) [see p. ]. one of the favourite objections, brought against the science of logic by its detractors, is that a syllogism has no real validity as an argument, since it involves the fallacy of _petitio principii_ (i.e. "begging the question", the essence of which is that the whole conclusion is involved in _one_ of the premisses). this formidable objection is refuted, with beautiful clearness and simplicity, by these three diagrams, which show us that, in each of the three figures, the conclusion is really involved in the _two_ premisses taken together, each contributing its share. thus, in fig. i., the premiss xm_{ } empties the _inner_ cell of the n.w. quarter, while the premiss ym_{ } empties its _outer_ cell. hence it needs the _two_ premisses to empty the _whole_ of the n.w. quarter, and thus to prove the conclusion xy_{ }. again, in fig. ii., the premiss xm_{ } empties the inner cell of the n.w. quarter. the premiss ym_{ } merely tells us that the inner portion of the w. half is _occupied_, so that we may place a 'i' in it, _somewhere_; but, if this were the _whole_ of our information, we should not know in _which_ cell to place it, so that it would have to 'sit on the fence': it is only when we learn, from the other premiss, that the _upper_ of these two cells is _empty_, that we feel authorised to place the 'i' in the _lower_ cell, and thus to prove the conclusion x'y_{ }. lastly, in fig. iii., the information, that m _exists_, merely authorises us to place a 'i' _somewhere_ in the inner square----but it has large choice of fences to sit upon! it needs the premiss xm_{ } to drive it out of the n. half of that square; and it needs the premiss ym_{ } to drive it out of the w. half. hence it needs the _two_ premisses to drive it into the inner portion of the s.e. quarter, and thus to prove the conclusion x'y'_{ }. pg appendix, addressed to teachers. § . _introductory._ there are several matters, too hard to discuss with _learners_, which nevertheless need to be explained to any _teachers_, into whose hands this book may fall, in order that they may thoroughly understand what my symbolic method _is_, and in what respects it differs from the many other methods already published. these matters are as follows:-- the "existential import" of propositions. the use of "is-not" (or "are-not") as a copula. the theory "two negative premisses prove nothing." euler's method of diagrams. venn's method of diagrams. my method of diagrams. the solution of a syllogism by various methods. my method of treating syllogisms and sorites. some account of parts ii, iii. § . _the "existential import" of propositions._ the writers, and editors, of the logical text-books which run in the ordinary grooves----to whom i shall hereafter refer by the (i hope inoffensive) title "the logicians"----take, on this subject, what seems to me to be a more humble position than is at all necessary. they speak of the copula of a proposition "with bated breath", almost as if it were a living, conscious entity, capable of declaring for itself what it chose to mean, and that we, poor human creatures, had nothing to do but to ascertain _what_ was its sovereign will and pleasure, and submit to it. pg in opposition to this view, i maintain that any writer of a book is fully authorised in attaching any meaning he likes to any word or phrase he intends to use. if i find an author saying, at the beginning of his book, "let it be understood that by the word '_black_' i shall always mean '_white_', and that by the word '_white_' i shall always mean '_black_'," i meekly accept his ruling, however injudicious i may think it. and so, with regard to the question whether a proposition is or is not to be understood as asserting the existence of its subject, i maintain that every writer may adopt his own rule, provided of course that it is consistent with itself and with the accepted facts of logic. let us consider certain views that may _logically_ be held, and thus settle which of them may _conveniently_ be held; after which i shall hold myself free to declare which of them _i_ intend to hold. the _kinds_ of propositions, to be considered, are those that begin with "some", with "no", and with "all". these are usually called propositions "in _i_", "in _e_", and "in _a_". first, then, a proposition in _i_ may be understood as asserting, or else as _not_ asserting, the existence of its subject. (by "existence" i mean of course whatever kind of existence suits its nature. the two propositions, "_dreams_ exist" and "_drums_ exist", denote two totally different kinds of "existence". a _dream_ is an aggregate of ideas, and exists only in the _mind of a dreamer_: whereas a _drum_ is an aggregate of wood and parchment, and exists in _the hands of a drummer_.) first, let us suppose that _i_ "asserts" (i.e. "asserts the existence of its subject"). here, of course, we must regard a proposition in _a_ as making the _same_ assertion, since it necessarily _contains_ a proposition in _i_. we now have _i_ and _a_ "asserting". does this leave us free to make what supposition we choose as to _e_? my answer is "no. we are tied down to the supposition that _e_ does _not_ assert." this can be proved as follows:-- if possible, let _e_ "assert". then (taking x, y, and z to represent attributes) we see that, if the proposition "no xy are z" be true, some things exist with the attributes x and y: i.e. "some x are y." pg also we know that, if the proposition "some xy are z" be true, the same result follows. but these two propositions are contradictories, so that one or other of them _must_ be true. hence this result is _always_ true: i.e. the proposition "some x are y" is _always_ true! _quod est absurdum._ (see note (a), p. ). we see, then, that the supposition "_i_ asserts" necessarily leads to "_a_ asserts, but _e_ does not". and this is the _first_ of the various views that may conceivably be held. next, let us suppose that _i_ does _not_ "assert." and, along with this, let us take the supposition that _e_ _does_ "assert." hence the proposition "no x are y" means "some x exist, and none of them are y": i.e. "_all_ of them are _not_-y," which is a proposition in _a_. we also know, of course, that the proposition "all x are not-y" proves "no x are y." now two propositions, each of which proves the other, are _equivalent_. hence every proposition in _a_ is equivalent to one in _e_, and therefore "_asserts_". hence our _second_ conceivable view is "_e_ and _a_ assert, but _i_ does not." this view does not seen to involve any necessary contradiction with itself or with the accepted facts of logic. but, when we come to _test_ it, as applied to the actual _facts_ of life, we shall find i think, that it fits in with them so badly that its adoption would be, to say the least of it, singularly inconvenient for ordinary folk. let me record a little dialogue i have just held with my friend jones, who is trying to form a new club, to be regulated on strictly _logical_ principles. _author._ "well, jones! have you got your new club started yet?" _jones_ (_rubbing his hands_). "you'll be glad to hear that some of the members (mind, i only say '_some_') are millionaires! rolling in gold, my boy!" _author._ "that sounds well. and how many members have entered?" _jones_ (_staring_). "none at all. we haven't got it started yet. what makes you think we have?" _author._ "why, i thought you said that some of the members----" pg _jones_ (_contemptuously_). "you don't seem to be aware that we're working on strictly _logical_ principles. a _particular_ proposition does _not_ assert the existence of its subject. i merely meant to say that we've made a rule not to admit _any_ members till we have at least _three_ candidates whose incomes are over ten thousand a year!" _author._ "oh, _that's_ what you meant, is it? let's hear some more of your rules." _jones._ "another is, that no one, who has been convicted seven times of forgery, is admissible." _author._ "and here, again, i suppose you don't mean to assert there _are_ any such convicts in existence?" _jones._ "why, that's exactly what i _do_ mean to assert! don't you know that a universal negative _asserts_ the existence of its subject? _of course_ we didn't make that rule till we had satisfied ourselves that there are several such convicts now living." the reader can now decide for himself how far this _second_ conceivable view would fit in with the facts of life. he will, i think, agree with me that jones' view, of the 'existential import' of propositions, would lead to some inconvenience. thirdly, let us suppose that neither _i_ nor _e_ "asserts". now the supposition that the two propositions, "some x are y" and "no x are not-y", do _not_ "assert", necessarily involves the supposition that "all x are y" does _not_ "assert", since it would be absurd to suppose that they assert, when combined, more than they do when taken separately. hence the _third_ (and last) of the conceivable views is that neither _i_, nor _e_, nor _a_, "asserts". the advocates of this third view would interpret the proposition "some x are y" to mean "if there _were_ any x in existence, some of them _would_ be y"; and so with _e_ and _a_. it admits of proof that this view, as regards _a_, conflicts with the accepted facts of logic. let us take the syllogism _darapti_, which is universally accepted as valid. its form is "all m are x; all m are y. .'. some y are x". pg this they would interpret as follows:-- "if there were any m in existence, all of them would be x; if there were any m in existence, all of them would be y. .'. if there were any y in existence, some of them would be x". that this conclusion does _not_ follow has been so briefly and clearly explained by mr. keynes (in his "formal logic", dated , pp. , ), that i prefer to quote his words:-- "_let no proposition imply the existence either of its subject or of its predicate._ "take, as an example, a syllogism in _darapti_:-- '_all m is p_, _all m is s_, _.'. some s is p_.' "taking s, m, p, as the minor, middle, and major terms respectively, the conclusion will imply that, if there is an s, there is some p. will the premisses also imply this? if so, then the syllogism is valid; but not otherwise. "the conclusion implies that if s exists p exists; but, consistently with the premisses, s may be existent while m and p are both non-existent. an implication is, therefore, contained in the conclusion, which is not justified by the premisses." this seems to _me_ entirely clear and convincing. still, "to make sicker", i may as well throw the above (_soi-disant_) syllogism into a concrete form, which will be within the grasp of even a _non_-logical reader. let us suppose that a boys' school has been set up, with the following system of rules:-- "all boys in the first (the highest) class are to do french, greek, and latin. all in the second class are to do greek only. all in the third class are to do latin only." suppose also that there _are_ boys in the third class, and in the second; but that no boy has yet risen into the first. it is evident that there are no boys in the school doing french: still we know, by the rules, what would happen if there _were_ any. pg we are authorised, then, by the _data_, to assert the following two propositions:-- "if there were any boys doing french, all of them would be doing greek; if there were any boys doing french, all of them would be doing latin." and the conclusion, according to "the logicians" would be "if there were any boys doing latin, some of them would be doing greek." here, then, we have two _true_ premisses and a _false_ conclusion (since we know that there _are_ boys doing latin, and that _none_ of them are doing greek). hence the argument is _invalid_. similarly it may be shown that this "non-existential" interpretation destroys the validity of _disamis_, _datisi_, _felapton_, and _fresison_. some of "the logicians" will, no doubt, be ready to reply "but we are not _aldrichians_! why should _we_ be responsible for the validity of the syllogisms of so antiquated an author as aldrich?" very good. then, for the _special_ benefit of these "friends" of mine (with what ominous emphasis that name is sometimes used! "i must have a private interview with _you_, my young _friend_," says the bland dr. birch, "in my library, at a.m. tomorrow. and you will please to be _punctual_!"), for their _special_ benefit, i say, i will produce _another_ charge against this "non-existential" interpretation. it actually invalidates the ordinary process of "conversion", as applied to proposition in '_i_'. _every_ logician, aldrichian or otherwise, accepts it as an established fact that "some x are y" may be legitimately converted into "some y are x." but is it equally clear that the proposition "if there _were_ any x, some of them _would_ be y" may be legitimately converted into "if there _were_ any y, some of them would be x"? i trow not. the example i have already used----of a boys' school with a non-existent first class----will serve admirably to illustrate this new flaw in the theory of "the logicians." pg let us suppose that there is yet _another_ rule in this school, viz. "in each class, at the end of the term, the head boy and the second boy shall receive prizes." this rule entirely authorises us to assert (in the sense in which "the logicians" would use the words) "some boys in the first class will receive prizes", for this simply means (according to them) "if there _were_ any boys in the first class, some of them _would_ receive prizes." now the converse of this proposition is, of course, "some boys, who will receive prizes, are in the first class", which means (according to "the logicians") "if there _were_ any boys about to receive prizes, some of them _would_ be in the first class" (which class we know to be _empty_). of this pair of converse propositions, the first is undoubtedly _true_: the second, _as_ undoubtedly, _false_. it is always sad to see a batsman knock down his own wicket: one pities him, as a man and a brother, but, as a _cricketer_, one can but pronounce him "out!" we see, then, that, among all the conceivable views we have here considered, there are only _two_ which can _logically_ be held, viz. _i_ and _a_ "assert", but _e_ does not. _e_ and _a_ "assert", but _i_ does not. the _second_ of these i have shown to involve great practical inconvenience. the _first_ is the one adopted in this book. (see p. .) some further remarks on this subject will be found in note (b), at p. . § . _the use of "is-not" (or "are-not") as a copula._ is it better to say "john _is-not_ in-the-house" or "john _is_ not-in-the-house"? "some of my acquaintances _are-not_ men-i-should-like-to-be-seen-with" or "some of my acquaintances _are_ men-i-should-_not_-like-to-be-seen-with"? that is the sort of question we have now to discuss. pg this is no question of logical right and wrong: it is merely a matter of _taste_, since the two forms mean exactly the same thing. and here, again, "the logicians" seem to me to take much too humble a position. when they are putting the final touches to the grouping of their proposition, just before the curtain goes up, and when the copula----always a rather fussy 'heavy father', asks them "am _i_ to have the 'not', or will you tack it on to the predicate?" they are much too ready to answer, like the subtle cab-driver, "leave it to _you_, sir!" the result seems to be, that the grasping copula constantly gets a "not" that had better have been merged in the predicate, and that propositions are differentiated which had better have been recognised as precisely similar. surely it is simpler to treat "some men are jews" and "some men are gentiles" as being both of them, _affirmative_ propositions, instead of translating the latter into "some men are-not jews", and regarding it as a _negative_ propositions? the fact is, "the logicians" have somehow acquired a perfectly _morbid_ dread of negative attributes, which makes them shut their eyes, like frightened children, when they come across such terrible propositions as "all not-x are y"; and thus they exclude from their system many very useful forms of syllogisms. under the influence of this unreasoning terror, they plead that, in dichotomy by contradiction, the _negative_ part is too large to deal with, so that it is better to regard each thing as either included in, or excluded from, the _positive_ part. i see no force in this plea: and the facts often go the other way. as a personal question, dear reader, if _you_ were to group your acquaintances into the two classes, men that you _would_ like to be seen with, and men that you would _not_ like to be seen with, do you think the latter group would be so _very_ much the larger of the two? for the purposes of symbolic logic, it is so _much_ the most convenient plan to regard the two sub-divisions, produced by dichotomy, on the _same_ footing, and to say, of any thing, either that it "is" in the one, or that it "is" in the other, that i do not think any reader of this book is likely to demur to my adopting that course. pg § . _the theory that "two negative premisses prove nothing"._ this i consider to be _another_ craze of "the logicians", fully as morbid as their dread of a negative attribute. it is, perhaps, best refuted by the method of _instantia contraria_. take the following pairs of premisses:-- "none of my boys are conceited; none of my girls are greedy". "none of my boys are clever; none but a clever boy could solve this problem". "none of my boys are learned; some of my boys are not choristers". (this last proposition is, in _my_ system, an _affirmative_ one, since i should read it "are not-choristers"; but, in dealing with "the logicians," i may fairly treat it as a _negative_ one, since _they_ would read it "are-not choristers".) if you, dear reader, declare, after full consideration of these pairs of premisses, that you cannot deduce a conclusion from _any_ of them----why, all i can say is that, like the duke in patience, you "will have to be contented with our heart-felt sympathy"! [see note (c), p. .] § . _euler's method of diagrams._ diagrams seem to have been used, at first, to represent _propositions_ only. in euler's well-known circles, each was supposed to contain a class, and the diagram consisted of two circles, which exhibited the relations, as to inclusion and exclusion, existing between the two classes. _____ _/ ___ \_ / / y \ \ | \___/ | \_ x _/ \_____/ thus, the diagram, here given, exhibits the two classes, whose respective attributes are x and y, as so related to each other that the following propositions are all simultaneously true:--"all x are y", "no x are not-y", "some x are y", "some y are not-x", "some not-y are not-x", and, of course, the converses of the last four. pg _____ _/ ___ \_ / / y \ \ | \___/ | \_ x _/ \_____/ similarly, with this diagram, the following propositions are true:--"all y are x", "no y are not-x", "some y are x", "some x are not-y", "some not-x are not-y", and, of course, the converses of the last four. _____ _____ _/ \_ _/ \_ / \ / \ | x | | y | \_ _/ \_ _/ \_____/ \_____/ similarly, with this diagram, the following are true:--"all x are not-y", "all y are not-x", "no x are y", "some x are not-y", "some y are not-x", "some not-x are not-y", and the converses of the last four. _____ _____ _/ \_/ \_ / / \ \ | x | | y | \_ \_/ _/ \_____/ \_____/ similarly, with this diagram, the following are true:--"some x are y", "some x are not-y", "some not-x are y", "some not-x are not-y", and of course, their four converses. note that _all_ euler's diagrams assert "some not-x are not-y." apparently it never occured to him that it might _sometimes_ fail to be true! now, to represent "all x are y", the _first_ of these diagrams would suffice. similarly, to represent "no x are y", the _third_ would suffice. but to represent any _particular_ proposition, at least _three_ diagrams would be needed (in order to include all the possible cases), and, for "some not-x are not-y", all the _four_. § . _venn's method of diagrams._ let us represent "not-x" by "x'". mr. venn's method of diagrams is a great advance on the above method. he uses the last of the above diagrams to represent _any_ desired relation between x and y, by simply shading a compartment known to be _empty_, and placing a + in one known to be _occupied_. thus, he would represent the three propositions "some x are y", "no x are y", and "all x are y", as follows:-- _____ _____ _/ \_/ \_ / / \ \ | | + | | \_ \_/ _/ \_____/ \_____/ _____ _____ _/ \_/ \_ / /#\ \ | |###| | \_ \#/ _/ \_____/ \_____/ _____ _____ _/#####\_/ \_ /#######/ \ \ |#######| + | | \#######\_/ _/ \#####/ \_____/ pg it will be seen that, of the _four_ classes, whose peculiar sets of attributes are xy, xy', x'y, and x'y', only _three_ are here provided with closed compartments, while the _fourth_ is allowed the rest of the infinite plane to range about in! this arrangement would involve us in very serious trouble, if we ever attempted to represent "no x' are y'." mr. venn _once_ (at p. ) encounters this awful task; but evades it, in a quite masterly fashion, by the simple foot-note "we have not troubled to shade the outside of this diagram"! to represent _two_ propositions (containing a common term) _together_, a _three_-letter diagram is needed. this is the one used by mr. venn. _____ _/ \_ _/___ x ___\_ _/| \_/ |\_ / \_ / \ _/ \ | \|___|/ | \_ m \_/ y _/ \_____/ \_____/ here, again, we have only _seven_ closed compartments, to accommodate the _eight_ classes whose peculiar sets of attributes are xym, xym', &c. "with four terms in request," mr. venn says, "the most simple and symmetrical diagram seems to me that produced by making four ellipses intersect one another in the desired manner". this, however, provides only _fifteen_ closed compartments. b ____ ____ c / \ / \ a ___/___ \/ ___\___ d / \ \ /\ / / \ / \ \/ \/ / \ \ \ /\ /\ / / \ \/ \/ \/ / \ /\ /\ /\ / \ \ \/ \/ / / \ \/\ /\/ / \ /\_\/_/\ / \__\______/__/ for _five_ letters, "the simplest diagram i can suggest," mr. venn says, "is one like this (the small ellipse in the centre is to be regarded as a portion of the _outside_ of c; i.e. its four component portions are inside b and d but are no part of c). it must be admitted that such a diagram is not quite so simple to draw as one might wish it to be; but then consider what the alternative is of one undertakes to deal with five terms and all their combinations--nothing short of the disagreeable task of writing out, or in some way putting before us, all the combinations involved." b c d ______ ____ ______ ______/_ \/ \/ _\______ a / / \ /\ /\ / \ \ e / / \ / \ / \ / \ \ / \ \/ \/ \/ / \ / \ /\ /\ /\ / \ / \ / \ / \ / \ / \ | \/ \/ __ \/ \/ | | /\ /\/ \/\ /\ | | / \ / /\ /\ \ / \ | | | \/ | \/ | \/ | | | | /\ | /\ | /\ | | | \ / \ \/ \/ / \ / | \ \/ \/\__/\/ \/ / \ /\ /\ /\ /\ / \ / \ / \ / \ / \ / \ / \/ \/ \/ \ / \ \ /\ /\ /\ / / \ \ / \ / \ / \ / / \ \/ \/ \/ \/ / \ /\____/\____/\____/\ / \ / \ / \| |/ \____________________/ pg this diagram gives us closed compartments. for _six_ letters, mr. venn suggests that we might use _two_ diagrams, like the above, one for the f-part, and the other for the not-f-part, of all the other combinations. "this", he says, "would give the desired subdivisions." this, however, would only give closed compartments, and _one_ infinite area, which the two classes, a'b'c'd'e'f and a'b'c'd'e'f', would have to share between them. beyond _six_ letters mr. venn does not go. § . _my method of diagrams._ my method of diagrams _resembles_ mr. venn's, in having separate compartments assigned to the various classes, and in marking these compartments as _occupied_ or as _empty_; but it _differs_ from his method, in assigning a _closed_ area to the _universe of discourse_, so that the class which, under mr. venn's liberal sway, has been ranging at will through infinite space, is suddenly dismayed to find itself "cabin'd, cribb'd, confined", in a limited cell like any other class! also i use _rectilinear_, instead of _curvilinear_, figures; and i mark an _occupied_ cell with a 'i' (meaning that there is at least _one_ thing in it), and an _empty_ cell with a 'o' (meaning that there is _no_ thing in it). for _two_ letters, i use this diagram, in which the north half is assigned to 'x', the south to 'not-x' (or 'x''), the west to y, and the east to y'. thus the n.w. cell contains the xy-class, the n.e. cell the xy'-class, and so on. ·-------· | | | |---|---| | | | ·-------· for _three_ letters, i subdivide these four cells, by drawing an _inner_ square, which i assign to m, the _outer_ border being assigned to m'. i thus get _eight_ cells that are needed to accommodate the eight classes, whose peculiar sets of attributes are xym, xym', &c. ·---------------· | | | | ·---|---· | | | | | | |---|---|---|---| | | | | | | ·---|---· | | | | ·---------------· this last diagram is the most complex that i use in the _elementary_ part of my 'symbolic logic.' but i may as well take this opportunity of describing the more complex ones which will appear in part ii. pg for _four_ letters (which i call a, b, c, d) i use this diagram; assigning the north half to a (and of course the _rest_ of the diagram to a'), the west half to b, the horizontal oblong to c, and the upright oblong to d. we have now got cells. ·---------------------· | | | | ·---|---· | | | | | | | ·---|---|---|---· | | | | | | | | |--|---|---|---|---|--| | | | | | | | | ·---|---|---|---· | | | | | | | ·---|---· | | | | ·---------------------· for _five_ letters (adding e) i subdivide the cells of the previous diagram by _oblique_ partitions, assigning all the _upper_ portions to e, and all the _lower_ portions to e'. here, i admit, we lose the advantage of having the e-class all _together_, "in a ring-fence", like the other classes. still, it is very easy to find; and the operation, of erasing it, is nearly as easy as that of erasing any other class. we have now got cells. ·---------------------· | / | / | | / ·---|---· / | | / | / | / | / | | ·---|---|---|---· | | | / | / | / | / | | |--|---|---|---|---|--| | | / | / | / | / | | | ·---|---|---|---· | | / | / | / | / | | / ·---|---· / | | / | / | ·---------------------· for _six_ letters (adding h, as i avoid _tailed_ letters) i substitute upright crosses for the oblique partitions, assigning the portions, into which each of the cells is thus divided, to the four classes eh, eh', e'h, e'h'. we have now got cells. #=============================# h | h | h h | #=====h=====# | h h | h | h | h | h h-----|--h--|--h--|--h--|-----h h | h | h | h | h h #=====h=====h=====h=====# h h h | h | h | h | h h h h--|--h--|--h--|--h--|--h h h h | h | h | h | h h h==h=====h=====h=====h=====h--h h h | h | h | h | h h h h--|--h--|--h--|--h--|--h h h h | h | h | h | h h h #=====h=====h=====h=====# h h | h | h | h | h h-----|--h--|--h--|--h--|-----h h | h | h | h | h h | #=====h=====# | h h | h | h #=============================# pg for _seven_ letters (adding k) i add, to each upright cross, a little inner square. all these little squares are assigned to the k-class, and all outside them to the k'-class; so that little cells (into which each of the cells is divided) are respectively assigned to the classes ehk, ehk', &c. we have now got cells. #=====================================================# h | h | h h | #===========h===========# | h h | h | h | h | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | | | h | | | h | | | h | | | h h-----|--|--|--h--|--|--|--h--|--|--|--h--|--|--|-----h h | | | h | | | h | | | h | | | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | h | h | h | h h #===========h===========h===========h===========# h h h | h | h | h | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | | | h | | | h | | | h | | | h h h h--|--|--|--h--|--|--|--h--|--|--|--h--|--|--|--h h h h | | | h | | | h | | | h | | | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | h | h | h | h h h==h===========h===========h===========h===========h==h h h | h | h | h | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | | | h | | | h | | | h | | | h h h h--|--|--|--h--|--|--|--h--|--|--|--h--|--|--|--h h h h | | | h | | | h | | | h | | | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | h | h | h | h h h #===========h===========h===========h===========# h h | h | h | h | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | | | h | | | h | | | h | | | h h-----|--|--|--h--|--|--|--h--|--|--|--h--|--|--|-----h h | | | h | | | h | | | h | | | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | h | h | h | h h | #===========h===========# | h h | h | h ·=====================================================# for _eight_ letters (adding l) i place, in each of the cells, a _lattice_, which is a reduced copy of the whole diagram; and, just as the large cells of the whole diagram are assigned to the classes abcd, abcd', &c., so the little cells of each lattice are assigned to the classes ehkl, ehkl', &c. thus, the lattice in the n.w. corner serves to accommodate the classes abc'd'ehkl, abc'd'eh'kl', &c. this octoliteral diagram (see next page) contains cells. for _nine_ letters, i place octoliteral diagrams side by side, assigning one of them to m, and the other to m'. we have now got cells. pg #=====================================================================# h | h | h h | #===============h===============# | h h | h | h | h | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | | | h | | | h | | | h | | | h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h | | | | | h | | | | | h | | | | | h | | | | | h h----|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|----h h | | | | | h | | | | | h | | | | | h | | | | | h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h | | | h | | | h | | | h | | | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | h | h | h | h h #===============h===============h===============h===============# h h h | h | h | h | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | | | h | | | h | | | h | | | h h h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h h h | | | | | h | | | | | h | | | | | h | | | | | h h h h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h h h h | | | | | h | | | | | h | | | | | h | | | | | h h h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h h h | | | h | | | h | | | h | | | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | h | h | h | h h h==h===============h===============h===============h===============h==h h h | h | h | h | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | | | h | | | h | | | h | | | h h h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h h h | | | | | h | | | | | h | | | | | h | | | | | h h h h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h h h h | | | | | h | | | | | h | | | | | h | | | | | h h h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h h h | | | h | | | h | | | h | | | h h h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h h h | h | h | h | h h h #===============h===============h===============h===============# h h | h | h | h | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | | | h | | | h | | | h | | | h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h | | | | | h | | | | | h | | | | | h | | | | | h h----|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|-h-|--|--|--|--|----h h | | | | | h | | | | | h | | | | | h | | | | | h h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h ·--|--|--|--· h h | | | h | | | h | | | h | | | h h ·--|--· h ·--|--· h ·--|--· h ·--|--· h h | h | h | h | h h | #===============h===============# | h h | h | h #=====================================================================# finally, for _ten_ letters, i arrange octoliteral diagrams, like the above, in a square, assigning them to the classes mn, mn', m'n, m'n'. we have now got cells. § . _solution of a syllogism by various methods._ the best way, i think, to exhibit the differences between these various methods of solving syllogisms, will be to take a concrete example, and solve it by each method in turn. let us take, as our example, no. (see p. ). "no philosophers are conceited; some conceited persons are not gamblers. .'. some persons, who are not gamblers, are not philosophers." pg ( ) _solution by ordinary method._ these premisses, as they stand, will give no conclusion, as they are both negative. if by 'permutation' or 'obversion', we write the minor premiss thus, 'some conceited persons are not-gamblers,' we can get a conclusion in _fresison_, viz. "no philosophers are conceited; some conceited persons are not-gamblers. .'. some not-gamblers are not philosophers" this can be proved by reduction to _ferio_, thus:-- "no conceited persons are philosophers; some not-gamblers are conceited. .'. some not-gamblers are not philosophers". the validity of _ferio_ follows directly from the axiom '_de omni et nullo_'. ( ) _symbolic representation._ before proceeding to discuss other methods of solution, it is necessary to translate our syllogism into an _abstract_ form. let us take "persons" as our 'universe of discourse'; and let x = "philosophers", m = "conceited", and y = "gamblers." then the syllogism may be written thus:-- "no x are m; some m are y'. .'. some y' are x'." ( ) _solution by euler's method of diagrams._ the major premiss requires only _one_ diagram, viz. _____ _____ _/ \_ _/ \_ / \ / \ | x | | m | \_ _/ \_ _/ \_____/ \_____/ pg the minor requires _three_, viz. _____ _____ _/ \_ _/ \_ / \ / \ | y | | m | \_ _/ \_ _/ \_____/ \_____/ _____ _____ _/ \_/ \_ / / \ \ | y | | m | \_ \_/ _/ \_____/ \_____/ _____ _/ ___ \_ / / y \ \ | \___/ | \_ m _/ \_____/ the combination of major and minor, in every possible way requires _nine_, viz. figs. and give _____ _____ _____ _/ \_ _/ \_ _/ \_ / \ / \ / \ | x | | y | | m | \_ _/ \_ _/ \_ _/ \_____/ \_____/ \_____/ _____ _____ _____ _/ \_/ \_ _/ \_ / / \ \ / \ | x | | y | | m | \_ \_/ _/ \_ _/ \_____/ \_____/ \_____/ _____ _____ _/ \_ _/ \_ / \ / \ | xy | | m | \_ _/ \_ _/ \_____/ \_____/ _____ _____ _/ ___ \_ _/ \_ / / x \ \ / \ | \___/ | | m | \_ y _/ \_ _/ \_____/ \_____/ _____ _____ _/ ___ \_ _/ \_ / / y \ \ / \ | \___/ | | m | \_ x _/ \_ _/ \_____/ \_____/ figs. and give _____ _____ _____ _/ \_ _/ \_/ \_ / \ / / \ \ | x | | y | | m | \_ _/ \_ \_/ _/ \_____/ \_____/ \_____/ _____ _____ _____ _/ \_/ \_/ \_ / / \ / \ \ | x | | y | | m | \_ \_/ \_/ _/ \_____/ \_____/ \_____/ _____ _____ _/___ \_/ \_ / / x \ / \ \ | \___/| | m | \_ y \_/ _/ \_____/ \_____/ figs. and give _____ _____ _/ \_ _/ ___ \_ / \ / / y \ \ | x | | \___/ | \_ _/ \_ m _/ \_____/ \_____/ from this group (figs. to ) we have, by disregarding m, to find the relation of x and y. on examination we find that figs. , , express the relation of entire mutual exclusion; that figs. , express partial inclusion and partial exclusion; that fig. expresses coincidence; that figs. , express entire inclusion of x in y; and that fig. expresses entire inclusion of y in x. pg we thus get five biliteral diagrams for x and y, viz. _____ _____ _/ \_ _/ \_ / \ / \ | x | | y | \_ _/ \_ _/ \_____/ \_____/ _____ _____ _/ \_/ \_ / / \ \ | x | | y | \_ \_/ _/ \_____/ \_____/ _____ _/ \_ / \ | xy | \_ _/ \_____/ _____ _/ ___ \_ / / x \ \ | \___/ | \_ y _/ \_____/ _____ _/ ___ \_ / / y \ \ | \___/ | \_ x _/ \_____/ where the only proposition, represented by them all, is "some not-y are not-x," i.e. "some persons, who are not gamblers, are not philosophers"----a result which euler would hardly have regarded as a _valuable_ one, since he seems to have assumed that a proposition of this form is _always_ true! ( ) _solution by venn's method of diagrams._ the following solution has been kindly supplied to me mr. venn himself. "the minor premiss declares that some of the constituents in my' must be saved: mark these constituents with a cross. _____ _/ + \_ _/___ ___\_ _/|##+#\_/ |\_ / \###/#\ _/ \ | + \|_#_|/ | \_ m \_/ y _/ \_____/ \_____/ the major declares that all xm must be destroyed; erase it. then, as some my' is to be saved, it must clearly be my'x'. that is, there must exist my'x'; or eliminating m, y'x'. in common phraseology, 'some y' are x',' or, 'some not-gamblers are not-philosophers.'" pg ( ) _solution by my method of diagrams._ the first premiss asserts that no xm exist: so we mark the xm-compartment as empty, by placing a 'o' in each of its cells. the second asserts that some my' exist: so we mark the my'-compartment as occupied, by placing a 'i' in its only available cell. ·---------------· | | | | ·---|---· | | |(o)|(o)| | |---|---|---|---| | | |(i)| | | ·---|---· | | | | ·---------------· the only information, that this gives us as to x and y, is that the x'y'-compartment is _occupied_, i.e. that some x'y' exist. hence "some x' are y'": i.e. "some persons, who are not philosophers, are not gamblers". ( ) _solution by my method of subscripts._ xm_{ } + my'_{ } ¶ x'y'_{ } i.e. "some persons, who are not philosophers, are not gamblers." § . _my method of treating syllogisms and sorites._ of all the strange things, that are to be met with in the ordinary text-books of formal logic, perhaps the strangest is the violent contrast one finds to exist between their ways of dealing with these two subjects. while they have elaborately discussed no less than _nineteen_ different forms of _syllogisms_----each with its own special and exasperating rules, while the whole constitute an almost useless machine, for practical purposes, many of the conclusions being incomplete, and many quite legitimate forms being ignored----they have limited _sorites_ to _two_ forms only, of childish simplicity; and these they have dignified with special _names_, apparently under the impression that no other possible forms existed! as to _syllogisms_, i find that their nineteen forms, with about a score of others which they have ignored, can all be arranged under _three_ forms, each with a very simple rule of its own; and the only question the reader has to settle, in working any one of the examples given at p. of this book, is "does it belong to fig. i., ii., or iii.?" pg as to _sorites_, the only two forms, recognised by the text-books, are the _aristotelian_, whose premisses are a series of propositions in a, so arranged that the predicate of each is the subject of the next, and the _goclenian_, whose premisses are the very same series, written backwards. goclenius, it seems, was the first who noticed the startling fact that it does not affect the force of a syllogism to invert the order of its premisses, and who applied this discovery to a sorites. if we assume (as surely we may?) that he is the _same_ man as that transcendent genius who first noticed that times is the same thing as times , we may apply to him what somebody (edmund yates, i think it was) has said of tupper, viz., "here is a man who, beyond all others of his generation, has been favoured with glimpses of the obvious!" these puerile----not to say infantine----forms of a sorites i have, in this book, ignored from the very first, and have not only admitted freely propositions in _e_, but have purposely stated the premisses in random order, leaving to the reader the useful task of arranging them, for himself, in an order which can be worked as a series of regular syllogisms. in doing this, he can begin with _any one_ of them he likes. i have tabulated, for curiosity, the various orders in which the premisses of the aristotelian sorites . all a are b; . all b are c; . all c are d; . all d are e; . all e are h. .'. all a are h. may be syllogistically arranged, and i find there are no less than _sixteen_ such orders, viz., , , , , , , , , , , , , , , , . of these the _first_ and the _last_ have been dignified with names; but the other _fourteen_----first enumerated by an obscure writer on logic, towards the end of the nineteenth century----remain without a name! pg § . _some account of parts ii, iii._ in part ii. will be found some of the matters mentioned in this appendix, viz., the "existential import" of propositions, the use of a _negative_ copula, and the theory that "two negative premisses prove nothing." i shall also extend the range of syllogisms, by introducing propositions containing alternatives (such as "not-all x are y"), propositions containing or more terms (such as "all ab are c", which, taken along with "some bc' are d", would prove "some d are a'"), &c. i shall also discuss sorites containing entities, and the _very_ puzzling subjects of hypotheticals and dilemmas. i hope, in the course of part ii., to go over all the ground usually traversed in the text-books used in our schools and universities, and to enable my readers to solve problems of the same kind as, and far harder than, those that are at present set in their examinations. in part iii. i hope to deal with many curious and out-of-the-way subjects, some of which are not even alluded to in any of the treatises i have met with. in this part will be found such matters as the analysis of propositions into their elements (let the reader, who has never gone into this branch of the subject, try to make out for himself what _additional_ proposition would be needed to convert "some a are b" into "some a are bc"), the treatment of numerical and geometrical problems, the construction of problems, and the solution of syllogisms and sorites containing propositions more complex than any that i have used in part ii. i will conclude with eight problems, as a taste of what is coming in part ii. i shall be very glad to receive, from any reader, who thinks he has solved any one of them (more especially if he has done so _without_ using any method of symbols), what he conceives to be its complete conclusion. it may be well to explain what i mean by the _complete_ conclusion of a syllogism or a sorites. i distinguish their terms as being of two kinds----those which _can_ be eliminated (e.g. the middle term of a syllogism), which i call the "eliminands," and those which _cannot_, which i call the "retinends"; and i do not call the conclusion _complete_, unless it states _all_ the relations among the retinends only, which can be deduced from the premisses. pg . all the boys, in a certain school, sit together in one large room every evening. they are of no less than _five_ nationalities----english, scotch, welsh, irish, and german. one of the monitors (who is a great reader of wilkie collins' novels) is very observant, and takes ms. notes of almost everything that happens, with the view of being a good sensational witness, in case any conspiracy to commit a murder should be on foot. the following are some of his notes:-- ( ) whenever some of the english boys are singing "rule britannia", and some not, some of the monitors are wide-awake; ( ) whenever some of the scotch are dancing reels, and some of the irish fighting, some of the welsh are eating toasted cheese; ( ) whenever all the germans are playing chess, some of the eleven are _not_ oiling their bats; ( ) whenever some of the monitors are asleep, and some not, some of the irish are fighting; ( ) whenever some of the germans are playing chess, and none of the scotch are dancing reels, some of the welsh are _not_ eating toasted cheese; ( ) whenever some of the scotch are _not_ dancing reels, and some of the irish _not_ fighting, some of the germans are playing chess; ( ) whenever some of the monitors are awake, and some of the welsh are eating toasted cheese, none of the scotch are dancing reels; ( ) whenever some of the germans are _not_ playing chess, and some of the welsh are _not_ eating toasted cheese, none of the irish are fighting; pg ( ) whenever all the english are singing "rule britannia," and some of the scotch are _not_ dancing reels, none of the germans are playing chess; ( ) whenever some of the english are singing "rule britannia", and some of the monitors are asleep, some of the irish are _not_ fighting; ( ) whenever some of the monitors are awake, and some of the eleven are _not_ oiling their bats, some of the scotch are dancing reels; ( ) whenever some of the english are singing "rule britannia", and some of the scotch are _not_ dancing reels, * * * * here the ms. breaks off suddenly. the problem is to complete the sentence, if possible. [n.b. in solving this problem, it is necessary to remember that the proposition "all x are y" is a _double_ proposition, and is equivalent to "some x are y, and none are y'." see p. .] . ( ) a logician, who eats pork-chops for supper, will probably lose money; ( ) a gambler, whose appetite is not ravenous, will probably lose money; ( ) a man who is depressed, having lost money and being likely to lose more, always rises at a.m.; ( ) a man, who neither gambles nor eats pork-chops for supper, is sure to have a ravenous appetite; ( ) a lively man, who goes to bed before a.m., had better take to cab-driving; ( ) a man with a ravenous appetite, who has not lost money and does not rise at a.m., always eats pork-chops for supper; ( ) a logician, who is in danger of losing money, had better take to cab-driving; ( ) an earnest gambler, who is depressed though he has not lost money, is in no danger of losing any; ( ) a man, who does not gamble, and whose appetite is not ravenous, is always lively; pg ( ) a lively logician, who is really in earnest, is in no danger of losing money; ( ) a man with a ravenous appetite has no need to take to cab-driving, if he is really in earnest; ( ) a gambler, who is depressed though in no danger of losing money, sits up till a.m. ( ) a man, who has lost money and does not eat pork-chops for supper, had better take to cab-driving, unless he gets up at a.m. ( ) a gambler, who goes to bed before a.m., need not take to cab-driving, unless he has a ravenous appetite; ( ) a man with a ravenous appetite, who is depressed though in no danger of losing, is a gambler. univ. "men"; a = earnest; b = eating pork-chops for supper; c = gamblers; d = getting up at ; e = having lost money; h = having a ravenous appetite; k = likely to lose money; l = lively; m = logicians; n = men who had better take to cab-driving; r = sitting up till . [n.b. in this problem, clauses, beginning with "though", are intended to be treated as _essential_ parts of the propositions in which they occur, just as if they had begun with "and".] . ( ) when the day is fine, i tell froggy "you're quite the dandy, old chap!"; ( ) whenever i let froggy forget that £ he owes me, and he begins to strut about like a peacock, his mother declares "he shall _not_ go out a-wooing!"; ( ) now that froggy's hair is out of curl, he has put away his gorgeous waistcoat; ( ) whenever i go out on the roof to enjoy a quiet cigar, i'm sure to discover that my purse is empty; ( ) when my tailor calls with his little bill, and i remind froggy of that £ he owes me, he does _not_ grin like a hyæna; pg ( ) when it is very hot, the thermometer is high; ( ) when the day is fine, and i'm not in the humour for a cigar, and froggy is grinning like a hyæna, i never venture to hint that he's quite the dandy; ( ) when my tailor calls with his little bill and finds me with an empty purse, i remind froggy of that £ he owes me; ( ) my railway-shares are going up like anything! ( ) when my purse is empty, and when, noticing that froggy has got his gorgeous waistcoat on, i venture to remind him of that £ he owes me, things are apt to get rather warm; ( ) now that it looks like rain, and froggy is grinning like a hyæna, i can do without my cigar; ( ) when the thermometer is high, you need not trouble yourself to take an umbrella; ( ) when froggy has his gorgeous waistcoat on, but is _not_ strutting about like a peacock, i betake myself to a quiet cigar; ( ) when i tell froggy that he's quite the dandy, he grins like a hyæna; ( ) when my purse is tolerably full, and froggy's hair is one mass of curls, and when he is _not_ strutting about like a peacock, i go out on the roof; ( ) when my railway-shares are going up, and when it is chilly and looks like rain, i have a quiet cigar; ( ) when froggy's mother lets him go a-wooing, he seems nearly mad with joy, and puts on a waistcoat that is gorgeous beyond words; ( ) when it is going to rain, and i am having a quiet cigar, and froggy is _not_ intending to go a-wooing, you had better take an umbrella; ( ) when my railway-shares are going up, and froggy seems nearly mad with joy, _that_ is the time my tailor always chooses for calling with his little bill; ( ) when the day is cool and the thermometer low, and i say nothing to froggy about his being quite the dandy, and there's not the ghost of a grin on his face, i haven't the heart for my cigar! pg . ( ) any one, fit to be an m.p., who is not always speaking, is a public benefactor; ( ) clear-headed people, who express themselves well, have had a good education; ( ) a woman, who deserves praise, is one who can keep a secret; ( ) people, who benefit the public, but do not use their influence for good purpose, are not fit to go into parliament; ( ) people, who are worth their weight in gold and who deserve praise, are always unassuming; ( ) public benefactors, who use their influence for good objects, deserve praise; ( ) people, who are unpopular and not worth their weight in gold, never can keep a secret; ( ) people, who can talk for ever and are fit to be members of parliament, deserve praise; ( ) any one, who can keep a secret and who is unassuming, is a never-to-be-forgotten public benefactor; ( ) a woman, who benefits the public, is always popular; ( ) people, who are worth their weight in gold, who never leave off talking, and whom it is impossible to forget, are just the people whose photographs are in all the shop-windows; ( ) an ill-educated woman, who is not clear-headed, is not fit to go into parliament; ( ) any one, who can keep a secret and is not for ever talking, is sure to be unpopular; ( ) a clear-headed person, who has influence and uses it for good objects, is a public benefactor; ( ) a public benefactor, who is unassuming, is not the sort of person whose photograph is in every shop-window; ( ) people, who can keep a secret and who use their influence for good purposes, are worth their weight in gold; ( ) a person, who has no power of expression and who cannot influence others, is certainly not a _woman_; pg ( ) people, who are popular and worthy of praise, either are public benefactors or else are unassuming. univ. "persons"; a = able to keep a secret; b = clear-headed; c = constantly talking; d = deserving praise; e = exhibited in shop-windows; h = expressing oneself well; k = fit to be an m.p.; l = influential; m = never-to-be-forgotten; n = popular; r = public benefactors; s = unassuming; t = using one's influence for good objects; v = well-educated; w = women; z = worth one's weight in gold. . six friends, and their six wives, are staying in the same hotel; and they all walk out daily, in parties of various size and composition. to ensure variety in these daily walks, they have agree to observe the following rules:-- ( ) if acres is with (i.e. is in the same party with) his wife, and barry with his, and eden with mrs. hall, cole must be with mrs. dix; ( ) if acres is with his wife, and hall with his, and barry with mrs. cole, dix must _not_ be with mrs. eden; ( ) if cole and dix and their wives are all in the same party, and acres _not_ with mrs. barry, eden must _not_ be with mrs. hall; ( ) if acres is with his wife, and dix with his, and barry _not_ with mrs. cole, eden must be with mrs. hall; ( ) if eden is with his wife, and hall with his, and cole with mrs. dix, acres must _not_ be with mrs. barry; ( ) if barry and cole and their wives are all in the same party, and eden _not_ with mrs. hall, dix must be with mrs. eden. the problem is to prove that there must be, every day, at least _one_ married couple who are not in the same party. pg . after the six friends, named in problem , had returned from their tour, three of them, barry, cole, and dix, agreed, with two other friends of theirs, lang and mill, that the five should meet, every day, at a certain _table d'hôte_. remembering how much amusement they had derived from their code of rules for walking-parties, they devised the following rules to be observed whenever beef appeared on the table:-- ( ) if barry takes salt, then either cole or lang takes _one_ only of the two condiments, salt and mustard: if he takes mustard, then either dix takes neither condiment, or mill takes both. ( ) if cole takes salt, then either barry takes only _one_ condiment, or mill takes neither: if he takes mustard, then either dix or lang takes both. ( ) if dix takes salt, then either barry takes neither condiment or cole take both: if he takes mustard, then either lang or mill takes neither. ( ) if lang takes salt, then barry or dix takes only _one_ condiment: if he takes mustard, then either cole or mill takes neither. ( ) if mill takes salt, then either barry or lang takes both condiments: if he takes mustard, then either cole or dix takes only _one_. the problem is to discover whether these rules are _compatible_; and, if so, what arrangements are possible. [n.b. in this problem, it is assumed that the phrase "if barry takes salt" allows of _two_ possible cases, viz. ( ) "he takes salt _only_"; ( ) "he takes _both_ condiments". and so with all similar phrases. it is also assumed that the phrase "either cole or lang takes _one_ only of the two condiments" allows _three_ possible cases, viz. ( ) "cole takes _one_ only, lang takes both or neither"; ( ) "cole takes both or neither, lang takes _one_ only"; ( ) "cole takes _one_ only, lang takes _one_ only". and so with all similar phrases. it is also assumed that every rule is to be understood as implying the words "and _vice versâ_." thus the first rule would imply the addition "and, if either cole or lang takes only _one_ condiment, then barry takes salt."] pg . ( ) brothers, who are much admired, are apt to be self-conscious; ( ) when two men of the same height are on opposite sides in politics, if one of them has his admirers, so also has the other; ( ) brothers, who avoid general society, look well when walking together; ( ) whenever you find two men, who differ in politics and in their views of society, and who are not both of them ugly, you may be sure that they look well when walking together; ( ) ugly men, who look well when walking together, are not both of them free from self-consciousness; ( ) brothers, who differs in politics, and are not both of them handsome, never give themselves airs; ( ) john declines to go into society, but never gives himself airs; ( ) brothers, who are apt to be self-conscious, though not _both_ of them handsome, usually dislike society; ( ) men of the same height, who do not give themselves airs, are free from self-consciousness; ( ) men, who agree on questions of art, though they differ in politics, and who are not both of them ugly, are always admired; ( ) men, who hold opposite views about art and are not admired, always give themselves airs; ( ) brothers of the same height always differ in politics; ( ) two handsome men, who are neither both of them admired nor both of them self-conscious, are no doubt of different heights; ( ) brothers, who are self-conscious, and do not both of them like society, never look well when walking together. [n.b. see note at end of problem .] pg . ( ) a man can always master his father; ( ) an inferior of a man's uncle owes that man money; ( ) the father of an enemy of a friend of a man owes that man nothing; ( ) a man is always persecuted by his son's creditors; ( ) an inferior of the master of a man's son is senior to that man; ( ) a grandson of a man's junior is not his nephew; ( ) a servant of an inferior of a friend of a man's enemy is never persecuted by that man; ( ) a friend of a superior of the master of a man's victim is that man's enemy; ( ) an enemy of a persecutor of a servant of a man's father is that man's friend. the problem is to deduce some fact about great-grandsons. [n.b. in this problem, it is assumed that all the men, here referred to, live in the same town, and that every pair of them are either "friends" or "enemies," that every pair are related as "senior and junior", "superior and inferior", and that certain pairs are related as "creditor and debtor", "father and son", "master and servant", "persecutor and victim", "uncle and nephew".] . "jack sprat could eat no fat: his wife could eat no lean: and so, between them both, they licked the platter clean." solve this as a sorites-problem, taking lines and as the conclusion to be proved. it is permitted to use, as premisses, not only all that is here _asserted_, but also all that we may reasonably understand to be _implied_. pg notes to appendix. (a) [see p. , line .] it may, perhaps, occur to the reader, who has studied formal logic that the argument, here applied to the propositions i and e, will apply equally well to the propositions i and a (since, in the ordinary text-books, the propositions "all xy are z" and "some xy are not z" are regarded as contradictories). hence it may appear to him that the argument might have been put as follows:-- "we now have i and a 'asserting.' hence, if the proposition 'all xy are z' be true, some things exist with the attributes x and y: i.e. 'some x are y.' "also we know that, if the proposition 'some xy are not-z' be true the same result follows. "but these two propositions are contradictories, so that one or other of them _must_ be true. hence this result is always true: i.e. the proposition 'some x are y' is _always_ true! "_quod est absurdum._ hence i _cannot_ assert." this matter will be discussed in part ii; but i may as well give here what seems to me to be an irresistable proof that this view (that _a_ and _i_ are contradictories), though adopted in the ordinary text-books, is untenable. the proof is as follows:-- with regard to the relationship existing between the class 'xy' and the two classes 'z' and 'not-z', there are _four_ conceivable states of things, viz. ( ) some xy are z, and some are not-z; ( ) " " none " ( ) no xy " some " ( ) " " none " of these four, no. ( ) is equivalent to "all xy are z", no. ( ) is equivalent to "all xy are not-z", and no. ( ) is equivalent to "no xy exist." now it is quite undeniable that, of these _four_ states of things, each is, _a priori_, _possible_, some _one must_ be true, and the other three _must_ be false. hence the contradictory to ( ) is "either ( ) or ( ) or ( ) is true." now the assertion "either ( ) or ( ) is true" is equivalent to "some xy are not-z"; and the assertion "( ) is true" is equivalent to "no xy exist." hence the contradictory to "all xy are z" may be expressed as the alternative proposition "either some xy are not-z, or no xy exist," but _not_ as the categorical proposition "some y are not-z." pg (b) [see p. , at end of section .] there are yet _other_ views current among "the logicians", as to the "existential import" of propositions, which have not been mentioned in this section. one is, that the proposition "some x are y" is to be interpreted, neither as "some x _exist_ and are y", nor yet as "if there _were_ any x in existence, some of them _would_ be y", but merely as "some x _can be_ y; i.e. the attributes x and y are _compatible_". on _this_ theory, there would be nothing offensive in my telling my friend jones "some of your brothers are swindlers"; since, if he indignantly retorted "what do you _mean_ by such insulting language, you scoundrel?", i should calmly reply "i merely mean that the thing is _conceivable_----that some of your brothers _might possibly_ be swindlers". but it may well be doubted whether such an explanation would _entirely_ appease the wrath of jones! another view is, that the proposition "all x are y" _sometimes_ implies the actual _existence_ of x, and _sometimes_ does _not_ imply it; and that we cannot tell, without having it in _concrete_ form, _which_ interpretation we are to give to it. _this_ view is, i think, strongly supported by common usage; and it will be fully discussed in part ii: but the difficulties, which it introduces, seem to me too formidable to be even alluded to in part i, which i am trying to make, as far as possible, easily intelligible to mere _beginners_. (c) [see p. , § .] the three conclusions are "no conceited child of mine is greedy"; "none of my boys could solve this problem"; "some unlearned boys are not choristers." pg index. § . _tables._ i. biliteral diagram. attributes of classes, and compartments, or cells, assigned to them ii. do. representation of uniliteral propositions of existence iii. do. representation of biliteral propositions of existence and of relation iv. triliteral diagram. attributes of classes, and compartments, or cells, assigned to them v. do. representation of particular and universal negative propositions, of existence and of relation, in terms of x and m vi. do. do., in terms of y and m vii. do. representation of universal affirmative propositions of relation, in terms of x and m viii. do. do. in terms of y and m ix. method of subscripts. formulæ and rules for syllogisms § . _words &c. explained._ 'abstract' proposition 'adjuncts' 'affirmative' proposition 'attributes' 'biliteral' diagram " proposition 'class' ½ classes, arbitrary limits of ½ " , subdivision of pg 'classification' ½ 'codivisional' classes 'complete' conclusion of a sorites 'conclusion' of a sorites " " " syllogism 'concrete' proposition 'consequent' in a sorites " " syllogism 'converse' propositions 'conversion' of a proposition " 'copula' of a proposition 'definition' 'dichotomy' ½ 'differentia' ½ 'division' 'eliminands' of a sorites " " syllogism 'entity' 'equivalent' propositions 'fallacy' 'genus' ½ 'imaginary' class " " name ½ 'individual' 'like', and 'unlike', signs of terms 'name' 'negative' proposition 'normal' form of a proposition " " of existence " " of relation 'nullity' 'partial' conclusion of a sorites 'particular' proposition 'peculiar' attributes ½ 'predicate' of a proposition " of a proposition of existence " " relation 'premisses' of a sorites " " syllogism pg 'proposition' " 'in _i_', 'in _e_', and 'in _a_' " 'in terms of' certain letters " of existence " of relation 'real' class ½ 'retinends' of a sorites " " syllogism 'sign of quantity' in a proposition 'sitting on the fence' 'some', technical meaning of 'sorites' 'species' ½ 'subject' of a proposition " " of existence " " of relation 'subscripts' of terms 'syllogism' symbol ".'." 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[_in preparation._ three sunsets, and other poems. with twelve illustrations by e. gertrude thomson. fcap. to, cloth, gilt edges. n.b.--this will be a reprint, possibly with a few additions, of the serious portion of "phantasmagoria, and other poems," published in . * * * * * advice to writers. buy "the wonderland case for postage-stamps," invented by lewis carrol, oct. , , size inches by , containing separate pockets for stamps of different values, coloured pictorial surprises taken from _alice in wonderland_, and or wise words about letter-writing. it is published by messrs. emberlin & son, magdalene street, oxford. price _s._ n.b.--if ordered by post, an additional payment will be required, to cover cost of postage, as follows:-- one copy, ½_d._ two or three do., _d._ four do., ½_d._ five to fourteen do., _d._ each subsequent fourteen or fraction thereof, ½_d._ * * * * * * * * * * transcriber's note this book makes extensive use of page references. to assist the reader, page markers in the forms "pg-ix", "pg " & "px- " have been included in the right margin at points corresponding closely to the tops of the original pages. these may be searched for to locate the material referred to. in the main section, these page markers are always given with digits including, if necessary, leading zeroes. this book contains a large number of line drawn illustrations which are un-credited. as these cannot be rendered here in the original manner they have been reproduced as well as possible in the manner known as "ascii art". a number of transcription errors were found in the original book. as these were clearly not part of the author's intention they have, as far as possible, been identified and corrected in accordance with the methods given by the author. these corrections are listed here below with their locations and original text. in these notes the word 'natural' identifies a letter symbol occurring without a prime mark. page viii: " " corrected to " ". page viii: " " corrected to " ". page xv, '=real=' and '=unreal=', or '=imaginary=', classes: " ½" corrected to " ". page xix, propositions beginning with "some": " " corrected to " ". page xix, rules: " " corrected to " ". page xix, the west and east halves ...: " " corrected to " ". page xxi, the proposition "all x are y" ...: was originally shown as occurring in page . page xxii, and of three other similar arrangements: " " corrected to " ". page xxiii, the proposition 'no xm exist': " " corrected to " ". page : "contruct" corrected to "construct". page , paper v: missing word "it" supplied. page , # : "no h are k-natural" corrected to "no h are k-prime". page , # : "no a are h-natural" corrected to "no a are h-prime". page , # : "no c are n-natural" corrected to "no c are n-prime". page , # (d): "mortally offended if i fail to notice them" corrected to "mortally offended". page , # : "some x-prime are y" corrected to "some x-natural are y". page , # : "x_{ }m-prime_{ }" corrected to "x_{ }m-natural_{ }". page , # : "xm-natural_{ }" corrected to "xm-prime_{ }". page , # ( / ): "be" corrected to "be-sub:zero". page , # ( / ): "ch" corrected to "ch-sub:zero". page , # ( / ): second underline corrected from single to double. page , # ( / ): first underline corrected from single to double. page , # (¶ ): "h_{ }c" corrected to "h_{ }c-sub:zero". page , # ( / ): "a_{ }c-natural_{ }" corrected to "a_{ }c-prime_{ }". page , # (¶ ): "e_{ }c-natural_{ }" corrected to "e_{ }c-prime_{ }". page , # ( / ): first underline corrected from single to double. page , # ( / ): "e'd-prime" corrected to "e'd-natural". page , # ( / ): "c-prime+d" corrected to "c-natural+d". page , # : "a" and "b" interchanged. page , # ( / ): "b-natural_{ }e_{ }" corrected to "b-prime_{ }e_{ }". page , # ( / ): "h'k-prime_{ }" corrected to "h'k-natural_{ }". page , # ( / ): "c'd-prime" corrected to "c'd-natural". page , # ( / ): "h-natural+d'" corrected to "h-prime+d'". in the original book at the top of page , the following text occurred: [n.b. the numbers at the foot of each page indicate the pages where the corresponding matter may be found.] in accordance with the un-paged medium here this has been changed to: [n.b. reference tags for examples, answers & solutions will be found in the right margin.] the part of the book to which this relates contains, by sections, "examples" (exercises for the student), "answers" (to the examples) & "solutions" (worked answers). all example sections have corresponding answer sections. for sections & , worked solutions are not supplied; for sections - , solutions are given by different methods. in association with this, the original text contained editorial notes at the foot of each page giving the page numbers for the related sections. in this version, these notes are replaced with marginal tags such as ex , an , sl , & sl -a and sl -b which are placed at the top of each section to identify the current location. as with page tags, these may be searched for to locate the material refered to. (a search for "sl " should find successively both "sl -a" & "sl -b".) these tags are unique regardless of case. university manuals edited by professor knight logic inductive and deductive published may, _reprinted december, _ " _november, _ " _january, _ " _august, _ " _june, _ " _september, _ " _july, _ " _january, _ logic inductive and deductive by william minto, m.a. hon. ll.d. st. andrews late professor of logic in the university of aberdeen london john murray, albemarle street, w. preface. in this little treatise two things are attempted that at first might appear incompatible. one of them is to put the study of logical formulæ on a historical basis. strangely enough, the scientific evolution of logical forms, is a bit of history that still awaits the zeal and genius of some great scholar. i have neither ambition nor qualification for such a _magnum opus_, and my life is already more than half spent; but the gap in evolutionary research is so obvious that doubtless some younger man is now at work in the field unknown to me. all that i can hope to do is to act as a humble pioneer according to my imperfect lights. even the little i have done represents work begun more than twenty years ago, and continuously pursued for the last twelve years during a considerable portion of my time. the other aim, which might at first appear inconsistent with this, is to increase the power of logic as a practical discipline. the main purpose of this practical science, or scientific art, is conceived to be the organisation of reason against error, and error in its various kinds is made the basis of the division of the subject. to carry out this practical aim along with the historical one is not hopeless, because throughout its long history logic has been a practical science; and, as i have tried to show at some length in introductory chapters, has concerned itself at different periods with the risks of error peculiar to each. to enumerate the various books, ancient and modern, to which i have been indebted, would be a vain parade. where i have consciously adopted any distinctive recent contribution to the long line of tradition, i have made particular acknowledgment. my greatest obligation is to my old professor, alexander bain, to whom i owe my first interest in the subject, and more details than i can possibly separate from the general body of my knowledge. w. m. aberdeen, _january, _. since these sentences were written, the author of this book has died; and professor minto's _logic_ is his last contribution to the literature of his country. it embodies a large part of his teaching in the philosophical class-room of his university, and doubtless reflects the spirit of the whole of it. scottish philosophy has lost in him one of its typical representatives, and the university of the north one of its most stimulating teachers. there have been few more distinguished men than william minto in the professoriate of aberdeen; and the memory of what he was, of his wide and varied learning, his brilliant conversation, his urbanity, and his rare power of sympathy with men with whose opinions he did not agree, will remain a possession to many who mourn his loss. it will be something if this little book keeps his memory alive, both amongst the students who owed so much to him, and in the large circle of friends who used to feel the charm of his personality. william knight. _general plan of the series._ _this series is primarily designed to aid the university extension movement throughout great britain and america, and to supply the need so widely felt by students, of text-books for study and reference, in connexion with the authorised courses of lectures._ _the manuals differ from those already in existence in that they are not intended for school use, or for examination purposes; and that their aim is to educate, rather than to inform. the statement of details is meant to illustrate the working of general laws, and the development of principles; while the historical evolution of the subject dealt with is kept in view, along with its philosophical significance._ _the remarkable success which has attended university extension in britain has been partly due to the combination of scientific treatment with popularity, and to the union of simplicity with thoroughness. this movement, however, can only reach those resident in the larger centres of population, while all over the country there are thoughtful persons who desire the same kind of teaching. it is for them also that this series is designed. its aim is to supply the general reader with the same kind of teaching as is given in the lectures, and to reflect the spirit which has characterised the movement, viz., the combination of principles with facts, and of methods with results._ _the manuals are also intended to be contributions to the literature of the subjects with which they respectively deal, quite apart from university extension; and some of them will be found to meet a general rather than a special want._ _they will be issued simultaneously in england and america. volumes dealing with separate sections of literature, science, philosophy, history, and art have been assigned to representative literary men, to university professors, or to extension lecturers connected with oxford, cambridge, london, and the universities of scotland and ireland._ _a list of the works in this series will be found at the end of the volume._ contents. introduction. i. page the origin and scope of logic, ii. logic as a preventive of error or fallacy--the inner sophist, iii. the axioms of dialectic and of syllogism, book i. the logic of consistency--syllogism and definition. part i. the elements of propositions. chapter i. general names and allied distinctions, chapter ii. the syllogistic analysis of proposition, into terms. ( ) the bare analytic forms. ( ) the practice of syllogistic analysis. ( ) some technical difficulties, part ii. definition. chapter i. ( ) imperfect understanding of words. ( ) verification of the meaning--dialectic. ( ) fixation of the meaning--division or classification, definition, naming, chapter ii. the five predicables--verbal and real predication, chapter iii. aristotle's categories, chapter iv. the controversy about universals--difficulties concerning the relation of general names to thought and to reality, part iii. the interpretation of propositions. chapter i. theories of predication--theories of judgment, chapter ii. the "opposition" of propositions--the interpretation of "no," chapter iii. the implication of propositions--immediate formal inference --eduction, chapter iv. the counter-implication of propositions, part iv. the interdependence of propositions. chapter i. the syllogism, chapter ii. the figures and moods of the syllogism. ( ) the first figure. ( ) the minor figures and their reduction to the first. ( ) sorites, chapter iii. the demonstration of the syllogistic moods--the canons of the syllogism, chapter iv. the analysis of arguments into syllogistic forms, chapter v. enthymemes, chapter vi. the utility of the syllogism, chapter vii. conditional arguments--hypothetical syllogism, disjunctive syllogism and dilemma, chapter viii. fallacies in deductive argument--_petitio principii_ and _ignoratio elenchi_, chapter ix. formal or aristotelian induction--inductive argument--the inductive syllogism, book ii. inductive logic, or the logic of science. introduction, chapter i. the data of experience as grounds of inference or rational belief, chapter ii. ascertainment of simple facts in their order--personal observation--hearsay evidence--method of testing traditional evidence, chapter iii. ascertainment of facts of causation. ( ) _post hoc ergo propter hoc._ ( ) meaning of cause--methods of observation --mill's experimental methods, chapter iv. method of observation--single difference. ( ) the principle of single difference. ( ) application of the principle, chapter v. methods of observation--elimination--single agreement. ( ) the principle of elimination. ( ) the principle of single agreement. ( ) mill's "joint method of agreement and difference," chapter vi. methods of observation--minor methods. ( ) concomitant variations. ( ) single residue, chapter vii. the method of explanation. ( ) the four stages of orderly procedure. ( ) obstacles to explanation--plurality of causes and intermixture of effects. ( ) the proof of a hypothesis, chapter viii. supplementary methods of investigation. ( ) the maintenance of averages--supplement to the method of difference. ( ) the presumption from extra-casual coincidence, chapter ix. probable inference to particulars--the measurement of probability, chapter x. inference from analogy, introduction. i.--the origin and scope of logic. the question has sometimes been asked, where should we begin in logic? particularly within the present century has this difficulty been felt, when the study of logic has been revived and made intricate by the different purposes of its cultivators. where did the founder of logic begin? where did aristotle begin? this seems to be the simplest way of settling where we should begin, for the system shaped by aristotle is still the trunk of the tree, though there have been so many offshoots from the old stump and so many parasitic plants have wound themselves round it that logic is now almost as tangled a growth as the yews of borrowdale-- an intertwisted mass of fibres serpentine upcoiling and inveterately convolved. it used to be said that logic had remained for two thousand years precisely as aristotle left it. it was an example of a science or art perfected at one stroke by the genius of its first inventor. the bewildered student must often wish that this were so: it is only superficially true. much of aristotle's nomenclature and his central formulæ have been retained, but they have been very variously supplemented and interpreted to very different purposes--often to no purpose at all. the cambridge mathematician's boast about his new theorem--"the best of it all is that it can never by any possibility be made of the slightest use to anybody for anything"--might be made with truth about many of the later developments of logic. we may say the same, indeed, about the later developments of any subject that has been a playground for generation after generation of acute intellects, happy in their own disinterested exercise. educational subjects--subjects appropriated for the general schooling of young minds--are particularly apt to be developed out of the lines of their original intention. so many influences conspire to pervert the original aim. the convenience of the teacher, the convenience of the learner, the love of novelty, the love of symmetry, the love of subtlety; easy-going indolence on the one hand and intellectual restlessness on the other--all these motives act from within on traditional matter without regard to any external purpose whatever. thus in logic difficulties have been glossed over and simplified for the dull understanding, while acute minds have revelled in variations and new and ingenious manipulations of the old formulæ, and in multiplication and more exact and symmetrical definition of the old distinctions. to trace the evolution of the forms and theories of logic under these various influences during its periods of active development is a task more easily conceived than executed, and one far above the ambition of an introductory treatise. but it is well that even he who writes for beginners should recognise that the forms now commonly used have been evolved out of a simpler tradition. without entering into the details of the process, it is possible to indicate its main stages, and thus furnish a clue out of the modern labyrinthine confusion of purposes. how did the aristotelian logic originate? its central feature is the syllogistic forms. in what circumstances did aristotle invent these? for what purpose? what use did he contemplate for them? in rightly understanding this, we shall understand the original scope or province of logic, and thus be in a position to understand more clearly how it has been modified, contracted, expanded, and supplemented. logic has always made high claims as the _scientia scientiarum_, the science of sciences. the builders of this tower of babel are threatened in these latter days with confusion of tongues. we may escape this danger if we can recover the designs of the founder, and of the master-builders who succeeded him. aristotle's logic has been so long before the world in abstract isolation that we can hardly believe that its form was in any way determined by local accident. a horror as of sacrilege is excited by the bare suggestion that the author of this grand and venerable work, one of the most august monuments of transcendent intellect, was in his day and generation only a pre-eminent tutor or schoolmaster, and that his logical writings were designed for the accomplishment of his pupils in a special art in which every intellectually ambitious young athenian of the period aspired to excel. yet such is the plain fact, baldly stated. aristotle's logic in its primary aim was as practical as a treatise on navigation, or "cavendish on whist". the latter is the more exact of the two comparisons. it was in effect in its various parts a series of handbooks for a temporarily fashionable intellectual game, a peculiar mode of disputation or dialectic,[ ] the game of question and answer, the game so fully illustrated in the dialogues of plato, the game identified with the name of socrates. we may lay stress, if we like, on the intellectuality of the game, and the high topics on which it was exercised. it was a game that could flourish only among a peculiarly intellectual people; a people less acute would find little sport in it. the athenians still take a singular delight in disputation. you cannot visit athens without being struck by it. you may still see groups formed round two protagonists in the cafés or the squares, or among the ruins of the acropolis, in a way to remind you of socrates and his friends. they do not argue as gil blas and his hibernians did with heat and temper, ending in blows. they argue for the pure love of arguing, the audience sitting or standing by to see fair play with the keenest enjoyment of intellectual thrust and parry. no other people could argue like the greeks without coming to blows. it is one of their characteristics now, and so it was in old times two thousand years ago. and about a century before aristotle reached manhood, they had invented this peculiarly difficult and trying species of disputative pastime, in which we find the genesis of aristotle's logical treatises. to get a proper idea of this debate by question and answer, which we may call socratic disputation after its most renowned master, one must read some of the dialogues of plato. i will indicate merely the skeleton of the game, to show how happily it lent itself to aristotle's analysis of arguments and propositions. a thesis or proposition is put up for debate, _e.g._, that knowledge is nothing else than sensible perception,[ ] that it is a greater evil to do wrong than to suffer wrong,[ ] that the love of gain is not reprehensible.[ ] there are two disputants, but they do not speak on the question by turns, so many minutes being allowed to each as in a modern encounter of wits. one of the two, who may be called the questioner, is limited to asking questions, the other, the respondent, is limited to answering. further, the respondent can answer only "yes" or "no," with perhaps a little explanation: on his side the questioner must ask only questions that admit of the simple answer "yes" or "no". the questioner's business is to extract from the respondent admissions involving the opposite of what he has undertaken to maintain. the questioner tries in short to make him contradict himself. only a very stupid respondent would do this at once: the questioner plies him with general principles, analogies, plain cases; leads him on from admission to admission, and then putting the admissions together convicts him out of his own mouth of inconsistency.[ ] now mark precisely where aristotle struck in with his invention of the syllogism, the invention on which he prided himself as specially his own, and the forms of which have clung to logic ever since, even in the usage of those who deride aristotle's moods and figures as antiquated superstitions. suppose yourself the questioner, where did he profess to help you with his mechanism? in effect, as the word syllogism indicates, it was when you had obtained a number of admissions, and wished to reason them together, to demonstrate how they bore upon the thesis in dispute, how they hung together, how they necessarily involved what you were contending for. and the essence of his mechanism was the reduction of the admitted propositions to common terms, and to certain types or forms which are manifestly equivalent or inter-dependent. aristotle advised his pupils also in the tactics of the game, but his grand invention was the form or type of admissions that you should strive to obtain, and the effective manipulation of them when you had got them. an example will show the nature of this help, and what it was worth. to bring the thing nearer home, let us, instead of an example from plato, whose topics often seem artificial to us now, take a thesis from last century, a paradox still arguable, mandeville's famous--some would say infamous--paradox that private vices are public benefits. undertake to maintain this, and you will have no difficulty in getting a respondent prepared to maintain the negative. the plain men, such as socrates cross-questioned, would have declared at once that a vice is a vice, and can never do any good to anybody. your respondent denies your proposition simply: he upholds that private vices never are public benefits, and defies you to extract from him any admission inconsistent with this. your task then is to lure him somehow into admitting that in some cases what is vicious in the individual may be of service to the state. this is enough: you are not concerned to establish that this holds of all private vices. a single instance to the contrary is enough to break down his universal negative. you cannot, of course, expect him to make the necessary admission in direct terms: you must go round about. you know, perhaps, that he has confidence in bishop butler as a moralist. you try him with the saying: "to aim at public and private good are so far from being inconsistent that they mutually promote each other". does he admit this? perhaps he wants some little explanation or exemplification to enable him to grasp your meaning. this was within the rules of the game. you put cases to him, asking for his "yes" or "no" to each. suppose a man goes into parliament, not out of any zeal for the public good, but in pure vainglory, or to serve his private ends, is it possible for him to render the state good service? or suppose a milk-seller takes great pains to keep his milk pure, not because he cares for the public health, but because it pays, is this a benefit to the public? let these questions be answered in the affirmative, putting you in possession of the admission that some actions undertaken for private ends are of public advantage, what must you extract besides to make good your position as against the respondent? to see clearly at this stage what now is required, though you have to reach it circuitously, masking your approach under difference of language, would clearly be an advantage. this was the advantage that aristotle's method offered to supply. a disputant familiar with his analysis would foresee at once that if he could get the respondent to admit that all actions undertaken for private ends are vicious, the victory was his, while nothing short of this would serve. here my reader may interject that he could have seen this without any help from aristotle, and that anybody may see it without knowing that what he has to do is, in aristotelian language, to construct a syllogism in bokardo. i pass this over. i am not concerned at this point to defend the utility of aristotle's method. all that i want is to illustrate the kind of use that it was intended for. perhaps if aristotle had not habituated men's minds to his analysis, we should none of us have been able to discern coherence and detect incoherence as quickly and clearly as we do now. but to return to our example. as aristotle's pupil, you would have seen at the stage we are speaking of that the establishment of your thesis must turn upon the definition of virtue and vice. you must proceed, therefore, to cross-examine your respondent about this. you are not allowed to ask him what he means by virtue, or what he means by vice. in accordance with the rules of the dialectic, it is your business to propound definitions, and demand his yes or no to them. you ask him, say, whether he agrees with shaftesbury's definition of a virtuous action as an action undertaken purely for the good of others. if he assents, it follows that an action undertaken with any suspicion of a self-interested motive cannot be numbered among the virtues. if he agrees, further, that every action must be either vicious or virtuous, you have admissions sufficient to prove your original thesis. all that you have now to do to make your triumph manifest, is to display the admissions you have obtained in common terms. some actions done with a self-interested motive are public benefits. all actions done with a self-interested motive are private vices. from these premisses it follows irresistibly that some private vices are public benefits. this illustration may serve to show the kind of disputation for which aristotle's logic was designed, and thus to make clear its primary uses and its limitations. to realise its uses, and judge whether there is anything analogous to them in modern needs, conceive the chief things that it behoved questioner and respondent in this game to know. all that a proposition necessarily implies; all that two propositions put together imply; on what conditions and to what extent one admission is inconsistent with another; when one admission necessarily involves another; when two necessarily involve a third. and to these ends it was obviously necessary to have an exact understanding of the terms used, so as to avoid the snares of ambiguous language. that a syllogistic or logic of consistency should emerge out of yes-and-no dialectic was natural. things in this world come when they are wanted: inventions are made on the spur of necessity. it was above all necessary in this kind of debate to avoid contradicting yourself: to maintain your consistency. a clever interrogator spread out proposition after proposition before you and invited your assent, choosing forms of words likely to catch your prejudices and lure you into self-contradiction. an organon, instrument, or discipline calculated to protect you as respondent and guide you as questioner by making clear what an admission led to, was urgently called for, and when the game had been in high fashion for more than a century aristotle's genius devised what was wanted, meeting at the same time, no doubt, collateral needs that had arisen from the application of dialectic to various kinds of subject-matter. the thoroughness of aristotle's system was doubtless due partly to the searching character of the dialectic in which it had its birth. no other mode of disputation makes such demands upon the disputant's intellectual agility and precision, or is so well adapted to lay bare the skeleton of an argument. the uses of aristotle's logical treatises remained when the fashion that had called them forth had passed.[ ] clear and consistent thinking, a mastery of the perplexities and ambiguities of language, power to detect identity of meaning under difference of expression, a ready apprehension of all that a proposition implies, all that may be educed or deduced from it--whatever helps to these ends must be of perpetual use. "to purge the understanding of those errors which lie in the confusion and perplexities of an inconsequent thinking," is a modern description of the main scope of logic.[ ] it is a good description of the branch of logic that keeps closest to the aristotelian tradition. the limitations as well as the uses of aristotle's logic may be traced to the circumstances of its origin. both parties to the disputation, questioner and respondent alike, were mainly concerned with the inter-dependence of the propositions put forward. once the respondent had given his assent to a question, he was bound in consistency to all that it implied. he must take all the consequences of his admission. it might be true or it might be false as a matter of fact: all the same he was bound by it: its truth or falsehood was immaterial to his position as a disputant. on the other hand, the questioner could not go beyond the admissions of the respondent. it has often been alleged as a defect in the syllogism that the conclusion does not go beyond the premisses, and ingenious attempts have been made to show that it is really an advance upon the premisses. but having regard to the primary use of the syllogism, this was no defect, but a necessary character of the relation. the questioner could not in fairness assume more than had been granted by implication. his advance could only be an argumentative advance: if his conclusion contained a grain more than was contained in the premisses, it was a sophistical trick, and the respondent could draw back and withhold his assent. he was bound in consistency to stand by his admissions; he was not bound to go a fraction of an inch beyond them. we thus see how vain it is to look to the aristotelian tradition for an organon of truth or a criterion of falsehood. directly and primarily, at least, it was not so; the circumstances of its origin gave it a different bent. indirectly and secondarily, no doubt, it served this purpose, inasmuch as truth was the aim of all serious thinkers who sought to clear their minds and the minds of others by dialectic. but in actual debate truth was represented merely by the common-sense of the audience. a dialectician who gained a triumph by outraging this, however cleverly he might outwit his antagonist, succeeded only in amusing his audience, and dialecticians of the graver sort aimed at more serious uses and a more respectful homage, and did their best to discountenance merely eristic disputation. further, it would be a mistake to conclude because aristotle's logic, as an instrument of dialectic, concerned itself with the syllogism of propositions rather than their truth, that it was merely an art of quibbling. on the contrary, it was essentially the art of preventing and exposing quibbling. it had its origin in quibbling, no doubt, inasmuch as what we should call verbal quibbling was of the essence of yes-and-no dialectic, and the main secret of its charm for an intellectual and disputatious people; but it came into being as a safeguard against quibbling, not a serviceable adjunct. the mediæval developments of logic retained and even exaggerated the syllogistic character of the original treatises. interrogative dialectic had disappeared in the middle ages whether as a diversion or as a discipline: but errors of inconsistency still remained the errors against which principally educated men needed a safeguard. men had to keep their utterances in harmony with the dogmas of the church. a clear hold of the exact implications of a proposition, whether singly or in combination with other propositions, was still an important practical need. the inductive syllogism was not required, and its treatment dwindled to insignificance in mediæval text-books, but the deductive syllogism and the formal apparatus for the definition of terms held the field. it was when observation of nature and its laws became a paramount pursuit that the defects of syllogistic logic began to be felt. errors against which this logic offered no protection then called for a safeguard--especially the errors to which men are liable in the investigation of cause and effect. "bring your thoughts into harmony one with another," was the demand of aristotle's age. "bring your thoughts into harmony with authority," was the demand of the middle ages. "bring them into harmony with fact," was the requirement most keenly felt in more recent times. it is in response to this demand that what is commonly but not very happily known as inductive logic has been formulated. in obedience to custom, i shall follow the now ordinary division of logic into deductive and inductive. the titles are misleading in many ways, but they are fixed by a weight of usage which it would be vain to try to unsettle. both come charging down the stream of time each with its cohort of doctrines behind it, borne forward with irresistible momentum. the best way of preventing confusion now is to retain the established titles, recognise that the doctrines behind each have a radically different aim or end, and supply the interpretation of this end from history. what they have in common may be described as the prevention of error, the organisation of reason against error. i have shown that owing to the bent impressed upon it by the circumstances of its origin, the errors chiefly safeguarded by the aristotelian logic were the errors of inconsistency. the other branch of logic, commonly called induction, was really a separate evolution, having its origin in a different practical need. the history of this i will trace separately after we have seen our way through the aristotelian tradition and its accretions. the experimental methods are no less manifestly the germ, the evolutionary centre or starting-point, of the new logic than the syllogism is of the old, and the main errors safeguarded are errors of fact and inference from fact. at this stage it will be enough to indicate briefly the broad relations between deductive logic and inductive logic. inductive logic, as we now understand it--the logic of observation and explanation--was first formulated and articulated to a system of logic by j. s. mill. it was he that added this wing to the old building. but the need of it was clearly expressed as early as the thirteenth century. roger bacon, the franciscan friar ( - ), and not his more illustrious namesake francis, lord verulam, was the real founder of inductive logic. it is remarkable that the same century saw syllogistic logic advanced to its most complete development in the system of petrus hispanus, a portuguese scholar who under the title of john xxi. filled the papal chair for eight months in - . a casual remark of roger bacon's in the course of his advocacy of experimental science in the _opus majus_ draws a clear line between the two branches of logic. "there are," he says, "two ways of knowing, by argument and by experience. argument concludes a question, but it does not make us feel certain, unless the truth be also found in experience." on this basis the old logic may be clearly distinguished from the new, taking as the general aim of logic the protection of the mind against the errors to which it is liable in the acquisition of knowledge. all knowledge, broadly speaking, comes either from authority, _i.e._, by argument from accepted premisses, or from experience. if it comes from authority it comes through the medium of words: if it comes from experience it comes through the senses. in taking in knowledge through words we are liable to certain errors; and in taking in knowledge through the senses we are liable to certain errors. to protect against the one is the main end of "deductive" logic: to protect against the other is the main end of "inductive" logic. as a matter of fact the pith of treatises on deduction and induction is directed to those ends respectively, the old meanings of deduction and induction as formal processes (to be explained afterwards) being virtually ignored. there is thus no antagonism whatever between the two branches of logic. they are directed to different ends. the one is supplementary to the other. the one cannot supersede the other. aristotelian logic can never become superfluous as long as men are apt to be led astray by words. its ultimate business is to safeguard in the interpretation of the tradition of language. the mere syllogistic, the bare forms of equivalent or consistent expression, have a very limited utility, as we shall see. but by cogent sequence syllogism leads to proposition, and proposition to term, and term to a close study of the relations between words and thoughts and things. [footnote : we know for certain--and it is one of the evidences of the importance attached to this trivial-looking pastime--that two of the great teacher's logical treatises, the topics and the sophistical refutations, were written especially for the guidance of questioners and respondents. the one instructs the disputant how to qualify himself methodically for discussion before an ordinary audience, when the admissions extracted from the respondent are matters of common belief, the questioner's skill being directed to make it appear that the respondent's position is inconsistent with these. the other is a systematic exposure of sophistical tricks, mostly verbal quibbles, whereby a delusive appearance of victory in debate may be obtained. but in the concluding chapter of the _elenchi_, where aristotle claims not only that his method is superior to the empirical methods of rival teachers, but that it is entirely original, it is the syllogism upon which he lays stress as his peculiar and chief invention. the syllogism, the pure forms of which are expounded in his prior analytics, is really the centre of aristotle's logical system, whether the propositions to which it is applied are matters of scientific truth as in the posterior analytics, or matters of common opinion as in the topics. the treatise on interpretation, _i.e._, the interpretation of the respondent's "yes" and "no," is preliminary to the syllogism, the reasoning of the admissions together. even in the half-grammatical half-logical treatise on the categories, the author always keeps an eye on the syllogistic analysis.] [footnote : theætetus, e.] [footnote : gorgias, d.] [footnote : hipparchus, a.] [footnote : in its leading and primary use, this was a mode of debate, a duel of wits, in which two men engaged before an audience. but the same form could be used, and was used, notably by socrates, not in an eristic spirit but as a means of awakening people to the consequences of certain admissions or first principles, and thus making vague knowledge explicit and clear. the mind being detained on proposition after proposition as assent was given to it, dialectic was a valuable instrument of instruction and exposition. but whatever the purpose of the exercise, controversial triumph, or solid grounding in the first principles--"the evolution of in-dwelling conceptions"--the central interest lay in the syllogising or reasoning together of the separately assumed or admitted propositions.] [footnote : like every other fashion, yes-and-no dialectic had its period, its rise and fall. the invention of it is ascribed to zeno the eleatic, the answering and questioning zeno, who flourished about the middle of the fifth century b.c. socrates ( - ) was in his prime at the beginning of the great peloponnesian war when pericles died in . in that year plato was born, and lived to , "the olive groves of academe" being established centre of his teaching from about onwards. aristotle ( - ), who was the tutor of alexander the great, established his school at the lyceum when alexander became king in and set out on his career of conquest. that yes-and-no dialectic was then a prominent exercise, his logical treatises everywhere bear witness. the subsequent history of the game is obscure. it is probable that aristotle's thorough exposition of its legitimate arts and illegitimate tricks helped to destroy its interest as an amusement.] [footnote : hamilton's _lectures_, iii. p. .] ii.--logic as a preventive of error or fallacy.--the inner sophist. why describe logic as a system of defence against error? why say that its main end and aim is the organisation of reason against confusion and falsehood? why not rather say, as is now usual, that its end is the attainment of truth? does this not come to the same thing? substantially, the meaning is the same, but the latter expression is more misleading. to speak of logic as a body of rules for the investigation of truth has misled people into supposing that logic claims to be an art of discovery, that it claims to lay down rules by simply observing which investigators may infallibly arrive at new truths. now, this does not hold even of the logic of induction, still less of the older logic, the precise relation of which to truth will become apparent as we proceed. it is only by keeping men from going astray and by disabusing them when they think they have reached their destination that logic helps men on the road to truth. truth often lies hid in the centre of a maze, and logical rules only help the searcher onwards by giving him warning when he is on the wrong track and must try another. it is the searcher's own impulse that carries him forward: logic does not so much beckon him on to the right path as beckon him back from the wrong. in laying down the conditions of correct interpretation, of valid argument, of trustworthy evidence, of satisfactory explanation, logic shows the inquirer how to test and purge his conclusions, not how to reach them. to discuss, as is sometimes done, whether fallacies lie within the proper sphere of logic, is to obscure the real connexion between fallacies and logic. it is the existence of fallacies that calls logic into existence; as a practical science logic is needed as a protection against fallacies. such historically is its origin. we may, if we like, lay down an arbitrary rule that a treatise on logic should be content to expound the correct forms of interpretation and reasoning and should not concern itself with the wrong. if we take this view we are bound to pronounce fallacies extra-logical. but to do so is simply to cripple the usefulness of logic as a practical science. the manipulation of the bare logical forms, without reference to fallacious departures from them, is no better than a nursery exercise. every correct form in logic is laid down as a safeguard against some erroneous form to which men are prone, whether in the interpretation of argument or the interpretation of experience, and the statement and illustration of the typical forms of wrong procedure should accompany _pari passu_ the exposition of the right procedure. in accordance with this principle, i shall deal with special fallacies, special snares or pitfalls--misapprehension of words, misinterpretation of propositions, misunderstanding of arguments, misconstruction of facts, evidences, or signs--each in connexion with its appropriate safeguard. this seems to me the most profitable method. but at this stage, it may be worth while, by way of emphasising the need for logic as a science of rational belief, to take a survey of the most general tendencies to irrational belief, the chief kinds of illusion or bias that are rooted in the human constitution. we shall then better appreciate the magnitude of the task that logic attempts in seeking to protect reason against its own fallibility and the pressure of the various forces that would usurp its place. it is a common notion that we need logic to protect us against the arts of the sophist, the dishonest juggler with words and specious facts. but in truth the inner sophist, whose instruments are our own inborn propensities to error, is a much more dangerous enemy. for once that we are the victims of designing sophists, we are nine times the victims of our own irrational impulses and prejudices. men generally deceive themselves before they deceive others. francis bacon drew attention to these inner perverting influences, these universal sources of erroneous belief, in his _de augmentis_ and again in his _novum organum_, under the designation of _idola_ ([greek: eidôla]), deceptive appearances of truth, illusions. his classification of _idola--idola tribus_, illusions common to all men, illusions of the race; _idola specus_, personal illusions, illusions peculiar to the "den" in which each man lives; _idola fori_, illusions of conversation, vulgar prejudices embodied in words; _idola theatri_, illusions of illustrious doctrine, illusions imposed by the dazzling authority of great names--is defective as a classification inasmuch as the first class includes all the others, but like all his writings it is full of sagacious remarks and happy examples. not for the sake of novelty, but because it is well that matters so important should be presented from more than one point of view, i shall follow a division adapted from the more scientific, if less picturesque, arrangement of professor bain, in his chapter on the fallacious tendencies of the human mind.[ ] the illusions to which we are all subject may best be classified according to their origin in the depths of our nature. let us try to realise how illusory beliefs arise. what is a belief? one of the uses of logic is to set us thinking about such simple terms. an exhaustive analysis and definition of belief is one of the most difficult of psychological problems. we cannot enter upon that: let us be content with a few simple characters of belief. first, then, belief is a state of mind. second, this state of mind is outward-pointing: it has a reference beyond itself, a reference to the order of things outside us. in believing, we hold that the world as it is, has been, or will be, corresponds to our conceptions of it. third, belief is the guide of action: it is in accordance with what we believe that we direct our activities. if we want to know what a man really believes, we look at his action. this at least is the clue to what he believes at the moment. "i cannot," a great orator once said, "read the minds of men." this was received with ironical cheers. "no," he retorted, "but i can construe their acts." promoters of companies are expected to invest their own money as a guarantee of good faith. if a man says he believes the world is coming to an end in a year, and takes a lease of a house for fifteen years, we conclude that his belief is not of the highest degree of strength. the close connexion of belief with our activities, enables us to understand how illusions, false conceptions of reality, arise. the illusions of feeling and the illusions of custom are well understood, but other sources of illusion, which may be designated impatient impulse and happy exercise, are less generally recognised. an example or two will show what is meant. we cannot understand the strength of these perverting influences till we realise them in our own case. we detect them quickly enough in others. seeing that in common speech the word illusion implies a degree of error amounting almost to insanity, and the illusions we speak of are such as no man is ever quite free from, it is perhaps less startling to use the word _bias_. _the bias of impatient impulse._ as a being formed for action, not only does healthy man take a pleasure in action, physical and mental, for its own sake, irrespective of consequences, but he is so charged with energy that he cannot be comfortable unless it finds a free vent. in proportion to the amount and excitability of his energy, restraint, obstruction, delay is irksome, and soon becomes a positive and intolerable pain. any bar or impediment that gives us pause is hateful even to think of: the mere prospect annoys and worries. hence it arises that belief, a feeling of being prepared for action, a conviction that the way is clear before us for the free exercise of our activities, is a very powerful and exhilarating feeling, as much a necessity of happy existence as action itself. we see this when we consider how depressing and uncomfortable a condition is the opposite state to belief, namely, doubt, perplexity, hesitation, uncertainty as to our course. and realising this, we see how strong a bias we have in this fact of our nature, this imperious inward necessity for action; how it urges us to act without regard to consequences, and to jump at beliefs without inquiry. for, unless inquiry itself is our business, a self-sufficient occupation, it means delay and obstruction. this ultimate fact of our nature, this natural inbred constitutional impatience, explains more than half of the wrong beliefs that we form and persist in. we must have a belief of some kind: we cannot be happy till we get it, and we take up with the first that seems to show the way clear. it may be right or it may be wrong: it is not, of course, necessarily always wrong: but that, so far as we are concerned, is a matter of accident. the pressing need for a belief of some sort, upon which our energies may proceed in anticipation at least, will not allow us to stop and inquire. any course that offers a relief from doubt and hesitation, any conviction that lets the will go free, is eagerly embraced. it may be thought that this can apply only to beliefs concerning the consequences of our own personal actions, affairs in which we individually play a part. it is from them, no doubt, that our nature takes this set: but the habit once formed is extended to all sorts of matters in which we have no personal interest. tell an ordinary englishman, it has been wittily said, that it is a question whether the planets are inhabited, and he feels bound at once to have a confident opinion on the point. the strength of the conviction bears no proportion to the amount of reason spent in reaching it, unless it may be said that as a general rule the less a belief is reasoned the more confidently it is held. "a grocer," writes mr. bagehot in an acute essay on "the emotion of conviction,"[ ] "has a full creed as to foreign policy, a young lady a complete theory of the sacraments, as to which neither has any doubt. a girl in a country parsonage will be sure that paris never can be taken, or that bismarck is a wretch." an attitude of philosophic doubt, of suspended judgment, is repugnant to the natural man. belief is an independent joy to him. this bias works in all men. while there is life, there is pressure from within on belief, tending to push reason aside. the force of the pressure, of course, varies with individual temperament, age, and other circumstances. the young are more credulous than the old, as having greater energy: they are apt, as bacon puts it, to be "carried away by the sanguine element in their temperament". shakespeare's laertes is a study of the impulsive temperament, boldly contrasted with hamlet, who has more discourse of reason. when laertes hears that his father has been killed, he hurries home, collects a body of armed sympathisers, bursts into the presence of the king, and threatens with his vengeance--the wrong man. he never pauses to make inquiry: like hotspur he is "a wasp-stung and impatient fool"; he must wreak his revenge on somebody, and at once. hamlet's father also has been murdered, but his reason must be satisfied before he proceeds to his revenge, and when doubtful proof is offered, he waits for proof more relative. bacon's _idola tribus_ and dr. bain's illustrations of incontinent energy, are mostly examples of unreasoning intellectual activity, hurried generalisations, unsound and superficial analogies, rash hypotheses. bacon quotes the case of the sceptic in the temple of poseidon, who, when shown the offerings of those who had made vows in danger and been delivered, and asked whether he did not now acknowledge the power of the god, replied: "but where are they who made vows and yet perished?" this man answered rightly, says bacon. in dreams, omens, retributions, and such like, we are apt to remember when they come true and to forget the cases when they fail. if we have seen but one man of a nation, we are apt to conclude that all his countrymen are like him; we cannot suspend our judgment till we have seen more. confident belief, as dr. bain remarks, is the primitive attitude of the human mind: it is only by slow degrees that this is corrected by experience. the old adage, "experience teaches fools," has a meaning of its own, but in one sense it is the reverse of the truth. the mark of a fool is that he is not taught by experience, and we are all more or less intractable pupils, till our energies begin to fail. _the bias of happy exercise._ if an occupation is pleasant in itself, if it fully satisfies our inner craving for action, we are liable to be blinded thereby to its consequences. happy exercise is the fool's paradise. the fallacy lies not in being content with what provides a field for the full activity of our powers: to be content in such a case may be the height of wisdom: but the fallacy lies in claiming for our occupation results, benefits, utilities that do not really attend upon it. thus we see subjects of study, originally taken up for some purpose, practical, artistic, or religious, pursued into elaborate detail far beyond their original purpose, and the highest value, intellectual, spiritual, moral, claimed for them by their votaries, when in truth they merely serve to consume so much vacant energy, and may be a sheer waste of time that ought to be otherwise employed. but as i am in danger of myself furnishing an illustration of this bias--it is nowhere more prevalent than in philosophy--i will pass to our next head. _the bias of the feelings._ this source of illusion is much more generally understood. the blinding and perverting influence of passion on reason has been a favourite theme with moralists ever since man began to moralise, and is acknowledged in many a popular proverb. "love is blind;" "the wish is father to the thought;" "some people's geese are all swans;" and so forth. we need not dwell upon the illustration of it. fear and sloth magnify dangers and difficulties; affection can see no imperfection in its object: in the eyes of jealousy a rival is a wretch. from the nature of the case we are much more apt to see examples in others than in ourselves. if the strength of this bias were properly understood by everybody, the mistake would not so often be committed of suspecting bad faith, conscious hypocrisy, when people are found practising the grossest inconsistencies, and shutting their eyes apparently in deliberate wilfulness to facts held under their very noses. men are inclined to ascribe this human weakness to women. reasoning from feeling is said to be feminine logic. but it is a human weakness. to take one very powerful feeling, the feeling of self-love or self-interest--this operates in much more subtle ways than most people imagine, in ways so subtle that the self-deceiver, however honest, would fail to be conscious of the influence if it were pointed out to him. when the slothful man saith, there is a lion in the path, we can all detect the bias to his belief, and so we can when the slothful student says that he will work hard to-morrow, or next week, or next month; or when the disappointed man shows an exaggerated sense of the advantages of a successful rival or of his own disadvantages. but self-interest works to bias belief in much less palpable ways than those. it is this bias that accounts for the difficulty that men of antagonistic interests have in seeing the arguments or believing in the honesty of their opponents. you shall find conferences held between capitalists and workmen in which the two sides, both represented by men incapable of consciously dishonest action, fail altogether to see the force of each other's arguments, and are mutually astonished each at the other's blindness. _the bias of custom._ that custom, habits of thought and practice, affect belief, is also generally acknowledged, though the strength and wide reach of the bias is seldom realised. very simple cases of unreasoning prejudice were adduced by locke, who was the first to suggest a general explanation of them in the "association of ideas" (_human understanding_, bk. ii. ch. xxxiii.). there is, for instance, the fear that overcomes many people when alone in the dark. in vain reason tells them that there is no real danger; they have a certain tremor of apprehension that they cannot get rid of, because darkness is inseparably connected in their minds with images of horror. similarly we contract unreasonable dislikes to places where painful things have happened to us. equally unreasoning, if not unreasonable, is our attachment to customary doctrines or practices, and our invincible antipathy to those who do not observe them. words are very common vehicles for the currency of this kind of prejudice, good or bad meanings being attached to them by custom. the power of words in this way is recognised in the proverb: "give a dog a bad name, and then hang him". these verbal prejudices are bacon's _idola fori_, illusions of conversation. each of us is brought up in a certain sect or party, and accustomed to respect or dishonour certain sectarian or party names, whig, tory, radical, socialist, evolutionist, broad, low, or high church. we may meet a man without knowing under what label he walks and be charmed with his company: meet him again when his name is known, and all is changed. such errors are called fallacies of association to point to the psychological explanation. this is that by force of association certain ideas are brought into the mind, and that once they are there, we cannot help giving them objective reality. for example, a doctor comes to examine a patient, and finds certain symptoms. he has lately seen or heard of many cases of influenza, we shall say; influenza is running in his head. the idea once suggested has all the advantage of possession. but why is it that a man cannot get rid of an idea? why does it force itself upon him as a belief? association, custom, explains how it got there, but not why it persists in staying. to explain this we must call in our first fallacious principle, the impatience of doubt or delay, the imperative inward need for a belief of some sort. and this leads to another remark, that though for convenience of exposition, we separate these various influences, they are not separated in practice. they may and often do act all together, the inner sophist concentrating his forces. finally, it may be asked whether, seeing that illusions are the offspring of such highly respectable qualities as excess of energy, excess of feeling, excess of docility, it is a good thing for man to be disillusioned. the rose-colour that lies over the world for youth is projected from the abundant energy and feeling within: disillusion comes with failing energies, when hope is "unwilling to be fed". is it good then to be disillusioned? the foregoing exposition would be egregiously wrong if the majority of mankind did not resent the intrusion of reason and its organising lieutenant logic. but really there is no danger that this intrusion succeeds to the extent of paralysing action and destroying feeling, and uprooting custom. the utmost that logic can do is to modify the excess of these good qualities by setting forth the conditions of rational belief. the student who masters those conditions will soon see the practical wisdom of applying his knowledge only in cases where the grounds of rational belief are within his reach. to apply it to the consequences of every action would be to yield to that bias of incontinent activity which is, perhaps, our most fruitful source of error. [footnote : bain's _logic_, bk. vi. chap. iii. bacon intended his _idola_ to bear the same relation to his _novum organum_ that aristotle's fallacies or sophistical tricks bore to the old organum. but in truth, as i have already indicated, what bacon classifies is our inbred tendencies to form _idola_ or false images, and it is these same tendencies that make us liable to the fallacies named by aristotle. some of aristotle's, as we shall see, are fallacies of induction.] [footnote : bagehot's _literary studies_, ii. .] iii.--the axioms of dialectic and of syllogism. there are certain principles known as the laws of thought or the maxims of consistency. they are variously expressed, variously demonstrated, and variously interpreted, but in one form or another they are often said to be the foundation of all logic. it is even said that all the doctrines of deductive or syllogistic logic may be educed from them. let us take the most abstract expression of them, and see how they originated. three laws are commonly given, named respectively the law of identity, the law of contradiction and the law of excluded middle. . _the law of identity._ a is a. socrates is socrates. guilt is guilt. . _the law of contradiction._ a is not not-a. socrates is not other than socrates. guilt is not other than guilt. or a is not at once _b_ and not-_b_. socrates is not at once good and not-good. guilt is not at once punishable and not-punishable. . _the law of excluded middle._ everything is either a or not-a; or, a is either _b_ or not-_b_. a given thing is either socrates or not-socrates, either guilty or not-guilty. it must be one or the other: no middle is possible. why lay down principles so obvious, in some interpretations, and so manifestly sophistical in others? the bare forms of modern logic have been reached by a process of attenuation from a passage in aristotle's _metaphysics_[ ] (iii. , , _b_ - ). he is there laying down the first principle of demonstration, which he takes to be that "it is impossible that the same predicate can both belong, and not belong, to the same subject, at the same time, and in the same sense".[ ] that socrates knows grammar, and does not know grammar--these two propositions cannot both be true at the same time, and in the same sense. two contraries cannot exist together in the same subject. the double answer yes and no cannot be given to one and the same question understood in the same sense. but why did aristotle consider it necessary to lay down a principle so obvious? simply because among the subtle dialecticians who preceded him the principle had been challenged. the platonic dialogue euthydemus shows the farcical lengths to which such quibbling was carried. the two brothers vanquish all opponents, but it is by claiming that the answer no does not preclude the answer yes. "is not the honourable honourable, and the base base?" asks socrates. "that is as i please," replies dionysodorus. socrates concludes that there is no arguing with such men: they repudiate the first principles of dialectic. there were, however, more respectable practitioners who canvassed on more plausible grounds any form into which ultimate doctrines about contraries and contradictions, truth and falsehood, could be put, and therefore aristotle considered it necessary to put forth and defend at elaborate length a statement of a first principle of demonstration. "contradictions cannot both be true of the same subject at the same time and in the same sense." this is the original form of the law of contradiction. the words "of the same subject," "at the same time," and "in the same sense," are carefully chosen to guard against possible quibbles. "_socrates knows grammar._" by socrates we must mean the same individual man. and even of the same man the assertion may be true at one time and not at another. there was a time when socrates did not know grammar, though he knows it now. and the assertion may be true in one sense and not in another. it may be true that socrates knows grammar, yet not that he knows everything that is to be known about grammar, or that he knows as much as aristarchus. aristotle acknowledges that this first principle cannot itself be demonstrated, that is, deduced from any other. if it is denied, you can only reduce the denier to an absurdity. and in showing how to proceed in so doing, he says you must begin by coming to an agreement about the words used, that they signify the same for one and the other disputant.[ ] no dialectic is possible without this understanding. this first principle of dialectic is the original of the law of identity. while any question as to the truth or falsehood of a question is pending, from the beginning to the end of any logical process, the words must continue to be accepted in the same sense. words must have an identical reference to things. incidentally in discussing the axiom of contradiction ([greek: axiôma tês antiphaseôs]),[ ] aristotle lays down what is now known as the law of excluded middle. of two contradictories one or other must be true: we must either affirm or deny any one thing of any other: no mean or middle is possible. in their origin, then, these so-called laws of thought were simply the first principles of dialectic and demonstration. consecutive argument, coherent ratiocination, is impossible unless they are taken for granted. if we divorce or abstract them from their original application, and consider them merely as laws of thinking or of being, any abstract expression, or illustration, or designation of them may easily be pushed into antagonism with other plain truths or first principles equally rudimentary. without entering into the perplexing and voluminous discussion to which these laws have been subjected by logicians within the last hundred years, a little casuistry is necessary to enable the student to understand within what limits they hold good. _socrates is socrates._ the name socrates is a name for something to which you and i refer when we use the name. unless we have the same reference, we cannot hold any argument about the thing, or make any communication one to another about it. but if we take _socrates is socrates_ to mean that, "an object of thought or thing is identical with itself," "an object of thought or thing cannot be other than itself," and call this a law of thought, we are met at once by a difficulty. thought, properly speaking, does not begin till we pass beyond the identity of an object with itself. thought begins only when we recognise the likeness between one object and others. to keep within the self-identity of the object is to suspend thought. "socrates was a native of attica," "socrates was a wise man," "socrates was put to death as a troubler of the commonweal"--whenever we begin to think or say anything about socrates, to ascribe any attributes to him, we pass out of his self-identity into his relations of likeness with other men, into what he has in common with other men. hegelians express this plain truth with paradoxical point when they say: "of any definite existence or thought, therefore, it may be said with quite as much truth that it _is not_, as that it _is_, its own bare self".[ ] or, "a thing must other itself in order to be itself". controversialists treat this as a subversion of the laws of identity and contradiction. but it is only hegel's fun--his paradoxical way of putting the plain truth that any object has more in common with other objects than it has peculiar to itself. till we enter into those aspects of agreement with other objects, we cannot truly be said to think at all. if we say merely that a thing is itself, we may as well say nothing about it. to lay down this is not to subvert the law of identity, but to keep it from being pushed to the extreme of appearing to deny the law of likeness, which is the foundation of all the characters, attributes, or qualities of things in our thoughts. that self-same objects are like other self-same objects, is an assumption distinct from the law of identity, and any interpretation of it that excludes this assumption is to be repudiated. but does not the law of identity as well as the law of the likeness of mutually exclusive identities presuppose that there are objects self-same, like others, and different from others? certainly: this is one of the presuppositions of logic.[ ] we assume that the world of which we talk and reason is separated into such objects in our thoughts. we assume that such words as _socrates_ represent individual objects with a self-same being or substance; that such words as _wisdom_, _humour_, _ugliness_, _running_, _sitting_, _here_, _there_, represent attributes, qualities, characters or predicates of individuals; that such words as _man_ represent groups or classes of individuals. some logicians in expressing the law of identity have their eye specially upon the objects signified by general names or abstract names, _man_, _education_.[ ] "a concept is identical with the sum of its characters," or, "classes are identical with the sum of the individuals composing them". the assumptions thus expressed in technical language which will hereafter be explained are undoubtedly assumptions that logic makes: but since they are statements of the internal constitution of some of the identities that words represent, to call them the law of identity is to depart confusingly from traditional usage.[ ] that throughout any logical process a word must signify the same object, is one proposition: that the object signified by a general name is identical with the sum of the individuals to each of whom it is applicable, or with the sum of the characters that they bear in common, is another proposition. logic assumes both: aristotle assumed both: but it is the first that is historically the original of all expressions of the law of identity in modern text-books. yet another expression of a law of identity which is really distinct from and an addition to aristotle's original. _socrates was an athenian, a philosopher, an ugly man, an acute dialectician, etc._ let it be granted that the word socrates bears the same signification throughout all these and any number more of predicates, we may still ask: "but what is it that socrates signifies?" the title law of identity is sometimes given[ ] to a theory on this point. _socrates is socrates._ "an individual is the identity running through the totality of its attributes." is this not, it may be asked, to confuse thought and being, to resolve socrates into a string of words? no: real existence is one of the admissible predicates of socrates: one of the attributes under which we conceive him. but whether we accept or reject this "law of identity," it is an addition to aristotle's dialectical "law of identity"; it is a theory of the metaphysical nature of the identity signified by a singular name. and the same may be said of yet another theory of identity, that, "an individual is identical with the totality of its predicates," or (another way of putting the same theory), "an individual is a conflux of generalities". to turn next to the laws of contradiction and excluded middle. these also may be subjected to casuistry, making clearer what they assert by showing what they do not deny. they do not deny that things change, and that successive states of the same thing may pass into one another by imperceptible degrees. a thing may be neither here nor there: it may be on the passage from here to there: and, while it is in motion, we may say, with equal truth, that it is neither here nor there, or that it is both here and there. youth passes gradually into age, day into night: a given man or a given moment may be on the borderland between the two. logic does not deny the existence of indeterminate margins: it merely lays down that for purposes of clear communication and coherent reasoning the line must be drawn somewhere between _b_, and not-_b_. a difference, however, must be recognised between logical negation and the negations of common thought and common speech. the latter are definite to a degree with which the mere logic of consistency does not concern itself. to realise this is to understand more clearly the limitations of formal logic. in common speech, to deny a quality of anything is by implication to attribute to it some other quality of the same kind. let any man tell me that "the streets of such and such a town are not paved with wood," i at once conclude that they are paved with some other material. it is the legitimate effect of his negative proposition to convey this impression to my mind. if, proceeding on this, i go on to ask: "then they are paved with granite or asphalt, or this or that?" and he turns round and says: "i did not say they were paved at all," i should be justified in accusing him of a quibble. in ordinary speech, to deny one kind of pavement is to assert pavement of some kind. similarly, to deny that so-and-so is not in the twenty-first regiment, is to imply that he is in another regiment, that he is in the army in some regiment. to retort upon this inference: "he is not in the army at all," is a quibble: as much so as it would be to retort: "there is no such person in existence". now logic does not take account of this implication, and nothing has contributed more to bring upon it the reproach of quibbling. in logic, to deny a quality is simply to declare a repugnance between it and the subject; negation is mere sublation, taking away, and implies nothing more. not-_b_ is entirely indefinite: it may cover anything except _b_. is logic then really useless, or even misleading, inasmuch as it ignores the definite implication of negatives in ordinary thought and speech? in ignoring this implication, does logic oppose this implication as erroneous? does logic shelter the quibbler who trades upon it? by no means: to jump to this conclusion were a misunderstanding. the fact only is that nothing beyond the logical law of contradiction needs to be assumed for any of the processes of formal logic. aristotle required to assume nothing more for his syllogistic formulæ, and logic has not yet included in its scope any process that requires any further assumption. "if not-_b_ represent everything except _b_, everything outside _b_, then that a is _b_, and that a is not-_b_, cannot both be true, and one or other of them must be true." whether the scope of logic ought to be extended is another question. it seems to me that the scope of logic may legitimately be extended so as to take account both of the positive implication of negatives and the negative implication of positives. i therefore deal with this subject in a separate chapter following on the ordinary doctrines of immediate inference, where i try to explain the simple law of thought involved. when i say that the extension is legitimate, i mean that it may be made without departing from the traditional view of logic as a practical science, conversant with the nature of thought and its expression only in so far as it can provide practical guidance against erroneous interpretations and inferences. the extension that i propose is in effect an attempt to bring within the fold of practical logic some of the results of the dialectic of hegel and his followers, such as mr. bradley and mr. bosanquet, professor caird and professor wallace.[ ] the logical processes formulated by aristotle are merely stages in the movement of thought towards attaining definite conceptions of reality. to treat their conclusions as positions in which thought may dwell and rest, is an error, against which logic itself as a practical science may fairly be called upon to guard. it may even be conceded that the aristotelian processes are artificial stages, courses that thought does not take naturally, but into which it has to be forced for a purpose. to concede this is not to concede that the aristotelian logic is useless, as long as we have reason on our side in holding that thought is benefited and strengthened against certain errors by passing through those artificial stages. [footnote : the first statement of the law of identity in the form _ens est ens_ is ascribed by hamilton (_lectures_, iii. ) to antonius andreas, a fourteenth century commentator on the _metaphysics_. but andreas is merely expounding what aristotle sets forth in iii. , _a, b_. _ens est ens_ does not mean in andreas what a is a means in hamilton.] [footnote : greek: to gar auto hama huparchein te kai mê huparchein adynaton tô autô kai kata to auto, . . . ahutê dê pasôn esti bebaiotatê tôn archôn. iii. , _b_, - .] [footnote : hamilton credits andreas with maintaining, "against aristotle," that "the principle of identity, and not the principle of contradiction, is the one absolutely first". which comes first, is a scholastic question on which ingenuity may be exercised. but in fact aristotle put the principle of identity first in the above plain sense, and andreas only expounded more formally what aristotle had said.] [footnote : [greek: metaxu antiphaseôs endechetai einai outhen, all' anankê ê phanai ê apophanai en kath henos hotioun.] _metaph._ iii. , _b_, - .] [footnote : prof. caird's _hegel_, p. .] [footnote : see venn, _empirical logic_, - .] [footnote : _e.g._, hamilton, lect. v.; veitch's _institutes of logic_, chaps, xii., xiii.] [footnote : the confusion probably arises in this way. first, these "laws" are formulated as laws of thought that logic assumes. second, a notion arises that these laws are the only postulates of logic: that all logical doctrines can be "evolved" from them. third, when it is felt that more than the identical reference of words or the identity of a thing with itself must be assumed in logic, the law of identity is extended to cover this further assumption.] [footnote : _e.g._, bosanquet's _logic_, ii. .] [footnote : bradley, _principles of logic_; bosanquet, _logic or the morphology of knowledge_; caird, _hegel_ (in blackwood's philosophical classics); wallace, _the logic of hegel_.] book i. the logic of consistency. syllogism and definition. part i. the elements of propositions. chapter i. general names and allied distinctions. to discipline us against the errors we are liable to in receiving knowledge through the medium of words--such is one of the objects of logic, the main object of what may be called the logic of consistency. strictly speaking, we may receive knowledge about things through signs or single words, as a nod, a wink, a cry, a call, a command. but an assertory sentence, proposition, or predication, is the unit with which logic concerns itself--a sentence in which a subject is named and something is said or predicated about it. let a man once understand the errors incident to this regular mode of communication, and he may safely be left to protect himself against the errors incident to more rudimentary modes. a proposition, whether long or short, is a unit, but it is an analysable unit. and the key to syllogistic analysis is the general name. every proposition, every sentence in which we convey knowledge to another, contains a general name or its equivalent. that is to say, every proposition may be resolved into a form in which the predicate is a general name. a knowledge of the function of this element of speech is the basis of all logical discipline. therefore, though we must always remember that the proposition is the real unit of speech, and the general name only an analytic element, we take the general name and its allied distinctions in thought and reality first. how propositions are analysed for syllogistic purposes will be shown by-and-by, but we must first explain various technical terms that logicians have devised to define the features of this cardinal element. the technical terms class, concept, notion, attribute, extension or denotation, intension or connotation, genus, species, differentia, singular name, collective name, abstract name, all centre round it. a general name is a name applicable to a number of different things on the ground of some likeness among them, as _man_, _ratepayer_, _man of courage_, _man who fought at waterloo_. from the examples it will be seen that a general name logically is not necessarily a single word. any word or combination of words that serves a certain function is technically a general name. the different ways of making in common speech the equivalent of a general name logically are for the grammarian to consider. in the definition of a general name attention is called to two distinct considerations, the individual objects to each of which the name is applicable, and the points of resemblance among them, in virtue of which they have a common name. for those distinctions there are technical terms. class is the technical term for the objects, different yet agreeing, to each of which a general name may be applied. the points of resemblance are called the common attributes of the class. a class may be constituted on one attribute or on several. _ratepayer_, _woman ratepayer_, _unmarried woman ratepayer_; _soldier_, _british soldier_, _british soldier on foreign service_. but every individual to which the general name can be applied must possess the common attribute or attributes. these common attributes are also called the notion of the class, inasmuch as it is these that the mind notes or should note when the general name is applied. concept is a synonym perhaps in more common use than notion; the rationale of this term (derived from _con_ and _capere_, to take or grasp together) being that it is by means of the points of resemblance that the individuals are grasped or held together by the mind. these common points are the one in the many, the same amidst the different, the identity signified by the common name. the name of an attribute as thought of by itself without reference to any individual or class possessing it, is called an abstract name. by contradistinction, the name of an individual or a class is concrete. technical terms are wanted also to express the relation of the individuals and the attributes to the general name. the individuals jointly are spoken of as the denotation, or extension or scope of the name; the common attributes as its connotation, intension, comprehension, or ground. the whole denotation, etc., is the class; the whole connotation, etc., is the concept.[ ] the limits of a "class" in logic are fixed by the common attributes. any individual object that possesses these is a member. the statement of them is the definition. to predicate a general name of any object, as, "this is a cat," "this is a very sad affair," is to refer that object to a class, which is equivalent to saying that it has certain features of resemblance with other objects, that it reminds us of them by its likeness to them. thus to say that the predicate of every proposition is a general name, expressed or implied, is the same as to say that every predication may be taken as a reference to a class. ordinarily our notion or concept of the common features signified by general names is vague and hazy. the business of logic is to make them clear. it is to this end that the individual objects of the class are summoned before the mind. in ordinary thinking there is no definite array or muster of objects: when we think of "dog" or "cat," "accident," "book," "beggar," "ratepayer," we do not stop to call before the mind a host of representatives of the class, nor do we take precise account of their common attributes. the concept of "house" is what all houses have in common. to make this explicit would be no easy matter, and yet we are constantly referring objects to the class "house". we shall see presently that if we wish to make the connotation or concept clear we must run over the denotation or class, that is to say, the objects to which the general name is applied in common usage. try, for example, to conceive clearly what is meant by house, tree, dog, walking-stick. you think of individual objects, so-called, and of what they have in common. a class may be constituted on one property or on many. there are several points common to all houses, enclosing walls, a roof, a means of exit and entrance. for the full concept of the natural kinds, _men_, _dogs_, _mice_, etc., we should have to go to the natural historian. degrees of generality. one class is said to be of higher generality than another when it includes that other and more. thus animal includes man, dog, horse, etc.; man includes aryan, semite, etc.; aryan includes hindoo, teuton, celt, etc. the technical names for higher and lower classes are genus and species. these terms are not fixed as in natural history to certain grades, but are purely relative one to another, and movable up and down a scale of generality. a class may be a species relatively to one class, which is above it, and a genus relatively to one below it. thus aryan is a species of the genus man, teuton a species of the genus aryan. in the graded divisions of natural history genus and species are fixed names for certain grades. thus: vertebrates form a "division"; the next subdivision, _e.g._, mammals, birds, reptiles, etc., is called a "class"; the next, _e.g_., rodents, carnivora, ruminants, an "order"; the next, _e.g._, rats, squirrels, beavers, a "genus"; the next, _e.g._, brown rats, mice, a "species". vertebrates (division). | mammals, birds, reptiles, etc. (class). | rodents, ruminants, carnivors, etc. (order). | rats, squirrels, beavers, etc. (genus). | brown rats, mice, etc. (species). if we subdivide a large class into smaller classes, and, again, subdivide these subdivisions, we come at last to single objects. men | ------------ europeans, asiatics, etc. | ------------- englishmen, frenchmen, etc. | --------------------- john doe, richard roe, etc. a table of higher and lower classes arranged in order has been known from of old as a _tree_ of division or classification. the following is porphyry's "tree":-- being / \ corporeal incorporeal \ / (body) / \ animate inanimate \ / (living being) / \ sensible insensible \ / (animal) / \ rational irrational \ / (man) | --------------------------------------- socrates, plato, and other individuals. the single objects are called individuals, because the division cannot be carried farther. the highest class is technically the summum genus, or _genus generalissimum_; the next highest class to any species is the proximum genus; the lowest group before you descend to individuals is the infima species, or _species specialissima_. the attribute or attributes whereby a species is distinguished from other species of the same genus, is called its differentia or differentiÆ. the various species of houses are differentiated by their several uses, dwelling-house, town-house, ware-house, public-house. poetry is a species of fine art, its differentia being the use of metrical language as its instrument. a lower class, indicated by the name of its higher class qualified by adjectives or adjective phrases expressing its differential property or properties, is said to be described per genus et differentiam. examples: "black-bird," "note-book," "clever man," "man of kent," "eminent british painter of marine subjects". by giving a combination of attributes common to him with nobody else, we may narrow down the application of a name to an individual: "the commander-in-chief of the british forces at the battle of waterloo". other attributes of classes as divided and defined, have received technical names. an attribute common to all the individuals of a class, found in that class only, and following from the essential or defining attributes, though not included among them, is called a proprium. an attribute that belongs to some, but not to all, or that belongs to all, but is not a necessary consequence of the essential attributes, is called an accident. the clearest examples of propria are found in mathematical figures. thus, the defining property of an equilateral triangle is the equality of the sides: the equality of the angles is a proprium. that the three angles of a triangle are together equal to two right angles is a proprium, true of all triangles, and deducible from the essential properties of a triangle. outside mathematics, it is not easy to find _propria_ that satisfy the three conditions of the definition. it is a useful exercise of the wits to try for such. educability--an example of the proprium in mediæval text-books--is common to men, and results from man's essential constitution; but it is not peculiar; other animals are educable. that man cooks his food is probably a genuine proprium. that horses run wild in thibet: that gold is found in california: that clergymen wear white ties, are examples of accidents. learning is an accident in man, though educability is a proprium. what is known technically as an inseparable accident, such as the black colour of the crow or the ethiopian, is not easy to distinguish from the proprium. it is distinguished only by the third character, deducibility from the essence.[ ] accidents that are both common and peculiar are often useful for distinguishing members of a class. distinctive dresses or badges, such as the gown of a student, the hood of a d.d., are accidents, but mark the class of the individual wearer. so with the colours of flowers. _genus_, _species_, _differentia_, _proprium_, and _accidens_ have been known since the time of porphyry as the five predicables. they are really only terms used in dividing and defining. we shall return to them and endeavour to show that they have no significance except with reference to fixed schemes, scientific or popular, of division or classification. given such a fixed scheme, very nice questions may be raised as to whether a particular attribute is a defining attribute, or a proprium, or an accident, or an inseparable accident. such questions afford great scope for the exercise of the analytic intellect. we shall deal more particularly with degrees of generality when we come to definition. this much has been necessary to explain an unimportant but much discussed point in logic, what is known as the inverse variation of connotation and denotation. connotation and denotation are often said to vary inversely in quantity. the larger the connotation the smaller the denotation, and _vice versâ_. with certain qualifications the statement is correct enough, but it is a rough compendious way of expressing the facts and it needs qualification. the main fact to be expressed is that the more general a name is, the thinner is its meaning. the wider the scope, the shallower the ground. as you rise in the scale of generality, your classes are wider but the number of common attributes is less. inversely, the name of a species has a smaller denotation than the name of its genus, but a richer connotation. _fruit-tree_ applies to fewer objects than _tree_, but the objects denoted have more in common: so with _apple_ and _fruit-tree_, _ribston pippin_ and _apple_. again, as a rule, if you increase the connotation you contract the area within which the name is applicable. take any group of things having certain attributes in common, say, _men of ability_: add _courage_, _beauty_, _height of six feet_, _chest measurement of inches_, and with each addition fewer individuals are to be found possessing all the common attributes. this is obvious enough, and yet the expression inverse variation is open to objection. for the denotation may be increased in a sense without affecting the connotation. the birth of an animal may be said to increase the denotation: every year thousands of new houses are built: there are swarms of flies in a hot summer and few in a cold. but all the time the connotation of _animal_, _house_, or _fly_ remains the same: the word does not change its meaning. it is obviously wrong to say that they vary in inverse proportion. double or treble the number of attributes, and you do not necessarily reduce the denotation by one-half or one-third. it is, in short, the meaning or connotation that is the main thing. this determines the application of a word. as a rule if you increase meaning, you restrict scope. let your idea, notion, or concept of _culture_ be a knowledge of mathematics, latin and greek: your _men of culture_ will be more numerous than if you require from each of them these qualifications _plus_ a modern language, an acquaintance with the fine arts, urbanity of manners, etc. it is just possible to increase the connotation without decreasing the denotation, to thicken or deepen the concept without diminishing the class. this is possible only when two properties are exactly co-extensive, as equilaterality and equiangularity in triangles. singular and proper names. a proper or singular name is a name used to designate an individual. its function, as distinguished from that of the general name, is to be used purely for the purpose of distinctive reference. a man is not called tom or dick because he is like in certain respects to other toms or other dicks. the toms or the dicks do not form a logical class. the names are given purely for purposes of distinction, to single out an individual subject. the arabic equivalent for a proper name, _alam_, "a mark," "a sign-post," is a recognition of this. in the expressions "a napoleon," "a hotspur," "a harry," the names are not singular names logically, but general names logically, used to signify the possession of certain attributes. a man may be nicknamed on a ground, but if the name sticks and is often used, the original meaning is forgotten. if it suggests the individual in any one of his qualities, any point in which he resembles other individuals, it is no longer a proper or singular name logically, that is, in logical function. that function is fulfilled when it has called to mind the individual intended. to ask, as is sometimes done, whether proper names are connotative or denotative, is merely a confusion of language. the distinction between connotation and denotation, extension and intension, applies only to general names. unless a name is general, it has neither extension nor intension:[ ] a proper or singular name is essentially the opposite of a general name and has neither the one nor the other. a nice distinction may be drawn between proper and singular names, though they are strict synonyms for the same logical function. it is not essential to the discharge of that function that the name should be strictly appropriated to one object. there are many toms and many dicks. it is enough that the word indicates the individual without confusion in the particular circumstances. this function may be discharged by words and combinations of words that are not proper in the grammatical sense. "this man," "the cover of this book," "the prime minister of england," "the seer of chelsea," may be singular names as much as honolulu or lord tennyson. in common speech singular names are often manufactured _ad hoc_ by taking a general name and narrowing it down by successive qualifications till it applies only to one individual, as "the leading subject of the sovereign of england at the present time". if it so happens that an individual has some attribute or combination peculiar to himself, he may be suggested by the mention of that attribute or combination:--"the inventor of the steam-engine," "the author of hudibras". have such names a connotation? the student may exercise his wits on the question. it is a nice one, an excellent subject of debate. briefly, if we keep rigid hold of the meaning of connotation, this singular name has none. the combination is a singular name only when it is the subject of a predication or an attribution, as in the sentences, "the position of the leading subject of etc., is a difficult one," or "the leading subject of etc., wears an eyeglass". in such a sentence as "so-and-so is the leading subject of etc.," the combined name has a connotation, but then it is a general and not a singular name. collective names, as distinguished from general names. a collective name is a name for a number of similar units taken as a whole--a name for a totality of similar units, as army, regiment, mob, mankind, patrimony, personal estate. a group or collection designated by a collective name is so far like a class that the individual objects have something in common: they are not heterogeneous but homogeneous. a mob is a collection of human beings; a regiment of soldiers; a library of books. the distinction lies in this, that whatever is said of a collective name is said about the collection as a whole, and does not apply to each individual; whatever is said of a general name applies to each individual. further, the collective name can be predicated only of the whole group, as a whole; the general name is predicable of each, distributively. "mankind has been in existence for thousands of years;" "the mob passed through the streets." in such expressions as "an honest man's the noblest work of god," the subject is functionally a collective name. a collective name may be used as a general name when it is extended on the ground of what is common to all such totalities as it designates. "an excited mob is dangerous;" "an army without discipline is useless." the collective name is then "connotative" of the common characters of the collection. material or substantial names. the question has been raised whether names of material, gold, water, snow, coal, are general or collective singular. in the case of pieces or bits of a material, it is true that any predicate made concerning the material, such as "sugar is sweet," or "water quenches thirst," applies to any and every portion. but the separate portions are not individuals in the whole signified by a material name as individuals are in a class. further, the name of material cannot be predicated of a portion as a class name can be of an individual. we cannot say, "this is a sugar". when we say, "this is a piece of sugar," sugar is a collective name for the whole material. there are probably words on the borderland between general names and collective names. in such expressions as "this is a _coal_," "the bonnie _water_ o' urie," the material name is used as a general name. the real distinction is between the distributive use and the collective use of a name; as a matter of grammatical usage, the same word may be used either way, but logically in any actual proposition it must be either one or the other. abstract names are names for the common attributes or concepts on which classes are constituted. a concrete name is a name directly applicable to an individual in all his attributes, that is, as he exists in the concrete. it may be written on a ticket and pinned to him. when we have occasion to speak of the point or points in which a number of individuals resemble one another, we use what is called an abstract name. "generous man," "clever man," "timid man," are concrete names; "generosity," "cleverness," "timidity," are abstract names. it is disputed whether abstract names are connotative. the question is a confused one: it is like asking whether the name of a town is municipal. an abstract name is the name of a connotation as a separate object of thought or reference, conceived or spoken of in abstraction from individual accidents. strictly speaking it is notative rather than _con_notative: it cannot be said to have a connotation because it is itself the symbol of what is called the connotation of a general name.[ ] the distinction between abstract names and concrete names is virtually a grammatical distinction, that is, a distinction in mode of predication. we may use concrete names or abstract names at our pleasure to express the same meaning. to say that "john is a timid man" is the same thing as saying that "timidity is one of the properties or characteristics or attributes of john". "pride and cruelty generally go together;" "proud men are generally cruel men." general names are predicable of individuals because they possess certain attributes: to predicate the possession of those attributes is the same thing as to predicate the general name. abstract forms of predication are employed in common speech quite as frequently as concrete, and are, as we shall see, a great source of ambiguity and confusion. [footnote : it has been somewhat too hastily assumed on the authority of mansel (note to aldrich, pp. , ) that mill inverted the scholastic tradition in his use of the word _connotative_. mansel puts his statement doubtfully, and admits that there was some licence in the use of the word connotative, but holds that in scholastic logic an adjective was said to "signify _primarily_ the attribute, and to _connote_ or _signify secondarily_ ([greek: prossêmainein]) the subject of inhesion". the truth is that mansel's view was a theory of usage not a statement of actual usage, and he had good reason for putting it doubtfully. as a matter of fact, the history of the distinction follows the simple type of increasing precision and complexity, and mill was in strict accord with standard tradition. by the nominalist commentators on the _summulæ_ of petrus hispanus certain names, adjectives grammatically, are called _connotativa_ as opposed to _absoluta_, simply because they have a double function. white is connotative as signifying both a subject, such as socrates, of whom "whiteness" is an attribute, and an attribute "whiteness": the names "socrates" and "whiteness" are absolute, as having but a single signification. occam himself speaks of the subject as the primary signification, and the attribute as the secondary, because the answer to "what is white?" is "something informed with whiteness," and the subject is in the nominative case while the attribute is in an oblique case (_logic_, part i. chap. x.). later on we find that tataretus (_expositio in summulas_, a.d. ), while mentioning (tract. sept. _de appellationibus_) that it is a matter of dispute among doctores whether a connotative name _connotat_ the subject or the attribute, is perfectly explicit in his own definition, "terminus connotativus est qui præter illud pro quo supponit connotat aliquid adjacere vel non adjacere rei pro qua supponit" (tract. sept. _de suppositionibus_). and this remained the standard usage as long as the distinction remained in logical text-books. we find it very clearly expressed by clichtoveus, a nominalist, quoted as an authority by guthutius in his _gymnasium speculativum_, paris, (_de terminorum cognitione_, pp. - ). "terminus absolutus est, qui solum illud pro quo in propositione supponit, significat. connotativus autem, qui ultra idipsum, aliud importat." thus _man_ and _animal_ are absolute terms, which simply stand for (supponunt pro) the things they signify. _white_ is a connotative name, because "it stands for (supponit pro) a subject in which it is an accident: and beyond this, still signifies an accident, which is in that subject, and is expressed by an abstract name". only clichtoveus drops the verb _connotat_, perhaps as a disputable term, and says simply _ultra importat_. so in the port royal logic ( ), from which possibly mill took the distinction: "les noms qui signifient les choses comme modifiées, marquant premièrement et directement la chose, quoique plus confusément, et indirectement le mode, quoique plus distinctement, sont appelés _adjectifs_ ou _connotatifs_; comme rond, dur, juste, prudent" (part i. chap ii.). what mill did was not to invert scholastic usage but to revive the distinction, and extend the word connotative to general names on the ground that they also imported the possession of attributes. the word has been as fruitful of meticulous discussion as it was in the renaissance of logic, though the ground has changed. the point of mill's innovation was, premising that general names are not absolute but are applied in virtue of a meaning, to put emphasis on this meaning as the cardinal consideration. what he called the connotation had dropped out of sight as not being required in the syllogistic forms. this was as it were the point at which he put in his horn to toss the prevalent conception of logic as syllogistic. the real drift of mill's innovation has been obscured by the fact that it was introduced among the preliminaries of syllogism, whereas its real usefulness and significance belongs not to syllogism in the strict sense but to definition. he added to the confusion by trying to devise forms of syllogism based on connotation, and by discussing the axiom of the syllogism from this point of view. for syllogistic purposes, as we shall see, aristotle's forms are perfect, and his conception of the proposition in extension the only correct conception. whether the centre of gravity in consistency logic should not be shifted back from syllogism to definition, the latter being the true centre of consistency, is another question. the tendency of mill's polemic was to make this change. and possibly the secret of the support it has recently received from mr. bradley and mr. bosanquet is that they, following hegel, are moving in the same direction. in effect, mill's doctrine of connotation helped to fix a conception of the general name first dimly suggested by aristotle when he recognised that names of genera and species signify quality, in showing what sort a thing is. occam carried this a step farther towards clear light by including among connotative terms such general names as "monk," name of classes that at once suggest a definite attribute. the third step was made by mill in extending the term connotation to such words as "man," "horse," the _infimæ species_ of the schoolmen, the species of modern science. whether connotation was the best term to use for this purpose, rather than extension, may be questioned: but at least it was in the line of tradition through occam.] [footnote : the history of the definition of the _proprium_ is an example of the tendency of distinctions to become more minute and at the same time more purposeless. aristotle's [greek: idion] was an attribute, such as the laugh of the man or the bark of the dog, common to all of a class and peculiar to the class (_quod convenit omni soli et semper_) yet not comprised in the definition of the class. porphyry recognised three varieties of [greek: idia] besides this, four in all, as follows:--( ) an attribute peculiar to a species but not possessed by all, as knowledge of medicine or geometry; ( ) possessed by a whole species but not peculiar to it, as being a biped in man; ( ) peculiar to a species, and possessed by all at a certain time, as turning grey in old age; ( ) aristotle's "proprium," peculiar and possessed by all, as risibility. the idea of the proprium as deducible from or consequent on the essence would seem to have originated in the desire to find something common to all poryphyry's four varieties.] [footnote : it is a plausible contention that in the case of the singular name the extension is at a minimum and the intension at a maximum, the extension being one individual, and the intension the totality of his attributes. but this is an inexact and confused use of words. a name does not _extend_ beyond the individual except when it is used to signify one or more of his prominent qualities, that is, is used with the function of a general name. the _ex_tension of a singular name is zero: it has no extension. on the other hand, it suggests, in its function as a singular name, no properties or qualities; it suggests only a subject; _i.e._, it has no intension. the ambiguity of the term denotation helps the confusion in the case of singular names. "denote" in common speech means to indicate, to distinguish. but when in logic we say that a general name denotes individuals, we have no thought of indicating or distinguishing: we mean only that it is applicable to any one, without respect of individuals, either in predication or epithetic description.] [footnote : strictly speaking, as i have tried to indicate all along, the words connotation and denotation, or extension and intension, apply only to general names. outside general names, they have no significance. an adjective with its noun is a general name, of which the adjective gives part of the connotation. if we apply the word connotation to signify merely the suggestion of an attribute in whatever grammatical connexion, then an abstract name is undoubtedly as much connotative as an adjective. the word _sweetness_ has the same meaning as _sweet_: it indicates or signifies, conveys to the mind of the reader the same attribute: the only difference is that it does not at the same time indicate a subject in which the attribute is found, as _sweet apple_. the meaning is not _con_noted.] chapter ii. the syllogistic analysis of propositions into terms. i.--the bare analytic forms. the word "term" is loosely used as a mere synonym for a name: strictly speaking, a term ([greek: horos], a boundary) is one of the parts of a proposition as analysed into subject and predicate. in logic, a term is a technical word in an analysis made for a special purpose, that purpose being to test the mutual consistency of propositions. for this purpose, the propositions of common speech may be viewed as consisting of two terms, a linkword called the copula (positive or negative) expressing a relation between them, and certain symbols of quantity used to express that relation more precisely. let us indicate the subject term by s, and the predicate term by p. all propositions may be analysed into one or other of four forms:-- all s is p, no s is p, some s is p, some s is not p. all s is p is called the universal affirmative, and is indicated by the symbol a (the first vowel of affirmo). no s is p is called the universal negative, symbol e (the first vowel of nego). some s is p is called the particular affirmative, symbol i (the second vowel of _aff_irmo). some s is not p is called the particular negative, symbol o (the second vowel of _neg_o). the distinction between universal and particular is called a distinction in quantity; between affirmative and negative, a distinction in quality. a and e, i and o, are of the same quantity, but of different quality: a and i, e and o, same in quality, different in quantity. in this symbolism, no provision is made for expressing degrees of particular quantity. _some_ stands for any number short of all: it may be one, few, most, or all but one. the debates in which aristotle's pupils were interested turned mainly on the proof or disproof of general propositions; if only a proposition could be shown to be not universal, it did not matter how far or how little short it came. in the logic of probability, the degree becomes of importance. distinguish, in this analysis, to avoid subsequent confusion, between the subject and the subject term, the predicate and the predicate term. the subject is the subject term quantified: in a and e,[ ] "all s"; in i and o, "some s". the predicate is the predicate term with the copula, positive or negative: in a and i, "is p"; in e and o, "is not p". it is important also, in the interest of exactness, to note that s and p, with one exception, represent general names. they are symbols for classes. p is so always: s also except when the subject is an individual object. in the machinery of the syllogism, predications about a singular term are treated as universal affirmatives. "socrates is a wise man" is of the form all s is p. s and p being general names, the signification of the symbol "is" is not the same as the "is" of common speech, whether the substantive verb or the verb of incomplete predication. in the syllogistic form, "is" means _is contained in_, "is not," _is not contained in_. the relations between the terms in the four forms are represented by simple diagrams known as euler's circles. [illustration: concentric circles of p and s - s in centre a s and p in the same circle a s and p each in a circle, overlapping circle. i & o s in one circle and p in another circle. e concentric circles of s and p - p in centre i? ] diagram is a purely artificial form, having no representative in common speech. in the affirmations of common speech, p is always a term of greater extent than s. no. represents the special case where s and p are coextensive, as in all equiangular triangles are equilateral. s and p being general names, they are said to be distributed when the proposition applies to them in their whole extent, that is, when the assertion covers every individual in the class. in e, the universal negative, both terms are distributed: "no s is p" wholly excludes the two classes one from the other, imports that not one individual of either is in the other. in a, s is distributed, but not p. s is wholly in p, but nothing is said about the extent of p beyond s. in o, s is undistributed, p is distributed. a part of s is declared to be wholly excluded from p. in i, neither s nor p is distributed. it will be seen that the predicate term of a negative proposition is always distributed, of an affirmative, always undistributed. a little indistinctness in the signification of p crept into mediæval text-books, and has tended to confuse modern disputation about the import of predication. unless p is a class name, the ordinary doctrine of distribution is nonsense; and euler's diagrams are meaningless. yet many writers who adopt both follow mediæval usage in treating p as the equivalent of an adjective, and consequently "is" as identical with the verb of incomplete predication in common speech. it should be recognised that these syllogistic forms are purely artificial, invented for a purpose, namely, the simplification of syllogising. aristotle indicated the precise usage on which his syllogism is based (_prior analytics_, i. and ). his form[ ] for all s is p, is s is wholly in p; for no s is p, s is wholly not in p. his copula is not "is," but "is in," and it is a pity that this usage was not kept. "all s is in p" would have saved much confusion. but, doubtless for the sake of simplicity, the besetting sin of tutorial handbooks, all s is p crept in instead, illustrated by such examples as "all men are mortal". thus the "is" of the syllogistic form became confused with the "is" of common speech, and the syllogistic view of predication as being equivalent to inclusion in, or exclusion from a class, was misunderstood. the true aristotelian doctrine is not that predication consists in referring subjects to classes, but only that for certain logical purposes it may be so regarded. the syllogistic forms are artificial forms. they were not originally intended to represent the actual processes of thought expressed in common speech. to argue that when i say "all crows are black," i do not form a class of black things, and contemplate crows within it as one circle is within another, is to contradict no intelligent logical doctrine. the root of the confusion lies in quoting sentences from common speech as examples of the logical forms, forgetting that those forms are purely artificial. "omnis homo est mortalis," "all men are mortal," is not an example formally of all s is p. p is a symbol for a substantive word or combination of words, and mortal is an adjective. strictly speaking, there is no formal equivalent in common speech, that is, in the forms of ordinary use--no strict grammatical formal equivalent--for the syllogistic propositional symbols. we can make an equivalent, but it is not a form that men would use in ordinary intercourse. "all man is in mortal being" would be a strict equivalent, but it is not english grammar. instead of disputing confusedly whether all s is p should be interpreted in extension or in comprehension, it would be better to recognise the original and traditional use of the symbols s and p as class names, and employ other symbols for the expression in comprehension or connotation. thus, let _s_ and _p_ stand for the connotation. then the equivalent for all s is p would be all s has _p_, or _p_ always accompanies _s_, or _p_ belongs to all s. it may be said that if predication is treated in this way, logic is simplified to the extent of childishness. and indeed, the manipulation of the bare forms with the help of diagrams and mnemonics is a very humble exercise. the real discipline of syllogistic logic lies in the reduction of common speech to these forms. this exercise is valuable because it promotes clear ideas about the use of general names in predication, their ground in thought and reality, and the liabilities to error that lurk in this fundamental instrument of speech. [footnote : for perfect symmetry, the form of e should be all s is not p. "no s is p" is adopted for e to avoid conflict with a form of common speech, in which all s is not p conveys the meaning of the particular negative. "all advices are not safe" does not mean that safeness is denied of all advices, but that safeness cannot be affirmed of all, _i.e._, not all advices are safe, _i.e._, some are not.] [footnote : his most precise form, i should say, for in "p is predicated of every s" he virtually follows common speech.] ii.--the practice of syllogistic analysis. the basis of the analysis is the use of general names in predication. to say that in predication a subject is referred to a class, is only another way of saying that in every categorical sentence the predicate is a general name express or implied: that it is by means of general names that we convey our thoughts about things to others. "milton is a great poet." "quoth hudibras, _i smell a rat_." _great poet_ is a general name: it means certain qualities, and applies to anybody possessing them. _quoth_ implies a general name, a name for persons _speaking_, connoting or meaning a certain act and applicable to anybody in the performance of it. _quoth_ expresses also past time: thus it implies another general name, a name for persons _in past time_, connoting a quality which differentiates a species in the genus persons speaking, and making the predicate term "persons speaking in past time". thus the proposition _quoth hudibras_, analysed into the syllogistic form s is in p, becomes s (hudibras) is in p (persons speaking in past time). the predicate term p is a class constituted on those properties. _smell a rat_ also implies a general name, meaning an act or state predicable of many individuals. even if we add the grammatical object of _quoth_ to the analysis, the predicate term is still a general name. hudibras is only one of the persons speaking in past time who have spoken of themselves as being in a certain mood of suspicion.[ ] the learner may well ask what is the use of twisting plain speech into these uncouth forms. the use is certainly not obvious. the analysis may be directly useful, as aristotle claimed for it, when we wish to ascertain exactly whether one proposition contradicts another, or forms with another or others a valid link in an argument. this is to admit that it is only in perplexing cases that the analysis is of direct use. the indirect use is to familiarise us with what the forms of common speech imply, and thus strengthen the intellect for interpreting the condensed and elliptical expression in which common speech abounds. there are certain technical names applied to the components of many-worded general names, categorematic and syncategorematic, subject and attributive. the distinctions are really grammatical rather than logical, and of little practical value. a word that can stand by itself as a term is said to be categorematic. _man_, _poet_, or any other common noun. a word that can only form part of a term is syncategorematic. under this definition come all adjectives and adverbs. the student's ingenuity may be exercised in applying the distinction to the various parts of speech. a verb may be said to be _hypercategorematic_, implying, as it does, not only a term, but also a copula. a nice point is whether the adjective is categorematic or syncategorematic. the question depends on the definition of "term" in logic. in common speech an adjective may stand by itself as a predicate, and so might be said to be categorematic. "this heart is merry." but if a term is a class, or the name of a class, it is not categorematic in the above definition. it can only help to specify a class when attached to the name of a higher genus. mr. fowler's words subject and attributive express practically the same distinction, except that attributive is of narrower extent than syncategorematic. an attributive is a word that connotes an attribute or property, as _hot_, _valorous_, and is always grammatically an adjective. the expression of quantity, that is, of universality or non-universality, is all-important in syllogistic formulæ. in them universality is expressed by _all_ or _none_. in ordinary speech universality is expressed in various forms, concrete and abstract, plain and figurative, without the use of "all" or "none". uneasy lies the head that wears a crown. he can't be wrong whose life is in the right. what cat's averse to fish? can the leopard change his spots? the longest road has an end. suspicion ever haunts the guilty mind. irresolution is always a sign of weakness. treason never prospers. a proposition in which the quantity is not expressed is called by aristotle indefinite ([greek: adioristos]). for "indefinite"[ ] hamilton suggests preindesignate, undesignated, that is, before being received from common speech for the syllogistic mill. a proposition is predesignate when the quantity is definitely indicated. all the above propositions are "predesignate" universals, and reducible to the form all s is p, or no s is p. the following propositions are no less definitely particular, reducible to the form i or o. in them as in the preceding quantity is formally expressed, though the forms used are not the artificial syllogistic forms:-- afflictions are often salutary. not every advice is a safe one. all that glitters is not gold. rivers generally[ ] run into the sea. often, however, it is really uncertain from the form of common speech whether it is intended to express a universal or a particular. the quantity is not formally expressed. this is especially the case with proverbs and loose floating sayings of a general tendency. for example:-- haste makes waste. knowledge is power. light come, light go. left-handed men are awkward antagonists. veteran soldiers are the steadiest in fight. such sayings are in actual speech for the most part delivered as universals.[ ] it is a useful exercise of the socratic kind to decide whether they are really so. this can only be determined by a survey of facts. the best method of conducting such a survey is probably ( ) to pick out the concrete subject, "hasty actions," "men possessed of knowledge," "things lightly acquired"; ( ) to fix the attribute or attributes predicated; ( ) to run over the individuals of the subject class and settle whether the attribute is as a matter of fact meant to be predicated of each and every one. this is the operation of induction. if one individual can be found of whom the attribute is not meant to be predicated, the proposition is not intended as universal. mark the difference between settling what is intended and settling what is true. the conditions of truth and the errors incident to the attempt to determine it, are the business of the logic of rational belief, commonly entitled inductive logic. the kind of "induction" here contemplated has for its aim merely to determine the quantity of a proposition in common acceptation, which can be done by considering in what cases the proposition would generally be alleged. this corresponds nearly as we shall see to aristotelian induction, the acceptance of a universal statement when no instance to the contrary is alleged. it is to be observed that for this operation we do not practically use the syllogistic form all s is p. we do not raise the question is all s, p? that is, we do not constitute in thought a class p: the class in our minds is s, and what we ask is whether an attribute predicated of this class is truly predicated of every individual of it. suppose we indicate by _p_ the attribute, knot of attributes, or concept on which the class p is constituted, then all s is p is equivalent to "all s has _p_": and has all s _p_? is the form of a question that we have in our minds when we make an inductive survey on the above method. i point this out to emphasise the fact that there is no prerogative in the form all s is p except for syllogistic purposes. this inductive survey may be made a useful collateral discipline. the bare forms of syllogistic are a useless item of knowledge unless they are applied to concrete thought. and determining the quantity of a common aphorism or saw, the limits within which it is meant to hold good, is a valuable discipline in exactness of understanding. in trying to penetrate to the inner intention of a loose general maxim, we discover that what it is really intended to assert is a general connexion of attributes, and a survey of concrete cases leads to a more exact apprehension of those attributes. thus in considering whether _knowledge is power_ is meant to be asserted of all knowledge, we encounter along with such examples as the sailor's knowledge that wetting a rope shortens it, which enabled some masons to raise a stone to its desired position, or the knowledge of french roads possessed by the german invaders,--along with such examples as these we encounter cases where a knowledge of difficulties without a knowledge of the means of overcoming them is paralysing to action. samuel daniel says:-- where timid knowledge stands considering audacious ignorance has done the deed. studying numerous cases where "knowledge is power" is alleged or denied, we find that what is meant is that a knowledge of the right means of doing anything is power--in short, that the predicate is not made of all knowledge, but only of a species of knowledge. take, again, _custom blunts sensibility_. putting this in the concrete, and inquiring what predicate is made about "men accustomed to anything" (s), we have no difficulty in finding examples where such men are said to become indifferent to it. we find such illustrations as lovelace's famous "paradox":-- through foul we follow fair for had the world one face and earth been bright as air we had known neither place. indians smell not their nest the swiss and finn taste best the spices of the east. so men accustomed to riches are not acutely sensible of their advantages: dwellers in noisy streets cease to be distracted by the din: the watchmaker ceases to hear the multitudinous ticking in his shop: the neighbours of chemical works are not annoyed by the smells like the casual passenger. but we find also that wine-tasters acquire by practice an unusual delicacy of sense; that the eyes once accustomed to a dim light begin to distinguish objects that were at first indistinguishable; and so on. what meanings of "custom" and of "sensibility" will reconcile these apparently conflicting examples? what are the exact attributes signified by the names? we should probably find that by sensibility is meant emotional sensibility as distinguished from intellectual discrimination, and that by custom is meant familiarity with impressions whose variations are not attended to, or subjection to one unvarying impression. to verify the meaning of abstract proverbs in this way is to travel over the road by which the greek dialecticians were led to feel the importance of definition. of this more will be said presently. if it is contended that such excursions are beyond the bounds of formal logic, the answer is that the exercise is a useful one and that it starts naturally and conveniently from the formulæ of logic. it is the practice and discipline that historically preceded the aristotelian logic, and in the absence of which the aristotelian formulæ would have a narrowing and cramping effect. can all propositions be reduced to the syllogistic form? probably: but this is a purely scientific inquiry, collateral to practical logic. the concern of practical logic is chiefly with forms of proposition that favour inaccuracy or inexactness of thought. when there is no room for ambiguity or other error, there is no virtue in artificial syllogistic form. the attempt so to reduce any and every proposition may lead, however, to the study of what mr. bosanquet happily calls the "morphology" of judgment, judgment being the technical name for the mental act that accompanies the utterance of a proposition. even in such sentences as "how hot it is!" or "it rains," the rudiment of subject and predicate may be detected. when a man says "how hot it is," he conveys the meaning, though there is no definitely formed subject in his mind, that the outer world at the moment of his speaking has a certain quality or attribute. so with "it rains". the study of such examples in their context, however, reveals the fact that the same form of common speech may cover different subjects and predicates in different connexions. thus in the argument:-- "whatever is, is best. it rains!"-- the subject is _rain_ and the predicate _is now_, "is at the present time," "is in the class of present events". [footnote : remember that when we speak of a general name, we do not necessarily mean a single word. a general name, logically viewed, is simply the name of a _genus_, kind, or class: and whether this is single-worded or many-worded is, strictly speaking, a grammatical question. "man," "man-of-ability," "man-of-ability-and-courage," "man-of-ability-and-courage-and-gigantic-stature," "man-who-fought-at-marathon"--these are all general names in their logical function. no matter how the constitutive properties of the class are indicated, by one word or in combination, that word or combination is a general name. in actual speech we can seldom indicate by a single word the meaning predicated.] [footnote : the objection taken to the word "indefinite," that the quantity of particular propositions is indefinite, _some_ meaning any quantity less than all, is an example of the misplaced and frivolous subtlety that has done so much to disorder the tradition of logic. by "indefinite" is simply meant not definitely expressed as either universal or particular, total or partial. the same objection might be taken to any word used to express the distinction: the degree of quantity in some s is not "designate" any more than it is "definite" or "dioristic".] [footnote : _generally._ in this word we have an instance of the frequent conflict between the words of common speech and logical terminology. how it arises shall be explained in next chapter. a general proposition is a synonym for a universal proposition (if the forms a and e are so termed): but "generally" in common speech means "for the most part," and is represented by the symbol of particular quantity, _some_.] [footnote : with some logicians it is a mechanical rule in reducing to syllogistic form to treat as i or o all sentences in which there is no formal expression of quantity. this is to err on the safe side, but common speakers are not so guarded, and it is to be presumed rather that they have a universal application in their minds when they do not expressly qualify.] iii.--some technical difficulties. _the formula for_ exclusive propositions. "none but the brave deserve the fair": "no admittance except on business": "only protestants can sit on the throne of england". these propositions exemplify different ways in common speech of naming a subject _exclusively_, the predication being made of all outside a certain term. "none that are not brave, etc.;" "none that are not on business, etc.;" "none that are not protestants, etc.". no not-s is p. it is only about all outside the given term that the universal assertion is made: we say nothing universally about the individuals within the term: we do not say that all protestants are eligible, nor that all persons on business are admitted, nor that every one of the brave deserves the fair. all that we say is that the possession of the attribute named is an indispensable condition: a person may possess the attribute, and yet on other grounds may not be entitled to the predicate. the justification for taking special note of this form in logic is that we are apt by inadvertence to make an inclusive inference from it. let it be said that none but those who work hard can reasonably expect to pass, and we are apt to take this as meaning that all who work hard may reasonably expect to pass. but what is denied of every not-s is not necessarily affirmed of every s. _the expression of_ tense or time _in the syllogistic forms_. seeing that the copula in s is p or s is in p does not express time, but only a certain relation between s and p, the question arises where are we to put time in the analytic formula? "wheat is dear;" "all had fled;" time is expressed in these propositions, and our formula should render the whole content of what is given. are we to include it in the predicate term or in the subject term? if it must not be left out altogether, and we cannot put it with the copula, we have a choice between the two terms. it is a purely scholastic question. the common technical treatment is to view the tense as part of the predicate. "all had fled," all s is p, _i.e._, the whole subject is included in a class constituted on the attributes of flight at a given time. it may be that the predicate is solely a predicate of time. "the board met yesterday at noon." s is p, _i.e._, the meeting of the board is one of the events characterised by having happened at a certain time, agreeing with other events in that respect. but in some cases the time is more properly regarded as part of the subject. _e.g._, "wheat is dear". s does not here stand for wheat collectively, but for the wheat now in the market, the wheat of the present time: it is concerning this that the attribute of dearness is predicated; it is this that is in the class of dear things. _the expression of_ modality _in the syllogistic forms_. propositions in which the predicate is qualified by an expression of necessity, contingency, possibility or impossibility [_i.e._, in english by _must_, _may_, _can_, or _cannot_], were called in mediæval logic _modal_ propositions. "two and two _must_ make four." "grubs _may_ become butterflies." "z _can_ paint." "y _cannot_ fly." there are two recognised ways of reducing such propositions to the form s is p. one is to distinguish between the _dictum_ and the _mode_, the proposition and the qualification of its certainty, and to treat the _dictum_ as the subject and the _mode_ as the predicate. thus: "that two and two make four is necessary"; "that y can fly is impossible". the other way is to treat the mode as part of the predicate. the propriety of this is not obvious in the case of necessary propositions, but it is unobjectionable in the case of the other three modes. thus: "grubs are things that have the potentiality of becoming butterflies"; "z has the faculty of painting"; "y has not the faculty of flying". the chief risk of error is in determining the quantity of the subject about which the contingent or possible predicate is made. when it is said that "victories may be gained by accident," is the predicate made concerning all victories or some only? here we are apt to confuse the meaning of the contingent assertion with the matter of fact on which in common belief it rests. it is true only that some victories have been gained by accident, and it is on this ground that we assert in the absence of certain knowledge concerning any victory that it may have been so gained. the latter is the effect of the contingent assertion: it is made about any victory in the absence of certain knowledge, that is to say, formally about all. the history of modals in logic is a good illustration of intricate confusion arising from disregard of a clear traditional definition. the treatment of them by aristotle was simple, and had direct reference to tricks of disputation practised in his time. he specified four "modes," the four that descended to mediæval logic, and he concerned himself chiefly with the import of contradicting these modals. what is the true contradictory of such propositions as, "it is possible to be" ([greek: dynaton einai]), "it admits of being" ([greek: endechetai einai]), "it must be" ([greek: anankaion einai]), "it is impossible to be" ([greek: adynaton einai])? what is implied in saying "no" to such propositions put interrogatively? "is it possible for socrates to fly?" "no." does this mean that it is not possible for socrates to fly, or that it is possible for socrates not to fly? a disputant who had trapped a respondent into admitting that it is possible for socrates not to fly, might have pushed the concession farther in some such way as this: "is it possible for socrates not to walk?" "certainly." "is it possible for him to walk?" "yes." "when you say that it is possible for a man to do anything do you not believe that it is possible for him to do it?" "yes." "but you have admitted that it is possible for socrates not to fly?" it was in view of such perplexities as these that aristotle set forth the true contradictories of his four modals. we may laugh at such quibbles now and wonder that a grave logician should have thought them worth guarding against. but historically this is the origin of the modals of formal logic, and to divert the names of them to signify other distinctions than those between modes of qualifying the certainty of a statement is to introduce confusion. thus we find "alexander was a great general," given as an example of a contingent modal, on the ground that though as a matter of fact alexander was so he might have been otherwise. it was not _necessary_ that alexander should be a great general: therefore the proposition is _contingent_. now the distinction between necessary truth and contingent truth may be important philosophically: but it is merely confusing to call the character of propositions as one or the other by the name of modality. the original modality is a mode of expression: to apply the name to this character is to shift its meaning. a more simple and obviously unwarrantable departure from tradition is to extend the name modality to any grammatical qualification of a single verb in common speech. on this understanding "alexander conquered darius" is given by hamilton as a _pure_ proposition, and "alexander conquered darius honourably" as a _modal_. this is a merely grammatical distinction, a distinction in the mode of composing the predicate term in common speech. in logical tradition modality is a mode of qualifying the certainty of an affirmation. "the conquest of darius by alexander was honourable," or "alexander in conquering darius was an honourable conqueror," is the syllogistic form of the proposition: it is simply assertory, not qualified in any "mode". there is a similar misunderstanding in mr. shedden's treatment of "generally" as constituting a modal in such sentences, as "rivers _generally_ flow into the sea". he argues that as _generally_ is not part either of the subject term or of the predicate term, it must belong to the copula, and is therefore a _modal_ qualification of the whole assertion. he overlooked the fact that the word "generally" is an expression of quantity: it determines the quantity of the subject term. finally it is sometimes held (_e.g._, by mr. venn) that the question of modality belongs properly to scientific or inductive logic, and is out of place in formal logic. this is so far accurate that it is for inductive logic to expound the conditions of various degrees of certainty. the consideration of modality is pertinent to formal logic only in so far as concerns special perplexities in the expression of it. the treatment of it by logicians has been rendered intricate by torturing the old tradition to suit different conceptions of the end and aim of logic. part ii. definition. chapter i. imperfect understanding of words and the remedies therefor.--dialectic.--definition. we cannot inquire far into the meaning of proverbs or traditional sayings without discovering that the common understanding of general and abstract names is loose and uncertain. common speech is a quicksand. consider how we acquire our vocabulary, how we pick up the words that we use from our neighbours and from books, and why this is so soon becomes apparent. theoretically we know the full meaning of a name when we know all the attributes that it connotes, and we are not justified in extending it except to objects that possess all the attributes. this is the logical ideal, but between the _ought to be_ of logic and the _is_ of practical life, there is a vast difference. how seldom do we conceive words in their full meaning! and who is to instruct us in the full meaning? it is not as in the exact sciences, where we start with a knowledge of the full meaning. in geometry, for example, we learn the definitions of the words used, _point_, _line_, _parallel_, etc., before we proceed to use them. but in common speech, we learn words first in their application to individual cases. nobody ever defined _good_ to us, or _fair_, or _kind_, or _highly educated_. we hear the words applied to individual objects: we utter them in the same connexion: we extend them to other objects that strike us as like without knowing the precise points of likeness that the convention of common speech includes. the more exact meaning we learn by gradual induction from individual cases. _ugly_, _beautiful_, _good_, _bad_--we learn the words first as applicable to things and persons: gradually there arises a more or less definite sense of what the objects so designated have in common. the individual's extension of the name proceeds upon what in the objects has most impressed him when he caught the word: this may differ in different individuals; the usage of neighbours corrects individual eccentricities. the child in arms shouts _da_ at the passing stranger who reminds him of his father: for him at first it is a general name applicable to every man: by degrees he learns that for him it is a singular name. the mode in which words are learnt and extended may be studied most simply in the nursery. a child, say, has learnt to say _mambro_ when it sees its nurse. the nurse works a hand-turned sewing machine, and sings to it as she works. in the street the child sees an organ-grinder singing as he turns his handle: it calls _mambro_: the nurse catches the meaning and the child is overjoyed. the organ-grinder has a monkey: the child has an india-rubber monkey toy: it calls this also _mambro_. the name is extended to a monkey in a picture-book. it has a toy musical box with a handle: this also becomes _mambro_, the word being extended along another line of resemblance. a stroller with a french fiddle comes within the denotation of the word: a towel-rail is also called _mambro_ from some fancied resemblance to the fiddle. a very swarthy hunch-back _mambro_ frightens the child: this leads to the transference of the word to a terrific coalman with a bag of coals on his back. in a short time the word has become a name for a great variety of objects that have nothing whatever common to all of them, though each is strikingly like in some point to a predecessor in the series. when the application becomes too heterogeneous, the word ceases to be of use as a sign and is gradually abandoned, the most impressive meaning being the last to go. in a child's vocabulary where the word _mambro_ had a run of nearly two years, its last use was as an adjective signifying ugly or horrible. the history of such a word in a child's language is a type of what goes on in the language of men. in the larger history we see similar extensions under similar motives, checked and controlled in the same way by surrounding usage. it is obvious that to avoid error and confusion, the meaning or connotation of names, the concepts, should somehow be fixed: names cannot otherwise have an identical reference in human intercourse. we may call this ideal fixed concept the logical concept: or we may call it the scientific concept, inasmuch as one of the main objects of the sciences is to attain such ideals in different departments of study. but in actual speech we have also the personal concept, which varies more or less with the individual user, and the popular or vernacular concept, which, though roughly fixed, varies from social sect to social sect and from generation to generation. the variations in popular concepts may be traced in linguistic history. words change with things and with the aspects of things, as these change in public interest and importance. as long as the attributes that govern the application of words are simple, sensible attributes, little confusion need arise: the variations are matters of curious research for the philologist, but are logically insignificant. murray's dictionary, or such books as trench's _english past and present_, supply endless examples, as many, indeed as there are words in the language. _clerk_ has almost as many connotations as our typical _mambro_: clerk in holy orders, church clerk, town clerk, clerk of assize, grocer's clerk. in early english, the word meant "man in a religious order, cleric, clergyman"; ability to read, write, and keep accounts being a prominent attribute of the class, the word was extended on this simple ground till it has ceased altogether to cover its original field except as a formal designation. but no confusion is caused by the variation, because the property connoted is simple.[ ] so with any common noun: street, carriage, ship, house, merchant, lawyer, professor. we might be puzzled to give an exact definition of such words, to say precisely what they connote in common usage; but the risk of error in the use of them is small. when we come to words of which the logical concept is a complex relation, an obscure or intangible attribute, the defects of the popular conception and its tendencies to change and confusion, are of the greatest practical importance. take such words as _monarchy_, _tyranny_, _civil freedom_, _freedom of contract_, _landlord_, _gentleman_, _prig_, _culture_, _education_, _temperance_, _generosity_. not merely should we find it difficult to give an analytic definition of such words: we might be unable to do so, and yet flatter ourselves that we had a clear understanding of their meaning. but let two men begin to discuss any proposition in which any such word is involved, and it will often be found that they take the word in different senses. if the relation expressed is complex, they have different sides or lines of it in their minds; if the meaning is an obscure quality, they are guided in their application of it by different outward signs. monarchy, in its original meaning, is applied to a form of government in which the will of one man is supreme, to make laws or break them, to appoint or dismiss officers of state and justice, to determine peace or war, without control of statute or custom. but supreme power is never thus uncontrolled in reality; and the word has been extended to cover governments in which the power of the titular head is controlled in many different modes and degrees. the existence of a head, with the title of king or emperor, is the simplest and most salient fact: and wherever this exists, the popular concept of a monarchy is realised. the president of the united states has more real power than the sovereign of great britain; but the one government is called a republic and the other a monarchy. people discuss the advantages and disadvantages of monarchy without first deciding whether they take the word in its etymological sense of unlimited power, or its popular sense of titular kingship, or its logical sense of power definitely limited in certain ways. and often in debate, monarchy is really a singular term for the government of great britain. _culture_, _religious_, _generous_, are names for inward states or qualities: with most individuals some simple outward sign directs the application of the word--it may be manner, or bearing, or routine observances, or even nothing more significant than the cut of the clothes or of the hair. small things undoubtedly are significant, and we must judge by small things when we have nothing else to go by: but instead of trying to get definite conceptions for our moral epithets, and suspending judgment till we know that the use of the epithet is justified, the trifling superficial sign becomes for us practically the whole meaning of the word. we feel that we must have a judgment of some sort at once: only simple signs are suited to our impatience. it was with reference to this state of things that hegel formulated his paradox that the true abstract thinker is the plain man who laughs at philosophy as what he calls abstract and unpractical. he holds decided opinions for or against this or the other abstraction, _freedom_, _tyranny_, _revolution_, _reform_, _socialism_, but what these words mean and within what limits the things signified are desirable or undesirable, he is in too great a hurry to pause and consider. the disadvantages of this kind of "abstract" thinking are obvious. the accumulated wisdom of mankind is stored in language. until we have cleared our conceptions, and penetrated to the full meaning of words, that wisdom is a sealed book to us. wise maxims are interpreted by us hastily in accordance with our own narrow conceptions. all the vocables of a language may be more or less familiar to us, and yet we may not have learnt it as an instrument of thought. outside the very limited range of names for what we see and use in the daily routine of life, food and clothes and the common occupations of men, words have little meaning for us, and are the vehicles merely of thin preconceptions and raw prejudices. the remedy for "abstract" thinking is more thinking, and in pursuing this two aims may be specified for the sake of clearness, though they are closely allied, and progress towards both may often be made by one and the same operation. ( ) we want to reach a clear and full conception of the meaning of names as used now or at a given time. let us call this the _verification of the meaning_. ( ) we want to fix such conceptions, and if necessary readjust their boundaries. this is the province of _definition_, which cannot be effectually performed without _scientific classification_ or _division_. i.--verification of the meaning--dialectic. this can only be done by assembling the objects to which the words are applied, and considering what they have in common. to ascertain the actual connotation we must run over the actual denotation. and since in such an operation two or more minds are better than one, discussion or dialectic is both more fruitful and more stimulating than solitary reflection or reading. the first to practise this process on a memorable scale, and with a distinct method and purpose, was socrates. to insist upon the necessity of clear conceptions, and to assist by his dialectic procedure in forming them, was his contribution to philosophy. his plan was to take a common name, profess ignorance of its meaning, and ask his interlocutor whether he would apply it in such and such an instance, producing one after another. according to xenophon's _memorabilia_ he habitually chose the commonest names, _good_, _unjust_, _fitting_, and so forth, and tried to set men thinking about them, and helped them by his questions to form an intelligent conception of the meaning. for example, what is the meaning of injustice? would you say that the man who cheats or deceives is unjust? suppose a man deceives his enemies, is there any injustice in that? can the definition be that a man who deceives his friends is unjust? but there are cases where friends are deceived for their own good: are these cases of injustice? a general may inspirit his soldiers by a falsehood. a man may cajole a weapon out of his friend's hand when he sees him about to commit suicide. a father may deceive his son into taking medicine. would you call these men unjust? by some such process of interrogation we are brought to the definition that a man is unjust who deceives his friends to their hurt. observe that in much of his dialectic the aim of socrates was merely to bring out the meaning lying vague and latent, as it were, in the common mind. his object was simply what we have called the verification of the meaning. and a dialectic that confines itself to the consideration of what is ordinarily meant as distinct from what ought to be meant may often serve a useful purpose. disputes about words are not always as idle as is sometimes supposed. mr. h. sidgwick truly remarks (_à propos_ of the terms of political economy) that there is often more profit in seeking a definition than in finding it. conceptions are not merely cleared but deepened by the process. mr. sidgwick's remarks are so happy that i must take leave to quote them: they apply not merely to the verification of ordinary meaning but also to the study of special uses by authorities, and the reasons for those special uses. "the truth is--as most readers of plato know, only it is a truth difficult to retain and apply--that what we gain by discussing a definition is often but slightly represented in the superior fitness of the formula that we ultimately adopt; it consists chiefly in the greater clearness and fulness in which the characteristics of the matter to which the formula refers have been brought before the mind in the process of seeking for it. while we are apparently aiming at definitions of terms, our attention should be really fixed on distinctions and relations of fact. these latter are what we are concerned to know, contemplate, and as far as possible arrange and systematise; and in subjects where we cannot present them to the mind in ordinary fulness by the exercise of the organs of sense, there is no way of surveying them so convenient as that of reflecting on our use of common terms.... in comparing different definitions our aim should be far less to decide which we ought to adopt, than to apprehend and duly consider the grounds on which each has commended itself to reflective minds. we shall generally find that each writer has noted some relation, some resemblance or difference, which others have overlooked; and we shall gain in completeness, and often in precision, of view by following him in his observations, whether or not we follow him in his conclusions."[ ] mr. sidgwick's own discussions of _wealth_, _value_, and _money_ are models. a clue is often found to the meaning in examining startlingly discrepant statements connected with the same leading word. thus we find some authorities declaring that "style" cannot be taught or learnt, while others declare that it can. but on trying to ascertain what they mean by "style," we find that those who say it cannot be taught mean either a certain marked individual character or manner of writing--as in buffon's saying, _le style c'est l'homme même_--or a certain felicity and dignity of expression, while those who say style can be taught mean lucid method in the structure of sentences or in the arrangement of a discourse. again in discussions on the rank of poets, we find different conceptions of what constitutes greatness in poetry lying at the root of the inclusion of this or the other poet among great poets. we find one poet excluded from the first rank of greatness because his poetry was not serious; another because his poetry was not widely popular; another because he wrote comparatively little; another because he wrote only songs or odes and never attempted drama or epic. these various opinions point to different conceptions of what constitutes greatness in poets, different connotations of "great poet". comparing different opinions concerning "education" we may be led to ask whether it means more than instruction in the details of certain subjects, whether it does not also import the formation of a disposition to learn or an interest in learning or instruction in a certain method of learning. historically, dialectic turning on the use of words preceded the attempt to formulate principles of definition, and attempts at precise definition led to division and classification, that is to systematic arrangement of the objects to be defined. attempt to define any such word as "education," and you gradually become sensible of the needs in respect of method that forced themselves upon mankind in the history of thought. you soon become aware that you cannot define it by itself alone; that you are beset by a swarm of more or less synonymous words, _instruction_, _discipline_, _culture_, _training_, and so on; that these various words represent distinctions and relations among things more or less allied; and that, if each must be fixed to a definite meaning, this must be done with reference to one another and to the whole department of things that they cover. the first memorable attempts at scientific arrangement were aristotle's treatises on ethics and politics, which had been the subjects of active dialectic for at least a century before. that these the most difficult of all departments to subject to scientific treatment should have been the first chosen was due simply to their preponderating interest: "the proper study of mankind is man". the systems of what are known as the natural sciences are of modern origin: the first, that of botany, dates from cesalpinus in the sixteenth century. but the principles on which aristotle proceeded in dividing and defining, principles which have gradually themselves been more precisely formulated, are principles applicable to all systematic arrangements for purposes of orderly study. i give them in the precise formulæ which they have gradually assumed in the tradition of logic. the principles of division are often given in formal logic, and the principles of classification in inductive logic, but there is no valid reason for the separation. the classification of objects in the natural sciences, of animals, plants, and stones, with a view to the thorough study of them in form, structure, and function, is more complex than classifications for more limited purposes, and the tendency is to restrict the word classification to these elaborate systems. but really they are only a series of divisions and subdivisions, and the same principles apply to each of the subordinate divisions as well as to the division of the whole department of study. ii.--principles of division or classification and definition. confusion in the boundaries of names arises from confused ideas regarding the resemblances and differences of things. as a protective against this confusion, things must be clearly distinguished in their points of likeness and difference, and this leads to their arrangement in systems, that is, to division and classification. a name is not secure against variation until it has a distinct place in such a system as a symbol for clearly distinguished attributes. nor must we forget, further, that systems have their day, that the best system attainable is only temporary, and may have to be recast to correspond with changes of things and of man's way of looking at them. the leading principles of division may be stated as follows:-- i. every division is made on the ground of differences in some attribute common to all the members of the whole to be divided. this is merely a way of stating what a logical division is. it is a division of a generic whole or _genus_, an indefinite number of objects thought of together as possessing some common character or attribute. all have this attribute, which is technically called the _fundamentum divisionis_, or generic attribute. but the whole is divisible into smaller groups (_species_), each of which possesses the common character with a difference (_differentia_). thus, mankind may be divided into white men, black men, yellow men, on ground of the differences in the colour of their skins: all have skins of some colour: this is the _fundamentum divisionis_: but each subdivision or species has a different colour: this is the _differentia_. rectilineal figures are divided into triangles, quadrangles, pentagons, etc., on the ground of differences in the number of angles. unless there is a _fund. div._, _i.e._, unless the differences are differences in a common character, the division is not a logical division. to divide men into europeans, opticians, tailors, blondes, brunettes, and dyspeptics is not to make a logical division. this is seen more clearly in connexion with the second condition of a perfect division. ii. in a perfect division, the subdivisions or species are mutually exclusive. every object possessing the common character should be in one or other of the groups, and none should be in more than one. confusion between classes, or overlapping, may arise from two causes. it may be due ( ) to faulty division, to want of unity in the _fundamentum divisionis_; ( ) to the indistinct character of the objects to be defined. ( ) unless the division is based upon a single ground, unless each species is based upon some mode of the generic character, confusion is almost certain to arise. suppose the field to be divided, the objects to be classified, are three-sided rectilineal plane figures, each group must be based upon some modification of the three sides. divide them into equilateral, isosceles, and scalene according as the three sides are all of equal length, or two of equal length, or each of different length, and you have a perfect division. similarly you can divide them perfectly according to the character of the angles into acute-angled, right-angled and obtuse-angled. but if you do not keep to a single basis, as in dividing them into equilateral, isosceles, scalene, and right-angled, you have a cross-division. the same triangle might be both right-angled and isosceles. ( ) overlapping, however, may be unavoidable in practice owing to the nature of the objects. there may be objects in which the dividing characters are not distinctly marked, objects that possess the differentiæ of more than one group in a greater or less degree. things are not always marked off from one another by hard and fast lines. they shade into one another by imperceptible gradations. a clear separation of them may be impossible. in that case you must allow a certain indeterminate margin between your classes, and sometimes it may be necessary to put an object into more than one class. to insist that there is no essential difference unless a clear demarcation can be made is a fallacy. a sophistical trick called the _sorites_ or heap from the classical example of it was based upon this difficulty of drawing sharp lines of definition. assuming that it is possible to say how many stones constitute a heap, you begin by asking whether three stones form a heap. if your respondent says no, you ask whether four stones form a heap, then five, and so on and he is puzzled to say when the addition of a single stone makes that a heap which was not a heap before. or you may begin by asking whether twenty stones form a heap, then nineteen, then eighteen, and so on, the difficulty being to say when what was a heap ceases to be so. where the objects classified are mixed states or affections, the products of interacting factors, or differently interlaced or interfused growths from common roots, as in the case of virtues, or emotions, or literary qualities, sharp demarcations are impossible. to distinguish between wit and humour, or humour and pathos, or pathos and sublimity is difficult because the same composition may partake of more than one character. the specific characters cannot be made rigidly exclusive one of another. even in the natural sciences, where the individuals are concrete objects of perception, it may be difficult to decide in which of two opposed groups an object should be included. sydney smith has commemorated the perplexities of naturalists over the newly discovered animals and plants of botany bay, in especial with the _ornithorynchus_,--"a quadruped as big as a large cat, with the eyes, colour, and skin of a mole, and the bill and web-feet of a duck--puzzling dr. shaw, and rendering the latter half of his life miserable, from his utter inability to determine whether it was a bird or a beast". iii. the classes in any scheme of division should be of co-ordinate rank. the classes may be mutually exclusive, and yet the division imperfect, owing to their not being of equal rank. thus in the ordinary division of the parts of speech, parts, that is, of a sentence, prepositions and conjunctions are not co-ordinate in respect of function, which is the basis of the division, with nouns, adjectives, verbs, and adverbs. the preposition is a part of a phrase which serves the same function as an adjective, _e.g._, _royal_ army, army _of the king_; it is thus functionally part of a part, or a particle. so with the conjunction: it also is a part of a part, _i.e._, part of a clause serving the function of adjective or adverb. iv. the basis of division (_fundamentum divisionis_) should be an attribute admitting of important differences. the importance of the attribute chosen as basis may vary with the purpose of the division. an attribute that is of no importance in one division, may be important enough to be the basis of another division. thus in a division of houses according to their architectural attributes, the number of windows or the rent is of little importance; but if houses are taxed or rated according to the number of windows or the rent, these attributes become important enough to be a basis of division for purposes of taxation or rating. they then admit of important differences. that the importance is relative to the purpose of the division should be borne in mind because there is a tendency to regard attributes that are of importance in any familiar or pre-eminent division as if they had an absolute importance. in short, disregard of this relativity is a fallacy to be guarded against. in the sciences, the purpose being the attainment and preservation of knowledge, the objects of study are divided so as to serve that purpose. groups must be formed so as to bring together the objects that have most in common. the question, who are to be placed together? in any arrangement for purposes of study, receives the same answer for individuals and for classes that have to be grouped into higher classes, namely, those that have most in common. this is what dr. bain happily calls "the golden rule" of scientific classification: "of the various groupings of resembling things, preference is given to such as have the greatest number of attributes in common". i slightly modify dr. bain's statement: he says "the most numerous and the most important attributes in common". but for scientific purposes number of attributes constitutes importance, as is well recognised by dr. fowler when he says that the test of importance in an attribute proposed as a basis of classification is the number of other attributes of which it is an index or invariable accompaniment. thus in zoology the squirrel, the rat, and the beaver are classed together as rodents, the difference between their teeth and the teeth of other mammalia being the basis of division, because the difference in teeth is accompanied by differences in many other properties. so the hedge-hog, the shrew-mouse, and the mole, though very unlike in outward appearance and habits, are classed together as insectivora, the difference in what they feed on being accompanied by a number of other differences. _the principles of_ definition. the word "definition" as used in logic shows the usual tendency of words to wander from a strict meaning and become ambiguous. throughout most of its uses it retains this much of a common signification, the fixing or determining of the boundaries of a class[ ] by making clear its constituent attributes. now in this making clear two processes may be distinguished, a material process and a verbal process. we have ( ) the clearing up of the common attributes by a careful examination of the objects included in the class: and we have ( ) the statement of these common attributes in language. the rules of definition given by dr. bain, who devotes a separate book in his logic to the subject of definition, concern the first of these processes: the rules more commonly given concern mainly the second. one eminent merit in dr. bain's treatment is that it recognises the close connexion between definition and classification. his cardinal rules are reduced to two. i. _assemble for comparison representative individuals of the class._ ii. _assemble for comparison representative individuals of the contrasted class or classes._ seeing that the contrasted classes are contrasted on some basis of division, this is in effect to recognise that you cannot clearly define any class except in a scheme of classification. you must have a wide _genus_ with its _fundamentum divisionis_, and, within this, _species_ distinguished by their several _differentiæ_. next, as to the verbal process, rules are commonly laid down mostly of a trifling and obvious character. that "a definition should state neither more nor less than the common attributes of the class," or than the attributes signified by the class-name, is sometimes given as a rule of definition. this is really an explanation of what a definition is, a definition of a definition. and as far as mere statement goes it is not strictly accurate, for when the attributes of a genus are known it is not necessary to give all the attributes of the species, which include the generic attributes as well, but it is sufficient to give the generic name and the differentia. thus poetry may be defined as "a fine art having metrical language as its instrument". this is technically known as definition _per genus et differentiam_. this mode of statement is a recognition of the connexion between definition and division. the rule that "a definition should not be a synonymous repetition of the name of the class to be defined," is too obvious to require formal statement. to describe a viceroy as a man who exercises viceregal functions, may have point as an epigram in the case of a _faineant_ viceroy, but it is not a definition. so with the rule that "a definition should not be couched in ambiguous unfamiliar, or figurative language". to call the camel "the ship of the desert" is a suggestive and luminous description of a property, but it is not a definition. so with the noble description of faith as "the substance of things hoped for, the evidence of things not seen". but if one wonders why so obvious a "rule" should be laid down, the answer is that it has its historical origin in the caprices of two classes of offenders, mystical philosophers and pompous lexicographers.[ ] that "the definition should be simply convertible with the term for the class defined," so that we may say, for example, either: "wine is the juice of the grape," or, "the juice of the grape is wine," is an obvious corollary from the nature of definition, but should hardly be dignified with the name of a "rule". _the principles of_ naming. rules have been formulated for the choice of names in scientific definition and classification, but it may be doubted whether such choice can be reduced to precise rule. it is enough to draw attention to certain considerations obvious enough on reflection. we may take for granted that there should be distinct names for every defining attribute (a _terminology_) and for every group or class (a _nomenclature_). what about the selection of the names? suppose an investigator is struck with likenesses and differences that seem to him important enough to be the basis of a new division, how should he be guided in his choice of names for the new groups that he proposes? should he coin new names, or should he take old names and try to fit them with new definitions? the balance of advantages is probably in favour of dr. whewell's dictum that "in framing scientific terms, the appropriation of old words is preferable to the invention of new ones". only care must be taken to keep as close as possible to the current meaning of the old word, and not to run counter to strong associations. this is an obvious precept with a view to avoiding confusion. suppose, for example, that in dividing governments you take the distribution of political power as your basis of division and come to the conclusion that the most important differences are whether this power is vested in a few or in the majority of the community. you want names to fix this broad division. you decide instead of coining the new word _pollarchy_ to express the opposite of _oligarchy_ to use the old words _republic_ and _oligarchy_. you would find, as sir george cornewall lewis found, that however carefully you defined the word republic, a division under which the british government had to be ranked among republics would not be generally understood and accepted. using the word in the sense explained above, mr. bagehot maintained that the constitution of great britain was more republican than that of the united states, but his meaning was not taken except by a few. the difficulty in choosing between new words and old words to express new meanings is hardly felt in the exact sciences. it is at least at a minimum. the innovator may encounter violent prejudice, but, arguing with experts, he can at least make sure of being understood, if his new division is based upon real and important differences. but in other subjects the difficulty of transmitting truth or of expressing it in language suited for precise transmission, is almost greater than the difficulty of arriving at truth. between new names and old names redefined, the possessor of fresh knowledge, assuming it to be perfectly verified, is in a quandary. the objects with which he deals are already named in accordance with loose divisions resting on strong prejudices. the names in current use are absolutely incapable of conveying his meaning. he must redefine them if he is to use them. but in that case he runs the risk of being misunderstood from people being too impatient to master his redefinition. his right to redefine may even be challenged without any reference to the facts to be expressed: he may simply be accused of circulating false linguistic coin, of debasing the verbal currency. the other alternative open to him is to coin new words. in that case he runs the risk of not being read at all. his contribution to verified knowledge is passed by as pedantic and unintelligible. there is no simple rule of safety: between scylla and charybdis the mariner must steer as best he may. practically the advantage lies with old words redefined, because thereby discussion is provoked and discussion clears the air. whether it is best to attempt a formal definition or to use words in a private, peculiar, or esoteric sense, and leave this to be gathered by the reader from the general tenor of your utterances, is a question of policy outside the limits of logic. it is for the logician to expound the method of definition and the conditions of its application: how far there are subjects that do not admit of its application profitably must be decided on other grounds. but it is probably true that no man who declines to be bound by a formal definition of his terms is capable of carrying them in a clear unambiguous sense through a heated controversy. [footnote : except, perhaps, in new offices to which the name is extended, such as _clerk_ of school board. the name, bearing its most simple and common meaning, may cause popular misapprehension of the nature of the duties. any uncertainty in meaning may be dangerous in practice: elections have been affected by the ambiguity of this word.] [footnote : sidgwick's _political economy_, pp. - . ed. .] [footnote : some logicians, however, speak of defining a thing, and illustrate this as if by a thing they meant a concrete individual, the realistic treatment of universals lending itself to such expressions. but though the authority of aristotle might be claimed for this, it is better to confine the name in strictness to the main process of defining a class. since, however, the method is the same whether it is an individual or a class that we want to make distinct, there is no harm in the extension of the word definition to both varieties. see davidson's _logic of definition_, chap. ii.] [footnote : see davidson's _logic of definition_, chap. iii.] chapter ii. the five predicables.--verbal and real predication. we give a separate chapter to this topic out of respect for the space that it occupies in the history of logic. but except as an exercise in subtle distinction for its own sake, all that falls to be said about the predicables might be given as a simple appendix to the chapter on definition. primarily, the five predicables or heads of predicables--genus, species, differentia, proprium, and accidens--are not predicables at all, but merely a list or enumeration of terms used in dividing and defining on the basis of attributes. they have no meaning except in connexion with a fixed scheme of division. given such a scheme, and we can distinguish in it the whole to be divided (the _genus_), the subordinate divisions (the _species_), the attribute or combination of attributes on which each species is constituted (the _differentia_), and other attributes, which belong to some or all of the individuals but are not reckoned for purposes of division and definition (_propria_ and _accidentia_). the list is not itself a logical division: it is heterogeneous, not homogeneous; the two first are names of classes, the three last of attributes. but corresponding to it we might make a homogeneous division of attributes, as follows:-- attributes ___________|____________ | | defining non-defining _____|______ ____|__________ | | | | generic specific proprium accidens (differentia) the origin of the title predicables as applied to these five terms is curious, and may be worth noting as an instance of the difficulty of keeping names precise, and of the confusion arising from forgetting the purpose of a name. porphyry in his [greek: eisagôgê] or introduction explains the five words ([greek: phônai]) simply as terms that it is useful for various purposes to know, expressly mentioning definition and division. but he casually remarks that singular names, "this man," "socrates," can be predicated only of one individual, whereas _genera_, _species_, _differentiæ_, etc., are predicables of many. that is to say he describes them as predicables simply by contradistinction from singular names. a name, however, was wanted for the five terms taken all together, and since they are not a logical division, but merely a list of terms used in dividing and defining, there was no apt general designation for them such as would occur spontaneously. thus it became the custom to refer to them as the predicables, a means of reference to them collectively being desiderated, while the meaning of this descriptive title was forgotten. to call the five divisional elements or _divisoria_ predicables is to present them as a division of predicate terms on the basis of their relation to the subject term: to suggest that every predicate term must be either a genus or a species, or a differentia, or a proprium, or an accidens of the subject term. they are sometimes criticised as such, and it is rightly pointed out that the predicate is never a species of or with reference to the subject. but, in truth, the five so-called predicables were never meant as a division of predicates in relation to the subject: it is only the title that makes this misleading suggestion. to complete the confusion it so happens that aristotle used three of the five terms in what was virtually a division of predicates inasmuch as it was a division of problems or questions. in expounding the methods of dialectic in the topica he divided problems into four classes according to the relation of the predicate to the subject. the predicate must either be simply convertible with the subject or not. if simply convertible, the two must be coextensive, and the predicate must be either a proprium or the definition. if not simply convertible, the predicate must either be part of the definition or not. if part of the definition it must be either a generic property or a differentia (both of which in this connexion aristotle includes under genus): if not part of the definition, it is an accident. aristotle thus arrives at a fourfold division of problems or predicates:--[greek: genos] (_genus_, including _differentia_, [greek: diaphora]); [greek: horos] (definition); [greek: to idion] (_proprium_); and [greek: to symbebêkos] (_accidens_). the object of it was to provide a basis for his systematic exposition; each of the four kinds admitted of differences in dialectic method. for us it is a matter of simple curiosity and ingenuity. it serves as a monument of how much greek dialectic turned on definition, and it corresponds exactly to the division of attributes into defining and non-defining given above. it is sometimes said that aristotle showed a more scientific mind than porphyry in making the predicables four instead of five. this is true if porphyry's list had been meant as a division of attributes: but it was not so meant. the distinction between verbal or analytic and real or synthetic predication corresponds to the distinction between defining and non-defining attributes, and also has no significance except with reference to some scheme of division, scientific and precise or loose and popular. when a proposition predicates of a subject something contained in the full notion, concept, or definition of the subject term, it is called verbal, analytic, or explicative: _verbal_, inasmuch as it merely explains the meaning of a name; _explicative_ for the same reason; _analytic_, inasmuch as it unties the bundle of attributes held together in the concept and pays out one, or all one by one. when the attributes of the predicate are not contained in the concept of the subject, the proposition is called _real_, _synthetic_, or _ampliative_, for parallel reasons. thus: "a triangle is a three-sided rectilinear figure" is verbal or analytic; "triangles have three angles together equal to two right angles," or "triangles are studied in schools," is real or synthetic. according to this distinction, predications of the whole definition or of a generic attribute or of a specific attribute are verbal; predications of accident are real. a nice point is whether propria are verbal or real. they can hardly be classed with verbal, inasmuch as one may know the full meaning of the name without knowing them: but it might be argued that they are analytic, inasmuch as they are implicitly contained in the defining attributes as being deducible from them. observe, however, that the whole distinction is really valid only in relation to some fixed or accepted scheme of classification or division. otherwise, what is verbal or analytic to one man may be real or synthetic to another. it might even be argued that every proposition is analytic to the man who utters it and synthetic to the man who receives it. we must make some analysis of a whole of thought before paying it out in words: and in the process of apprehending the meaning of what we hear or read we must add the other members of the sentence on to the subject. whether or not this is super-subtle, it clearly holds good that what is verbal (in the sense defined) to the learned man of science may be real to the learner. that the horse has six incisors in each jaw or that the domestic dog has a curly tail, is a verbal proposition to the natural historian, a mere exposition of defining marks; but the plain man has a notion of horse or dog into which this defining attribute does not enter, and to him accordingly the proposition is real. but what of propositions that the plain man would at once recognise as verbal? charles lamb, for example, remarks that the statement that "a good name shows the estimation in which a man is held in the world" is a verbal proposition. where is the fixed scheme of division there? the answer is that by a fixed scheme of division we do not necessarily mean a scheme that is rigidly, definitely and precisely fixed. to make such schemes is the business of science. but the ordinary vocabulary of common intercourse as a matter of fact proceeds upon schemes of division, though the names used in common speech are not always scientifically accurate, not always the best that could be devised for the easy acquisition and sure transmission of thorough knowledge. the plain man's vocabulary, though often twisted aside by such causes as we have specified, is roughly moulded on the most marked distinguishing attributes of things. this was practically recognised by aristotle when he made one of his modes of definition consist in something like what we have called verifying the meaning of a name, ascertaining the attributes that it signifies in common speech or in the speech of sensible men. this is to ascertain the essence, [greek: ousia], or _substantia_, of things, the most salient attributes that strike the common eye either at once or after the closer inspection that comes of long companionship, and form the basis of the ordinary vocabulary. "properly speaking," mansel says,[ ] "all definition is an inquiry into _attributes_. our complex notions of substances can only be resolved into various attributes, with the addition of an unknown _substratum_: a something to which we are compelled to regard these attributes as belonging. _man_, for example, is analysed into animality, rationality, and the something which exhibits these phenomena. pursue the analysis and the result is the same. we have a something corporeal, animated, sensible, rational. an unknown constant must always be added to complete the integration." this "unknown constant" was what locke called the _real_ essence, as distinguished from the _nominal_ essence, or complex of attributes. it is upon this nominal essence, upon divisions of things according to attributes, that common speech rests, and if it involves many cross-divisions, this is because the divisions have been made for limited and conflicting purposes. [footnote : aldrich's compendium, appendix, note c. the reader may be referred to mansel's notes a and c for valuable historical notices of the predicables and definition.] chapter iii. aristotle's categories. in deference to tradition a place must be found in every logical treatise for aristotle's categories. no writing of the same length has exercised a tithe of its influence on human thought. it governed scholastic thought and expression for many centuries, being from its shortness and consequent easiness of transcription one of the few books in every educated man's library. it still regulates the subdivisions of parts of speech in our grammars. its universality of acceptance is shown in the fact that the words _category_ ([greek: katêgoria]) and _predicament_, its latin translation, have passed into common speech. the categories have been much criticised and often condemned as a division, but, strange to say, few have inquired what they originally professed to be a division of, or what was the original author's basis of division. whether the basis is itself important, is another question: but to call the division imperfect, without reference to the author's intention, is merely confusing, and serves only to illustrate the fact that the same objects may be differently divided on different principles of division. ramus was right in saying that the categories had no logical significance, inasmuch as they could not be made a basis for departments of logical method; and kant and mill in saying that they had no philosophical significance, inasmuch as they are founded upon no theory of knowing and being: but this is to condemn them for not being what they were never intended to be. the sentence in which aristotle states the objects to be divided, and his division of them is so brief and bold that bearing in mind the subsequent history of the categories, one first comes upon it with a certain surprise. he says simply:-- "of things expressed without syntax (_i.e._, single words), each signifies either substance, or quantity, or quality, or relation, or place, or time, or disposition (_i.e._, attitude or internal arrangement), or appurtenance, or action (doing), or suffering (being done to)."[ ] the objects, then, that aristotle proposed to classify were single words (the _themata simplicia_ of the schoolmen). he explains that by "out of syntax" ([greek: aneu symplokês]) he means without reference to truth or falsehood: there can be no declaration of truth or falsehood without a sentence, a combination, or syntax: "man runs" is either true or false, "man" by itself, "runs" by itself, is neither. his division, therefore, was a division of single words according to their differences of signification, and without reference to the truth or falsehood of their predication.[ ] signification was thus the basis of division. but according to what differences? the categories themselves are so abstract that this question might be discussed on their bare titles interminably. but often when abstract terms are doubtful, an author's intention may be gathered from his examples. and when aristotle's examples are ranged in a table, certain principles of subdivision leap to the eyes. thus:-- substance man } common { substance ([greek: ousia]) ([greek: anthrôpos]) } noun { (_substantia_) -------------------------------------------------------------- quantity five-feet-five } { ([greek: poson]) ([greek: tripêchu]) } { (_quantitas_) } { quality scholarly } { permanent ([greek: poion]) ([greek: grammatikon])} adjective { attribute (_qualitas_) } { relation bigger } { ([greek: pros ti]) ([greek: meizon]) } { (_relatio_) } { -------------------------------------------------------------- place in-the-lyceum } { ([greek: pou]) ([greek: en lykeiô]) } { (_ubi_) } adverb { temporary time yesterday } { attribute ([greek: pote]) ([greek: chthes]) } { (_quando_) } { -------------------------------------------------------------- disposition reclines } { ([greek: keisthai]) ([greek: anakeitai]) } { (_positio_) } { appurtenance has-shoes-on } { ([greek: echein]) ([greek: hypodedetai])} { (_habitus_) } verb { action cuts } { temporary ([greek: poiein]) ([greek: temnei]) } { attribute (_actio_) } { passion is cut } { ([greek: paschein]) ([greek: temnetai]) } { (_passio_) } { in looking at the examples, our first impression is that aristotle has fallen into a confusion. he professes to classify words out of syntax, yet he gives words with the marks of syntax on them. thus his division is accidentally grammatical, a division of parts of speech, parts of a sentence, into nouns, adjectives, adverbs, and verbs. and his subdivisions of these parts are still followed in our grammars. but really it is not the grammatical function that he attends to, but the signification: and looking further at the examples, we see what differences of signification he had in his mind. it is differences relative to a concrete individual, differences in the words applied to him according as they signify the substance of him or his attributes, permanent or temporary. take any concrete thing, socrates, this book, this table. it must be some kind of a thing, a man, a book. it must have some size or quantity, six feet high, three inches broad. it must have some quality, white, learned, hard. it must have relations with other things, half this, double that, the son of a father. it must be somewhere, at some time, in some attitude, with some "havings," appendages, appurtenances, or belongings, doing something, or having something done to it. can you conceive any name (simple or composite) applicable to any object of perception, whose signification does not fall into one or other of these classes? if you cannot, the categories are justified as an exhaustive division of significations. they are a complete list of the most general resemblances among individual things, in other words, of the _summa genera_, the _genera generalissima_ of predicates concerning this, that or the other concrete individual. no individual thing is _sui generis_: everything is like other things: the categories are the most general likenesses. the categories are exhaustive, but do they fulfil another requisite of a good division--are they mutually exclusive? aristotle himself raised this question, and some of his answers to difficulties are instructive. particularly his discussion of the distinction between second substances or essences and qualities. here he approximates to the modern doctrine of the distinction between substance and attribute as set forth in our quotation from mansel at p. . aristotle's second essences ([greek: deuterai ousiai]) are common nouns or general names, species and genera, _man_, _horse_, _animal_, as distinguished from singular names, _this man_, _this horse_, which he calls first substances ([greek: prôtai ousiai]), essences _par excellence_, to which real existence in the highest sense is attributed. common nouns are put in the first category because they are predicated in answer to the question, what is this? but he raises the difficulty whether they may not rather be regarded as being in the third category, that of quality ([greek: to poion]). when we say, "this is a man," do we not declare what sort of a thing he is? do we not declare his quality? if aristotle had gone farther along this line, he would have arrived at the modern point of view that a man is a man in virtue of his possessing certain attributes, that general names are applied in virtue of their connotation. this would have been to make the line of distinction between the first category and the third pass between first essence and second, ranking the second essences with qualities. but aristotle did not get out of the difficulty in this way. he solved it by falling back on the differences in common speech. "man" does not signify the quality simply, as "whiteness" does. "whiteness" signifies nothing but the quality. that is to say, there is no separate name in common speech for the common attributes of man. his further obscure remark that general names "define quality round essence" [greek: peri ousian], inasmuch as they signify what sort a certain essence is, and that genera make this definition more widely than species, bore fruit in the mediæval discussions between realists and nominalists by which the signification of general names was cleared up. another difficulty about the mutual exclusiveness of the categories was started by aristotle in connexion with the fourth category, relation ([greek: pros ti] _ad aliquid_, _to something_). mill remarks that "that could not be a very comprehensive view of the nature of relation which would exclude action, passivity, and local situation from that category," and many commentators, from simplicius down to hamilton, have remarked that all the last six categories might be included under relation. this is so far correct that the word relation is one of the vaguest and most extensive of words; but the criticism ignores the strictness with which aristotle confined himself in his categories to the forms of common speech. it is clear from his examples that in his fourth category he was thinking only of "relation" as definitely expressed in common speech. in his meaning, any word is a relative which is joined with another in a sentence by means of a preposition or a case-inflection. thus "disposition" is a relative: it is the disposition _of_ something. this kind of relation is perfect when the related terms reciprocate grammatically; thus "master," "servant," since we can say either "the master of the servant," or "the servant of the master". in mediæval logic the term _relata_ was confined to these perfect cases, but the category had a wider scope with aristotle. and he expressly raised the question whether a word might not have as much right to be put in another category as in this. indeed, he went further than his critics in his suggestions of what relation might be made to include. thus: "big" signifies quality; yet a thing is big with reference to something else, and is so far a relative. knowledge must be knowledge of something, and is a relative: why then should we put "knowing" (_i.e._, learned) in the category of quality. "hope" is a relative, as being the hope _of_ a man and the hope of something. yet we say, "i have hope," and there hope would be in the category of having, appurtenance. for the solution of all such difficulties, aristotle falls back upon the forms of common speech, and decides the place of words in his categories according to them. this was hardly consistent with his proposal to deal with separate words out of syntax, if by this was meant anything more than dealing with them without reference to truth or falsehood. he did not and could not succeed in dealing with separate words otherwise than as parts of sentences, owing their signification to their position as parts of a transient plexus of thought. in so far as words have their being in common speech, and it is their being in this sense that aristotle considers in the categories, it is a transient being. what being they represent besides is, in the words of porphyry, a very deep affair, and one that needs other and greater investigation. [footnote : [greek: tôn kata mêdemian symplokên legomenôn hekaston êtoi ousian sêmainei, ê poson, ê poion, ê pros ti, ê pou, ê pote, ê keisthai, ê echein, ê poiein, ê paschein.] (categ. ii. .)] [footnote : to describe the categories as a grammatical division, as mansel does in his instructive appendix c to aldrich, is a little misleading without a qualification. they are non-logical inasmuch as they have no bearing on any logical purpose. but they are grammatical only in so far as they are concerned with words. they are not grammatical in the sense of being concerned with the function of words in predication. the unit of grammar in this sense is the sentence, a combination of words in syntax; and it is expressly with words out of syntax that aristotle deals, with single words not in relation to the other parts of a sentence, but in relation to the things signified. in any strict definition of the provinces of grammar and logic, the categories are neither grammatical nor logical: the grammarians have appropriated them for the subdivision of certain parts of the sentence, but with no more right than the logicians. they really form a treatise by themselves, which is in the main ontological, a discussion of substances and attributes as underlying the forms of common speech. in saying this i use the word substance in the modern sense: but it must be remembered that aristotle's [greek: ousia], translated substantia, covered the word as well as the thing signified, and that his categories are primarily classes of words. the union between names and things would seem to have been closer in the greek mind than we can now realise. to get at it we must note that every separate word [greek: to legomenon] is conceived as having a being or thing [greek: to on] corresponding to it, so that beings or things [greek: ta onta] are coextensive with single words: a being or thing is whatever receives a separate name. this is clear and simple enough, but perplexity begins when we try to distinguish between this nameable being and concrete being, which last is aristotle's category of [greek: ousia], the being signified by a proper or a common as distinguished from an abstract noun. as we shall see, it is relatively to the highest sense of this last kind of being, namely, the being signified by a proper name, that he considers the other kinds of being.] chapter iv. the controversy about universals.--difficulties concerning the relation of general names to thought and to reality. in the opening sentences of his isagoge, before giving his simple explanation of the five predicables, porphyry mentions certain questions concerning genera and species, which he passes over as being too difficult for the beginner. "concerning genera and species," he says, "the question whether they subsist (_i.e._, have real substance), or whether they lie in the mere thoughts only, or whether, granting them to subsist, they are corporeal or incorporeal, or whether they subsist apart, or in sensible things and cohering round them--this i shall pass over, such a question being a very deep affair and one that needs other and greater investigation." this passage, written about the end of the third century, a.d., is a kind of isthmus between greek philosophy and mediæval: it summarises questions which had been turned over on every side and most intricately discussed by plato and aristotle and their successors, and the bald summary became a starting-point for equally intricate discussions among the schoolmen, among whom every conceivable variety of doctrine found champions. the dispute became known as the dispute about universals, and three ultra-typical forms of doctrine were developed, known respectively as realism, nominalism, and conceptualism. undoubtedly the dispute, with all its waste of ingenuity, had a clearing effect, and we may fairly try now what porphyry shrank from, to gather some simple results for the better understanding of general names and their relations to thoughts and to things. the rival schools had each some aspect of the general name in view, which their exaggeration served to render more distinct. what does a general name signify? for logical purposes it is sufficient to answer--the points of resemblance as grasped in the mind, fixed by a name applicable to each of the resembling individuals. this is the signification of the general name _logically_, its connotation or concept, the identical element of objective reference in all uses of a general name. but other questions may be asked that cannot be so simply answered. what is this concept in thought? what is there in our minds corresponding to the general name when we utter it? how is its signification conceived? what is the signification _psychologically_? we may ask, further, what is there in nature that the general name signifies? what is its relation to reality? what corresponds to it in the real world? has the unity that it represents among individuals no existence except in the mind? calling this unity, this one in the many, the universal (_universale_, [greek: to pan]), what is the universal _ontologically_? it was this ontological question that was so hotly and bewilderingly debated among the schoolmen. before giving the ultra-typical answers to it, it may be well to note how this question was mixed up with still other questions of theology and cosmogony. recognising that there is a unity signified by the general name, we may go on to inquire into the ground of the unity. why are things essentially like one another? how is the unity maintained? how is it continued? where does the common pattern come from? the question of the nature of the universal thus links itself with metaphysical theories of the construction of the world, or even with the darwinian theory of the origin of species. passing by these remoter questions, we may give the answers of the three extreme schools to the ontological question, what is a universal? the answer of the ultra-realists, broadly put, was that a universal is a substance having an independent existence in nature. of the ultra-nominalists, that the universal is a name and nothing else, _vox et præterea nihil_; that this name is the only unity among the individuals of a species, all that they have in common. of the ultra-conceptualists, that the individuals have more in common than the name, that they have the name plus the meaning, _vox_ + _significatio_, but that the universals, the genera and species, exist only in the mind. now these extreme doctrines, as literally interpreted by opponents, are so easily refuted and so manifestly untenable, that it may be doubted whether they were ever held by any thinker, and therefore i call them ultra-realism, ultra-nominalism, and ultra-conceptualism. they are mere exaggerations or caricatures, set up by opponents because they can be easily knocked down. to the ultra-realists, it is sufficient to say that if there existed anywhere a substance having all the common attributes of a species and only these, having none of the attributes peculiar to any of the individuals of that species, corresponding to the general name as an individual corresponds to a proper or singular name, it would not be the universal, the unity pervading the individuals, but only another individual. to the ultra-nominalists, it is sufficient to say that the individuals must have more in common than the name, because the name is not applied arbitrarily, but on some ground. the individuals must have in common that on account of which they receive the common name: to call them by the same name is not to make them of the same species. to the ultra-conceptualists, it is sufficient to say that when we employ a general name, as when we say "socrates is a man," we do not refer to any passing thought or state of mind, but to certain attributes independent of what is passing in our minds. we cannot make a thing of this or that species by merely thinking of it as such. the ultra-forms of these doctrines are thus easily shown to be inadequate, yet each of the three, realism, nominalism, and conceptualism, represents a phase of the whole truth. thus, take realism. although it is not true that there is anything in reality corresponding to the general name such as there is corresponding to the singular name, the general name merely signifying attributes of what the singular name signifies, it does not follow, as the opponents of ultra-realism hastily assume, that there is nothing in the real world corresponding to the general name. three senses may be particularised in which realism is justified. ( ) the points of resemblance from which the concept is formed are as real as the individuals themselves. it is true in a sense that it is our thought that gives unity to the individuals of a class, that gathers the many into one, and so far the conceptualists are right. still we should not gather them into one if they did not resemble one another: that is the reason why we think of them together: and the respects in which they resemble one another are as much independent of us and our thinking as the individuals themselves, as much beyond the power of our thought to change. we must go behind the activity of the mind in unifying to the reason for the unification: and the ground of unity is found in what really exists. we do not confer the unity: we do not make all men or all dogs alike: we find them so. the curly tails in a thousand domestic dogs, which serve to distinguish them from wolves and foxes, are as real as the thousand individual domestic dogs. in this sense the aristotelian doctrine, _universalia in re_, expresses a plain truth. ( ) the platonic doctrine, formulated by the schoolmen as _universalia ante rem_, has also a plain validity. individuals come and go, but the type, the universal, is more abiding. men are born and die: man remains throughout. the snows of last year have vanished, but snow is still a reality to be faced. wisdom does not perish with the wise men of any generation. in this plain sense, at least, it is true that universals exist before individuals, have a greater permanence, or, if we like to say so, a higher, as it is a more enduring, reality. ( ) further, the "idea," concept, or universal, though it cannot be separated from the individual, and whether or not we ascribe to it the separate suprasensual existence of the archetypal forms of plato's poetical fancy, is a very potent factor in the real world. ideals of conduct, of manners, of art, of policy, have a traditional life: they do not pass away with the individuals in whom they have existed, in whom they are temporarily materialised: they survive as potent influences from age to age. the "idea" of chaucer's man of law, who always "seemed busier than he was," is still with us. mediæval conceptions of chivalry still govern conduct. the universal enters into the individual, takes possession of him, makes of him its temporary manifestation. nevertheless, the nominalists are right in insisting on the importance of names. what we call the real world is a common object of perception and knowledge to you and me: we cannot arrive at a knowledge of it without some means of communication with one another: our means of communication is language. it may be doubted whether even thinking could go far without symbols with the help of which conceptions may be made definite. a concept cannot be explained without reference to a symbol. there is even a sense in which the ultra-nominalist doctrine that the individuals in a class have nothing in common but the name is tenable. denotability by the same name is the only respect in which those individuals are absolutely identical: in this sense the name alone is common to them, though it is applied in virtue of their resemblance to one another. finally, the conceptualists are right in insisting on the mind's activity in connexion with general names. genera and species are not mere arbitrary subjective collections: the union is determined by the characters of the things collected. still it is with the concept in each man's mind that the name is connected: it is by the activity of thought in recognising likenesses and forming concepts that we are able to master the diversity of our impressions, to introduce unity into the manifold of sense, to reduce our various recollections to order and coherence. so much for the ontological question. now for the psychological. what is in the mind when we employ a general name? what is the universal psychologically? how is it conceived? what breeds confusion in these subtle inquiries is the want of fixed unambiguous names for the things to be distinguished. it is only by means of such names that we can hold on to the distinctions, and keep from puzzling ourselves. now there are three things to be distinguished in this inquiry, which we may call the concept, the conception, and the conceptual or generic image. let us call them by these names, and proceed to explain them. by the concept, i understand the meaning of the general name, what the general name signifies: by the conception, the mental act or state of him who conceives this meaning. the concept of "triangle," _i.e._, what you and i mean by the word, is not my act of mind or your act of mind when we think or speak of a triangle. the conception, which is this act, is an event or incident in our mental history, a psychical act or state, a distinct occurrence, a particular fact in time as much as the battle of waterloo. the concept is the objective reference of the name, which is the same, or at least is understood to be the same, every time we use it. i make a figure on paper with ink or on a blackboard with chalk, and recognise or conceive it as a triangle: you also conceive it as such: we do the same to-morrow: we did the same yesterday: each act of conception is a different event, but the concept is the same throughout. now the psychological question about the universal is, what is this conception? we cannot define it positively further than by saying that it consists in realising the meaning of a general name: the act being unique, we can only make it intelligible by producing an example of it. but we may define it negatively by distinguishing it from the conceptual image. whenever we conceive anything, "man," "horse," there is generally present to our minds an image of a man or horse, with accidents of size, colour, position or other categories. but this conceptual image is not the concept, and the mental act of forming it is not conception. this distinction between mental picturing or imaging and the conception of common attributes is variously expressed. the correlative terms _intuitive_ and _symbolical_ thinking, _presentative_ and _representative_ knowledge have been employed.[ ] but whatever terms we use, the distinction itself is vital, and the want of it leads to confusion. thus the fact that we cannot form a conceptual image composed solely of common attributes has been used to support the argument of ultra-nominalism, that the individuals classed under a common name have nothing in common but the name. what the word "dog" signifies, _i.e._, the "concept" of dog, is neither big nor little, neither black nor tan, neither here nor there, neither newfoundland, nor retriever, nor terrier, nor greyhound, nor pug, nor bulldog. the concept consists only of the attributes common to all dogs apart from any that are peculiar to any variety or any individual. now we cannot form any such conceptual image. our conceptual image is always of some definite size and shape. therefore, it is argued, we cannot conceive what a dog means, and dogs have nothing in common but the name. this, however, does not follow. the concept is not the conceptual image, and forming the image is not conception. we may even, as in the case of a chiliagon, or thousand-sided figure, conceive the meaning without being able to form any definite image. how then, do we ordinarily proceed in conceiving, if we cannot picture the common attributes alone and apart from particulars? we attend, or strive to attend, only to those aspects of an image which it has in common with the individual things denoted. and if we want to make our conception definite, we pass in review an indefinite number of the individuals, case after case. a minor psychological question concerns the nature of the conceptual image. is it a copy of some particular impression, or a confused blur or blend of many? possibly neither: possibly it is something like one of mr. galton's composite photographs, photographs produced by exposing the same surface to the impressions of a number of different photographs in succession. if the individuals are nearly alike, the result is an image that is not an exact copy of any one of the components and yet is perfectly distinct. possibly the image that comes into our mind's eye when we hear such a word as "horse" or "man" is of this character, the result of the impressions of a number of similar things, but not identical with any one. as, however, different persons have different conceptual images of the same concept, so we may have different conceptual images at different times. it is only the concept that remains the same. but how, it may be asked, can the concept remain the same? if the universal or concept psychologically is an intellectual act, repeated every time we conceive, what guarantee have we for the permanence of the concept? does this theory not do away with all possibility of defining and fixing concepts? this brings us back to the doctrine already laid down about the truth of realism. the theory of the concept is not exhausted when it is viewed only psychologically, as a psychic act. if we would understand it fully, we must consider the act in its relations to the real experience of ourselves and others. to fix this act, we give it a separate name, calling it the conception: and then we must go behind the activity of the mind to the objects on which it is exercised. the element of fixity is found in them. and here also the truth of nominalism comes in. by means of words we enter into communication with other minds. it is thus that we discover what is real, and what is merely personal to ourselves. [footnote : the only objection to these terms is that they have slipped from their moorings in philosophical usage. thus instead of leibnitz's use of intuitive and symbolical, which corresponds to the above distinction between imaging and conception, mr. jevons employs the terms to express a distinction among conceptions proper. we can understand what a chiliagon means, but we cannot form an image of it in our minds, except in a very confused and imperfect way; whereas we can form a distinct image of a triangle. mr. jevons would call the conception of the triangle _intuitive_, of the chiliagon _symbolical_. again, while mansel uses the words presentative and representative to express our distinction, a more common usage is to call actual perception presentative knowledge, and ideation or recollection in idea representative.] part iii. the interpretation of propositions.--opposition and immediate inference. chapter i. theories of predication.--theories of judgment. we may now return to the syllogistic forms, and the consideration of the compatibility or incompatibility, implication, and interdependence of propositions. it was to make this consideration clear and simple that what we have called the syllogistic form of propositions was devised. when are propositions incompatible? when do they imply one another? when do two imply a third? we have seen in the introduction how such questions were forced upon aristotle by the disputative habits of his time. it was to facilitate the answer that he analysed propositions into subject and predicate, and viewed the predicate as a reference to a class: in other words, analysed the predicate further into a copula and a class term. but before showing how he exhibited the interconnexion of propositions on this plan, we may turn aside to consider various so-called theories of predication or of judgment. strictly speaking, they are not altogether relevant to logic, that is to say, as a practical science: they are partly logical, partly psychological theories: some of them have no bearing whatever on practice, but are matters of pure scientific curiosity: but historically they are connected with the logical treatment of propositions as having been developed out of this. the least confusing way of presenting these theories is to state them and examine them both logically and psychologically. the logical question is, has the view any advantage for logical purposes? does it help to prevent error, to clear up confusion? does it lead to firmer conceptions of the truth? the psychological question is, is this a correct theory of how men actually think when they make propositions? it is a question of _what is_ in the one case, and of _what ought to be for a certain purpose_ in the other. whether we speak of proposition or of judgment does not materially affect our answer. a judgment is the mental act accompanying a proposition, or that may be expressed in a proposition and cannot be expressed otherwise: we can give no other intelligible definition or description of a judgment. so a proposition can only be defined as the expression of a judgment: unless there is a judgment underneath them, a form of words is not a proposition. let us take, then, the different theories in turn. we shall find that they are not really antagonistic, but only different: that each is substantially right from its own point of view: and that they seem to contradict one another only when the point of view is misunderstood. i. _that the predicate term may be regarded as a class in or from which the subject is included or excluded._ known as the class-inclusion, class-reference, or denotative view. this way of analysing propositions is possible, as we have seen, because every statement implies a general name, and the extension or denotation of a general name is a class defined by the common attribute or attributes. it is useful for syllogistic purposes: certain relations among propositions can be most simply exhibited in this way. but if this is called a theory of predication or judgment, and taken psychologically as a theory of what is in men's minds whenever they utter a significant sentence, it is manifestly wrong. when discussed as such, it is very properly rejected. when a man says "p struck q," he has not necessarily a class of "strikers of q" definitely in his mind. what he has in his mind is the logical equivalent of this, but it is not this directly. similarly, mr. bradley would be quite justified in speaking of two terms and a copula as a superstition, if it were meant that these analytic elements are present to the mind of an ordinary speaker. ii. _that every proposition may be regarded as affirming or denying an attribute of a subject._ known sometimes as the connotative or the denotative-connotative view. this also follows from the implicit presence of a general name in every sentence. but it should not be taken as meaning that the man who says: "tom came here yesterday," or "james generally sits there," has a clearly analysed subject and attribute in his mind. otherwise it is as far wrong as the other view. iii. _that every proposition may be regarded as an equation between two terms._ known as the equational view. this is obviously not true for common speech or ordinary thought. but it is a possible way of regarding the analytic components of a proposition, legitimate enough if it serves any purpose. it is a modification of the class-reference analysis, obtained by what is known as quantification of the predicate. in "all s is in p," p is undistributed, and has no symbol of quantity. but since the proposition imports that all s is a part of p, _i.e._, some p, we may, if we choose, prefix the symbol of quantity, and then the proposition may be read "all s = some p". and so with the other forms. is there any advantage in this? yes: it enables us to subject the formulæ to algebraic manipulation. but any logical advantage--any help to thinking? none whatever. the elaborate syllogistic systems of boole, de morgan, and jevons are not of the slightest use in helping men to reason correctly. the value ascribed to them is merely an illustration of the bias of happy exercise. they are beautifully ingenious, but they leave every recorded instance of learned scholastic trifling miles behind. iv. _that every proposition is the expression of a comparison between concepts._ sometimes called the conceptualist view. "to judge," hamilton says, "is to recognise the relation of congruence or confliction in which two concepts, two individual things, or a concept and an individual compared together stand to each other." this way of regarding propositions is permissible or not according to our interpretation of the words "congruence" and "confliction," and the word "concept". if by concept we mean a conceived attribute of a thing, and if by saying that two concepts are congruent or conflicting, we mean that they may or may not cohere in the same thing, and by saying that a concept is congruent or conflicting with an individual that it may or may not belong to that individual, then the theory is a corollary from aristotle's analysis. seeing that we must pass through that analysis to reach it, it is obviously not a theory of ordinary thought, but of the thought of a logician performing that analysis. the precise point of hamilton's theory was that the logician does not concern himself with the question whether two concepts are or are not as a matter of fact found in the same subject, but only with the question whether they are of such a character that they may be found, or cannot be found, in the same subject. in so far as his theory is sound, it is an abstruse and technical way of saying that we may consider the consistency of propositions without considering whether or not they are true, and that consistency is the peculiar business of syllogistic logic. v. _that the ultimate subject of every judgment is reality._ this is the form in which mr. bradley and mr. bosanquet deny the ultra-conceptualist position. the same view is expressed by mill when he says that "propositions are concerned with things and not with our ideas of them". the least consideration shows that there is justice in the view thus enounced. take a number of propositions:-- the streets are wet. george has blue eyes. the earth goes round the sun. two and two make four. obviously, in any of these propositions, there is a reference beyond the conceptions in the speaker's mind, viewed merely as incidents in his mental history. they express beliefs about things and the relations among things _in rerum natura_: when any one understands them and gives his assent to them, he never stops to think of the speaker's state of mind, but of what the words represent. when states of mind are spoken of, as when we say that our ideas are confused, or that a man's conception of duty influences his conduct, those states of mind are viewed as objective facts in the world of realities. even when we speak of things that have in a sense no reality, as when we say that a centaur is a combination of man and horse, or that centaurs were fabled to live in the vales of thessaly, it is not the passing state of mind expressed by the speaker as such that we attend to or think of; we pass at once to the objective reference of the words. psychologically, then, the theory is sound: what is its logical value? it is sometimes put forward as if it were inconsistent with the class-reference theory or the theory that judgment consists in a comparison of concepts. historically the origin of its formal statement is its supposed opposition to those theories. but really it is only a misconception of them that it contradicts. it is inconsistent with the class-reference view only if by a class we understand an arbitrary subjective collection, not a collection of things on the ground of common attributes. and it is inconsistent with the conceptualist theory only if by a concept we understand not the objective reference of a general name, but what we have distinguished as a conception or a conceptual image. the theory that the ultimate subject is reality is assumed in both the other theories, rightly understood. if every proposition is the utterance of a judgment, and every proposition implies a general name, and every general name has a meaning or connotation, and every such meaning is an attribute of things and not a mental state, it is implied that the ultimate subject of every proposition is reality. but we may consider whether or not propositions are consistent without considering whether or not they are true, and it is only their mutual consistency that is considered in the syllogistic formulæ. thus, while it is perfectly correct to say that every proposition expresses either truth or falsehood, or that the characteristic quality of a judgment is to be true or false, it is none the less correct to say that we may temporarily suspend consideration of truth or falsehood, and that this is done in what is commonly known as formal logic. vi. _that every proposition may be regarded as expressing relations between phenomena._ bain follows mill in treating this as the final import of predication. but he indicates more accurately the logical value of this view in speaking of it as important for laying out the divisions of inductive logic. they differ slightly in their lists of universal predicates based upon import in this sense--mill's being resemblance, coexistence, simple sequence, and causal sequence, and bain's being coexistence, succession, and equality or inequality. but both lay stress upon coexistence and succession, and we shall find that the distinctions between simple sequence and causal sequence, and between repeated and occasional coexistence, are all-important in the logic of investigation. but for syllogistic purposes the distinctions have no relevance. chapter ii. the "opposition" of propositions.--the interpretation of "no". propositions are technically said to be "opposed" when, having the same terms in subject and predicate, they differ in quantity, or in quality, or in both.[ ] the practical question from which the technical doctrine has been developed was how to determine the significance of contradiction. what is meant by giving the answer "no" to a proposition put interrogatively? what is the interpretation of "no"? what is the respondent committed to thereby? "have all ratepayers a vote?" if you answer "no," you are bound to admit that some ratepayers have not. o is the contradictory of a. if a is false, o must be true. so if you deny o, you are bound to admit a: one or other must be true: either some ratepayers have not a vote or all have. is it the case that no man can live without sleep? deny this, and you commit yourself to maintaining that some man, one at least, can live without sleep. i is the contradictory of e; and _vice versâ_. contradictory opposition is distinguished from contrary, the opposition of one universal to another, of a to e and e to a. there is a natural tendency to meet a strong assertion with the very reverse. let it be maintained that women are essentially faithless or that "the poor in a lump is bad," and disputants are apt to meet this extreme with another, that constancy is to be found only in women or true virtue only among the poor. both extremes, both a and e, may be false: the truth may lie between: some are, some not. logically, the denial of a or e implies only the admission of o or i. you are not committed to the full contrary. but the implication of the contradictory is absolute; there is no half-way house where the truth may reside. hence the name of excluded middle is applied to the principle that "of two contradictories one or other must be true: they cannot both be false". while both contraries may be false, they cannot both be true. it is sometimes said that in the case of singular propositions, the contradictory and the contrary coincide. a more correct doctrine is that in the case of singular propositions, the distinction is not needed and does not apply. put the question "is socrates wise?" or "is this paper white?" and the answer "no" admits of only one interpretation, provided the terms remain the same. socrates may become foolish, or this paper may hereafter be coloured differently, but in either case the subject term is not the same about which the question was asked. contrary opposition belongs only to general terms taken universally as subjects. concerning individual subjects an attribute must be either affirmed or denied simply: there is no middle course. such a proposition as "socrates is sometimes not wise," is not a true singular proposition, though it has a singular term as grammatical subject. logically, it is a particular proposition, of which the subject-term is the actions or judgments of socrates.[ ] opposition, in the ordinary sense, is the opposition of incompatible propositions, and it was with this only that aristotle concerned himself. but from an early period in the history of logic, the word was extended to cover mere differences in quantity and quality among the four forms a e i o, which differences have been named and exhibited symmetrically in a diagram known as: the square of opposition. a______contraries______e |\ /| | \ s | | c e | | o i | | n r | | t o | s r t s u a c u b \ i b a \ d a l \/ l t /\ t e / d e r / i r n a c n s r t s | t o | | n r | | o i | | c e | | / s | |/ \| i____sub-contraries____o the four forms being placed at the four corners of the square, and the sides and diagonals representing relations between them thus separated, a very pretty and symmetrical doctrine is the result. _contradictories_, a and o, e and i, differ both in quantity and in quality. _contraries_, a and e, differ in quality but not in quantity, and are both universal. _sub-contraries_, i and o, differ in quality but not in quantity, and are both particular. _subalterns_, a and i, e and o, differ in quantity but not in quality. again, in respect of concurrent truth and falsehood there is a certain symmetry. contradictories cannot both be true, nor can they both be false. contraries may both be false, but cannot both be true. sub-contraries may both be true, but cannot both be false. subalterns may both be false and both true. if the universal is true, its subalternate particular is true: but the truth of the particular does not similarly imply the truth of its subalternating universal. this last is another way of saying that the truth of the contrary involves the truth of the contradictory, but the truth of the contradictory does not imply the truth of the contrary. there, however, the symmetry ends. the sides and the diagonals of the square do not symmetrically represent degrees of incompatibility, or opposition in the ordinary sense. there is no incompatibility between two sub-contraries or a subaltern and its subalternant. both may be true at the same time. indeed, as aristotle remarked of i and o, the truth of the one commonly implies the truth of the other: to say that some of the crew were drowned, implies that some were not, and _vice versâ_. subaltern and subalternant also are compatible, and something more. if a man has admitted a or e, he cannot refuse to admit i or o, the particular of the same quality. if all poets are irritable, it cannot be denied that some are so; if none is, that some are not. the admission of the contrary includes the admission of the contradictory. consideration of subalterns, however, brings to light a nice ambiguity in some. it is only when i is regarded as the contradictory of e, that it can properly be said to be subalternate to a. in that case the meaning of some is "not none," _i.e._, "some at least". but when some is taken as the sign of particular quantity simply, _i.e._, as meaning "not all," or "some at most," i is not subalternate to a, but opposed to it in the sense that the truth of the one is incompatible with the truth of the other. again, in the diagram contrary opposition is represented by a side and contradictory by the diagonal; that is to say, the stronger form of opposition by the shorter line. the contrary is more than a denial: it is a counter-assertion of the very reverse, [greek: to enantion]. "are good administrators always good speakers?" "on the contrary, they never are." this is a much stronger opposition, in the ordinary sense, than a modest contradictory, which is warranted by the existence of a single exception. if the diagram were to represent incompatibility accurately, the contrary ought to have a longer line than the contradictory, and this it seems to have had in the diagram that aristotle had in mind (_de interpret._, c. ). it is only when opposition is taken to mean merely difference in quantity and quality that there can be said to be greater opposition between contradictories than between contraries. contradictories differ both in quantity and in quality: contraries, in quality only. there is another sense in which the particular contradictory may be said to be a stronger opposite than the contrary. it is a stronger position to take up argumentatively. it is easier to defend than a contrary. but this is because it offers a narrower and more limited opposition. we deal with what is called immediate inference in the next chapter. pending an exact definition of the process, it is obvious that two immediate inferences are open under the above doctrines, ( ) granted the truth of any proposition, you may immediately infer the falsehood of its contradictory. ( ) granted the truth of any contrary, you may immediately infer the truth of its subaltern.[ ] [footnote : this is the traditional definition of opposition from an early period, though the tradition does not start from aristotle. with him opposition ([greek: antikeisthai]) meant, as it still means in ordinary speech, incompatibility. the technical meaning of opposition is based on the diagram (given afterwards in the text) known as the square of opposition, and probably originated in a confused apprehension of the reason why it received that name. it was called the square of opposition, because it was intended to illustrate the doctrine of opposition in aristotle's sense and the ordinary sense of repugnance or incompatibility. what the square brings out is this. if the four forms a e i o are arranged symmetrically according as they differ in quantity, or quality, or both, it is seen that these differences do not correspond symmetrically to compatibility and incompatibility: that propositions may differ in quantity or in quality without being incompatible, and that they may differ in both (as contradictories) and be less violently incompatible than when they differ in one only (as contraries). the original purpose of the diagram was to bring this out, as is done in every exposition of it. hence it was called the square of opposition. but as a descriptive title this is a misnomer: it should have been the square of differences in quantity or quality. this misnomer has been perpetuated by appropriating opposition as a common name for difference in quantity or quality when the terms are the same and in the same order, and distinguishing it in this sense from repugnance or incompatibility (tataretus in summulas, _de oppositionibus_ [ ], keynes, _the opposition of propositions_ [ ]). seeing that there never is occasion to speak of opposition in the limited sense except in connexion with the square, there is no real risk of confusion. a common name is certainly wanted in that connexion, if only to say that opposition (in the limited or diagrammatic sense) does not mean incompatibility.] [footnote : cp. keynes, pt. ii. ch. ii. s. . aristotle laid down the distinction between contrary and contradictory to meet another quibble in contradiction, based on taking the universal as a whole and indivisible subject like an individual, of which a given predicate must be either affirmed or denied.] [footnote : i have said that there is little risk of confusion in using the word opposition in its technical or limited sense. there is, however, a little. when it is said that these inferences are based on opposition, or that opposition is a mode of immediate inference, there is confusion of ideas unless it is pointed out that when this is said, it is opposition in the ordinary sense that is meant. the inferences are really based on the rules of contrary and contradictory opposition; contraries cannot both be true, and of contradictories one or other must be.] chapter iii. the implication of propositions.--immediate formal inference. --education. the meaning of inference generally is a subject of dispute, and to avoid entering upon debatable ground at this stage, instead of attempting to define inference generally, i will confine myself to defining what is called formal inference, about which there is comparatively little difference of opinion. formal inference then is the apprehension of what is implied in a certain datum or admission: the derivation of one proposition, called the conclusion, from one or more given, admitted, or assumed propositions, called the premiss or premisses. when the conclusion is drawn from one proposition, the inference is said to be immediate; when more than one proposition is necessary to the conclusion, the inference is said to be mediate. given the proposition, "all poets are irritable," we can immediately infer that "nobody that is not irritable is a poet"; and the one admission implies the other. but we cannot infer immediately that "all poets make bad husbands". before we can do this we must have a second proposition conceded, that "all irritable persons make bad husbands". the inference in the second case is called mediate.[ ] the modes and conditions of valid mediate inference constitute syllogism, which is in effect the reasoning together of separate admissions. with this we shall deal presently. meantime of immediate inference. to state all the implications of a certain form of proposition, to make explicit all that it implies, is the same thing with showing what immediate inferences from it are legitimate. formal inference, in short, is the eduction of all that a proposition implies. most of the modes of immediate inference formulated by logicians are preliminary to the syllogistic process, and have no other practical application. the most important of them technically is the process known as conversion, but others have been judged worthy of attention. Æquipollent or equivalent forms--obversion. Æquipollence or equivalence ([greek: isodynamia]) is defined as the perfect agreement in sense of two propositions that differ somehow in expression.[ ] the history of Æquipollence in logical treatises illustrates two tendencies. there is a tendency on the one hand to narrow a theme down to definite and manageable forms. but when a useful exercise is discarded from one place it has a tendency to break out in another under another name. a third tendency may also be said to be specially well illustrated--the tendency to change the traditional application of logical terms. in accordance with the above definition of Æquipollence or equivalence, which corresponds with ordinary acceptation, the term would apply to all cases of "identical meaning under difference of expression". most examples of the reduction of ordinary speech into syllogistic form would be examples of æquipollence; all, in fact, would be so were it not that ordinary speech loses somewhat in the process, owing to the indefiniteness of the syllogistic symbol for particular quality, some. and in truth all such transmutations of expression are as much entitled to the dignity of being called immediate inferences as most of the processes so entitled. dr. bain uses the word with an approach to this width of application in discussing all that is now most commonly called immediate inference under the title of equivalent forms. the chief objection to this usage is that the converse _per accidens_ is not strictly equivalent. a debater may want for his argument less than the strict equivalent, and content himself with educing this much from his opponent's admission. (whether dr. bain is right in treating the minor and conclusion of a hypothetical syllogism as being equivalent to the major, is not so much a question of naming.) but in the history of the subject, the traditional usage has been to confine Æquipollence to cases of equivalence between positive and negative forms of expression. "not all are," is equivalent to "some are not": "not none is," to "some are". in pre-aldrichian text-books, Æquipollence corresponds mainly to what it is now customary to call (_e.g._, fowler, pt. iii. c. ii., keynes, pt. ii. c. vii.) immediate inference based on opposition. the denial of any proposition involves the admission of its contradictory. thus, if the negative particle "not" is placed before the sign of quantity, all or some, in a proposition, the resulting proposition is equivalent to the contradictory of the original. not all s is p = some s is not p. not any s is p = no s is p. the mediæval logicians tabulated these equivalents, and also the forms resulting from placing the negative particle after, or both before and after, the sign of quantity. under the title of Æquipollence, in fact, they considered the interpretation of the negative particle generally. if the negative is placed after the universal sign, it results in the contrary: if both before and after, in the subaltern. the statement of these equivalents is a puzzling exercise which no doubt accounts for the prominence given it by aristotle and the schoolmen. the latter helped the student with the following mnemonic line: _præ contradic., post contrar., præ postque subaltern._[ ] to Æquipollence belonged also the manipulation of the forms known after the _summulæ_ as _exponibiles_, notably _exclusive_ and _exceptive propositions_, such as none but barristers are eligible, the virtuous alone are happy. the introduction of a negative particle into these already negative forms makes a very trying problem in interpretation. the æquipollence of the exponibiles was dropped from text-books long before aldrich, and it is the custom to laugh at them as extreme examples of frivolous scholastic subtlety: but most modern text-books deal with part of the doctrine of the _exponibiles_ in casual exercises. curiously enough, a form left unnamed by the scholastic logicians because too simple and useless, has the name Æquipollent appropriated to it, and to it alone, by ueberweg, and has been adopted under various names into all recent treatises. bain calls it the formal obverse,[ ] and the title of obversion (which has the advantage of rhyming with conversion) has been adopted by keynes, miss johnson, and others. fowler (following karslake) calls it permutation. the title is not a happy one, having neither rhyme nor reason in its favour, but it is also extensively used. this immediate inference is a very simple affair to have been honoured with such a choice of terminology. "this road is long: therefore, it is not short," is an easy inference: the second proposition is the obverse, or permutation, or Æquipollent, or (in jevons's title) the immediate inference by privative conception, of the first. the inference, such as it is, depends on the law of excluded middle. either a term p, or its contradictory, not-p, must be true of any given subject, s: hence to affirm p of all or some s, is equivalent to denying not-p of the same: and, similarly, to deny p, is to affirm not-p. hence the rule of obversion;--substitute for the predicate term its contrapositive,[ ] and change the quality of the proposition. all s is p = no s is not-p. no s is p = all s is not-p. some s is p = some s is not not-p. some s is not p = some s is not-p. conversion. the process takes its name from the interchange of the terms. the predicate-term becomes the subject-term, and the subject-term the predicate-term. when propositions are analysed into relations of inclusion or exclusion between terms, the assertion of any such relation between one term and another, implies a converse relation between the second term and the first. the statement of this implied assertion is technically known as the converse of the original proposition, which may be called the _convertend_. three modes of conversion are commonly recognised:--(_a_) simple conversion; (_b_) conversion _per accidens_ or by limitation; (_c_) conversion by contraposition. (_a_) e and i can be simply converted, only the terms being interchanged, and quantity and quality remaining the same. if s is wholly excluded from p, p must be wholly excluded from s. if some s is contained in p, then some p must be contained in s. (_b_) a cannot be simply converted. to know that all s is contained in p, gives you no information about that portion of p which is outside s. it only enables you to assert that some p is s; that portion of p, namely, which coincides with s. o cannot be converted either simply or _per accidens_. some s is not p does not enable you to make any converse assertion about p. all p may be s, or no p may be s, or some p may be not s. all the three following diagrams are compatible with some s being excluded from p. [illustration: concentric circles of s and p - p in centre s in one circle and p in another circle. s and p each in a circle, overlapping circle. ] (_c_) another mode of conversion, known by mediæval logicians following boethius as _conversio per contra positionem terminorum_, is useful in some syllogistic manipulations. this converse is obtained by substituting for the predicate term its contrapositive or contradictory, not-p, making the consequent change of quality, and simply converting. thus all s is p is converted into the equivalent no not-p is s.[ ] some have called it "conversion by negation," but "negation" is manifestly too wide and common a word to be thus arbitrarily restricted to the process of substituting for one term its opposite. others (and this has some mediæval usage in its favour, though not the most intelligent) would call the form all not-p is not-s (the obverse or permutation of no not-p is s), the converse by contraposition. this is to conform to an imaginary rule that in conversion the converse must be of the same quality with the convertend. but the essence of conversion is the interchange of subject and predicate: the quality is not in the definition except by a bungle: it is an accident. no not-p is s, and some not-p is s are the forms used in syllogism, and therefore specially named. unless a form had a use, it was left unnamed, like the subalternate forms of syllogism: nomen habent nullum: nec, si bene colligis, usum. table of contrapositive converses. con. con. all s is p no not-p is s no s is p some not-p is s some s is not p some not-p is s some s is p none. when not-p is substituted for p, some s is p becomes some s is not not-p, and this form is inconvertible. other forms of immediate inference. i have already spoken of the immediate inferences based on the rules of contradictory and contrary opposition (see p. - part iii, ch. ii). another process was observed by thomson, and named _immediate inference by added determinants_. if it is granted that "a negro is a fellow-creature," it follows that "a negro in suffering is a fellow-creature in suffering". but that this does not follow for every attribute[ ] is manifest if you take another case:--"a tortoise is an animal: therefore, a fast tortoise is a fast animal". the form, indeed, holds in cases not worth specifying: and is a mere handle for quibbling. it could not be erected into a general rule unless it were true that whatever distinguishes a species within a class, will equally distinguish it in every class in which the first is included. modal consequence has also been named among the forms of immediate inference. by this is meant the inference of the lower degrees of certainty from the higher. thus _must be_ is said to imply _may be_; and _none can be_ to imply _none is_. dr. bain includes also _material obversion_, the analogue of _formal obversion_ applied to a subject. thus peace is beneficial to commerce, implies that war is injurious to commerce. dr. bain calls this material obversion because it cannot be practised safely without reference to the matter of the proposition. we shall recur to the subject in another chapter. [footnote : i purposely chose disputable propositions to emphasise the fact that formal logic has no concern with the truth, but only with the interdependence of its propositions.] [footnote : mark duncan, _inst. log._, ii. , .] [footnote : there can be no doubt that in their doctrine of Æquipollents, the schoolmen were trying to make plain a real difficulty in interpretation, the interpretation of the force of negatives. their results would have been more obviously useful if they had seen their way to generalising them. perhaps too they wasted their strength in applying it to the artificial syllogistic forms, which men do not ordinarily encounter except in the manipulation of syllogisms. their results might have been generalised as follows:-- ( ) a "not" placed before the sign of quantity contradicts the whole proposition. not "all s is p," not "no s is p," not "some s is p," not "some s is not p," are equivalent respectively to contradictories of the propositions thus negatived. ( ) a "not" placed after the sign of quantity affects the copula, and amounts to inverting its quality, thus denying the predicate term of the same quantity of the subject term of which it was originally affirmed, and _vice versâ_. all s is "not" p = no s is p. no s is "not" p = all s is p. some s is "not" p = some s is not p. some s is "not" not p = some s is p. ( ) if a "not" is placed before as well as after, the resulting forms are obviously equivalent (under rule ) to the assertion of the contradictories of the forms on the right (in the illustration of rule ). not | all s is "not" p = no s is p | = some s is p. not | no s is "not" p = all s is p | = some s is not p. not | some s is "not" p = some s is not p | = all s is p. not | some s is "not" not p = some s is p | = no s is p. ] [footnote : _formal_ to distinguish it from what he called the _material obverse_, about which more presently.] [footnote : the mediæval word for the opposite of a term, the word contradictory being confined to the propositional form.] [footnote : it is to be regretted that a practice has recently crept in of calling this form, for shortness, the contrapositive simply. by long-established usage, dating from boethius, the word contrapositive is a technical name for a terminal form, not-a, and it is still wanted for this use. there is no reason why the propositional form should not be called the converse by contraposition, or the contrapositive converse, in accordance with traditional usage.] [footnote : _cf._ stock, part iii. c. vii.; bain, _deduction_, p. .] chapter iv. the counter-implication of propositions. in discussing the axioms of dialectic, i indicated that the propositions of common speech have a certain negative implication, though this does not depend upon any of the so-called laws of thought, identity, contradiction, and excluded middle. since, however, the counter-implicate is an important guide in the interpretation of propositions, it is desirable to recognise it among the modes of immediate inference. i propose, then, first, to show that people do ordinarily infer at once to a counter-sense; second, to explain briefly the law of thought on which such an inference is justified; and, third, how this law may be applied in the interpretation of propositions, with a view to making subject and predicate more definite. every affirmation about anything is an implicit negation about something else. every say is a gainsay. that people ordinarily act upon this as a rule of interpretation a little observation is sufficient to show: and we find also that those who object to having their utterances interpreted by this rule often shelter themselves under the name of logic. suppose, for example, that a friend remarks, when the conversation turns on children, that john is a good boy, the natural inference is that the speaker has in his mind another child who is not a good boy. such an inference would at once be drawn by any actual hearer, and the speaker would protest in vain that he said nothing about anybody but john. suppose there are two candidates for a school appointment, a and b, and that stress is laid upon the fact that a is an excellent teacher. a's advocate would at once be understood to mean that b was not equally excellent as a teacher. the fairness of such inferences is generally recognised. a reviewer, for example, of one of mrs. oliphant's historical works, after pointing out some small errors, went on to say that to confine himself to censure of small points, was to acknowledge by implication that there were no important points to find fault with. yet such negative implications are often repudiated as illogical. it would be more accurate to call them extra-logical. they are not condemned by any logical doctrine: they are simply ignored. they are extra-logical only because they are not legitimated by the laws of identity, contradiction, and excluded middle: and the reason why logic confines itself to those laws is that they are sufficient for syllogism and its subsidiary processes. but, though extra-logical, to infer a counter-implicate is not unreasonable: indeed, if definition, clear vision of things in their exact relations, is our goal rather than syllogism, a knowledge of the counter-implicate is of the utmost consequence. such an implicate there must always be under an all-pervading law of thought which has not yet been named, but which may be called tentatively the law of homogeneous counter-relativity. the title, one hopes, is sufficiently technical-looking: though cumbrous, it is descriptive. the law itself is simple, and may be thus stated and explained. _the law of homogeneous counter-relativity._ every positive in thought has a contrapositive, and the positive and contrapositive are of the same kind. the first clause of our law corresponds with dr. bain's law of discrimination or relativity: it is, indeed, an expansion and completion of that law. nothing is known absolutely or in isolation; the various items of our knowledge are inter-relative; everything is known by distinction from other things. light is known as the opposite of darkness, poverty of riches, freedom of slavery, in of out; each shade of colour by contrast to other shades. what dr. bain lays stress upon is the element of difference in this inter-relativity. he bases this law of our knowledge on the fundamental law of our sensibility that change of impression is necessary to consciousness. a long continuance of any unvaried impression results in insensibility to it. we have seen instances of this in illustrating the maxim that custom blunts sensibility (p. ). poets have been beforehand with philosophers in formulating this principle. it is expressed with the greatest precision by barbour in his poem of "the bruce," where he insists that men who have never known slavery do not know what freedom is. thus contrar thingis evermare discoverings of t' other are. since, then, everything that comes within our consciousness comes as a change or transition from something else, it results that our knowledge is counter-relative. it is in the clash or conflict of impressions that knowledge emerges: every item of knowledge has its illuminating foil, by which it is revealed, over against which it is defined. every positive in thought has its contrapositive. so much for the element of difference. but this is not the whole of the inter-relativity. the hegelians rightly lay stress on the common likeness that connects the opposed items of knowledge. "thought is not only _distinction_; it is, at the same time, _relation_.[ ] if it marks off one thing from another, it, at the same time, connects one thing with another. nor can either of these functions of thought be separated from the other: as aristotle himself said, the knowledge of opposites is one. a thing which has nothing to distinguish it is unthinkable, but equally unthinkable is a thing which is so separated from all other things as to have no community with them. if then the law of contradiction be taken as asserting the self-identity of things or thoughts in a sense that excludes their community--in other words, if it be not taken as limited by another law which asserts the _relativity_ of the things or thoughts distinguished--it involves a false abstraction.... if, then, the world, as an intelligible world, is a world of distinction, differentiation, individuality, it is equally true that in it as an intelligible world there are no absolute separations or oppositions, no antagonisms which cannot be reconciled."[ ] in the penultimate sentence of this quotation dr. caird _differentiates_ his theory against a logical counter-theory of the law of identity, and in the last sentence against an ethical counter-theory: but the point here is that he insists on the relation of likeness among opposites. every impression felt is felt as a change or transition from something else: but it is a variation of the same impression--the something else, the contrapositive, is not entirely different. change itself is felt as the opposite of sameness, difference of likeness, and likeness of difference. we do not differentiate our impression against the whole world, as it were, but against something nearly akin to it--upon some common ground. the positive and the contrapositive are of the same kind. let us surprise ourselves in the act of thinking and we shall find that our thoughts obey this law. we take note, say, of the colour of the book before us: we differentiate it against some other colour actually before us in our field of vision or imagined in our minds. let us think of the blackboard as black: the blackness is defined against the whiteness of the figures chalked or chalkable upon it, or against the colour of the adjacent wall. let us think of a man as a soldier; the opposite in our minds is not the colour of his hair, or his height, or his birthplace, or his nationality, but some other profession--soldier, sailor, tinker, tailor. it is always by means of some contrapositive that we make the object of our thoughts definite; it is not necessarily always the same opposite, but against whatever opposite it is, they are always homogeneous. one colour is contradistinguished from another colour, one shade from another shade: colour may be contradistinguished from shape, but it is within the common genus of sensible qualities. a curious confirmation of this law of our thinking has been pointed out by mr. carl abel.[ ] in egyptian hieroglyphics, the oldest extant language, we find, he says, a large number of symbols with two meanings, the one the exact opposite of the other. thus the same symbol represents _strong_ and _weak_; _above_--_below_; _with_--_without_; _for_--_against_. this is what the hegelians mean by the reconciliation of antagonisms in higher unities. they do not mean that black is white, but only that black and white have something in common--they are both colours. i have said that this law of homogeneous counter-relativity has not been recognised by logicians. this, however, is only to say that it has not been explicitly formulated and named, as not being required for syllogism; a law so all-pervading could not escape recognition, tacit or express. and accordingly we find that it is practically assumed in definition: it is really the basis of definition _per genus et differentiam_. when we wish to have a definite conception of anything, to apprehend what it is, we place it in some genus and distinguish it from species of the same. in fact our law might be called the law of specification: in obeying the logical law of what we ought to do with a view to clear thinking, we are only doing with exactness and conscious method what we all do and cannot help doing with more or less definiteness in our ordinary thinking. it is thus seen that logicians conform to this law when they are not occupied with the narrow considerations proper to syllogism. and another unconscious recognition of it may be found in most logical text-books. theoretically the not-a of the law of contradiction--(a is not not-a)--is an infinite term. it stands for everything but a. this is all that needs to be assumed for conversion and syllogism. but take the examples given of the formal obverse or permutation, "all men are fallible". most authorities would give as the formal obverse of this, "no men are infallible". but, strictly speaking, "infallible" is of more limited and definite signification than not-fallible. not-fallible, other than fallible, is brown, black, chair, table, and every other nameable thing except fallible. thus in obversion and conversion by contraposition, the homogeneity of the negative term is tacitly assumed; it is assumed that a and not-a are of the same kind. now to apply this law of our thought to the interpretation of propositions. whenever a proposition is uttered we are entitled to infer at once (or _immediately_) that the speaker has in his mind some counter-proposition, in which what is overtly asserted of the ostensible subject is covertly denied of another subject. and we must know what this counter-proposition, the counter-implicate is, before we can fully and clearly understand his meaning. but inasmuch as any positive may have more than one contrapositive, we cannot tell immediately or without some knowledge of the circumstances or context, what the precise counter-implicate is. the peculiar fallacy incident to this mode of interpretation is, knowing that there must be some counter-implicate, to jump rashly or unwarily to the conclusion that it is some definite one. dr. bain applies the term material obverse to the form, not-s is not p, as distinguished from the form s is not not-p, which he calls the formal obverse, on the ground that we can infer the predicate-contrapositive at once from the form, whereas we cannot tell the subject-contrapositive without an examination of the matter. but in truth we cannot tell either predicate-contrapositive or subject-contrapositive as it is in the mind of the speaker from the bare utterance. we can only tell that if he has in his mind a proposition definitely analysed into subject and predicate, he must have contrapositives in his mind of both, and that they must be homogeneous. let a man say, "this book is a quarto". for all that we know he may mean that it is not a folio or that it is not an octavo: we only know for certain, under the law of homogeneous counter-relativity, that he means some definite other size. under the same law, we know that he has a homogeneous contrapositive of the subject, a subject that admits of the same predicate, some other book in short. what the particular book is we do not know. it would however be a waste of ingenuity to dwell upon the manipulation of formulæ founded on this law. the practical concern is to know that for the interpretation of a proposition, a knowledge of the counter-implicate, a knowledge of what it is meant to deny, is essential. the manipulation of formulæ, indeed, has its own special snare. we are apt to look for the counterparts of them in the grammatical forms of common speech. thus, it might seem to be a fair application of our law to infer from the sentence, "wheat is dear," that the speaker had in his mind that oats or sugar or shirting or some other commodity is cheap. but this would be a rash conclusion. the speaker may mean this, but he _may_ also mean that wheat is dear now as compared with some other time: that is, the positive subject in his mind may be "wheat as now," and the contrapositive "wheat as then". so a man may say, "all men are mortal," meaning that the angels never taste death, "angels" being the contrapositive of his subject "men". or he may mean merely that mortality is a sad thing, his positive subject being men as they are, and his contrapositive men as he desires them to be. or his emphasis may be upon the _all_, and he may mean only to deny that some one man in his mind (mr. gladstone, for example) is immortal. it would be misleading, therefore, to prescribe propositions as exercises in material obversion, if we give that name to the explicit expression of the contrapositive subject: it is only from the context that we can tell what this is. the man who wishes to be clearly understood gives us this information, as when the epigrammatist said: "we are all fallible--even the youngest of us". but the chief practical value of the law is as a guide in studying the development of opinions. every doctrine ever put forward has been put forward in opposition to a previous doctrine on the same subject. until we know what the opposed doctrine is, we cannot be certain of the meaning. we cannot gather it with precision from a mere study of the grammatical or even (in the narrow sense of the word) the logical content of the words used. this is because the framers of doctrines have not always been careful to put them in a clear form of subject and predicate, while their impugners have not moulded their denial exactly on the language of the original. no doubt it would have been more conducive to clearness if they had done so. but they have not, and we must take them as they are. thus we have seen that the hegelian doctrine of relativity is directed against certain other doctrines in logic and in ethics; that ultra-nominalism is a contradiction of a certain form of ultra-realism; and that various theories of predication each has a backward look at some predecessor. i quote from mr. a.b. walkley a very happy application of this principle of interpretation:-- "it has always been a matter for speculation why so sagacious an observer as diderot should have formulated the wild paradox that the greatest actor is he who feels his part the least. mr. archer's bibliographical research has solved this riddle. diderot's paradox was a protest against a still wilder one. it seems that a previous eighteenth century writer on the stage, a certain saint-albine, had advanced the fantastic propositions that none but a magnanimous man can act magnanimity, that only lovers can do justice to a love scene, and kindred assertions that read like variations on the familiar 'who drives fat oxen must himself be fat'. diderot saw the absurdity of this; he saw also the essentially artificial nature of the french tragedy and comedy of his own day; and he hastily took up the position which mr. archer has now shown to be untenable." this instance illustrates another principle that has to be borne in mind in the interpretation of doctrines from their historical context of counter-implication. this is the tendency that men have to put doctrines in too universal a form, and to oppose universal to universal, that is, to deny with the flat contrary, the very reverse, when the more humble contradictory is all that the truth admits of. if a name is wanted for this tendency, it might be called the tendency to over-contradiction. between "all are" and "none are," the sober truth often is that "some are" and "some are not," and the process of evolution has often consisted in the substitution of these sober forms for their more violent predecessors. [footnote : it is significant of the unsuitableness of the vague unqualified word relativity to express a logical distinction that dr. bain calls his law the law of relativity simply, having regard to the relation of difference, _i.e._, to counter-relativity, while dr. caird applies the name relativity simply to the relation of likeness, _i.e._, to co-relativity. it is with a view to taking both forms of relation into account that i name our law the law of homogeneous counter-relativity. the protagorean law of relativity has regard to yet another relation, the relation of knowledge to the knowing mind: these other logical laws are of relations among the various items of knowledge. aristotle's category of relation is a fourth kind of relation not to be confused with the others. "father--son," "uncle--nephew," "slave--master," are _relata_ in aristotle's sense: "father," "uncle" are homogeneous counter-relatives, varieties of kinship; so "slave," "freeman" are counter-relatives in social status.] [footnote : dr. caird's _hegel_, p. .] [footnote : see article on counter-sense, _contemporary review_, april, .] part iv. the interdependence of propositions.--mediate inference. --syllogism. chapter i. the syllogism. we have already defined mediate inference as the derivation of a conclusion from more than one proposition. the type or form of a mediate inference fully expressed consists of three propositions so related that one of them is involved or implied in the other two. distraction is exhausting. modern life is full of distraction [.'.] modern life is exhausting. we say nothing of the truth of these propositions. i purposely choose questionable ones. but do they hang together? if you admit the first two, are you bound in consistency to admit the third? is the truth of the conclusion a necessary consequence of the truth of the premisses? if so, it is a valid mediate inference from them. when one of the two premisses is more general than the conclusion, the argument is said to be deductive. you lead down from the more general to the less general. the general proposition is called the major premiss, or grounding proposition, or sumption: the other premiss the minor, or applying proposition, or subsumption. undue haste makes waste. this is a case of undue hasting. [.'.] it is a case of undue wasting. we may, and constantly do, apply principles and draw conclusions in this way without making any formal analysis of the propositions. indeed we reason mediately and deductively whenever we make any application of previous knowledge, although the process is not expressed in propositions at all and is performed so rapidly that we are not conscious of the steps. for example, i enter a room, see a book, open it and begin to read. i want to make a note of something: i look round, see a paper case, open it, take a sheet of paper and a pen, dip the pen in the ink and proceed to write. in the course of all this, i act upon certain inferences which might be drawn out in the form of syllogisms. first, in virtue of previous knowledge i recognise what lies before me as a book. the process by which i reach the conclusion, though it passes in a flash, might be analysed and expressed in propositions. whatever presents certain outward appearances, contains readable print. this presents such appearances. [.'.]it contains readable print. so with the paper case, and the pen, and the ink. i infer from peculiar appearances that what i see contains paper, that the liquid will make a black mark on the white sheet, and so forth. we are constantly in daily life subsuming particulars under known universals in this way. "whatever has certain visible properties, has certain other properties: this has the visible ones: therefore, it has the others" is a form of reasoning constantly latent in our minds. the syllogism may be regarded as the explicit expression of this type of deductive reasoning; that is, as the analysis and formal expression of this every-day process of applying known universals to particular cases. thus viewed it is simply the analysis of a mental process, as a psychological fact; the analysis of the procedure of all men when they reason from signs; the analysis of the kind of assumptions they make when they apply knowledge to particular cases. the assumptions may be warranted, or they may not: but as a matter of fact the individual who makes the confident inference has such assumptions and subsumptions latent in his mind. but practically viewed, that is _logically_ viewed, if you regard logic as a practical science, the syllogism is a contrivance to assist the correct performance of reasoning together or syllogising in difficult cases. it applies not to mental processes but to results of such expressed in words, that is, to propositions. where the syllogism comes in as a useful form is when certain propositions are delivered to you _ab extra_ as containing a certain conclusion; and the connexion is not apparent. these propositions are analysed and thrown into a form in which it is at once apparent whether the alleged connexion exists. this form is the syllogism: it is, in effect, an analysis of given arguments. it was as a practical engine or organon that it was invented by aristotle, an organon for the syllogising of admissions in dialectic. the germ of the invention was the analysis of propositions into terms. the syllogism was conceived by aristotle as a reasoning together of terms. his prime discovery was that whenever two propositions necessarily contain or imply a conclusion, they have a common term, that is, only three terms between them: that the other two terms which differ in each are the terms of the conclusion; and that the relation asserted in the conclusion between its two terms is a necessary consequence of their relations with the third term as declared in the premisses. such was aristotle's conception of the syllogism and such it has remained in logic. it is still, strictly speaking, a syllogism of terms: of propositions only secondarily and after they have been analysed. the conclusion is conceived analytically as a relation between two terms. in how many ways may this relation be established through a third term? the various moods and figures of the syllogism give the answer to that question. the use of the very abstract word "relation" makes the problem appear much more difficult than it really is. the great charm of aristotle's syllogism is its simplicity. the assertion of the conclusion is reduced to its simplest possible kind, a relation of inclusion or exclusion, contained or not contained. to show that the one term is or is not contained in the other we have only to find a third which contains the one and is contained or not contained in the other. the practical difficulties, of course, consist in the reduction of the conclusions and arguments of common speech to definite terms thus simply related. once they are so reduced, their independence or the opposite is obvious. therein lies the virtue of the syllogism. before proceeding to show in how many ways two terms may be syllogised through a third, we must have technical names for the elements. the third term is called the middle (m) ([greek: to meson]): the other two the extremes ([greek: akra]). the extremes are the subject (s) and the predicate (p) of the conclusion. in an affirmative proposition (the normal form) s is contained in p: hence p is called the major[ ] term ([greek: to meixon]), and s the minor ([greek: to elatton]), being respectively larger and smaller in extension. all difficulty about the names disappears if we remember that in bestowing them we start from the conclusion. that was the problem ([greek: problêma]) or thesis in dialectic, the question in dispute. the two premisses, or propositions giving the relations between the two extremes and the middle, are named on an equally simple ground. one of them gives the relation between the minor term, s, and the middle, m. s, all or some, is or is not in m. this is called the minor premiss. the other gives the relation between the major term and the middle. m, all or some, is or is not in p. this is called the major premiss.[ ] [footnote : aristotle calls the major the first ([greek: to prôton]) and the minor the last ([greek: to eschaton]), probably because that was their order in the conclusion when stated in his most usual form, "p is predicated of s," or "p belongs to s".] [footnote : when we speak of the minor or the major simply, the reference is to the terms. to avoid a confusion into which beginners are apt to stumble, and at the same time to emphasise the origin of the names, the premisses might be spoken of at first as the minor's premiss and the major's premiss. it was only in the middle ages when the origin of the syllogism had been forgotten, that the idea arose that the terms were called major and minor because they occurred in the major and the minor premiss respectively.] chapter ii. figures and moods of the syllogism. i.--the first figure. the forms (technically called moods, _i.e._, modes) of the first figure are founded on the simplest relations with the middle that will yield or that necessarily involve the disputed relation between the extremes. the simplest type is stated by aristotle as follows: "when three terms are so related that the last (the minor) is wholly in the middle, and the middle wholly either in or not in the first (the major) there must be a perfect syllogism of the extremes".[ ] when the minor is partly in the middle, the syllogism holds equally good. thus there are four possible ways in which two terms ([greek: oroi], plane enclosures) may be connected or disconnected through a third. they are usually represented by circles as being the neatest of figures, but any enclosing outline answers the purpose, and the rougher and more irregular it is the more truly will it represent the extension of a word. conclusion a. all m is in p. all s is in m. all s is in p. [illustration: concentric circles of p, m and s - s in centre] conclusion e. no m is in p. all s is in m. no s is in p. [illustration: concentric circles of m and s, s in centre and separate circle of p] conclusion i. all m is in p. some s is in m. some s is in p. [illustration: concentric circles of p and m, m in centre, both overlapped by circle of s] conclusion o. no m is in p. some s is in m. some s is not in p. [illustration: circles of m and p touching, each overlapped by circle of s] these four forms constitute what are known as the moods of the first figure of the syllogism. seeing that all propositions may be reduced to one or other of the four forms, a, e, i, or o, we have in these premisses abstract types of every possible valid argument from general principles. it is all the same whatever be the matter of the proposition. whether the subject of debate is mathematical, physical, social or political, once premisses in these forms are conceded, the conclusion follows irresistibly, _ex vi formæ, ex necessitate formæ_. if an argument can be analysed into these forms, and you admit its propositions, you are bound in consistency to admit the conclusion--unless you are prepared to deny that if one thing is in another and that other in a third, the first is in the third, or if one thing is in another and that other wholly outside a third, the first is also outside the third. this is called the axiom of syllogism. the most common form of it in logic is that known as the _dictum_, or _regula de omni et nullo:_ "whatever is predicated of all or none of a term, is predicated of whatever is contained in that term". it has been expressed with many little variations, and there has been a good deal of discussion as to the best way of expressing it, the relativity of the word best being often left out of sight. _best_ for what purpose? practically that form is the best which best commands general assent, and for this purpose there is little to choose between various ways of expressing it. to make it easy and obvious it is perhaps best to have two separate forms, one for affirmative conclusions and one for negative. thus: "whatever is affirmed of all m, is affirmed of whatever is contained in m: and whatever is denied of all m, is denied of whatever is contained in m". the only advantage of including the two forms in one expression, is compendious neatness. "a part of a part is a part of the whole," is a neat form, it being understood that an individual or a species is part of a genus. "what is said of a whole, is said of every one of its parts," is really a sufficient statement of the principle: the whole being the middle term, and the minor being a part of it, the major is predicable of the minor affirmatively or negatively if it is predicable similarly of the middle. this axiom, as the name imports, is indemonstrable. as aristotle pointed out in the case of the axiom of contradiction, it can be vindicated, if challenged, only by reducing the challenger to a practical absurdity. you can no more deny it than you can deny that if a leaf is in a book and the book is in your pocket, the leaf is in your pocket. if you say that you have a sovereign in your purse and your purse is in your pocket, and yet that the sovereign is not in your pocket: will you give me what is in your pocket for the value of the purse? ii.--the minor figures of the syllogism, and their reduction to the first. the word figure ([greek: schêma]) applies to the form or figure of the premisses, that is, the order of the terms in the statement of the premisses, when the major premiss is put first, and the minor second. in the first figure the order is m p s m but there are three other possible orders or figures, namely:-- fig. ii. fig. iii. fig. iv. pm mp pm sm ms ms. it results from the doctrines of conversion that valid arguments may be stated in these forms, inasmuch as a proposition in one order of terms may be equivalent to a proposition in another. thus no m is in p is convertible with no p is in m: consequently the argument no p is in m all s is in m, in the second figure is as much valid as when it is stated in the first-- no m is in p all s is in m. similarly, since all m is in s is convertible into some s is in m, the following arguments are equally valid:-- fig. iii. fig. i. all m is in p all m is in p = all m is in s some s is in m. using both the above converses in place of their convertends, we have-- fig. iv. fig. i. no p is in m no m is in p = all m is in s some s is in m. it can be demonstrated (we shall see presently how) that altogether there are possible four valid forms or moods of the second figure, six of the third, and five of the fourth. an ingenious mnemonic of these various moods and their reduction to the first figure by the transposition of terms and premisses has come down from the thirteenth century. the first line names the moods of the first, normal, or standard figure. ba_rb_a_r_a, ce_l_a_r_e_nt_, da_r_ii, fe_r_io_que_ prioris; ce_s_a_r_e, ca_m_e_str_e_s_, fe_st_i_n_o, ba_r_o_k_o, secundæ; tertia da_r_a_pt_i, di_s_a_m_i_s_, da_t_i_s_i, fe_l_a_pt_o_n_, bo_k_a_rd_o, fe_r_i_s_o_que_, habet; quarta insuper addit, b_r_a_m_a_nt_ip, ca_m_e_n_e_s_, di_m_a_r_i_s_, fe_s_a_p_o, f_r_e_s_i_s_o_n_. the vowels in the names of the moods indicate the propositions of the syllogism in the four forms, a e i o. to write out any mood at length you have only to remember the figure, and transcribe the propositions in the order of major premiss, minor premiss, and conclusion. thus, the second figure being pm sm fe_st_i_n_o is written-- no p is in m. some s is in m. some s is not in p. the fourth figure being pm ms di_m_a_r_i_s_ is some p is in m. all m is in s. some s is in p. the initial letter in a minor mood indicates that mood of the first to which it may be reduced. thus festino is reduced to ferio, and dimaris to darii. in the cases of baroko and bokardo, b indicates that you may employ barbara to bring any impugner to confusion, as shall be afterwards explained. the letters _s_, _m_, and _p_ are also significant. placed after a vowel, _s_ indicates that the proposition has to be simply converted. thus, fe_st_i_n_o:-- no p is in m. some s is in m. some s is not in p. simply convert the major premiss, and you get fe_r_io, of the first. no m is in p. some s is in m. some s is not in p. _m_ (_muta_, or _move_) indicates that the premisses have to be transposed. thus, in ca_m_e_str_e_s_, you have to transpose the premisses, as well as simply convert the minor premiss before reaching the figure of ce_l_a_r_e_nt_. all p is in m no m is in s = no s is in m all p is in m. from this it follows in ce_l_a_r_e_nt_ that no p is in s, and this simply converted yields no s is in p. a simple transposition of the premisses in di_m_a_r_i_s_ of the fourth some p is in m all m is in s yields the premisses of da_r_ii all m is in s some p is in m, but the conclusion some p is in s has to be simply converted. placed after a vowel, _p_ indicates that the proposition has to be converted _per accidens_. thus in fe_l_a_pt_o_n_ of the third (mp, ms) no m is in p all m is in s some s is not in p you have to substitute for all m is in s its converse by limitation to get the premisses of fe_r_io. two of the minor moods, baroko of the second figure, and bokardo of the third, cannot be reduced to the first figure by the ordinary processes of conversion and transposition. it is for dealing with these intractable moods that contraposition is required. thus in ba_r_o_k_o of the second (pm, sm) all p is in m. some s is not in m. substitute for the major premiss its converse by contraposition, and for the minor its formal obverse or permutation, and you have fe_r_io of the first, with not-m as the middle. no not-m is in p. some s is in not-m, some s is not in p. the processes might be indicated by the mnemonic fa_cs_o_c_o, with _c_ indicating the contraposition of the predicate term or formal obversion. the reduction of bo_k_a_rd_o, some m is not in p all m is in s some s is not in p, is somewhat more intricate. it may be indicated by do_cs_a_m_o_sc_. you substitute for the major premiss its converse by contraposition, transpose the premisses and you have da_r_ii. all m is in s. some not-p is in m. some not-p is in s. convert now the conclusion by contraposition, and you have some s is not in p. the author of the mnemonic apparently did not recognise contraposition, though it was admitted by boethius; and, it being impossible without this to demonstrate the validity of baroko and bokardo by showing them to be equivalent with valid moods of the first figure, he provided for their demonstration by the special process known as _reductio ad absurdum_. b indicates that barbara is the medium. the rationale of the process is this. it is an imaginary opponent that you reduce to an absurdity or self-contradiction. you show that it is impossible with consistency to admit the premisses and at the same time deny the conclusion. for, let this be done; let it be admitted as in ba_r_o_k_o that, all p is in m some s is not in m, but denied that some s is not in p. the denial of a proposition implies the admission of its contradictory. if it is not true that some s is not in p, it must be true that all s is in p. take this along with the admission that all p is in m, and you have a syllogism in ba_rb_a_r_a, all p is in m all s is in p, yielding the conclusion all s is in m. if then the original conclusion is denied, it follows that all s is in m. but this contradicts the minor premiss, which has been admitted to be true. it is thus shown that an opponent cannot admit the premisses and deny the conclusion without contradicting himself. the same process may be applied to bokardo. some m is not in p. all m is in s. some s is not in p. deny the conclusion, and you must admit that all s is in p. syllogised in barbara with all m is in s, this yields the conclusion that all m is in p, the contradictory of the major premiss. the beginner may be reminded that the argument _ad absurdum_ is not necessarily confined to baroko and bokardo. it is applied to them simply because they are not reducible by the ordinary processes to the first figure. it might be applied with equal effect to other moods, di_m_a_r_i_s_, _e.g._, of the third. some m is in p. all m is in s. some s is in p. let some s is in p be denied, and no s is in p must be admitted. but if no s is in p and all m is in s, it follows (in celarent) that no m is in p, which an opponent cannot hold consistently with his admission that some m is in p. the beginner sometimes asks: what is the use of reducing the minor figures to the first? the reason is that it is only when the relations between the terms are stated in the first figure that it is at once apparent whether or not the argument is valid under the axiom or _dictum de omni_. it is then undeniably evident that if the dictum holds the argument holds. and if the moods of the first figure hold, their equivalents in the other figures must hold too. aristotle recognised only two of the minor figures, the second and third, and thus had in all only fourteen valid moods. the recognition of the fourth figure is attributed by averroes to galen. averroes himself rejects it on the ground that no arguments expressed naturally, that is, in accordance with common usage, fall into that form. this is a sufficient reason for not spending time upon it, if logic is conceived as a science that has a bearing upon the actual practice of discussion or discursive thought. and this was probably the reason why aristotle passed it over. if however the syllogism of terms is to be completed as an abstract doctrine, the fourth figure must be noticed as one of the forms of premisses that contain the required relation between the extremes. there is a valid syllogism between the extremes when the relations of the three terms are as stated in certain premisses of the fourth figure. iii.--the sorites. a chain of syllogisms is called a sorites. thus:-- all a is in b. all b is in c. all c is in d. : : : : all x is in z. [.'.] all a is in z. a minor premiss can thus be carried through a series of universal propositions each serving in turn as a major to yield a conclusion which can be syllogised with the next. obviously a sorites may contain one particular premiss, provided it is the first; and one universal negative premiss, provided it is the last. a particular or a negative at any other point in the chain is an insuperable bar. [footnote : [greek: hotan oun horoi treis autôs echôsi pros allêlous ôste ton eschaton en holô einai tô mesô, kai ton meson en holô tô krôtô ê einai ê mê einai, anankê tôn akrôn einai syllogismon teleion.] (anal. prior., i. .)] chapter iii. the demonstration of the syllogistic moods.--the canons of the syllogism. how do we know that the nineteen moods are the only possible forms of valid syllogism? aristotle treated this as being self-evident upon trial and simple inspection of all possible forms in each of his three figures. granted the parity between predication and position in or out of a limited enclosure (term, [greek: horos]), it is a matter of the simplest possible reasoning. you have three such terms or enclosures, s, p and m; and you are given the relative positions of two of them to the third as a clue to their relative positions to one another. is s in or out of p, and is it wholly in or wholly out or partly in or partly out? you know how each of them lies toward the third: when can you tell from this how s lies towards p? we have seen that when m is wholly in or out of p, and s wholly or partly in m, s is wholly or partly in or out of p. try any other given positions in the first figure, and you find that you cannot tell from them how s lies relatively to p. unless the major premiss is universal, that is, unless m lies wholly in or out of p, you can draw no conclusion, whatever the minor premiss may give. given, _e.g._, all s is in m, it may be that all s is in p, or that no s is in p, or that some s is in p, or that some s is not in p. [illustration: circles of m and p, overlapping, with instances of a circle of s: . s in m, but not in p; . s in the overlap of m and p; . s in m, some s in p. ] again, unless the minor premiss is affirmative, no matter what the major premiss may be, you can draw no conclusion. for if the minor premiss is negative, all that you know is that all s or some s lies somewhere outside m; and however m may be situated relatively to p, that knowledge cannot help towards knowing how s lies relatively to p. all s may be p, or none of it, or part of it. given all m is in p; the all s (or some s) which we know to be outside of m may lie anywhere in p or out of it. [illustration: concentric circles of p and m, m in center, with instances of circle of s: . s wholly outside p and m; . s partly overlapping both p and m, and partly outside both; . s overlapping p, but outside m; . s wholly within p, but wholly outside m; . s touching circle of p, but outside both circles. ] similarly, in the second figure, trial and simple inspection of all possible conditions shows that there can be no conclusion unless the major premiss is universal, and one of the premisses negative. another and more common way of eliminating the invalid forms, elaborated in the middle ages, is to formulate principles applicable irrespective of figure, and to rule out of each figure the moods that do not conform to them. these regulative principles are known as the canons of the syllogism. _canon i._ in every syllogism there should be three, and not more than three, terms, and the terms must be used throughout in the same sense. it sometimes happens, owing to the ambiguity of words, that there seem to be three terms when there are really four. an instance of this is seen in the sophism:-- he who is most hungry eats most. he who eats least is most hungry. [.'.] he who eats least eats most. this canon, however, though it points to a real danger of error in the application of the syllogism to actual propositions, is superfluous in the consideration of purely formal implication, it being a primary assumption that terms are univocal, and remain constant through any process of inference. under this canon, mark duncan says (_inst. log._, iv. , ), is comprehended another commonly expressed in this form: there should be nothing in the conclusion that was not in the premisses: inasmuch as if there were anything in the conclusion that was in neither of the premisses, there would be four terms in the syllogism. the rule that in every syllogism there must be three, and only three, propositions, sometimes given as a separate canon, is only a corollary from canon i. _canon ii._ the middle term must be distributed once at least in the premisses. the middle term must either be wholly in, or wholly out of, one or other of the extremes before it can be the means of establishing a connexion between them. if you know only that it is partly in both, you cannot know from that how they lie relatively to one another: and similarly if you know only that it is partly outside both. the canon of distributed middle is a sort of counter-relative supplement to the _dictum de omni_. whatever is predicable of a whole distributively is predicable of all its several parts. if in neither premiss there is a predication about the whole, there is no case for the application of the axiom. _canon iii._ no term should be distributed in the conclusion that was not distributed in the premisses. if an assertion is not made about the whole of a term in the premisses, it cannot be made about the whole of that term in the conclusion without going beyond what has been given. the breach of this rule in the case of the major term is technically known as the illicit process of the major: in the case of the minor term, illicit process of the minor. great use is made of this canon in cutting off invalid moods. it must be remembered that the predicate term is "distributed" or taken universally in o (some s is not in p) as well as in e (no s is in p); and that p is never distributed in affirmative propositions. _canon iv._ no conclusion can be drawn from two negative premisses. two negative premisses are really tantamount to a declaration that there is no connexion whatever between the major and minor (as quantified in the premisses) and the term common to both premisses; in short, that this is not a middle term--that the condition of a valid syllogism does not exist. there is an apparent exception to this when the real middle in an argument is a contrapositive term, not-m. thus:-- nobody who is not thirsty is suffering from fever. this person is not thirsty. [.'.] he is not suffering from fever. but in such cases it is really the absence of a quality or rather the presence of an opposite quality on which we reason; and the minor premiss is really affirmative of the form s is in not-m. _canon v._ if one premiss is negative, the conclusion must be negative. if one premiss is negative, one of the extremes must be excluded in whole or in part from the middle term. the other must therefore (under canon iv.) declare some coincidence between the middle term and the other extreme; and the conclusion can only affirm exclusion in whole or in part from the area of this coincidence. _canon vi._ no conclusion can be drawn from two particular premisses. this is evident upon a comparison of terms in all possible positions, but it can be more easily demonstrated with the help of the preceding canons. the premisses cannot both be particular and yield a conclusion without breaking one or other of those canons. suppose both are affirmative, ii, the middle is not distributed in either premiss. suppose one affirmative and the other negative, io, or oi. then, whatever the figure may be, that is, whatever the order of the terms, only one term can be distributed, namely, the predicate of o. this (canon ii.) must be the middle. but in that case there must be illicit process of the major (canon iii.), for one of the premisses being negative, the conclusion is negative (canon v.), and p its predicate is distributed. briefly, in a negative mood, both major and middle must be distributed, and if both premisses are particular this cannot be. _canon vii._ if one premiss is particular the conclusion is particular. this canon is sometimes combined with what we have given as canon v., in a single rule: "the conclusion follows the weaker premiss". it can most compendiously be demonstrated with the help of the preceding canons. suppose both premisses affirmative, then, if one is particular, only one term can be distributed in the premisses, namely, the subject of the universal affirmative premiss. by canon ii., this must be the middle, and the minor, being undistributed in the premisses, cannot be distributed in the conclusion. that is, the conclusion cannot be universal--must be particular. suppose one premiss negative, the other affirmative. one premiss being negative, the conclusion must be negative, and p must be distributed in the conclusion. before, then, the conclusion can be universal, all three terms, s, m, and p, must, by canons ii. and iii., be distributed in the premisses. but whatever the figure of the premisses, only two terms can be distributed. for if one of the premisses be o, the other must be a, and if one of them is e, the other must be i. hence the conclusion must be particular, otherwise there will be illicit process of the minor, or of the major, or of the middle. the argument may be more briefly put as follows: in an affirmative mood, with one premiss particular, only one term can be distributed in the premisses, and this cannot be the minor without leaving the middle undistributed. in a negative mood, with one premiss particular, only two terms can be distributed, and the minor cannot be one of them without leaving either the middle or the major undistributed. armed with these canons, we can quickly determine, given any combination of three propositions in one of the figures, whether it is or is not a valid syllogism. observe that though these canons hold for all the figures, the figure must be known, in all combinations containing a or o, before we can settle a question of validity by canons ii. and iii., because the distribution of terms in a and o depends on their order in predication. take aee. in fig. i.-- all m is in p no s is in m no s is in p-- the conclusion is invalid as involving an illicit process of the major. p is distributed in the conclusion and not in the premisses. in fig. ii. aee-- all p is in m no s is in m no s is in p-- the conclusion is valid (camestres). in fig. iii. aee-- all m is in p no m is in s no s is in p-- the conclusion is invalid, there being illicit process of the major. in fig. iv. aee is valid (camenes). take eio. a little reflection shows that this combination is valid in all the figures if in any, the distribution of the terms in both cases not being affected by their order in predication. both e and i are simply convertible. that the combination is valid is quickly seen if we remember that in negative moods both major and middle must be distributed, and that this is done by e. eie is invalid, because you cannot have a universal conclusion with one premiss particular. aii is valid in fig. i. or fig. iii., and invalid in figs. ii. and iv., because m is the subject of a in i. and iii. and predicate in ii. and iv. oao is valid only in fig. iii., because only in that figure would this combination of premisses distribute both m and p. simple exercises of this kind may be multiplied till all possible combinations are exhausted, and it is seen that only the recognised moods stand the test. if a more systematic way of demonstrating the valid moods is desired, the simplest method is to deduce from the canons special rules for each figure. aristotle arrived at these special rules by simple inspection, but it is easier to deduce them. i. in the first figure, the major premiss must be universal, and the minor premiss affirmative. to make this evident by the canons, we bear in mind the scheme or figure-- m in p s in m-- and try the alternatives of affirmative moods and negative moods. obviously in an affirmative mood the middle is undistributed unless the major premiss is universal. in a negative mood, ( ) if the major premiss is o, the minor must be affirmative, and m is undistributed; ( ) if the major premiss is i, m may be distributed by a negative minor premiss, but in that case there would be an illicit process of the major--p being distributed in the conclusion (canon v.) and not in the premisses. thus the major premiss can neither be o nor i, and must therefore be either a or e, _i.e._, must be universal. that the minor must be affirmative is evident, for if it were negative, the conclusion must be negative (canon v.) and the major premiss must be affirmative (canon iv.), and this would involve illicit process of the major, p being distributed in the conclusion and not in the premisses. these two special rules leave only four possible valid forms in the first figure. there are sixteen possible combinations of premisses, each of the four types of proposition being combinable with itself and with each of the others. aa ea ia oa ae ee ie oe ai ei ii oi ao eo io oo special rule i. wipes out the columns on the right with the particular major premisses; and ae, ee, ao, and eo are rejected by special rule ii., leaving ba_rb_a_r_a, ce_l_a_r_e_nt_, da_r_ii and fe_r_io. ii. in the second figure, only negative moods are possible, and the major premiss must be universal. only negative moods are possible, for unless one premiss is negative, m being the predicate term in both-- p in m s in m-- is undistributed. only negative moods being possible, there will be illicit process of the major unless the major premiss is universal, p being its subject term. these special rules reject aa and ai, and the two columns on the right. to get rid of ee and eo, we must call in the general canon iv.; which leaves us with ea, ae, ei, and ao--ce_s_a_r_e, ca_m_e_str_e_s_, fe_st_i_n_o ba_r_o_k_o. iii. in the third figure, the minor premiss must be affirmative. otherwise, the conclusion would be negative, and the major premiss affirmative, and there would be illicit process of the major, p being the predicate term in the major premiss. m in p m in s. this cuts off ae, ee, ie, oe, ao, eo, io, oo,--the second and fourth rows in the above list. ii and oi are inadmissible by canon vi.; which leaves aa, ia, ai, ea, oa, ei--da_r_a_pt_i, di_s_a_m_i_s_, da_t_i_s_i, fe_l_a_pt_o_n_, bo_k_a_rd_o, fe_r_i_s_o--three affirmative moods and three negative. iv. the fourth figure is fenced by three special rules. ( ) in negative moods, the major premiss is universal. ( ) if the minor is negative, both premisses are universal. ( ) if the major is affirmative, the minor is universal. ( ) otherwise, the figure being p in m m in s, there would be illicit process of the major. ( ) the major must be universal by special rule ( ), and if the minor were not also universal, the middle would be undisturbed. ( ) otherwise m would be undistributed. rule ( ) cuts off the right-hand column, oa, oe, oi, and oo; also ie and io. rule ( ) cuts off ao, eo. rule ( ) cuts off ai, ii. ee goes by general canon iv.; and we are left with aa, ae, ia, ea, ei--b_r_a_m_a_nt_i_p_, ca_m_e_n_e_s_, di_m_a_r_i_s_, fe_s_a_p_o, f_r_e_s_i_s_o_n_. chapter iv. the analysis of arguments into syllogistic forms. turning given arguments into syllogistic form is apt to seem as trivial and useless as it is easy and mechanical. in most cases the necessity of the conclusion is as apparent in the plain speech form as in the artificial logical form. the justification of such exercises is that they give familiarity with the instrument, serving at the same time as simple exercises in ratiocination: what further uses may be made of the instrument once it is mastered, we shall consider as we proceed. i.--first figure. given the following argument to be put into syllogistic form: "no war is long popular: for every war increases taxation; and the popularity of anything that touches the pocket is short-lived". the simplest method is to begin with the conclusion--"no war is long popular"--no s is p--then to examine the argument to see whether it yields premisses of the necessary form. keeping the form in mind, celarent of fig. i.-- no m is p all s is m no s is p-- we see at once that "every war increases taxation" is of the form all s is m. does the other sentence yield the major premiss no m is p, when m represents the increasing of taxation, _i.e._, a class bounded by that attribute? we see that the last sentence of the argument is equivalent to saying that "nothing that increases taxation is long popular"; and this with the minor yields the conclusion in celarent. nothing that increases taxation is long popular. every war increases taxation. no war is long popular. observe, now, what in effect we have done in thus reducing the argument to the first figure. in effect, a general principle being alleged as justifying a certain conclusion, we have put that principle into such a form that it has the same predicate with the conclusion. all that we have then to do in order to inspect the validity of the argument is to see whether the subject of the conclusion is contained in the subject of the general principle. is war one of the things that increase taxation? is it one of that class? if so, then it cannot long be popular, long popularity being an attribute that cannot be affirmed of any of that class. reducing to the first figure, then, amounts simply to making the predication of the proposition alleged as ground uniform with the conclusion based upon it. the minor premiss or applying proposition amounts to saying that the subject of the conclusion is contained in the subject of the general principle. is the subject of the conclusion contained in the subject of the general principle when the two have identical predicates? if so, the argument falls at once under the _dictum de omni et nullo_. two things may be noted concerning an argument thus simplified. . it is not necessary, in order to bring an argument under the _dictum de omni_, to reduce the predicate to the form of an extensive term. in whatever form, abstract or concrete, the predication is made of the middle term, it is applicable in the same form to that which is contained in the middle term. . the quantity of the minor term does not require special attention, inasmuch as the argument does not turn upon it. in whatever quantity it is contained in the middle, in that quantity is the predicate of the middle predicable of it. these two points being borne in mind, the attention may be concentrated on the middle term and its relations with the extremes. that the predicate may be left unanalysed without affecting the simplicity of the argument or in any way obscuring the exhibition of its turning-point, has an important bearing on the reduction of modals. the modality may be treated as part of the predicate without in any way obscuring what it is the design of the syllogism to make clear. we have only to bear in mind that however the predicate may be qualified in the premisses, the same qualification must be transferred to the conclusion. otherwise we should have the fallacy of four terms, _quaternio terminorum_. to raise the question: what is the proper form for a modal of possibility, a or i? is to clear up in an important respect our conceptions of the universal proposition, "victories may be gained by accident". should this be expressed as a or i? is the predicate applicable to all victories or only to some? obviously the meaning is that of any victory it may be true that it was gained by accident, and if we treat the "mode" as part of the predicate term "things that may be gained by accident," the form of the proposition is all s is in p. but, it may be asked, does not the proposition that victories may be gained by accident rest, as a matter of fact, on the belief that some victories have been gained in this way? and is not, therefore, the proper form of proposition some s is p? this, however, is a misunderstanding. what we are concerned with is the formal analysis of propositions as given. and some victories have been gained by accident is not the formal analysis of victories may be gained by accident. the two propositions do not give the same meaning in different forms: the meaning as well as the form is different. the one is a statement of a matter of fact: the other of an inference founded on it. the full significance of the modal proper may be stated thus: in view of the fact that some victories have been gained by accident, we are entitled to say of any victory, in the absence of certain knowledge, that it may be one of them. a general proposition, in short, is a proposition about a genus, taken universally. ii.--second figure. for testing arguments from general principles, the first figure is the simplest and best form of analysis. but there is one common class of arguments that fall naturally, as ordinarily expressed, into the second figure, namely, negative conclusions from the absence of distinctive signs or symptoms, or necessary conditions. thirst, for example, is one of the symptoms of fever: if a patient is not thirsty, you can conclude at once that his illness is not fever, and the argument, fully expressed, is in the second figure. all fever-stricken patients are thirsty. this patient is not thirsty. [.'.] he is not fever-stricken. arguments of this type are extremely common. armed with the general principle that ill-doers are ill-dreaders, we argue from a man's being unsuspicious that he is not guilty. the negative diagnosis of the physician, as when he argues from the absence of sore throat or the absence of a white speck in the throat that the case before him is not one of scarlatina or diphtheria, follows this type: and from its utility in making such arguments explicit, the second figure may be called the figure of negative diagnosis. it is to be observed, however, that the character of the argument is best disclosed when the major premiss is expressed by its converse by contraposition. it is really from the absence of a symptom that the physician concludes; as, for example: "no patient that has not a sore throat is suffering from scarlatina". and the argument thus expressed is in the first figure. thus the reduction of baroko to the first figure by contraposition of the middle is vindicated as a really useful process. the real middle is a contrapositive term, and the form corresponds more closely to the reasoning when the argument is put in the first figure. the truth is that if the positive term or sign or necessary condition is prominent as the basis of the argument, there is considerable risk of fallacy. sore throat being one of the symptoms of scarlatina, the physician is apt on finding this symptom present to jump to a positive conclusion. this is equivalent technically to drawing a positive conclusion from premisses of the second figure. all scarlatina patients have sore throat. this patient has sore throat. a positive conclusion is technically known as a non-sequitur (doesn't follow). so with arguments from the presence of a necessary condition which is only one of many. given that it is impossible to pass without working at the subject, or that it is impossible to be a good marksman without having a steady hand, we are apt to argue that given also the presence of this condition, a conclusion is implicated. but really the premisses given are only two affirmatives of the second figure. "it is impossible to pass without working at the subject." this, put into the form no not-m is p, is to say that "none who have not worked can pass". this is equivalent, as the converse by contraposition, with-- all capable of passing have worked at the subject. but though q has worked at the subject, it does not follow that he is capable of passing. technically the middle is undistributed. on the other hand, if he has not worked at the subject, it follows that he is not capable of passing. we can draw a conclusion at once from the absence of the necessary condition, though none can be drawn from its presence alone. third figure. arguments are sometimes advanced in the form of the third figure. for instance: killing is not always murder: for tyrannicide is not murder, and yet it is undoubtedly killing. or again: unpleasant things are sometimes salutary: for afflictions are sometimes so, and no affliction can be called pleasant. these arguments, when analysed into terms, are, respectively, felapton and disamis. no tyrannicide is murder; all tyrannicide is killing; some killing is not murder. some afflictions are salutary things; all afflictions are unpleasant things; some unpleasant things are salutary things. the syllogistic form cannot in such cases pretend to be a simplification of the argument. the argument would be equally unmistakable if advanced in this form: some s is not p, for example, m. some killing is not murder, _e.g.,_ tyrannicide. some unpleasant things are salutary, _e.g.,_ some afflictions. there is really no "deduction" in the third figure, no leading down from general to particular. the middle term is only an example of the minor. it is the syllogism of contradictory examples. in actual debate examples are produced to disprove a universal assertion, affirmative or negative. suppose it is maintained that every wise man has a keen sense of humour. you doubt this: you produce an instance of the opposite, say milton. the force of your contradictory instance is not increased by exhibiting the argument in syllogistic form: the point is not made clearer. the third figure was perhaps of some use in yes and no dialectic. when you had to get everything essential to your conclusion definitely admitted, it was useful to know that the production of an example to refute a generality involved the admission of two propositions. you must extract from your opponent both that milton was a wise man, and that milton had not a keen sense of humour, before you could drive him from the position that all wise men possess that quality. _examples for analysis._ scarlet flowers have no fragrance: this flower has no fragrance: does it follow that this flower is of a scarlet colour? interest in the subject is an indispensable condition of learning easily; z is interested in the subject: he is bound, therefore, to learn easily. it is impossible to be a good shot without having a steady hand: john has a steady hand: he is capable, therefore, of becoming a good shot. some victories have been won by accident; for example, maiwand. intemperance is more disgraceful than cowardice, because people have more opportunities of acquiring control of their bodily appetites. "some men are not fools, yet all men are fallible." what follows? "some men allow that their memory is not good: every man believes in his own judgment." what is the conclusion, and in what figure and mood may the argument be expressed? "an honest man's the noblest work of god: z is an honest man": therefore, he is--what? examine the logical connexion between the following "exclamation" and "answer": "but i hear some one exclaiming that wickedness is not easily concealed. to which i answer, nothing great is easy." "if the attention is actively aroused, sleep becomes impossible: hence the sleeplessness of anxiety, for anxiety is a strained attention upon an impending disaster." "to follow truth can never be a subject of regret: free inquiry does lead a man to regret the days of his childish faith; therefore it is not following truth."--_j. h. newman._ he would not take the crown: therefore 'tis certain he was not ambitious. as he was valiant, i honour him; as he was ambitious, i slew him. the utopians learned the language of the greeks with more readiness because they were originally of the same race with them. nothing which is cruel can be expedient, for cruelty is most revolting to the nature of man. "the fifth century saw the foundation of the frank dominion in gaul, and the first establishment of the german races in britain. the former was effected in a single long reign, by the energy of one great ruling tribe, which had already modified its traditional usages, and now, by the adoption of the language and religion of the conquered, prepared the way for a permanent amalgamation with them." in the second of the above sentences a general proposition is assumed. show in syllogistic form how the last proposition in the sentence depends upon it. "i do not mean to contend that active benevolence may not hinder a man's advancement in the world: for advancement greatly depends upon a reputation for excellence in some one thing of which the world perceives that it has present need: and an obvious attention to other things, though perhaps not incompatible with the excellence itself, may easily prevent a person from obtaining a reputation for it." pick out the propositions here given as interdependent. examine whether the principle alleged is sufficiently general to necessitate a conclusion. in what form would it be so? chapter v. enthymemes. there is a certain variety in the use of the word enthymeme among logicians. in the narrowest sense, it is a valid formal syllogism, with one premiss suppressed. in the widest sense it is simply an argument, valid or invalid, formal in expression or informal, with only one premiss put forward or hinted at, the other being held in the mind ([greek: en thymô]). this last is the aristotelian sense. it is only among formal logicians of the straitest sect that the narrowest sense prevails. hamilton divides enthymemes into three classes according as it is the major premiss, the minor premiss, or the conclusion that is suppressed. thus, a full syllogism being:-- all liars are cowards: caius is a liar: [.'.] caius is a coward:-- this may be enthymematically expressed in three ways. i. enthymeme of the first order (_major understood_). caius is a coward; for caius is a liar. ii. enthymeme of the second order (_minor understood_). caius is a coward; for all liars are cowards. iii. enthymeme of the third order (_conclusion understood_). all liars are cowards, and caius is a liar. the third order is a contribution of hamilton's own. it is superfluous, inasmuch as the conclusion is never suppressed except as a rhetorical figure of speech. hamilton confines the word enthymeme to valid arguments, in pursuance of his view that pure logic has no concern with invalid arguments. aristotle used enthymeme in the wider sense of an elliptically expressed argument. there has been some doubt as to the meaning of his definition, but that disappears on consideration of his examples. he defines an enthymeme (prior analyt., ii. ) as "a syllogism from probabilities or signs" ([greek: syllogismos ex eikotôn ê sêmeiôn]). the word syllogism in this connexion is a little puzzling. but it is plain from the examples he gives that he meant here by syllogism not even a correct reasoning, much less a reasoning in the explicit form of three terms and three propositions. he used syllogism, in fact, in the same loose sense in which we use the words reasoning and argument, applying without distinction of good and bad. the sign, he says, is taken in three ways, in as many ways as there are syllogistic figures. ( ) a sign interpreted in the first figure is conclusive. thus: "this person has been drowned, for he has froth in the trachea". taken in the first figure with "all who have froth in the trachea have been drowned" as a major premiss, this argument is valid. the sign is conclusive. ( ) "this patient is fever-stricken, for he is thirsty." assumed that "all fever-stricken patients are thirsty," this is an argument in the second figure, but it is not a valid argument. thirst is a sign or symptom of fever, but not a conclusive sign, because it is indicative of other ailments also. yet the argument has a certain probability. ( ) "wise men are earnest ([greek: spoudaioi]), for pittacus is earnest." here the suppressed premiss is that "pittacus is wise". fully expressed, the argument is in the third figure:-- pittacus is earnest. pittacus is wise. [.'.] wise men are earnest. here again the argument is inconclusive and yet it has a certain probability. the coincidence of wisdom with earnestness in one notable example lends a certain air of probability to the general statement. such are aristotle's examples or strict parallels to them. the examples illustrate also what he says in his _rhetoric_ as to the advantages of enthymemes. for purposes of persuasion enthymemes are better than explicit syllogisms, because any inconclusiveness there may be in the argument is more likely to pass undetected. as we shall see, one main use of the syllogism is to force tacit assumptions into light and so make their true connexion or want of connexion apparent. in logic enthymemes are recognised only to be shown up: the elliptical expression is a cover for fallacy, which it is the business of the logician to strip off. in aristotle's examples one of the premisses is expressed. but often the arguments of common speech are even less explicit than this. a general principle is vaguely hinted at: a subject is referred to a class the attributes of which are assumed to be definitely known. thus:-- he was too ambitious to be scrupulous in his choice of means. he was too impulsive not to have made many blunders. each of these sentences contains a conclusion and an enthymematic argument in support of it. the hearer is understood to have in his mind a definite idea of the degree of ambition at which a man ceases to be scrupulous, or the degree of impulsiveness that is incompatible with accuracy. one form of enthymeme is so common in modern rhetoric as to deserve a distinctive name. it may be called the enthymeme of the abstractly denominated principle. a conclusion is declared to be at variance with the principles of political economy, or contrary to the doctrine of evolution, or inconsistent with heredity, or a violation of the sacred principle of freedom of contract. it is assumed that the hearer is familiar with the principles referred to. as a safeguard against fallacy, it may be well to make the principle explicit in a proposition uniform with the conclusion. chapter vi. the utility of the syllogism. the main use of the syllogism is in dealing with incompletely expressed or elliptical arguments from general principals. this may be called enthymematic argument, understanding by enthymeme an argument with only one premiss put forward or hinted at, the other being held in the mind. in order to test whether such reasoning is sound or unsound, it is of advantage to make the argument explicit in syllogistic form. there have been heaps and mazes of discussion about the use of the syllogism, much of it being profitable as a warning against the neglect of formal logic. again and again it has been demonstrated that the syllogism is useless for certain purposes, and from this it has been concluded that the syllogism is of no use at all. the inventor of the syllogism had a definite practical purpose, to get at the simplest, most convincing, undeniable and irresistible way of putting admitted or self-evident propositions so that their implication should be apparent. his ambition was to furnish a method for the yes and no dialectician, and the expounder of science from self-evident principles. a question being put up for discussion, it was an advantage to analyse it, and formulate the necessary premisses: you could then better direct your interrogations or guard your answers. the analysis is similarly useful when you want to construct an argument from self-evident principles. all that the syllogism could show was the consistency of the premisses with the conclusion. the conclusion could not go beyond the premisses, because the questioner could not go beyond the admissions of the respondent. there is indeed an advance, but not an advance upon the two premisses taken together. there is an advance upon any one of them, and this advance is made with the help of the other. both must be admitted: a respondent may admit one without being committed to the conclusion. let him admit both and he cannot without self-contradiction deny the conclusion. that is all. dialectic of the yes and no kind is no longer practised. does any analogous use for the syllogism remain? is there a place for it as a safeguard against error in modern debate? as a matter of fact it is probably more useful now than it was for its original purpose, inasmuch as modern discussion, aiming at literary grace and spurning exact formality as smacking of scholasticism and pedantry, is much more flabby and confused. in the old dialectic play there was generally a clear question proposed. the interrogative form forced this much on the disputants. the modern debater of the unpedantic, unscholastic school is not so fettered, and may often be seen galloping wildly about without any game in sight or scent, his maxim being to-- spur boldly on, and dash through thick and thin, through sense and nonsense, never out nor in. now the syllogistic analysis may often be of some use in helping us to keep a clear head in the face of a confused argument. there is a brilliant defence of the syllogism as an analysis of arguments in the _westminster review_ for january, . the article was a notice of whately's logic: it was written by j. s. mill. for some reason it has never been reprinted, but it puts the utility of the syllogism on clearer ground than mill afterwards sought for it. can a fallacy in argument be detected at once? is common-sense sufficient? common-sense would require some inspection. how would it proceed? does common-sense inspect the argument in a lump or piecemeal? all at once or step by step? it analyses. how? first, it separates out the propositions which contribute to the conclusion from those which do not, the essential from the irrelevant. then it states explicitly all that may have been assumed tacitly. finally, it enumerates the propositions in order. some such procedure as this would be adopted by common-sense in analysing an argument. but when common-sense has done this, it has exhibited the argument in a series of syllogisms. such is mill's early defence of the syllogism. it is weak only in one point, in failing to represent how common-sense would arrive at the peculiar syllogistic form. it is the peculiar form of logical analysis that is the distinction of the syllogism. when you have disentangled the relevant propositions you have not necessarily put them in this form. the arguments given in text-books to be cast into syllogistic form, consist only as a rule of relevant propositions, but they are not yet formal syllogisms. but common-sense had only one other step to make to reach the distinctive form. it had only to ask after analysing the argument, is there any form of statement specially suitable for exhibiting the connexion between a conclusion and the general principle on which it is alleged to depend? ask yourself the question, and you will soon see that there would be an obvious advantage in making the conclusion and the general principle uniform, in stating them with the same predicate. but when you do this, as i have already shown (p. ) you state the argument in the first figure of the syllogism. it must, however, be admitted that it is chiefly for exhibiting, or forcing into light, tacit or lurking assumptions that the syllogistic form is of use. unless identity of meaning is disguised or distorted by puzzling difference of language, there is no special illuminative virtue in the syllogism. the argument in a euclidean demonstration would not be made clearer by being cast into formal syllogisms. again, when the subject matter is simple, the syllogistic form is not really required for protection against error. in such enthymemes as the following for example:-- she must be clever: she is so uncompromisingly ugly. romeo must be in love: for is he not seventeen? it is plain to the average intelligence without any knowledge of syllogism that the argument takes for granted a general proposition and what the general proposition is. another thing is plain to the average intelligence, perhaps plainer than to a proficient in the use of the syllogism. clearly we cannot infer with certainty that a woman is clever because she is ugly, unless it is the case that all ugly women are clever. but a syllogiser, seeing that no certain conclusion can be drawn except upon this condition, is apt to dismiss the argument as altogether worthless. this may be specified as an error incident to the practice of the syllogism, that it inclines us to look for necessarily conclusive premisses, and to deny all weight to anything short of this. now in ordinary life it is comparatively seldom that such premisses can be found. we are obliged to proceed on maxims that are not of universal scope, and which lend only a more or less strong colour of probability to cases that can be brought under them. "a little learning is a dangerous thing;" "haste makes waste;" "slowness of speech is a sign of depth of thought;" "vivacity is a sign of shallowness:" such are the "endoxes" or commonplaces of popular knowledge that men bring to bear in daily life. they are not true for all cases, but some of them are true for most or for a good many, and they may be applied with a certain probability though they are not rigidly conclusive. the plain man's danger is that he apply them unthinkingly as universals: the formal logician's danger is that, seeing them to be inapplicable as universals, he dismisses them as being void of all argumentative force. it helps to fix the limits of formal logic to remember that it lies outside its bounds to determine the degree of probability attaching to the application of approximate truths, such as are the staple of arguments in ordinary affairs. formal logic, we may repeat, is not concerned with degrees of truth or falsehood, probability or improbability. it merely shows the interdependency of certain arguments, the consistency of conclusion with premisses. this, however, is a function that might easily be underrated. its value is more indirect than direct. in showing what is required for a certain conclusion, it puts us on the road to a more exact estimate of the premisses alleged, a sounder judgment of their worth. well begun is half done: in undertaking the examination of any argument from authority, a formal syllogism is a good beginning. chapter vii. conditional arguments.--hypothetical syllogism, disjunctive syllogism, and dilemma. the justification of including these forms of argument in logic is simply that they are sometimes used in debate, and that confusion may arise unless the precise meaning of the premisses employed is understood. aristotle did not include them as now given in his exposition of the syllogism, probably because they have no connexion with the mode of reasoning together to which he appropriated the title. the fallacies connected with them are of such a simple kind that to discuss as a question of method the precise place they should occupy in a logical treatise is a waste of ingenuity.[ ] i.--hypothetical syllogisms. if a is b, c is d | a is b } modus [.'.]c is d | ponens. if a is b, c is d | c is not d } modus [.'.]a is not b | tollens. a so-called hypothetical syllogism is thus seen to be a syllogism in which the major premiss is a hypothetical proposition, that is to say, a complex proposition in which two propositions are given as so related that the truth of one follows necessarily from the truth of the other. two propositions so related are technically called the antecedent or reason, and the consequent. the meaning and implication of the form, if a is b, c is d, is expressed in what is known as the law of reason and consequent:-- "_when two propositions are related as reason and consequent, the truth of the consequent follows from the truth of the antecedent, and the falsehood of the antecedent, from the falsehood of the consequent_". if a is b, c is d, implies that if c is not d, a is not b. if this subject is educative, it quickens the wits; if it does not quicken the wits, it is not educative. admitted, then, that the law of reason and consequent holds between two propositions--that if a is b, c is d: admitted also the antecedent, the truth of the consequent follows. this is the modus ponens or positive mode, where you reach a conclusion by obtaining the admission of the antecedent. admit the antecedent and the truth of the consequent follows. with the same major premiss, you may also, under the law of reason and consequent reach a conclusion by obtaining the denial of the consequent. this is the modus tollens or negative mode. deny the consequent and one is bound to deny the antecedent. but to guard against the fallacy technically known as fallacia consequentis, we must observe what the relation of reason and consequent does not imply. the truth of the consequent does not involve the truth of the antecedent, and the falsehood of the antecedent does not involve the falsehood of the consequent. "if the harbour is frozen, the ships cannot come in." if the harbour is not frozen, it does not follow that the ships can come in: they may be excluded by other causes. and so, though they cannot come in, it does not follow that the harbour is frozen. questions connected with hypothetical syllogisms. ( ) _are they properly called syllogisms?_ this is purely a question of method and definition. if we want a separate technical name for forms of argument in which two terms are reasoned together by means of a third, the hypothetical syllogism, not being in such a form, is not properly so called. the fact is that for the purposes of the hypothetical argument, we do not require an analysis into terms at all: it is superfluous: we are concerned only with the affirmation or denial of the constituent propositions as wholes. but if we extend the word syllogism to cover all arguments in which two propositions necessarily involve a third, the hypothetical argument is on this understanding properly enough called a syllogism. ( ) _is the inference in the hypothetical syllogism mediate or immediate?_ to answer this question we have to consider whether the conclusion can be drawn from either of the two premisses without the help of the other. if it is possible immediately, it must be educible directly either from the major premiss or from the minor. (_a_) some logicians argue as if the conclusion were immediately possible from the major premiss. the minor premiss and the conclusion, they urge, are simply equivalent to the major premiss. but this is a misunderstanding. "if a is b, c is d," is not equivalent to "a is b, _therefore_ c is d". "if the harbour is frozen, the ships cannot come in" is not to say that "the harbour is frozen, and therefore," etc. the major premiss merely affirms the existence of the relation of reason and consequent between the two propositions. but we cannot thereupon assert the conclusion unless the minor premiss is also conceded; that is, the inference of the conclusion is mediate, as being from two premisses and not from one alone. (_b_) similarly with hamilton's contention that the conclusion is inferrible immediately from the minor premiss, inasmuch as the consequent is involved in the reason. true, the consequent is involved in the reason: but we cannot infer from "a is b" to "c is d," unless it is conceded that the relation of reason and consequent holds between them; that is, unless the major premiss is conceded as well as the minor. ( ) _can hypothetical syllogism be reduced to the categorical form?_ to oppose hypothetical syllogisms to categorical is misleading, unless we take note of the precise difference between them. it is only in the form of the major premiss that they differ: minor premiss and conclusion are categorical in both. and the meaning of a hypothetical major premiss (unless it is a mere arbitrary convention between two disputants, to the effect that the consequent will be admitted if the antecedent is proved, or that the antecedent will be relinquished if the consequent is disproved), can always be put in the form of a general proposition, from which, with the minor premiss as applying proposition, a conclusion identical with the original can be drawn in regular categorical form. thus:-- if the harbour is frozen, the ships cannot come in. the harbour is frozen. [.'.] the ships cannot come in. this is a hypothetical syllogism, _modus ponens_. express the hypothetical major in the form of the general proposition which it implies, and you reach a conclusion (in _barbara_) which is only grammatically different from the original. all frozen harbours exclude ships. the harbour is frozen. [.'.] it excludes ships. again, take an example of the _modus tollens_-- if rain has fallen, the streets are wet. the streets are not wet. [.'.] rain has not fallen. this is reducible, by formulating the underlying proposition, to _camestres_ or _baroko_ of the second figure. all streets rained upon are wet. the streets are not wet. [.'.] they are not streets rained upon. hypothetical syllogisms are thus reducible, by merely grammatical change[ ], or by the statement of self-evident implications, to the categorical form. and, similarly, any categorical syllogism may be reduced to the hypothetical form. thus:-- all men are mortal. socrates is a man. [.'.] socrates is mortal. this argument is not different, except in the expression of the major and the conclusion, from the following:-- if socrates is a man, death will overtake him. socrates is a man. [.'.] death will overtake him. the advantage of the hypothetical form in argument is that it is simpler. it was much used in mediæval disputation, and is still more popular than the categorical syllogism. perhaps the prominence given to hypothetical syllogisms as syllogisms in post-renaissance text-books is due to the use of them in the formal disputations of graduands in the universities. it was the custom for the disputant to expound his argument in this form:-- if so and so is the case, such and such follows. so and so is the case. [.'.] such and such follows. to which the respondent would reply: _accipio antecedentem, nego consequentiam_, and argue accordingly. petrus hispanus does not give the hypothetical syllogism as a syllogism: he merely explains the true law of reason and consequent in connexion with the fallacia consequentis in the section on fallacies. (_summulæ. tractatus sextus._) ii.--disjunctive syllogisms. a disjunctive syllogism is a syllogism in which the major premiss is a disjunctive proposition, _i.e._, one in which two propositions are declared to be mutually incompatible. it is of the form either a is b, or c is d.[ ] if the disjunction between the alternatives is really complete, the form implies four hypothetical propositions:-- ( ) if a is b, c is not d. ( ) if a is not b, c is d. ( ) if c is d, a is not b. ( ) if c is not d, a is b. suppose then that an antagonist has granted you a disjunctive proposition, you can, using this as a major premiss, extract from him four different conclusions, if you can get him also to admit the requisite minors. the mode of two of these is technically called modus ponendo tollens, the mode that denies the one alternative by granting the other--a is b, _therefore_ c is not d; c is d, _therefore_ a is not b. the other mode is also twice open, the modus tollendo ponens--a is not b, _therefore_ c is d; c is not d, _therefore_ a is b. fallacy is sometimes committed through the disjunctive form owing to the fact that in common speech there is a tendency to use it in place of a mere hypothetical, when there are not really two incompatible alternatives. thus it may be said "either the witness is perjured, or the prisoner is guilty," when the meaning merely is that if the witness is not perjured the prisoner is guilty. but really there is not a valid disjunction and a correct use of the disjunctive form, unless four hypotheticals are implied, that is, unless the concession of either involves the denial of the other, and the denial of either the concession of the other. now the prisoner may be guilty and yet the witness be perjured; so that two of the four hypotheticals, namely-- if the witness is perjured, the prisoner is not guilty, if the prisoner is guilty, the witness is not perjured-- do not necessarily hold. if, then, we would guard against fallacy, we must always make sure before assenting to a disjunctive proposition that there is really a complete disjunction or mutual incompatibility between the alternatives. iii.--the dilemma. a dilemma is a combination of hypothetical and disjunctive propositions. the word has passed into common speech, and its ordinary use is a clue to the logical structure. we are said to be in a dilemma when we have only two courses open to us and both of them are attended by unpleasant consequences. in argument we are in this position when we are shut into a choice between two admissions, and either admission leads to a conclusion which we do not like. the statement of the alternatives as the consequences hypothetically of certain conditions is the major premiss of the dilemma: once we admit that the relations of antecedent and consequent are as stated, we are in a trap, if trap it is: we are on the horns of the dilemma, ready to be tossed from one to the other. for example:-- if a is b, a is c, and if a is not b, a is d. but a either is or is not b. therefore, a either is c or is d. if a acted of his own motive, he is a knave; if a did not act of his own motive, he is a catspaw. but a either acted of his own motive or he did not. thereupon a is either a knave or a catspaw. this is an example of the _constructive_ dilemma, the form of it corresponding to the common use of the word as a choice between equally unpleasant alternatives. the standard example is the dilemma in which the custodians of the alexandrian library are said to have been put by the caliph omar in a.d. if your books are in conformity with the koran, they are superfluous; if they are at variance with it, they are pernicious. but they must either be in conformity with the koran or at variance with it. therefore they are either superfluous or pernicious. where caution has to be exercised is in accepting the clauses of the major. we must make sure that the asserted relations of reason and consequent really hold. it is there that fallacy is apt to creep in and hide its head. the alexandrian librarians were rash in accepting the first clause of the conqueror's major: it does not follow that the books are superfluous unless the doctrines of the koran are not merely sound but contain all that is worth knowing. the propounder of the dilemma covertly assumes this. it is in the facility that it affords for what is technically known as _petitio principii_ that the dilemma is a useful instrument for the sophist. we shall illustrate it further under that head. what is known as the _destructive_ dilemma is of a somewhat different form. it proceeds upon the denial of the consequent as involving the denial of the antecedent. in the major you obtain the admission that if a certain thing holds, it must be followed by one or other of two consequences. you then prove by way of minor that neither of the alternatives is true. the conclusion is that the antecedent is false. we had an example of this in discussing whether the inference in the hypothetical syllogism is immediate. our argument was in this form:-- if the inference is immediate, it must be drawn either from the major alone or from the minor alone. but it cannot be drawn from the major alone, neither can it be drawn from the minor alone. therefore, it is not immediate. in this form of dilemma, which is often serviceable for clearness of exposition, we must as in the other make sure of the truth of the major: we must take care that the alternatives are really the only two open. otherwise the imposing form of the argument is a convenient mask for sophistry. zeno's famous dilemma, directed to prove that motion is impossible, covers a _petitio principii_. if a body moves, it must move either where it is or where it is not. but a body cannot move where it is: neither can it move where it is not. conclusion, it cannot move at all, _i.e._, motion is impossible. the conclusion is irresistible if we admit the major, because the major covertly assumes the point to be proved. in truth, _if_ a body moves, it moves neither where it is nor where it is not, but from where it is to where it is not. motion consists in change of place: the major assumes that the place is unchanged, that is, that there is no motion. [footnote : for the history of hypothetical syllogism see mansel's _aldrich_, appendix i.] [footnote : it may be argued that the change is not merely grammatical, and that the implication of a general proposition in a hypothetical and _vice versâ_ is a strictly logical concern. at any rate such an implication exists, whether it is the function of the grammarian or the logician to expound it.] [footnote : some logicians prefer the form either a is, or b is. but the two alternatives are propositions, and if "a is" represents a proposition, the "is" is not the syllogistic copula. if this is understood it does not matter: the analysis of the alternative propositions is unessential.] chapter viii. fallacies in deductive argument.--petitio principii and ignoratio elenchi. the traditional treatment of fallacies in logic follows aristotle's special treatise [greek: peri sophistikôn elenchôn]--concerning sophistical refutations--pretended disproofs--argumentative tricks. regarding logic as in the main a protection against fallacies, i have been going on the plan of taking each fallacy in connexion with its special safeguard, and in accordance with that plan propose to deal here with the two great types of fallacy in deductive argument. both of them were recognised and named by aristotle: but before explaining them it is worth while to indicate aristotle's plan as a whole. some of his argumentative tricks were really peculiar to yes-and-no dialectic in its most sportive forms: but his leading types, both inductive and deductive, are permanent, and his plan as a whole has historical interest. young readers would miss them from logic: they appeal to the average argumentative boy. he divides fallacies broadly into verbal fallacies ([greek: para tên lexin], _in dictione_), and non-verbal fallacies ([greek: exô tês lexeôs], _extra dictionem_). the first class are mere verbal quibbles, and hardly deserve serious treatment, still less minute subdivision. the world was young when time was spent upon them. aristotle names six varieties, but they all turn on ambiguity of word or structure, and some of them, being dependent on greek syntax, cannot easily be paralleled in another tongue. ( ) ambiguity of word ([greek: homônymia]). as if one were to argue: "all cold can be expelled by heat: john's illness is a cold: therefore it can be expelled by heat". or: "some afflictions are cheering, for afflictions are sometimes light, and light is always cheering". the serious confusion of ambiguous words is met by definition, as explained at length in pt. ii. c i. ( ) _ambiguity of structure_ ([greek: amphibolia]). "what he was beaten with was what i saw him beaten with: what i saw him beaten with was my eye: therefore, what he was beaten with was my eye." "how do you do?" "do? do what?" "i mean, how do you feel?" "how do i feel? with my fingers, of course; but i can see very well." "no, no; i mean, how do you find yourself?" "then why did you not say so? i never exactly noticed, but i will tell you next time i lose myself." ( ) _illicit conjunction_ ([greek: synthesis]). socrates is good. socrates is a musician. therefore socrates is a good musician. ( ) _illicit disjunction_ ([greek: diairesis]). socrates is a good musician. therefore he is a good man. ( ) _ambiguity of pronunciation_ ([greek: prosôdia], _fallacia accentus_). analogies to words that differ only in accent, such as [greek: ou-with accents {psili and persipomeni}] and [greek: ou-with accents {psili and oxia}], may be found in differences of pronunciation. "hair very thick, sir," said a barber to a customer, whose hair was bushy, but beginning to turn grey. "yes, i daresay. but i would rather have it thick than thin." "ah, too thick to-day, sir." "but i don't want to dye it." "excuse me, sir, i mean the hair of the hatmosphere, t-o-d-a-y, to-day." "he said, saddle me the ass. and they saddled _him_." ( ) _ambiguity of inflexion_ ([greek: schêma tês lexeôs], _figura dictionis_). this is not easy to make intelligible in english. the idea is that a termination may be ambiguously interpreted, a neuter participle, _e.g._, taken for an active. thus: "george is ailing". "doing what, did you say? ailing? what is he ailing? ginger-aleing?" non-verbal fallacies, or fallacies in thought, are a more important division. aristotle distinguishes seven. of these, three are comparatively unimportant and trifling. one of them, known to the schoolmen as _fallacia plurium interrogationum_, was peculiar to interrogative disputation. it is the trick of putting more than one question as one, so that a simple yes commits the respondent to something implied. "have you left off beating your father?" if you answer yes, that implies that you have been in the habit of beating him. "has the practice of excessive drinking ceased in your part of the country?" such questions were unfair when the respondent could answer only yes or no. the modern disputant who demands a plain answer yes or no, is sometimes guilty of this trick. two others, the fallacies known as _a dicto simpliciter ad dictum secundum quid_, and _a dicto secundum quid ad dictum simpliciter_, are as common in modern dialectic as they were in ancient. the trick, conscious or unconscious, consists in getting assent to a statement with a qualification and proceeding to argue as if it had been conceded without qualification, and _vice versâ_. for example, it being admitted that culture is good, a disputant goes on to argue as if the admission applied to some sort of culture in special, scientific, æsthetic, philosophical or moral. the fallacy was also known as _fallacia accidentis_. proving that the syllogism is useless for a certain purpose, and then claiming to have proved that it is useless for any purpose is another example. getting a limited admission and then extending it indefinitely is perhaps the more common of the two forms. it is common enough to deserve a shorter name. the _fallacia consequentis_, or _non-sequitur_, which consists specially in ignoring the possibility of a plurality of causes, has already been partly explained in connexion with the hypothetical syllogism, and will be explained further in the logic of induction. _post hoc ergo proper hoc_ is a purely inductive fallacy, and will be explained in connexion with the experimental methods. there remain the two typical deductive fallacies, petitio principii (surreptitious assumption) and ignoratio elenchi (irrelevant argument) about which we must speak more at length. the phrase of which petitio principii or begging the question is a translation--[greek: to en archê aiteisthai]--was applied by aristotle to an argumentative trick in debate by question and answer. the trick consisted in taking for granted a proposition necessary to the refutation without having obtained the admission of it. another expression for the same thing--[greek: to en archê lambanein]--taking the principle for granted--is more descriptive. generally speaking, aristotle says, begging the question consists in not demonstrating the theorem. it would be in accordance with this general description to extend the name to all cases of tacitly or covertly, unwittingly to oneself or to one's opponent, assuming any premiss necessary to the conclusion. it is the fallacy of surreptitious assumption, and all cases of enthymematic or elliptical argument, where the unexpressed links in the chain of argument are not fully understood, are examples of it. by contrast, the articulate and explicit syllogism is an _expositio principii_. the only remedy for covert assumptions is to force them into the light.[ ] _ignoratio elenchi_, ignoring the refutation ([greek: tou elenchou agnoia]), is simply arguing beside the point, distracting the attention by irrelevant considerations. it often succeeds by proving some other conclusion which is not the one in dispute, but has a superficial resemblance to it, or is more or less remotely connected with it. it is easier to explain what these fallacies consist in than to illustrate them convincingly. it is chiefly in long arguments that the mischief is done. "a fallacy," says whately, "which when stated barely in a few sentences would not deceive a child, may deceive half the world if diluted in a quarto volume." very rarely is a series of propositions put before us in regular form and order, all bearing on a definite point. a certain conclusion is in dispute, not very definitely formulated perhaps, and a mixed host of considerations are tumbled out before us. if we were perfectly clear-headed persons, capable of protracted concentration of attention, incapable of bewilderment, always on the alert, never in a hurry, never over-excited, absolutely without prejudice, we should keep our attention fixed upon two things while listening to an argument, the point to be proved, and the necessary premisses. we should hold the point clearly in our minds, and watch indefatigably for the corroborating propositions. but none of us being capable of this, all of us being subject to bewilderment by a rapid whirl of statements, and all of us biased more or less for or against a conclusion, the sophist has facilities for doing two things--taking for granted that he has stated the required premisses (_petitio principii_), and proving to perfect demonstration something which is not the point in dispute, but which we are willing to mistake for it (_ignoratio elenchi_). it is chiefly in the heat of argument that either petitio or ignoratio succeeds. when a fallacy continues to perplex us in cold blood, it must have in its favour either some deeply-rooted prejudice or some peculiar intricacy in the language used, or some abstruseness in the matter. if we are not familiar with the matter of the argument, and have but a vague hold of the words employed, we are, of course, much more easily imposed upon. the famous sophisms of antiquity show the fascination exercised over us by proving something, no matter how irrelevant. if certain steps in an argument are sound, we seem to be fascinated by them so that we cannot apply our minds to the error, just as our senses are fascinated by an expert juggler. we have seen how plausibly zeno's argument against the possibility of motion hides a petitio: the fatalist dilemma is another example of the same sort. if it is fated that you die, you will die whether you call in a doctor or not, and if it is fated that you will recover, you will recover whether you call in a doctor or not. but it must be fated either that you die or that you recover. _therefore_, you will either die or recover whether you call in a doctor or not. here it is tacitly assumed in the major premiss that the calling in of a doctor cannot be a link in the fated chain of events. in the statement of both the alternative conditions, it is assumed that fate does not act through doctors, and the conclusion is merely a repetition of this assumption, a verbal proposition after an imposing show of argument. "if fate does not act through doctors, you will die whether you call in a doctor or not." the fallacy in this case is probably aided by our veneration for the grand abstraction of fate and the awful idea of death, which absorbs our attention and takes it away from the artful _petitio_. the sophism of achilles and the tortoise is the most triumphant of examples of _ignoratio elenchi_. the point that the sophism undertakes to prove is that achilles can never overtake a tortoise once it has a certain start: what it really proves, and proves indisputably, is that he cannot overtake the tortoise within a certain space or time. for simplicity of exposition, let us assume that the tortoise has yards start and that achilles runs ten times as fast. then, clearly, achilles will not come up with it at the end of yards, for while he has run , the tortoise has run ; nor at the end of , for then the tortoise has run more; nor at the end of , for then the tortoise has run / more; nor at the end of -­ / , for then the tortoise has gained / more. so while achilles runs this / , the tortoise runs / ; while he runs the / , it runs / . thus it would seem that the tortoise must always keep ahead: he can never overtake it. but the conclusion is only a confusion of ideas: all that is really proved is that achilles will not overtake the tortoise while running + + + / + / + / + / , etc. that is, that he will not overtake it till he has completed the sum of this series, - / yards. to prove this is an _ignoratio elenchi_; what the sophist undertakes to prove is that achilles will never overtake it, and he really proves that achilles passes it between the th and th yards. the exposure of this sophism is an example also of the value of a technical term. all attempts to expose it without using the term _ignoratio elenchi_ or something equivalent to it, succeed only in bewildering the student. it is customary to say that the root of the fallacy lies in assuming that the sum of an infinite series is equal to infinity. this profound error may be implied: but if any assumption so hard to understand were really required, the fallacy would have little force with the generality. it has often been argued that the syllogism involves a _petitio principii_, because the major premiss contains the conclusion, and would not be true unless the conclusion were true. but this is really an _ignoratio elenchi_. the fact adduced, that the major premiss contains the conclusion, is indisputable; but this does not prove the syllogism guilty of petitio. _petitio principii_ is an argumentative trick, a conscious or unconscious act of deception, a covert assumption, and the syllogism, so far from favouring this, is an _expositio principii_, an explicit statement of premisses such that, if they are true, the conclusion is true. the syllogism merely shows the interdependence of premisses and conclusion; its only tacit assumption is the _dictum de omni_. if, indeed, an opponent challenges the truth of the conclusion, and you adduce premisses necessarily containing it as a refutation, that is an _ignoratio elenchi_ unless your opponent admits those premisses. if he admits them and denies the conclusion, you convict him of inconsistency, but you do not prove the truth of the conclusion. suppose a man to take up the position: "i am not mortal, for i have procured the _elixir vitæ_". you do not disprove this by saying, "all men are mortal, and you are a man". in denying that he is mortal, he denies that all men are mortal. whatever is sufficient evidence that he is not mortal, is sufficient evidence that all men are not mortal. perhaps it might be said that in arguing, "all men are mortal, and you are a man," it is not so much _ignoratio elenchi_ as _petitio principii_ that you commit. but be it always remembered that you may commit both fallacies at once. you may both argue beside the point and beg the question in the course of one and the same argument. [footnote : cp. mr. sidgwick's instructive treatise on fallacies, international scientific series, p. .] chapter ix. formal or aristotelian induction.--inductive argument. the distinction commonly drawn between deduction and induction is that deduction is reasoning from general to particular, and induction reasoning from particular to general. but it is really only as modes of argumentation that the two processes can be thus clearly and fixedly opposed. the word induction is used in a much wider sense when it is the title of a treatise on the methods of scientific investigation. it is then used to cover all the processes employed in man's search into the system of reality; and in this search deduction is employed as well as induction in the narrow sense. we may call induction in the narrow sense formal induction or inductive argument, or we may simply call it aristotelian induction inasmuch as it was the steps of inductive argument that aristotle formulated, and for which he determined the conditions of validity. let us contrast it with deductive argument. in this the questioner's procedure is to procure the admission of a general proposition with a view to forcing the admission of a particular conclusion which is in dispute. in inductive argument, on the other hand, it is a general proposition that is in dispute, and the procedure is to obtain the admission of particular cases with a view to forcing the admission of this general proposition. let the question be whether all horned animals ruminate. you engage to make an opponent admit this. how do you proceed? you ask him whether he admits it about the various species. does the ox ruminate? the sheep? the goat? and so on. the bringing in of the various particulars is the induction ([greek: epagôgê]). when is this inductive argument complete? when is the opponent bound to admit that all horned animals ruminate? obviously, when he has admitted it about every one. he must admit that he has admitted it about every one, in other words, that the particulars enumerated constitute the whole, before he can be held bound in consistency to admit it about the whole. the condition of the validity of this argument is ultimately the same with that of deductive argument, the identity for purposes of predication of a generic whole with the sum of its constituent parts. the axiom of inductive argument is, _what is predicated of every one of the parts is predicable of the whole._ this is the simple converse of the axiom of deductive argument, the _dictum de omni_, "what is predicated of the whole is predicable about every one of the parts". the axiom is simply convertible because for purposes of predication generic whole and specific or individual parts taken all together are identical. practically in inductive argument an opponent is worsted when he cannot produce an instance to the contrary. suppose he admits the predicate in question to be true of this, that and the other, but denies that this, that and the other constitute the whole class in question, he is defeated in common judgement if he cannot instance a member of the class about which the predicate does not hold. hence this mode of induction became technically known as _inductio per enumerationem simplicem ubi non reperitur instantia contradictoria_. when this phrase is applied to a generalisation of fact, nature or experience is put figuratively in the position of a respondent unable to contradict the inquirer. such in plain language is the whole doctrine of inductive argument. aristotle's inductive syllogism is, in effect, an expression of this simple doctrine tortuously in terms of the deductive syllogism. the great master was so enamoured of his prime invention that he desired to impress its form upon everything: otherwise, there was no reason for expressing the process of induction syllogistically. here is his description of the inductive syllogism:-- "induction, then, and the inductive syllogism, consists in syllogising one extreme with the middle through the other extreme. for example, if b is middle to a and c, to prove through c that a belongs to b."[ ] this may be interpreted as follows: suppose a general proposition is in dispute, and that you wish to make it good by obtaining severally the admission of all the particulars that it sums up. the type of a general proposition in syllogistic terminology is the major premiss, all m is p. what is the type of the particulars that it sums up? obviously, the conclusion, s is p. this particular is contained in the major premiss, all m is p; its truth is accepted as contained in the truth of all m is p. s is one of the parts of the generic whole m; one of the individuals or species contained in the class m. if you wish, then, to establish p of all m by induction, you must establish p of all the parts, species, or individuals contained in m, that is, of all possible s_s:_ you must make good that this, that and the other s is p, and also that this, that and the other s constitute the whole of m. you are then entitled to conclude that all m is p: you have syllogised one extreme with the middle through the other extreme. the formal statement of these premisses and conclusion is the inductive syllogism. this, that and the other s is p, _major_. this, that and the other s is all m, _minor_. [.'.] all m is p, _conclusion_. this, that and the other magnet (_i.e._, magnets individually) attract iron. this, that and the other magnet (_i.e._, the individuals separately admitted) are all magnets. [.'.] all magnets attract iron. this, that and the other s being simply convertible with all m, you have only to make this conversion and you have a syllogism in barbara where this, that and the other s figures as the middle term. the practical value of this tortuous expression is not obvious. mediæval logicians shortened it into what was known as the inductive enthymeme: "this, that and the other, therefore all," an obvious conclusion when this, that and the other constitute all. it is merely an evidence of the great master's intoxication with his grand invention. it is a proof also that aristotle really looked at induction from the point of view of interrogative dialectic. his question was, when is a respondent bound to admit a general conclusion? and his answer was, when he has admitted a certain number of particulars, and cannot deny that those particulars constitute the whole whose predicate is in dispute. he was not concerned primarily with the analysis of the steps of an inquirer generalising from nature. [footnote : [greek: epagôgê men oun esti kai ho ex epagôgês syllogismos to dia tou eterou thateron akron tô mesô syllogisasthai; oion ei tôn a g meson to b, dia tou g deixai to a tô b hyparchon.] (an. prior., ii. .)] book ii. inductive logic, or the logic of science. introduction. perhaps the simplest way of disentangling the leading features of the departments of logic is to take them in relation to historical circumstances. these features are writ large, as it were, in history. if we recognise that all bodies of doctrine have their origin in practical needs, we may conceive different ages as controlled each by a distinctive spirit, which issues its mandate to the men of the age, assigning to them their distinctive work. the mandate issued to the age of plato and aristotle was _bring your beliefs into harmony one with another_. the aristotelian logic was framed in response to this order: its main aim was to devise instruments for making clear the coherence, the concatenation, the mutual implication of current beliefs. the mandate of the mediæval spirit was _bring your beliefs into harmony with dogma_. the mediæval logic was contracted from aristotle's under this impulse. induction as conceived by him was neglected, allowed to dwindle, almost to disappear from logic. greater prominence was given to deduction. then as dogmatic authority became aggressive, and the church through its officials claimed to pronounce on matters outside theology, a new spirit was roused, the mandate of which was, _bring your beliefs into harmony with facts_. it was under this impulse that a body of methodical doctrine vaguely called induction gradually originated. in dealing with the genesis of the old logic, we began with aristotle. none can dispute his title to be called its founder. but who was the founder of the new logic? in what circumstances did it originate? the credit of founding induction is usually given to francis bacon, lord verulam. that great man claimed it for himself in calling his treatise on the interpretation of nature the _novum organum_. the claim is generally conceded. reid's account of the matter represents the current belief since bacon's own time. "after man had laboured in the search of truth near two thousand years by the help of syllogisms, [lord] bacon proposed the method of induction as a more effectual engine for that purpose. his _novum organum_ gave a new turn to the thoughts and labours of the inquisitive, more remarkable and more useful than that which the _organon_ of aristotle had given before, and may be considered as a second grand era in the progress of human nature.... most arts have been reduced to rules after they had been brought to a considerable degree of perfection by the natural sagacity of artists; and the rules have been drawn from the best examples of the art that had been before exhibited; but the art of philosophical induction was delineated by [lord] bacon in a very ample manner before the world had seen any tolerable example of it."[ ] there is a radical misconception here, which, for reasons that i hope to make plain, imperatively needs to be cleared up. it obscures the very essence of "philosophical induction". there are three ways in which movement in any direction may be helped forward, exhortation, example, and precept. exhortation: a man may exhort to the practice of an art and thereby give a stimulus. example: he may practise the art himself, and show by example how a thing should be done. precept: he may formulate a clear method, and so make plain how to do it. let us see what was bacon's achievement in each of those three ways. undoubtedly bacon's powerful eloquence and high political position contributed much to make the study of nature fashionable. he was high in place and great in intellect, one of the commanding personalities of his time. taking "all knowledge for his province," though study was really but his recreation, he sketched out a plan of universal conquest with a clearness and confidence that made the mob eager to range themselves under his leadership. he was the magnificent demagogue of science. there had been champions of "induction" before him, but they had been comparatively obscure and tongue-tied. while, however, we admit to the full the great services of this mighty advocate in making an "inductive" method popular, we should not forget that he had pioneers even in hortatory leadership. his happiest watchword, the interpretation of nature, as distinguished from the interpretation of authoritative books, was not of his invention. if we read whewell's _history of the inductive sciences_, we shall find that many before him had aspired to "give a new turn to the labors of the inquisitive," and in particular to substitute inquisition for disquisition. one might compile from whewell a long catalogue of eminent men before bacon who held that the study of nature was the proper work of the inquisitive: leonardo da vinci ( - ), one of the wonders of mankind for versatility, a miracle of excellence in many things, painter, sculptor, engineer, architect, astronomer, and physicist; copernicus ( - ), the author of the heliocentric theory; telesius ( - ), a theoretical reformer, whose _de rerum natura_ ( ) anticipated not a little of the _novum organum_; cesalpinus ( - ), the botanist; gilbert ( - ), the investigator of magnetism. by all these men experiment and observation were advocated as the only way of really increasing knowledge. they all derided mere book-learning. the conception of the world of sense as the original ms. of which systems of philosophy are but copies, was a familiar image with them. so also was bacon's epigrammatic retort to those who wish to rest on the wisdom of the ancients, that antiquity is the youth of the world and that we are the true ancients. "we are older," said giordano bruno, "and have lived longer than our predecessors." this last argument, indeed, is much older than the sixteenth century. it was used by the doctor mirabilis of the thirteenth, the franciscan friar, roger bacon ( - ). "the later men are, the more enlightened they are; and wise men now are ignorant of much the world will some day know." the truth is that if you are in search of a father for inductive philosophy, the mediæval friar has better claims than his more illustrious namesake. his enthusiasm for the advancement of learning was not less nobly ambitious and far-reaching, and he was himself an ardent experimenter and inventor. his _opus majus_--an eloquent outline of his projects for a new learning, addressed in to pope clement iv., through whom he offered to give to the church the empire of the world as aristotle had given it to alexander--was almost incredibly bold, comprehensive and sagacious. fixing upon authority, custom, popular opinion, and the pride of supposed knowledge, as the four causes of human ignorance, he urged a direct critical study of the scriptures, and after an acute illustration of the usefulness of grammar and mathematics (widely interpreted), concluded with experimental science as the great source of human knowledge. i have already quoted (p. ) the friar's distinction between the two modes of knowing, argument and experience, wherein he laid down that it is only experience that makes us feel certain. it were better, he cried in his impatience, to burn aristotle and make a fresh start than to accept his conclusions without inquiry. experimental science, the sole mistress of speculative science, has three great prerogatives among other parts of knowledge. first, she tests by experiment the noblest conclusions of all other sciences. next, she discovers respecting the notions which other sciences deal with, magnificent truths to which these sciences can by no means attain. her third dignity is that she by her own power and without respect to other sciences investigates the secret of nature. so far, then, as exhortation goes, king james's great lawyer and statesman was not in advance of pope clement's friar. their first principle was the same. it is only by facts that theories can be tested. man must not impose his own preconceptions (_anticipationes mentis_) on nature. man is only the interpreter of nature. both were also at one in holding that the secrets of nature could not be discovered by discussion, but only by observation and experiment. francis bacon, however, went beyond all his predecessors in furnishing an elaborate method for the interpretation of nature. when he protested against the intellect's being left to itself (_intellectus sibi permissus_), he meant more than speculation left unchecked by study of the facts. he meant also that the interpreter must have a method. as man, he says, cannot move rocks by the mere strength of his hands without instruments, so he cannot penetrate to the secrets of nature by mere strength of his intellect without instruments. these instruments he undertakes to provide in his inductive method or _novum organum_. and it is important to understand precisely what his methods were, because it is on the ground of them that he is called the founder of inductive philosophy, and because this has created a misapprehension of the methods actually followed by men of science. ingenious, penetrating, wide-ranging, happy in nomenclature, the _novum organum_ is a wonderful monument of the author's subtle wit and restless energy; but, beyond giving a general impulse to testing speculative fancies by close comparison with facts, it did nothing for science. his method--with its tables of preliminary muster for the intellect (_tabulæ comparentiæ primæ instantiarum ad intellectum_, facts collected and methodically arranged for the intellect to work upon); its elimination upon first inspection of obviously accidental concomitants (_rejectio sive exclusiva naturarum_); its provisional hypothesis (_vindemiatio prima sive interpretatio inchoata_); its advance to a true induction or final interpretation by examination of special instances (he enumerates twenty-seven, × × , _prerogativas instantiarum_, trying to show the special value of each for the inquirer)[ ]--was beautifully regular and imposing, but it was only a vain show of a method. it was rendered so chiefly by the end or aim that bacon proposed for the inquirer. in this he was not in advance of his age; on the contrary, he was probably behind roger bacon, and certainly far behind such patient and concentrated thinkers as copernicus, gilbert, and galileo--no discredit to the grandeur of his intellect when we remember that science was only his recreation, the indulgence of his leisure from law and state. in effect, his method came to this. collect as many instances as you can of the effect to be investigated, and the absence of it where you would expect it, arrange them methodically, then put aside guesses at the cause which are obviously unsuitable, then draw up a probably explanation, then proceed to make this exact by further comparison with instances. it is when we consider what he directed the inquirer to search for that we see why so orderly a method was little likely to be fruitful. he starts from the principle that the ultimate object of all knowledge is use, practice (_scimus ut operemur_). we want to know how nature produces things that we may produce them for ourselves, if we can. the inquirer's first aim, therefore, should be to find out how the qualities of bodies are produced, to discover the _formæ_ or formal causes of each quality. an example shows what he meant by this. gold is a crowd or conjugation of various qualities or "natures"; it is yellow, it has a certain weight, it is malleable or ductile to a certain degree, it is not volatile (loses nothing under fire), it can be melted, it is soluble. if we knew the _forma_ or formal cause of each of those qualities, we could make gold, provided the causes were within our control. the first object, then, of the investigator of nature is to discover such _formæ_, in order to be able to effect the transformation of bodies. it may be desirable also to know the _latens processus_, any steps not apparent to the senses by which a body grows from its first germs or rudiments, and the _schematismus_ or ultimate inner constitution of the body. but the discovery of the _formæ_ of the constituent qualities (_naturæ singulæ_), heat, colour, density or rarity, sweetness, saltness, and so forth, is the grand object of the interpreter of nature; and it is for this that bacon prescribed his method. the _sylva sylvarum_, or natural history, a miscellaneous collection of facts and fictions, observations and traditions, with guesses at the explanation of them, affords us a measure of bacon's own advancement as an interpreter of nature. it was a posthumous work, and the editor, his secretary, tells us that he often said that if he had considered his reputation he would have withheld it from the world, because it was not digested according to his own method: yet he persuaded himself that the causes therein assigned were far more certain than those rendered by others, "not for any excellence of his own wit, but in respect of his continual conversation with nature and experience," and mankind might stay upon them till true axioms were more fully discovered. when, however, we examine the causes assigned, we find that in practice bacon could not carry out his own precepts: that he did not attempt to creep up to an explanation by slow and patient ascent, but jumped to the highest generalisations: and that his explanatory notions were taken not from nature, but from the ordinary traditions of mediæval physical science. he deceived himself, in short, in thinking that he could throw aside tradition and start afresh from observation. for example. he is struck by the phenomenon of bubbles on water: "it seemeth somewhat strange that the air should rise so swiftly, while it is in the water, and when it cometh to the top should be stayed by so weak a cover as that of the bubble is". the swift ascent of the air he explains as a "motion of percussion," the water descending and forcing up the air, and not a "motion of levity" in the air itself. "the cause of the enclosure of the bubble is for that the appetite to resist separation or discontinuance, which is strong in solids, is also in liquors, though fainter and weaker." "the same reason is of the roundness of the bubble, as well for the skin of water as for the air within. for the air likewise avoideth discontinuance, and therefore casteth itself into a round figure. and for the stop and arrest of the air a little while, it showeth that the air of itself hath little or no appetite of ascending."[ ] these notions were not taken direct from the facts: they descended from aristotle. he differs from aristotle, however, in his explanation of the colours of birds' feathers. "aristotle giveth the cause vainly" that birds are more in the beams of the sun than beasts. "but that is manifestly untrue; for cattle are more in the sun than birds, that live commonly in the woods or in some covert. the true cause is that the excrementitious moisture of living creatures, which maketh as well the feathers in birds as the hair in beasts, passeth in birds through a finer and more delicate strainer than it doth in beasts. for feathers pass through quills, and hair through skin." it is an instance of percolation or filtering: other effects of the same cause being the gums of trees, which are but a fine passage or straining of the juice through the wood and bark, and cornish diamonds and rock rubies, which are in like manner "fine exudations of stone".[ ] these examples of bacon's inductions are taken from the _sylva_ at random. but the example which best of all illustrates his attitude as a scientific investigator is the remark he makes in the _novum organum_ about the copernican theory. elsewhere he says that there is nothing to choose between it and the ptolemaic; and in the _novum organum_ (lib. ii. ) he remarks that "no one can hope to terminate the question whether in diurnal motion it is really the earth or the sky that rotates, unless he shall first have comprehended the nature of spontaneous rotation". that is, we must first find out the _forma_ or formal cause of spontaneous rotation. this is a veritable _instantia crucis_, as fixing bacon's place in the mediæval and not in the new world of scientific speculation. bacon, in short, in the practice of induction did not advance an inch beyond aristotle. rather he retrograded, inasmuch as he failed to draw so clear a line between the respective spheres of inductive collection of facts and explanation. there are two sources of general propositions, according to aristotle, induction and nous. by induction he meant the generalisation of facts open to sense, the summation of observed particulars, the _inductio per enumerationem simplicem_ of the schoolmen. by nous he meant the reason or speculative faculty, as exercised with trained sagacity by experts. thus by induction we gather that all horned animals ruminate. the explanation of this is furnished by the nous, and the explanation that commended itself to the trained sagacity of his time was that nature having but a limited amount of hard material and having spent this on the horns, had none left for teeth, and so provided four stomachs by way of compensation. bacon's guesses at causes are on the same scientific level with this, only he rather confused matters by speaking of them as if they were inductions from fact, instead of being merely fancies superinduced upon fact. his theory of interpretation, it is true, was so far an advance that he insisted on the necessity of verifying every hypothesis by further appeal to facts, though in practice he himself exercised no such patience and never realised the conditions of verification. against this, again, must be set the fact that by calling his method induction, and laying so much stress on the collection of facts, he fostered, and, indeed, fixed in the public mind the erroneous idea that the whole work of science consists in observation. the goal of science, as herschel said, is explanation, though every explanation must be made to conform to fact, and explanation is only another term for attaining to higher generalisations, higher unities. the truth is that induction, if that is the name we use for scientific method, is not, as reid conceived, an exception to the usual rule of arts in being the invention of one man. bacon neither invented nor practised it. it was perfected gradually in the practice of men of science. the birthplace of it as a conscious method was in the discussions of the royal society of london, as the birthplace of the aristotelian logic was in the discussions of the athenian schools. its first great triumph was newton's law of gravitation. if we are to name it after its first illustrious practitioner, we must call it the newtonian method, not the baconian. newton really stands to the scientific method of explanation as aristotle stands to the method of dialectic and deduction. he partly made it explicit in his _regulæ philosophandi_ ( ). locke, his friend and fellow-member of the royal society, who applied the method to the facts of mind in his _essay concerning human understanding_ ( ), made it still further explicit in the fourth book of that famous work. it was, however, a century and a half later that an attempt was first made to incorporate scientific method with logic under the name of induction, and add it as a new wing to the old aristotelian building. this was the work of john stuart mill, whose system of logic, deductive and inductive, was first published in . the genesis of mill's system of logic, as of other things, throws light upon its character. and in inquiries into the genesis of anything that man makes we may profitably follow aristotle's division of causes. the efficient cause is the man himself, but we have also to find out the final cause, his object or purpose in making the thing, the material cause, the sources of his material, and the formal cause, the reason why he shaped it as he did. in the case of mill's system we have to ask: what first moved him to formulate the methods of scientific investigation? whence did he derive his materials? why did he give his scientific method the form of a supplement to the old aristotelian logic? we cannot absolutely separate the three inquiries, but motive, matter and form each had a traceable influence on the leading features of his system. first, then, as to his motive. it is a mistake to suppose that mill's object was to frame an organon that might assist men of science as ordinarily understood in making discoveries. bacon, his secretary tells us, was wont to complain that he should be forced to be a workman and a labourer in science when he thought he deserved to be an architect in this building. and men of science have sometimes rebuked mill for his presumption in that, not being himself an investigator in any department of exact science, he should volunteer to teach them their business. but mill was really guilty of no such presumption. his object, on the contrary, was to learn their method with a view to its application to subjects that had not yet undergone scientific treatment. briefly stated, his purpose was to go to the practical workers in the exact sciences, astronomy, chemistry, heat, light, electricity, molar and molecular physics; ascertain, not so much how they made their discoveries as how they assured themselves and others that their conclusions were sound; and having ascertained their tests of truth and principles of proof, to formulate these tests so that they might be applied to propositions outside the range of the exact sciences, propositions in politics, ethics, history, psychology. more particularly he studied how scientific men verify, and when they accept as proved, propositions of causation, explanations of the causes of things. in effect, his survey of scientific method was designed to lead up to the sixth book in his system, the logic of the moral sciences. there are multitudes of floating endoxes or current opinions concerning man and his concerns, assigning causes for the conduct and character of individuals and of communities. mill showed himself quite aware that the same modes of investigation may not be practicable, and that it may not be possible, though men are always ready to assign causes with confidence, to ascertain causes with the same degree of certainty: but at least the conditions of exact verification should be the same, and it is necessary to see what they are in order to see how far they can be realised. that such was mill's design in the main is apparent on internal evidence, and it was the internal evidence that first struck me. but there is external evidence as well. we may first adduce some essays on the spirit of the age, published in the _examiner_ in , essays which drew from carlyle the exclamation, "here is a new mystic!" these essays have never been republished, but they contain mill's first public expression of the need for a method in social inquiries. he starts from the platonic idea that no state can be stable in which the judgment of the wisest in political affairs is not supreme. he foresees danger in the prevalent anarchy of opinion. how is it to be averted? how are men to be brought to accept loyally the judgment of the expert in public affairs? they accept at once and without question the decisions of the specially skilled in the physical sciences. why is this? for one reason, because there is complete agreement among experts. and why is there this complete agreement? because all accept the same tests of truth, the same conditions of proof. is it not possible to obtain among political investigators similar unanimity as to their methods of arriving at conclusions, so as to secure similar respect for their authority? we need not stop to ask whether this was a vain dream, and whether it must not always be the case that to ensure confidence in a political or moral adviser more is needed than faith in his special knowledge and trained sagacity. our point is that in mill was in search of a method of reasoning in social questions. opportunely soon after, early in , was published herschel's _discourse on the study of natural philosophy_, the first attempt by an eminent man of science to make the methods of science explicit. mill reviewed this book in the _examiner_, and there returns more definitely to the quest on which he was bent. "the uncertainty," he says, "that hangs over the very elements of moral and social philosophy proves that the means of arriving at the truth in those sciences are not yet properly understood. and whither can mankind so advantageously turn, in order to learn the proper means and to form their minds to the proper habits, as to that branch of knowledge in which by universal acknowledgment the greatest number of truths have been ascertained and the greatest possible degree of certainty arrived at?" we learn from mill himself that he made an attempt about this time, while his mind was full of herschel's discourse, to connect a scientific method with the body of the old logic. but he could not make the junction to his satisfaction, and abandoned the attempt in despair. a little later, in , upon the appearance of whewell's _history of the inductive sciences_, he renewed it, and this time with happier results. whewell's _philosophy of the inductive sciences_ was published in , but by that time mill's system was definitely shaped. it was, then, to herschel and whewell, but especially to the former, that mill owed the raw materials of his inductive method. but why did he desire to concatenate this with the old logic? probably because he considered that this also had its uses for the student of society, the political thinker. he had inherited a respect for the old logic from his father. but it was the point at which he sought to connect the new material with the old, the point of junction between the two, that determined the form of his system. we find the explanation of this in the history of the old logic. it so happened that whately's logic was in the ascendant, and whately's treatment of induction gives the key to mill's. towards the end of the first quarter of this century there was a great revival of the study of logic at oxford. the study had become mechanical, aldrich's compendium, an intelligent but exceedingly brief abstract of the scholastic logic, being the text-book beyond which no tutor cared to go. the man who seems to have given new life to the study was a tutor who subsequently became bishop of llandaff, edward copleston. the first public fruits of the revival begun by him was whately's article on logic in the _encyclopædia metropolitana_, published as a separate book in . curiously enough, one of whately's most active collaborators in the work was john henry newman, so that the common room of oriel, which mr. froude describes as the centre from which emanated the high church movement, may also be said to have been the centre from which emanated the movement that culminated in the revolution of logic. the publication of whately's logic made a great stir. it was reviewed by mill, then a young man of twenty-one, in the _westminster review_ ( ), and by hamilton, then forty-five years of age, in the _edinburgh_ ( ). there can be no doubt that it awakened mill's interest in the subject. a society formed for the discussion of philosophical questions, and called the speculative society, met at grote's house in , and for some years following. of this society young mill was a member, and their continuous topic in was logic, whately's treatise being used as a sort of text-book. it is remarkable that mill's review of whately, the outcome of these discussions, says very little about induction. at that stage mill's chief concern seems to have been to uphold the usefulness of deductive logic, and he even goes so far as to scoff at its eighteenth century detractors and their ambition to supersede it with a system of induction. the most striking feature of the article is the brilliant defence of the syllogism as an analysis of arguments to which i have already referred. he does not deny that an inductive logic might be useful as a supplement, but apparently he had not then formed the design of supplying such a supplement. when, however, that design seriously entered his mind, consequent upon the felt need of a method for social investigations, it was whately's conception of induction that he fell back upon. historically viewed, his system of logic was an attempt to connect the practical conditions of proof set forth in herschel's discourse with the theoretic view of induction propounded in whately's. the tag by which he sought to attach the new material to the old system was the inductive enthymeme of the schoolmen as interpreted by whately. whately's interpretation--or misinterpretation--of this enthymeme, and the conception of induction underlying it, since it became mill's ruling conception of induction, and virtually the formative principle of his system, deserves particular attention. "this, that and the other horned animal, ox, sheep, goat, ruminate; _therefore_, all horned animals ruminate." the traditional view of this enthymeme i have given in my chapter on formal induction (p. ). it is that a minor premiss is suppressed: "this, that and the other constitute the whole class". this is the form of the minor in aristotle's inductive syllogism. but, whately argued, how do we know that this, that and the other--the individuals we have examined--constitute the whole class? do we not assume that what belongs to the individuals examined belongs to the whole class? this tacit assumption, he contended, is really at the bottom of the enthymeme, and its proper completion is to take this as the major premiss, with the enumeration of individuals as the minor. thus:-- what belongs to the individuals examined belongs to the whole class. the property of the ruminating belongs to the individuals examined, ox, sheep, goat, etc. _therefore_, it belongs to all. in answer to this, hamilton repeated the traditional view, treating whately's view merely as an instance of the prevailing ignorance of the history of logic. he pointed out besides that whately's major was the postulate of a different kind of inference from that contemplated in aristotle's inductive syllogism, material as distinguished from formal inference. this is undeniable if we take this syllogism purely as an argumentative syllogism. the "all" of the conclusion simply covers the individuals enumerated and admitted to be "all" in the minor premiss. if a disputant admits the cases produced to be all and can produce none to the contrary, he is bound to admit the conclusion. now the inference contemplated by whately was not inference from an admission to what it implies, but inference from a series of observations to all of a like kind, observed and unobserved. it is not worth while discussing what historical justification whately had for his view of induction. it is at least arguable that the word had come to mean, if it did not mean with aristotle himself, more than a mere summation of particulars in a general statement. even aristotle's respondent in the concession of his minor admitted that the individuals enumerated constituted all in the truly general sense, not merely all observed but all beyond the range of observation. the point, however, is insignificant. what really signifies is that while hamilton, after drawing the line between formal induction and material, fell back and entrenched himself within that line, mill caught up whately's conception of induction, pushed forward, and made it the basis of his system of logic. in mill's definition, the mere summation of particulars, _inductio per enumerationem simplicem ubi non reperitur instantia contradictoria_, is induction improperly so called. the only process worthy of the name is material induction, inference to the unobserved. here only is there an advance from the known to the unknown, a veritable "inductive hazard". starting then with this conception of inference to the unobserved as the only true inference, and with an empirical law--a generality extended from observed cases to unobserved--as the type of such inference, mill saw his way to connecting a new logic with the old. we must examine this junction carefully, and the brilliant and plausible arguments by which he supported it; we shall find that, biased by this desire to connect the new with the old, he gave a misleading dialectic setting to his propositions, and, in effect, confused the principles of argumentative conclusion on the one hand and of scientific observation and inference on the other. the conception of inference which he adopted from whately was too narrow on both sides for the uses to which he put it. be it understood that in the central methods both of syllogistic and of science, mill was substantially in accord with tradition; it is in his mode of junction, and the light thereby thrown upon the ends and aims of both, that he is most open to criticism. as regards the relation between deduction and induction, mill's chief proposition was the brilliant paradox that all inference is at bottom inductive, that deduction is only a partial and accidental stage in a process the whole of which may be called induction. an opinion was abroad--fostered by the apparently exclusive devotion of logic to deduction--that all inference is essentially deductive. not so, answered mill, meeting this extreme with another: all inference is essentially inductive. he arrives at this through the conception that induction is a generalisation from observed particulars, while deduction is merely the extension of the generalisation to a new case, a new particular. the example that he used will make his meaning plain. take a common syllogism:-- all men are mortal. socrates is a man. socrates is mortal. "the proposition," mill says, "that socrates is mortal is evidently an inference. it is got at as a conclusion from something else. but do we in reality conclude it from the proposition, all men are mortal?" he answers that this cannot be, because if it is not true that socrates is mortal it cannot be true that all men are mortal. it is clear that our belief in the mortality of socrates must rest on the same ground as our belief in the mortality of men in general. he goes on to ask whence we derive our knowledge of the general truth, and answers: "of course from observation. now all which man can observe are individual cases.... a general truth is but an aggregate of particular truths. but a general proposition is not merely a compendious form for recording a number of particular facts.... it is also a process of inference. from instances which we have observed we feel warranted in concluding that what we have found true in those instances, holds in all similar ones, past, present, and future. we then record all that we have observed together with what we infer from our observations, in one concise expression." a general proposition is thus at once a summary of particular facts and a memorandum of our right to infer from them. and when we make a deduction we are, as it were, interpreting this memorandum. but it is upon the particular facts that the inference really rests, and mill contends that we might if we chose infer to the particular conclusion at once without going through the form of a general inference. thus mills seeks to make good his point that all inference is essentially inductive, and that it is only for convenience that the word induction has been confined to the general induction, while the word deduction is applied to the process of interpreting our memorandum. clear and consecutive as this argument is, it is fundamentally confusing. it confuses the nature of syllogistic conclusion or deduction, and at the same time gives a partial and incomplete account of the ground of material inference. the root of the first confusion lies in raising the question of the ground of material inference in connexion with the syllogism. as regards the usefulness of the syllogism, this is an ignoratio elenchi. that the major and the conclusion rest upon the same ground as matters of belief is indisputable: but it is irrelevant. in so far as "socrates is mortal" is an inference from facts, it is not the conclusion of a syllogism. this is implicitly and with unconscious inconsistency recognised by mill when he represents deduction as the interpretation of a memorandum. to represent deduction as the interpretation of a memorandum--a very happy way of putting it and quite in accordance with roger bacon's view--is really inconsistent with regarding deduction as an occasional step in the process of induction. if deduction is the interpretation of a memorandum, it is no part of the process of inference from facts. the conditions of correct interpretation as laid down in syllogism are one thing, and the methods of correct inference from the facts, the methods of science that he was in search of, are another. let us emphasise this view of deduction as the interpretation of a memorandum. it corresponds exactly with the view that i have taken in discussing the utility of the syllogism. suppose we want to know whether a particular conclusion is consistent with our memorandum, what have we to look to? we have to put our memorandum into such a form that it is at once apparent whether or not it covers our particular case. the syllogism aspires to be such a form. that is the end and aim of it. it does not enable us to judge whether the memorandum is a legitimate memorandum or not. it only makes clear that if the memorandum is legitimate, so is the conclusion. how to make clear and consistent memoranda of our beliefs in words is a sufficiently complete description of the main purpose of deductive logic. instead, then, of trying to present deduction and induction as parts of the same process, which he was led to do by his desire to connect the new and the old, mill ought rather, in consistency as well as in the interests of clear system, to have drawn a line of separation between the two as having really different ends, the conditions of correct conclusion from accepted generalities on the one hand, and the conditions of correct inference from facts on the other. whether the first should be called inference at all is a question of naming that ought to have been considered by itself. we may refuse to call it inference, but we only confuse ourselves and others if we do not acknowledge that in so doing we are breaking with traditional usage. perhaps the best way in the interests of clearness is to compromise with tradition by calling the one formal inference and the other material inference. it is with the latter that the physical sciences are mainly concerned, and it was the conditions and methods of its correct performance that mill desired to systematise in his inductive logic. we have next to see how his statement of the grounds of material inference was affected by his connexion of deduction and induction. here also we shall find a reason for a clearer separation between the two departments of logic. in his antagonism to a supposed doctrine that all reasoning is from general to particular, mill maintained _simpliciter_ that all reasoning is from particulars to particulars. now this is true only _secundum quid_, and although in the course of his argument mill introduced the necessary qualifications, the unqualified thesis was confusing. it is perfectly true that we may infer--we can hardly be said to reason--from observed particulars to unobserved. we may even infer, and infer correctly, from a single case. the village matron, called in to prescribe for a neighbour's sick child, infers that what cured her own child will cure the neighbour's, and prescribes accordingly. and she may be right. but it is also true that she may be wrong, and that no fallacy is more common than reasoning from particulars to particulars without the requisite precautions. this is the moral of one of the fables of camerarius. two donkeys were travelling in the same caravan, the one laden with salt, the other with hay. the one laden with salt stumbled in crossing a stream, his panniers dipped in the stream, the salt melted, and his burden was lightened. when they came to another stream, the donkey that was laden with hay dipped his panniers in the water, expecting a similar result. mill's illustrations of correct inference from particulars to particulars were really irrelevant. what we are concerned with in considering the grounds of inference, is the condition of correct inference, and no inference to an unobserved case is sound unless it is of a like kind with the observed case or cases on which it is founded, that is to say, unless we are entitled to make a general proposition. we need not go through the form of making a general proposition, but if a general proposition for all particulars of a certain description is not legitimate, no more is the particular inference. mill, of course, did not deny this, he was only betrayed by the turn of his polemic into an unqualified form of statement that seemed to ignore it. but this was not the worst defect of mill's attempt at a junction of old and new through whately's conception of induction. a more serious defect was due to the insufficiency of this conception to represent all the modes of scientific inference. when a certain attribute has been found in a certain connexion in this, that, and the other, to the extent of all observed instances, we infer that it will be found in all, that the connexion that has obtained within the range of our actual experience has obtained beyond that range and will obtain in the future. call this an observed uniformity of nature: we hold ourselves justified in expecting that the observed uniformities of nature will continue. such an observed uniformity--that all animals have a nervous system, that all animals die, that quinine cures ague--is also called an empirical law. but while we are justified in extending an empirical law beyond the limits within which it has been observed to hold good, it is a mistake to suppose that the main work of science is the collection of empirical laws, and that the only scientific inference is the inference from the observed prevalence of an empirical law to its continuance. with science the collection of empirical laws is only a preliminary: "the goal of science," in herschel's phrase, "is explanation". in giving such prominence to empirical laws in his theory, mill confined induction to a narrower scope than science ascribes to it. science aims at reaching "the causes of things": it tries to penetrate behind observed uniformities to the explanation of them. in fact, as long as a science consists only of observed uniformities, as long as it is in the empirical stage, it is a science only by courtesy. astronomy was in this stage before the discovery of the law of gravitation. medicine is merely empirical as long as its practice rests upon such generalisations as that quinine cures ague, without knowing why. it is true that this explanation may consist only in the discovery of a higher or deeper uniformity, a more recondite law of connexion: the point is that these deeper laws are not always open to observation, and that the method of reaching them is not merely observing and recording. in the body of his inductive logic, mill gave a sufficient account of the method of explanation as practised in scientific inquiry. it was only his mode of approaching the subject that was confusing, and made it appear as if the proper work of science were merely extending observed generalities, as when we conclude that all men will die because all men have died, or that all horned animals ruminate because all hitherto observed have had this attribute. a minor source of confusion incident to the same controversy was his refusing the title of induction proper to a mere summary of particulars. he seemed thereby to cast a slight upon the mere summation of particulars. and yet, according to his theory, it was those particulars that were the basis of the induction properly so called. that all men will die is an inference from the observation summed up in the proposition that all men have died. if we refuse the name of induction to the general proposition of fact, what are we to call it? the truth is that the reason why the word induction is applied indifferently to the general proposition of fact and the general proposition applicable to all time is that, once we are sure of the facts, the transition to the inference is so simple an affair that it has not been found necessary in practice to distinguish them by different names. our criticism of mill would itself mislead if it were taken to mean that the methods of science which he formulated are not the methods of science or that his system of those methods is substantially incomplete. his inductive logic as a system of scientific method was a great achievement in organisation, a veritable _novum organum_ of knowledge. what kept him substantially right was that the methods which he systematised were taken from the practice of men of science. our criticism amounts only to this, that in correlating the new system with the old he went upon a wrong track. for more than two centuries deduction had been opposed to induction, the _ars disserendi_ to the _ars inveniendi_. in trying to reconcile them and bring them under one roof, mill drew the bonds too tight. in stating the terms of the union between the two partners, he did not separate their spheres of work with sufficient distinctness. mill's theory of deduction and induction and the voluminous criticism to which in its turn it has been subjected have undoubtedly been of great service in clearing up the foundations of reasoning. but the moral of it is that if we are to make the methods of science a part of logic, and to name this department induction, it is better to discard altogether the questions of general and particular which are pertinent to syllogism, and to recognise the new department simply as being concerned with a different kind of inference, inference from facts to what lies beyond them, inference from the observed to the unobserved. that this is the general aim and proper work of science is evident from its history. get at the secrets of nature by the study of nature, penetrate to what is unknown and unexperienced by help of what is known and has been experienced, was the cry of the early reformers of science. thus only, in roger bacon's phrase, could certainty--assured, well grounded, rational belief--be reached. this doctrine, like every other, can be understood only by what it was intended to deny. the way of reaching certainty that roger bacon repudiated was argument, discussion, dialectic. this "concludes a question but does not make us feel certain, or acquiesce in the contemplation of truth that is not also found in experience". argument is not necessarily useless; the proposition combated is only that by it alone--by discussion that does not go beyond accepted theories or conceptions--rational belief about the unknown cannot be reached. the proposition affirmed is that to this end the conclusions of argument must be tested by experience. observation of facts then is a cardinal part of the method of science. the facts on which our inferences are based, by which our conclusions are tested, must be accurate. but in thus laying emphasis on the necessity of accurate observation, we must beware of rushing to the opposite extreme, and supposing that observation alone is enough. observation, the accurate use of the senses (by which we must understand inner as well as outer sense), is not the whole work of science. we may stare at facts every minute of our waking day without being a whit the wiser unless we exert our intellects to build upon them or under them. to make our examination fruitful, we must have conceptions, theories, speculations, to bring to the test. the comparison of these with the facts is the inductive verification of them. science has to exercise its ingenuity both in making hypotheses and in contriving occasions for testing them by observation. these contrived occasions are its artificial experiments, which have come to be called experiments simply by contrast with conclusive observations for which nature herself furnishes the occasion. the observations of science are not passive observations. the word experiment simply means trial, and every experiment, natural or artificial, is the trial of a hypothesis. in the language of leonardo da vinci, "theory is the general, experiments are the soldiers". observation and inference go hand in hand in the work of science, but with a view to a methodical exposition of its methods, we may divide them broadly into methods of observation and methods of inference. there are errors specially incident to observation, and errors specially incident to inference. how to observe correctly and how to make correct inferences from our observations are the two objects of our study in inductive logic: we study the examples of science because they have been successful in accomplishing those objects. that all inference to the unobserved is founded on facts, on the data of experience, need not be postulated. it is enough to say that inductive logic is concerned with inference in so far as it is founded on the data of experience. but inasmuch as all the data of experience are not of equal value as bases of inference, it is well to begin with an analysis of them, if we wish to take a comprehensive survey of the various modes of inference and the conditions of their validity. [footnote : hamilton's _reid_, p. .] [footnote : the _novum organum_ was never completed. of the nine heads of special aids to the intellect in the final interpretation he completed only the first, the list of prerogative instances.] [footnote : _sylva sylvarum_, century i, .] [footnote : _sylva sylvarum_, century i, .] chapter i. the data of experience as grounds of inference or rational belief. if we examine any of the facts or particulars on which an inference to the unobserved is founded, we shall find that they are not isolated individuals or attributes, separate objects of perception or thought, but relations among things and their qualities, constituents, or ingredients. take the "particular" from which mill's village matron inferred, the fact on which she based her expectation of a cure for her neighbour's child. it is a relation between things. we have the first child's ailment, the administration of the drug, and the recovery, a series of events in sequence. this observed sequence is the fact from which she is said to infer, the datum of experience. she expects this sequence to be repeated in the case of her neighbour's child. similarly we shall find that, in all cases where we infer, the facts are complex, are not mere isolated things, but relations among things--using the word thing in its widest sense--relations which we expect to find repeated, or believe to have occurred before, or to be occurring now beyond the range of our observation. these relations, which we may call coincidences or conjunctions, are the data of experience from which we start in our beliefs or inferences about the unexperienced. the problem of inductive logic being to determine when or on what conditions such beliefs are rational, we may begin by distinguishing the data of coincidence or conjunction accordingly. there are certain coincidences that we expect to find repeated beyond the occasions on which we have observed them, and others that we do not expect to find repeated. if it is a sound basis of inference that we are in search of, it is evidently to these first, the coincidences that we are assured of finding again, that we must direct our study. let us see whether they can be specified. ( ) if there is no causal connexion between a and b, using these as symbols for the members of a coincidence--the objects that are presented together--we do not expect the coincidence to be repeated. if a and b are connected as cause and effect, we expect the effect to recur in company with the cause. we expect that when the cause reappears in similar circumstances, the effect also will reappear. you are hit, _e.g._, by a snowball, and the blow is followed by a feeling of pain. the sun, we shall say, was shining at the moment of the impact of the snowball on your body. the sunshine preceded your feeling of pain as well as the blow. but you do not expect the pain to recur next time that the sun shines. you do expect it to recur next time you are hit by a snowball. the taking of food and a certain feeling of strength are causally connected. if we go without food, we are not surprised when faintness or weariness supervenes. suppose that when our village matron administered her remedy to her own child, a dog stood by the bedside and barked. the barking in that case would precede the cure. now, if the matron were what we should call a superstitious person, and believed that this concomitant had a certain efficacy, that the dog's barking and the cure were causally connected, she would take the dog with her when she went to cure her neighbour's child. otherwise she would not. she would say that the barking was an accidental, casual, fortuitous coincidence, and would build no expectation upon it. these illustrations may serve to remind us of the familiar fact that the causal nexus is at least one of the things that we depend on in our inferences to the unobserved. to a simple sequence we attach no importance, but a causal sequence or consequence that has been observed is a mainstay of inference. whether the causal sequence holds or not as a matter of fact, we depend upon it if we believe in it as a matter of fact. but unless it does hold as a matter of fact, it is valueless as a guide to the unknown, and our belief is irrational. clearly, therefore, if rational belief is what we aim at, it is of importance that we should make sure of cause and effect as matter of fact in the sequence of events. one large department of inductive logic, the so-called experimental methods, is designed to help us in thus making sure, _i.e._, in ascertaining causal sequence as a matter of fact. it is assumed that by careful observation of the circumstances, we can distinguish between mere simple sequence and causal sequence or consequence, and methods are recommended of observing with the proper precautions against error. observe that these methods, though called inductive, are not concerned with arriving at general propositions. the principle we go upon is simply this, that if it can be ascertained as matter of fact that a certain thing is related to another as cause and effect, we may count upon the same relation as holding in unobserved nature, on the general ground that like causes produce like effects in like circumstances. observe, also, that i deliberately speak of the causal relation as a relation among phenomena. whether this use of the words cause and effect is philosophically justifiable, is a question that will be raised and partly discussed later on. here i simply follow the common usage, in accordance with which objects of perception, _e.g._, the administration of a drug and the recovery of a patient, are spoken of as cause and effect. such observable sequences are causal sequences in the ordinary sense, and it is part of the work of science to observe them. i do not deny that the _true_ cause, of the cause that science aims ultimately at discovering, is to be found in the latent constitution or composition of the things concerned. only that, as we shall see more precisely, is a cause of another description. meantime, let us take the word to cover what it undoubtedly covers in ordinary speech, the perceptible antecedent of a perceptible consequent. strictly speaking, as we shall find, science has only one method of directly observing when events are in causal sequence. but there are various indirect methods, which shall be described in some sort of order. for the practical purposes of life, a single ascertained causal sequence is of little value as a basis of inference, because we can infer only to its repetition in identical circumstances. suppose our village matron had been able to ascertain as a matter of fact--a feat as we shall find not to be achieved by direct observation--that the drug did cure her child, this knowledge by itself would have been practically valueless, because the only legitimate inference would have been that an exactly similar dose would have the same effect in exactly similar circumstances. but, as we shall find, though practically valueless, a single ascertained causal sequence is of supreme value in testing scientific speculations as to the underlying causes. ( ) we have next to see whether there are any other rational expectations based on observed facts. we may lay down as a principle the following:-- _if a conjunction or coincidence has constantly been repeated within our experience, we expect it to recur and believe that it has recurred outside our experience._ how far such expectations are rational, and with what degrees of confidence they should be entertained, are the questions for the logic of inference, but we may first note that we do as a matter of habit found expectations on repeated coincidence, and indeed guide our daily life in this way. if we meet a man repeatedly in the street at a certain hour, we go out expecting to meet him: it is a shock to our expectations, a surprise, when we do not. if we are walking along a road and find poles set up at regular intervals, we continue our walk expecting to find a pole coincident with the end of each interval. what mill calls the uniformities of nature, the uniformities expressed in general propositions, are from the point of view of the observer, examples of repeated coincidence. birth, growth, decay, death, are not isolated or variable coincidences with organised being: all are born, all grow, all decay, and all die. these uniformities constitute the order of nature: the coincidences observed are not occasional, occurring once in a way or only now and then; they turn up again and again. trees are among the uniformities on the varied face of nature: certain relations between the soil and the plant, between trunk, branches, and leaves are common to them. for us who observe, each particular tree that comes under our observation is a repetition of the coincidence. and so with animals: in each we find certain tissues, certain organs, conjoined on an invariable plan. technically these uniformities have been divided into uniformities of sequence and uniformities of coexistence. thus the repeated alternation of day and night is a uniformity of sequence: the invariable conjunction of inertia with weight is a uniformity of coexistence. but the distinction is really immaterial to logic. what logic is concerned with is the observation of the facts and the validity of any inference based on them: and in these respects it makes no difference whether the uniformity that we observe and found upon is one of sequence or of coexistence. it was exclusively to such inferences, inferences from observed facts of repeated coincidence, that mill confined himself in his theory of induction, though not in his exposition of the methods. these are the inferences for which we must postulate what he calls the uniformity of nature. every induction, he says, following whately, may be thrown into the form of a syllogism, in which the principle of the uniformity of nature is the major premiss, standing to the inference in the relation in which the major premiss of a syllogism stands to the conclusion. if we express this abstractly denominated principle in propositional form, and take it in connexion with mill's other saying that the course of nature is not a uniformity but uniformities, we shall find, i think, that this postulated major premiss amounts to an assumption that the observed uniformities of nature continue. mill's inductive syllogism thus made explicit would be something like this:-- all the observed uniformities of nature continue. that all men have died is an observed uniformity. _therefore_, it continues; _i.e._, all men will die and did die before the beginning of record. there is no doubt that this is a perfectly sound postulate. like all ultimate postulates it is indemonstrable; mill's derivation of it from experience did not amount to a demonstration. it is simply an assumption on which we act. if any man cares to deny it, there is no argument that we can turn against him. we can only convict him of practical inconsistency, by showing that he acts upon this assumption himself every minute of his waking day. if we do not believe in the continuance of observed uniformities, why do we turn our eyes to the window expecting to find it in its accustomed order of place? why do we not look for it in another wall? why do we dip our pens in ink, and expect the application of them to white paper to be followed by a black mark? the principle is sound, but is it our only postulate in inference to the unobserved, and does the continuance of empirical laws represent all that science assumes in its inferences? mill was not satisfied about this question. he pointed out a difficulty which a mere belief in empirical continuity does not solve. why do we believe more confidently in some uniformities than in others? why would a reported breach of one be regarded with more incredulity than that of another? suppose a traveller to return from a strange country and report that he had met men with heads growing beneath their shoulders, why would this be pronounced more incredible than a report that he had seen a grey crow? all crows hitherto observed have been black, and in all men hitherto observed the heads have been above the shoulders: if the mere continuity of observed uniformities is all that we go upon in our inferences, a breach of the one uniformity should be just as improbable as a breach of the other, neither more nor less. mill admitted the difficulty, and remarked that whoever could solve it would have solved the problem of induction. now it seems to me that this particular difficulty may be solved, and yet leave another behind. it may be solved within the limits of the principle of emperical--meaning by that observational--continuity. the uniform blackness of the crow is an exception within a wider uniformity: the colour of animals is generally variable. hence we are not so much surprised at the reported appearance of a grey crow: it is in accordance with the more general law. on the other hand, the uniform position of the head relative to other parts of the body is a uniformity as wide as the animal kingdom: it is a coincidence repeated as often as animals have been repeated, and merely on the principle that uniformities continue, it has an absolutely uncontradicted series in its favour. but is this principle really all that we assume? do we not also assume that behind the observed fact uniformity, there is a cause for it, a cause that does not appear on the surface of the observation, but must be sought outside of its range? and do not the various degrees of confidence with which we expect a repetition of the coincidence, depend upon the extent of our knowledge of the producing causes and the mode of their operation? at bottom our belief in the continuance of the observed uniformities rests on a belief in the continuance of the producing causes, and till we know what these are our belief has an inferior warrant: there is less reason for our confidence. to go back to the illustrations with which we started. if we have met a man every day for months at a certain place at a certain hour, it is reasonable to expect to meet him there to-morrow, even if our knowledge does not go beyond the observed facts of repeated coincidence. but if we know also what brings him there, and that this cause continues, we have a stronger reason for our expectation. and so with the case of poles at regular intervals on a road. if we know why they are placed there, and the range of the purpose, we expect their recurrence more confidently within the limits of that purpose. this further knowledge is a warrant for stronger confidence, because if we know the producing causes, we are in a better position for knowing whether anything is likely to defeat the coincidence. a uniformity is said to be explained when its cause is known, and an inference from an explained uniformity is always more certain than an inference from a uniformity that is merely empirical in the sense of being simply observed. now, the special work of science is to explain, in the sense of discovering the causes at work beneath what lies open to observation. in so doing it follows a certain method, and obeys certain conditions of satisfactory explanation. its explanations are inferences from facts, inasmuch as it is conformity with observed facts, with outward signs of underlying causal nexus, that is the justification of them. but they are not inferences from facts in the sense above described as empirical inference. in its explanations also science postulates a principle that may be called the uniformity of nature. but this principle is not merely that observed uniformities continue. it may be expressed rather as an assumption that the underlying causes are uniform in their operation, that as they have acted beneath the recorded experiences of mankind, so they have acted before and will continue to act. the foregoing considerations indicate a plan for a roughly systematic arrangement of the methods of induction. seeing that all inference from the data of experience presupposes causal connexion among the data from which we infer, all efforts at establishing sound bases of inference, or rational ground for expectation fall, broadly speaking, under two heads: ( ) methods of ascertaining causal connexion among phenomena as a matter of fact, that is, methods of observation; and ( ) methods of ascertaining what the causal connexion is, that is, methods of explanation. these constitute the body of inductive logic. but there is a preliminary and a pendant. without raising the question of causal connexion, we are liable to certain errors in ascertaining in what sequence and with what circumstances events really occurred. these tendencies to error deserve to be pointed out by way of warning, and this i shall attempt in a separate chapter on observation of facts of simple sequence. this is preliminary to the special methods of observing causal sequence. then, by way of pendant, i shall consider two modes of empirical inference from data in which the causal connexion has not been ascertained or explained--inference from approximate generalisations to particular cases, and inference from analogy. most of these methods in one form or another were included by mill in his system of inductive logic, and the great merit of his work was that he did include them, though at some sacrifice of consistency with his introductory theory. with regard to the kind of empirical inference which that theory, following the lead of whately, took as the type of all inference, logic has really little to say. it was this probably that was in mill's mind when he said that there is no logic of observation, ignoring the fact that the experimental methods are really methods of observation, as well as the methods of eliminating chance by calculation of probability. there is no method of observing uniformities except simply observing them. nor indeed is there any "method" of inferring from them: we can only point out that in every particular inference from them we assume or postulate their continuance generally. as regards their observation, we may point out further that a special fallacy is incident to it, the fallacy of ignoring exceptions. if we are prepossessed or prejudiced in favour of a uniformity, we are apt to observe only the favourable instances, and to be blind to cases where the supposed invariable coincidence does not occur. thus, as bacon remarked among his _idola_, we are apt to remember when our dreams come true, and to forget when they do not. suppose we take up the notion that a new moon on a saturday is invariably followed by twenty days of unsettled weather, one or two or a few cases in which this notably holds good are apt to be borne in mind, while cases where the weather is neither conspicuously good nor bad are apt to be overlooked. but when a warning has been given against this besetting fallacy, logic has nothing further to say about empirical uniformities, except that we may infer from them with some degree of reasonable probability, and that if we want ground for a more certain inference we should try to explain them. chapter ii. ascertainment of simple facts in their order.--personal observation. --hearsay evidence--method of testing traditional evidence. all beliefs as to simple matter of fact must rest ultimately on observation. but, of course, we believe many things to have happened that we have never seen. as chaucer says:-- but god forbedë but men shouldë 'lieve wel morë thing than men han seen with eye. man shall not weenen everything a lie but if himself it seeth or elsë doth. for the great bulk of matters of fact that we believe we are necessarily dependent on the observations of others. and if we are to apply scientific method to the ascertainment of this, we must know what errors we are liable to in our recollections of what we have ourselves witnessed, and what errors are apt to arise in the tradition of what purports to be the evidence of eye-witnesses. i.--personal observation. it is hard to convince anybody that he cannot trust implicitly to his memory of what he has himself seen. we are ready enough to believe that others may be deceived: but not our own senses. seeing is believing. it is well, however, that we should realise that all observation is fallible, even our own. three great besetting fallacies or tendencies to error may be specified:-- . liability to have the attention fastened on special incidents, and so diverted from other parts of the occurrence. . liability to confuse and transpose the sequence of events. . liability to substitute inference for fact. it is upon the first of these weaknesses in man as an observing machine that jugglers chiefly depend on working their marvels. sleight of hand counts for much, but diverting the spectator's eyes for a good deal more. that is why they have music played and patter incessantly as they operate. their patter is not purposeless: it is calculated to turn our eyes away from the movements of their nimble hands. it must be borne in mind that in any field of vision there are many objects, and that in any rapid succession of incidents much more passes before the eyes than the memory can retain in its exact order. it is of course in moments of excitement and hurry, when our observation is distracted, that we are most subject to fallacious illusions of memory. unconsciously we make a coherent picture of what we have seen, and very often it happens that the sequence of events is not what actually passed, but what we were prejudiced in favour of seeing. hence the unlikelihood of finding exact agreement among the witnesses of any exciting occurrence, a quarrel, a railway accident, a collision at sea, the incidents of a battle. "it commonly happens," says mr. kinglake,[ ] "that incidents occurring in a battle are told by the most truthful bystanders with differences more or less wide." in the attack on the great redoubt in the battle of the alma, a young officer, anstruther, rushed forward and planted the colours of the royal welsh--but where? some distinctly remembered seeing him dig the butt-end of the flagstaff into the parapet: others as distinctly remembered seeing him fall several paces before he reached it. similarly with the incidents of the death of the prince imperial near the italezi hills in the zulu war. he was out as a volunteer with a reconnoitring party. they had off-saddled at a kraal and were resting, when a band of zulus crept up through the long grass, and suddenly opened fire and made a rush forward. our scouts at once took horse, as a reconnoitring party was bound to do, and scampered off, but the prince was overtaken and killed. at the court-martial which ensued, the five troopers gave the most conflicting accounts of particulars which an unskilled investigator would think could not possibly have been mistaken by eye-witnesses of the same event. one said that the prince had given the order to mount before the zulus fired: another that he gave the order directly after: a third was positive that he never gave the order at all, but that it was given after the surprise by the officer in command. one said that he saw the prince vault into the saddle as he gave the order: another that his horse bolted as he laid hold of the saddle, and that he ran alongside trying to get up. the evidence before any court of inquiry into an exciting occurrence is almost certain to reveal similar discrepancies. but what we find it hard to realise is that we ourselves can possibly be mistaken in what we have a distinct and positive recollection of having seen. it once happened to myself in a london street to see a drunken woman thrown under a cab by her husband. two cabs were running along, a four-wheeler and a hansom: the woman staggered almost under the first, and was thrown under the second. as it happened the case never got beyond the police station to which the parties were conveyed after fierce opposition from some neighbours, who sympathised entirely with the man. the woman herself, when her wounds were dressed, acknowledged the justice of her punishment, and refused to charge her husband. i was all the more willing to acquiesce in this because i found that while i had the most distinct impression of having seen the four-wheeler run over the woman's body, and should have been obliged to swear accordingly, there could be no doubt that it was really the hansom that had done so. this was not only the evidence of the neighbours, which i suspected at the time of being a trick, but of the cabdriver, who had stopped at the moment to abide the results of the accident. i afterwards had the curiosity to ask an eminent police magistrate, sir john bridge, whether this illusion of memory on my part--which i can only account for by supposing that my eyes had been fixed on the sufferer and that i had unconsciously referred her injuries to the heavier vehicle--would have entirely discredited my testimony in his court. his answer was that it would not; that he was constantly meeting with such errors, and that if he found a number of witnesses of the same occurrence exactly agreed in every particular, he would suspect that they had talked the matter over and agreed upon what they were to say. this was the opinion of an experienced judge, a skilled critic of the defects of personal observation. an old bailey counsel for the defence, who is equally acquainted with the weakness of human memory, takes advantage of the fact that it is not generally understood by a jury, and makes the fallacious assumption that glaring discrepancies are irreconcilable with the good faith of the witnesses who differ.[ ] ii.--tradition.--hearsay evidence. next in value to personal observation, we must place the report, oral or written, of an eye-witness. this is the best evidence we can get if we have not witnessed an occurrence ourselves. yet courts of law, which in consideration of the defects of personal observation require more than one witness to establish the truth, exclude hearsay evidence altogether in certain cases, and not without reason. in hearing a report we are in the position of observers of a series of significant sounds, and we are subject to all the fallacies of observation already mentioned. in an aggravated degree, for words are harder to observe than visible things. our attention is apt to be more listless than in presence of the actual events. our minds dwell upon parts of the narrative to the neglect of other parts, and in the coherent story or description that we retain in our memories, sequences are apt to be altered and missing links supplied in accordance with what we were predisposed to hear. thus hearsay evidence is subject to all the imperfections of the original observer, in addition to the still more insidious imperfections of the second observer. how quickly in the course of a few such transmissions hearsay loses all evidentiary value is simply illustrated by the game known as russian scandal. one of a company, a, writes down a short tale or sketch, and reads it to b. b repeats it to c, c to d, and so on. when it has thus gone the round of the company, the last hearer writes down his version, and it is compared with the original. with every willingness to play fair, the changes are generally considerable and significant. sometimes it is possible to compare an oral tradition with a contemporary written record. in one of mr. hayward's essays--"the pearls and mock pearls of history"--there are some examples of this disenchanting process. there is, for instance, a pretty story of an exchange of courtesies between the leaders of the french and english guards at the battle of fontenoy. the tradition runs that lord charles hay stepped in front of his men and invited the french guards to fire, to which m. d'auteroche with no less chivalry responded: "monsieur, we never fire first; you fire". what really passed we learn from a letter from lord charles hay to his mother, which happens to have been preserved. "i advanced before our regiment, and drank to the frenchmen, and told them we were the english guards, and hoped they would stand till we came, and not swim the scheldt as they did the maine at dettingen." tradition has changed this lively piece of buffoonery into an act of stately and romantic courtesy. the change was probably made quite unconsciously by some tenth or hundredth transmitter, who remembered only part of the story, and dressed the remainder to suit his own fancy. the question has been raised, for how long can oral tradition be trusted? newton was of opinion that it might be trusted for eighty years after the event. others have named forty years. but if this means that we may believe a story that we find in circulation forty years after the alleged events, it is wildly extravagant. it does injustice to the mythop[oe]ic faculty of man. the period of time that suffices for the creation of a full-blown myth, must be measured by hours rather than by years. i will give an instance from my own observation, if that has not been entirely discredited by my previous confessions. the bazaars of the east are generally supposed to be the peculiar home of myth, hotbeds in which myths grow with the most amazing speed, but the locality of my myth is aberdeen. in the summer of our town set up in one of its steeples a very fine carillon of belgian bells. there was much public excitement over the event: the descriptions of enthusiastic promoters had prepared us to hear silvery music floating all over the town and filling the whole air. on the day fixed for the inauguration, four hours after the time announced for the first ceremonial peal, not having heard the bells, i was in a shop and asked if anything had happened to put off the ceremony. "yes," i was told; "there had been an accident; they had not been properly hung, and when the wife of the lord provost had taken hold of a string to give the first pull, the whole machinery had come down." as a matter of fact all that had happened was that the sound of the bells was faint, barely audible a hundred yards from the belfry, and not at all like what had been expected. there were hundreds of people in the streets, and the myth had originated somehow among those who had not heard what they went out to hear. the shop where it was repeated circumstantially to me was in the main street, not more than a quarter of a mile from where the carillon had been played in the hearing of a large but disappointed crowd. i could not help reflecting that if i had been a mediæval chronicler, i should have gone home and recorded the story, which continued to circulate for some days in spite of the newspapers: and two hundred years hence no historian would have ventured to challenge the truth of the contemporary evidence. iii.--method of testing traditional evidence. it is obvious that the tests applied to descriptive testimony in courts of law cannot be applied to the assertions of history. it is a supreme canon of historical evidence that only the statements of contemporaries can be admitted: but most even of their statements must rest on hearsay, and even when the historian professes to have been an eye-witness, the range of his observation is necessarily limited, and he cannot be put into the witness-box and cross-examined. is there then no way of ascertaining historical fact? must we reject history as altogether unworthy of credit? the rational conclusion only is that very few facts can be established by descriptive testimony such as would satisfy a court of law. those who look for such ascertainment are on a wrong track, and are doomed to disappointment. it is told of sir walter raleigh that when he was writing his history of the world, he heard from his prison in the tower a quarrel outside, tried to find out the rights and the wrongs and the course of it, and failing to satisfy himself after careful inquiry, asked in despair how he could pretend to write the history of the world when he could not find out the truth about what occurred under his own windows. but this was really to set up an impossible standard of historical evidence. the method of testing historical evidence follows rather the lines of the newtonian method of explanation, which we shall afterwards describe. we must treat any historical record as being itself in the first place a fact to be explained. the statement at least is extant: our first question is, what is the most rational way of accounting for it? can it be accounted for most probably by supposing the event stated to have really occurred with all the circumstances alleged? or is it a more probable hypothesis that it was the result of an illusion of memory on the part of the original observer, if it professes to be the record of an eye-witness, or on the part of some intermediate transmitter, if it is the record of a tradition? to qualify ourselves to answer the latter kind of question with reasonable probability we must acquaint ourselves with the various tendencies to error in personal observation and in tradition, and examine how far any of them are likely to have operated in the given case. we must study the operation of these tendencies within our experience, and apply the knowledge thus gained. we must learn from actual observation of facts what the mythop[oe]ic faculty is capable of in the way of creation and transmutation, and what feats are beyond its powers, and then determine with as near a probability as we can how far it has been active in the particular case before us. [footnote : _the invasion of the crimea_, iii. ] [footnote : the truth is, that we see much less than is commonly supposed. not every impression is attended to that is made on the retina, and unless we do attend we cannot, properly speaking, be said to see. walking across to college one day, i was startled by seeing on the face of a clock in my way that it was ten minutes to twelve, whereas i generally passed that spot about twenty minutes to twelve. i hurried on, fearing to be late, and on my arrival found myself in very good time. on my way back, passing the clock again, i looked up to see how much it was fast. it marked ten minutes to eight. it had stopped at that time. when i passed before i had really seen only the minute hand. the whole dial must have been on my retina, but i had looked at or attended to only what i was in doubt about, taking the hour for granted. i am bound to add that my business friends hint that it is only absorbed students that are capable of such mistakes, and that alert men of business are more circumspect. that can only be because they are more alive to the danger of error.] chapter iii. ascertainment of facts of causation. i.--_post hoc ergo propter hoc_. one of the chief contributions of the old logic to inductive method was a name for a whole important class of misobservations. the fallacy entitled _post hoc ergo propter hoc_--"after, therefore, because of"--consisted in alleging mere sequence as a proof of consequence or causal sequence. the sophist appeals to experience, to observed facts: the sequence which he alleges has been observed. but the appeal is fallacious: the observation on which he relies amounts only to this, that the one event has followed upon the other. this much must be observable in all cases of causal sequence, but it is not enough for proof. _post hoc ergo propter hoc_ may be taken as a generic name for imperfect proof of causation from observed facts of succession. the standard example of the fallacy is the old kentish peasant's argument that tenterden steeple was the cause of goodwin sands. sir thomas more (as latimer tells the story in one of his sermons to ridicule incautious inference) had been sent down into kent as a commissioner to inquire into the cause of the silting up of sandwich haven. among those who came to his court was the oldest inhabitant, and thinking that he from his great age must at least have seen more than anybody else, more asked him what he had to say as to the cause of the sands. "forsooth, sir," was the greybeard's answer, "i am an old man: i think that tenterden steeple is the cause of goodwin sands. for i am an old man, and i may remember the building of tenterden steeple, and i may remember when there was no steeple at all there. and before that tenterden steeple was in building, there was no manner of speaking of any flats or sands that stopped the haven; and, therefore, i think that tenterden steeple is the cause of the destroying and decaying of sandwich haven." this must be taken as latimer meant it to be, as a ridiculous example of a purely imbecile argument from observation, but the appeal to experience may have more show of reason and yet be equally fallacious. the believers in kenelm digby's "ointment of honour" appealed to experience in support of its efficacy. the treatment was to apply the ointment, not to the wound, but to the sword that had inflicted it, to dress this carefully at regular intervals, and, meantime, having bound up the wound, to leave it alone for seven days. it was observed that many cures followed upon this treatment. but those who inferred that the cure was due to the bandaging of the sword, failed to observe that there was another circumstance that might have been instrumental, namely, the exclusion of the air and the leaving of the wound undisturbed while the natural healing processes went on. and it was found upon further observation that binding up the wound alone answered the purpose equally well whether the sword was dressed or not. in cases where _post hoc_ is mistaken for _propter hoc_, simple sequence for causal sequence, there is commonly some bias of prejudice or custom which fixes observation on some one antecedent and diverts attention from other circumstances and from what may be observed to follow in other cases. in the minds of digby and his followers there was probably a veneration for the sword as the weapon of honour, and a superstitious belief in some secret sympathy between the sword and its owner. so when the practice of poisoning was common, and suspicion was flurried by panic fear, observation was often at fault. pope clement viii. was said to have been killed by the fumes of a poisoned candle which was placed in his bedroom. undoubtedly candles were there, but those who attributed the pope's death to them took no notice of the fact that a brazier of burning charcoal was at the same time in the apartment with no sufficient outlet for its fumes. prince eugene is said to have received a poisoned letter, which he suspected and immediately threw from him. to ascertain whether his suspicions were well founded the letter was administered to a dog, which, to make assurance doubly sure, was fortified by an antidote. the dog died, but no inquiry seems to have been made into the character of the antidote. hotspur's retort to glendower showed a sound sense of the true value to be attached to mere priority. _glendower_. at my nativity the front of heaven was full of fiery shapes, of burning cressets: and at my birth the frame and huge foundation of the earth shaked like a coward. _hotspur_. why so it would have done at the same season, if your mother's cat had but kittened, though yourself had never been born. hen. iv., , , . we all admit at once that the retort was just. what principle of sound conclusion was involved in it? it is the business of inductive logic to make such principles explicit. taking _post hoc ergo propter hoc_ as a generic name for fallacious arguments of causation based on observed facts, for the fallacious proof of causation from experience, the question for logic is, what more than mere _sequence_ is required to prove _consequence?_ when do observations of _post hoc_ warrant the conclusion _propter hoc?_ ii.--meaning of "cause".--methods of observation--mill's experimental methods. the methods formulated by mill under the name of experimental methods are methods actually practised by men of science with satisfactory results, and are perfectly sound in principle. they were, indeed, in substance, taken by him from the practice of the scientific laboratory and study as generalised by herschel. in effect what mill did was to restate them and fit them into a system. but the controversies into which he was tempted in so doing have somewhat obscured their exact function in scientific inquiry. hostile critics, finding that they did not serve the ends that he seemed to claim for them, have jumped to the conclusion that they are altogether illusory and serve no purpose at all. first, we must dismiss the notion, encouraged by mill's general theory of inference, that the experimental methods have anything special to do with the observation and inferential extension of uniformities such as that death is common to all organised beings. one of the methods, as we shall see, that named by mill the method of agreement, does incidentally and collaterally establish empirical laws in the course of its observations, and this probably accounts for the prominence given to it in mill's system. but this is not its end and aim, and the leading method, that named by him the method of difference, establishes as fact only a particular case of causal coincidence. it is with the proof of theories of causation that the experimental methods are concerned: they are methods of observing with a view to such proof.[ ] the next point to be made clear is that the facts of causation with which the methods are concerned are observable facts, relations among phenomena, but that the causal relations or conditions of which they are the proof are not phenomena, in the meaning of being manifest to the senses, but rather noumena, inasmuch as they are reached by reasoning from what is manifest. take, for example, what is known as the _quaquaversus_ principle in hydrostatics, that pressure upon a liquid is propagated equally in all directions. we cannot observe this extension of pressure among the liquid particles directly. it cannot be traced among the particles by any of our senses. but we can assume that it is so, consider what ought to be visible if it is so, and then observe whether the visible facts are in accordance with the hypothesis. a box can be made, filled with water, and so fitted with pistons on top and bottom and on each of its four sides that they will indicate the amount of pressure on them from within. let pressure then be applied through a hole in the top, and the pistons show that it has been communicated to them equally. the application of the pressure and the yielding of the pistons are observable facts, facts in causal sequence: what happens among the particles of the liquid is not observed but reasonably conjectured, is not _phenomenal_ but _noumenal_. this distinction, necessary to an understanding of the scope of the methods, was somewhat obscured by mill in his preliminary discussion of the meaning of "cause". very rightly, though somewhat inconsistently with his first theory of induction, he insists that "the notion of cause being the root of the whole theory of induction, it is indispensable that this idea should at the very outset of our inquiry be, with the utmost practicable degree of precision, fixed and determined". but in this determination, not content with simply recognising that it is with phenomena that the experimental methods primarily deal, it being indeed only phenomena that can be the subjects of experimental management and observation, he starts by declaring that science has not to do with any causes except such as are phenomenal--"when i speak of the cause of any phenomenon, i do not mean a cause which is not itself a phenomenon"--and goes on to define as the only correct meaning of cause "the sum total of conditions," including among them conditions which are not phenomenal, in the sense of being directly open to observation. when mill protested that he had regard only to phenomenal causes, he spoke as the partisan of a philosophical tradition. it would have been well if he had acted upon his own remark that the proper understanding of the scientific method of investigating cause is independent of metaphysical analysis of what cause means. curiously enough, this remark is the preface to an analysis of cause which has but slight relevance to science, and is really the continuation of a dispute begun by hume. this is the key to his use of the word phenomenon: it must be interpreted with reference to this: when he spoke of causes as phenomenal, he opposed the word to "occult" in some supposed metaphysical sense.[ ] and this irrelevant discussion, into the vortex of which he allowed himself to be carried, obscured the fact, elsewhere fully recognised by mill himself, that science does attempt to get beyond phenomena at ultimate laws which are not themselves phenomena though they bind phenomena together. the "colligation" of the facts, to use whewell's phrase, is not a phenomenon, but a noumenon. the truth is that a very simple analysis of "cause" is sufficient for the purposes of scientific inquiry. it is enough to make sure that causal sequence or consequence shall not be confounded with simple sequence. causal sequence is simple sequence and something more, that something more being expressed by calling it causal. what we call a cause is not merely antecedent or prior in time to what we call its effect: it is so related to the effect that if it or an equivalent event had not happened the effect would not have happened. anything in the absence of which a phenomenon would not have come to pass as it did come to pass is a cause in the ordinary sense. we may describe it as an indispensable antecedent, with this reservation (which will be more fully understood afterwards), that if we speak of a general effect, such as death, the antecedents must be taken with corresponding generality. it is misleading to suggest, as mill does, by defining cause as "the sum total of conditions"--a definition given to back up his conception of cause as phenomenal--that science uses the word cause in a different meaning from that of ordinary speech. it is quite true that "the cause, philosophically speaking, is the sum total of the conditions, positive and negative, taken together: the whole of the contingencies of every description, which being realised, the consequent invariably follows". but this does not imply any discrepancy between the scientific or philosophical meaning and the ordinary meaning. it is only another way of saying that the business of science or philosophy is to furnish a complete explanation of an event, an account of all its indispensable antecedents. the plain man would not refuse the name of cause to anything that science or philosophy could prove to be an indispensable antecedent, but his interest in explanation is more limited. it is confined to what he wants to know for the purpose he has in hand. nor could the man of science consistently refuse the name of cause to what the plain man applies it to, if it really was something in consequence of which the event took place. only his interest in explanation is different. the indispensable antecedents that he wants to know may not be the same. science or philosophy applies itself to the satisfaction of a wider curiosity: it wants to know all the causes, the whole why, the sum total of conditions. to that end the various departments of science interest themselves in various species of conditions. but all understand the word cause in the ordinary sense. we must not conclude from accidental differences in explanation or statement of cause, dependent on the purpose in view, that the word cause is used in different senses. in answering a question as to the cause of anything, we limit ourselves to what we suppose our interrogator to be ignorant of and desirous of knowing. if asked why the bells are ringing, we mention a royal marriage, or a victory, or a church meeting, or a factory dinner hour, or whatever the occasion may be. we do not consider it necessary to mention that the bells are struck by a clapper. our hearer understands this without our mentioning it. nor do we consider it necessary to mention the acoustic condition, that the vibration of the bells is communicated to our ears through the air, or the physiological condition, that the vibrations in the drums of our ears are conveyed by a certain mechanism of bone and tissue to the nerves. our hearer may not care to know this, though quite prepared to admit that these conditions are indispensable antecedents. similarly, a physiographer, in stating the cause of the periodical inundation of the nile, would consider it enough to mention the melting of snow on the mountains in the interior of africa, without saying anything of such conditions as the laws of gravity or the laws of liquefaction by heat, though he knows that these conditions are also indispensable. death is explained by the doctor when referred to a gunshot wound, or a poison, or a virulent disease. the pathologist may inquire further, and the moral philosopher further still. but all inquiries into indispensable conditions are inquiries into cause. and all alike have to be on their guard against mistaking simple sequence for consequence. to speak of the sum total of conditions, as the cause in a distinctively scientific sense, is misleading in another direction. it rather encourages the idea that science investigates conditions in the lump, merely observing the visible relations between sets of antecedents and their consequents. now this is the very thing that science must avoid in order to make progress. it analyses the antecedent situation, tries to separate the various coefficients, and finds out what they are capable of singly. it must recognise that some of the antecedents of which it is in search are not open to observation. it is these, indeed, for the most part that constitute the special subject-matter of the sciences in molar as well as in molecular physics. for practical every-day purposes, it is chiefly the visible succession of phenomena that concerns us, and we are interested in the latent conditions only in as far as they provide safer ground for inference regarding such visible succession. but to reach the latent conditions is the main work of science. it is, however, only through observation of what is open to the senses that science can reach the underlying conditions, and, therefore, to understand its methods we must consider generally what is open to observation in causal succession. what can be observed when phenomena follow one another as cause and effect, that is, when the one happens in consequence of the happening of the other? in hume's theory, which mill formally adopted with a modification,[ ] there is nothing observable but the constancy or invariability of the connexion. when we say that fire burns, there is nothing to be observed except that a certain sensation invariably follows upon close proximity to fire. but this holds good only if our observation is arbitrarily limited to the facts enounced in the expression. if this theory were sound, science would be confined to the observation of empirical laws. but that there is something wrong with it becomes apparent when we reflect that it has been ascertained beyond doubt that in many observed changes, and presumably in all, there is a transference of energy from one form to another. the paralogism really lies in the assumption from which hume deduced his theory, namely, that every idea is a copy of some impression. as a matter of fact, we have ideas that are not copies of any one impression, but a binding together, colligation, or intellection of several impressions. psychological analysis shows us that even when we say that things exist with certain qualities, we are expressing not single impressions or mental phenomena, but supposed causes and conditions of such, _noumena_ in short, which connect our recollections of many separate impressions and expectations of more. the experimental methods proceed on the assumption that there is other outward and visible evidence of causal connexion than invariability of sequence. in the leading method it is assumed that when events may be observed to follow one another in a certain way, they are in causal sequence. if we can make sure that an antecedent change is the only change that has occurred in an antecedent situation, we have proof positive that any immediately subsequent change in the situation is a consequent, that the successive changes are in causal sequence. thus when pascal's barometer was carried to the top of puy le dome, and the mercury in it fell, the experimenters argued that the fall of the mercury was causally connected with the change of elevation, all the other circumstances remaining the same. this is the foundation of the so-called method of difference. to determine that the latent condition was a difference in the weight of the atmosphere, needed other observations, calculations and inferences; but if it could be shown that the elevation was the only antecedent changed in a single instance, causal connexion was established between this and the phenomenon of the fall of the barometer. it is obvious that in coming to this conclusion we assume what cannot be demonstrated but must simply be taken as a working principle to be confirmed by its accordance with experience, that nothing comes into being without some change in the antecedent circumstances. this is the assumption known as the law of causation--_ex nihilo nihil fit_. again, certain observable facts are taken as evidence that there is no causal connexion. on the assumption that any antecedent in whose absence a phenomenon takes place is not causally connected with it, we set aside or eliminate various antecedents as fortuitous or non-causal. this negative principle, as we shall see, is the foundation of what mill called the method of agreement. be it remarked, once for all, that before coming to a conclusion on the positive method or method of difference, we may often have to make many observations on the negative method. thus pascal's experimenters, before concluding that the change of altitude was the only influential change, tried the barometer in exposed positions and in sheltered, when the wind blew and when it was calm, in rain and in fog, in order to prove that these circumstances were indifferent. we must expound and illustrate the methods separately, but every method known to science may have in practice to be employed in arriving at a single conclusion. [footnote : this is implied, as i have already remarked, in the word experimental. an experiment is a proof or trial: of what? of a theory, a conjecture.] [footnote : if we remember, as becomes apparent on exact psychological analysis, that things and their qualities are as much _noumena_ and not, strictly speaking, _phenomena_ as the attraction of gravity or the quaquaversus principle in liquid pressure, the prejudice against occultism is mitigated.] [footnote : the modification was that causation is not only "invariable" but also "unconditional" sequence. this addition of unconditionality as part of the meaning of cause, after defining cause as the sum total of the conditions, is very much like arguing in a circle. after all, the only point recognised in the theory as observable is the invariability of the sequence. but this is less important than the fact that in his canons of the experimental methods mill recognised that more is observable.] chapter iv. methods of observation.--single difference. i.--the principle of single difference.--mill's "canon". on what principle do we decide, in watching a succession of phenomena, that they are connected as cause and effect, that one happened in consequence of the happening of another? it may be worded as follows:-- _when the addition of an agent is followed by the appearance or its subtraction by the disappearance of a certain effect, no other influential circumstance having been added or subtracted at the same time or in the meantime, and no change having occurred among the original circumstances, that agent is a cause of the effect._ on this principle we would justify our belief in the causal properties of common things--that fire burns, that food appeases hunger, that water quenches thirst, that a spark ignites gunpowder, that taking off a tight shoe relieves a pinched foot. we have observed the effect following when there was no other change in the antecedent circumstances, when the circumstance to which we refer it was simply added to or subtracted from the prior situation. suppose we doubt whether a given agent is or is not capable of producing a certain effect in certain circumstances, how do we put it to the proof? we add it singly or subtract it singly, taking care that everything else remains as before, and watch the result. if we wish to know whether a spoonful of sugar can sweeten a cup of tea, we taste the tea without the sugar, then add the sugar, and taste again. the isolated introduction of the agent is the proof, the experiment. if we wish to know whether a pain in the foot is due to a tight lacing, we relax the lacing and make no other change: if the pain then disappears, we refer it to the lacing as the cause. the proof is the disappearance of the pain on the subtraction of the single antecedent. the principle on which we decide that there is causal connexion is the same whether we make the experimental changes ourselves or merely watch them as they occur--the only course open to us with the great forces of nature which are beyond the power of human manipulation. in any case we have proof of causation when we can make sure that there was only one difference in the antecedent circumstances corresponding to the difference of result. mill's statement of this principle, which he calls the canon of the method of difference, is somewhat more abstract, but the proof relied upon is substantially the same. _if an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former, the circumstance in which alone the two instances differ is [the effect, or][ ] the cause, or an indispensable part of the cause, of the phenomenon._ mill's statement has the merit of exactness, but besides being too abstract to be easy of application, the canon is apt to mislead in one respect. the wording of it suggests that the two instances required must be two separate sets of circumstances, such as may be put side by side and compared, one exhibiting the phenomenon and the other not. now in practice it is commonly one set of circumstances that we observe with a special circumstance introduced or withdrawn: the two instances, the data of observation, are furnished by the scene before and the scene after the experimental interference. in the case, for example, of a man shot in the head and falling dead, death being the phenomenon in question, the instance where it does not occur is the man's condition before he received the wound, and the instance where it does occur is his condition after, the single circumstance of difference being the wound, a difference produced by the addition or introduction of a new circumstance. again, take the common coin and feather experiment, contrived to show that the resistance of the air is the cause of the feather's falling to the ground more slowly than the coin. the phenomenon under investigation is the retardation of the feather. when the two are dropped simultaneously in the receiver of an air-pump, the air being left in, the feather flutters to the ground after the coin. this is the instance where the phenomenon occurs. then the air is pumped out of the receiver, and the coin and the feather being dropped at the same instant reach the ground together. this is the instance where the phenomenon does not occur. the single circumstances of difference is the presence of air in the former instance, a difference produced by the subtraction of a circumstance. mill's canon is framed so as to suit equally whether the significant difference is produced by addition to or subtraction from an existing sum of circumstances. but that is misleading in so far as it suggests that the two instances must be separate sets of circumstances, is shown by the fact that it misled himself when he spoke of the application of the method in social investigations, such as the effect of protection on national wealth. "in order," he says, "to apply to the case the most perfect of the methods of experimental inquiry, the method of difference, we require to find two instances which tally in every particular except the one which is the subject of inquiry. we must have two nations alike in all natural advantages and disadvantages; resembling each other in every quality physical and moral; habits, usages, laws, and institutions, and differing only in the circumstance that the one has a prohibitory tariff and the other has not." it being impossible ever to find two such instances, he concluded that the method of difference could not be applied in social inquiries. but really it is not necessary in order to have two instances that we should have two different nations: the same nation before and after a new law or institution fulfils that requirement. the real difficulty, as we shall see, is to satisfy the paramount condition that the two instances shall differ in a single circumstance. every new enactment would be an experiment after the method of difference, if all circumstances but it remained the same till its results appeared. it is because this seldom or never occurs that decisive observation is difficult or impossible, and the simple method of difference has to be supplemented by other means. to introduce or remove a circumstance singly is the typical application of the principle; but it may be employed also to compare the effects of different agents, each added alone to exactly similar circumstances. a simple example is seen in mr. jamieson's agricultural experiments to determine the effects of different manures, such as coprolite and superphosphate, on the growth of crops. care is taken to have all the antecedent circumstances as exactly alike as possible, except as regards the agency whose effects are to be observed. a field is chosen of uniform soil and even exposure and divided into plots: it is equally drained so as to have the same degree of moisture throughout; the seed is carefully selected for the whole sowing. between the sowing and the maturing of the crop all parts of the field are open to the same weather. each plot may thus be regarded as practically composing the same set of conditions, and any difference in the product may with reasonable probability be ascribed to the single difference in the antecedents, the manures which it is desired to compare. ii.--application of the principle. the principle of referring a phenomenon to the only immediately preceding change in antecedent circumstances that could possibly have affected it, is so simple and so often employed by everybody every day, that at first we do not see how there can be any difficulty about it or any possibility of error. and once we understand how many difficulties there are in reaching exact knowledge even on this simple principle, and what care has to be taken, we are apt to overrate its value, and to imagine that it carries us further than it really does. the scientific expert must know how to apply this principle, and a single application of it with the proper precautions may take him days or weeks, and yet all that can be made good by it may carry but a little way towards the knowledge of which he is in search. when the circumstances are simple and the effect follows at once, as when hot water scalds, or a blow with a stick breaks a pane of glass, there can be no doubt of the causal connexion so far, though plenty of room for further inquiry into the why. but the mere succession of phenomena may be obscure. we may introduce more than one agent without knowing it, and if some time elapses between the experimental interference and the appearance of the effect, other agents may come in without our knowledge. we must know exactly what it is that we introduce and all the circumstances into which we introduce it. we are apt to ignore the presence of antecedents that are really influential in the result. a man heated by work in the harvest field hastily swallows a glass of water, and drops down dead. there is no doubt that the drinking of the water was a causal antecedent, but the influential circumstance may not have been the quantity or the quality of the liquid but its temperature, and this was introduced into the situation as well as a certain amount of the liquid components. in making tea we put in so much tea and so much boiling water. but the temperature of the pot is also an influential circumstance in the resulting infusion. so in chemical experiments, where one might expect the result to depend only upon the proportions of the ingredients, it is found that the quantity is also influential, the degree of heat evolved entering as a factor into the result. before we can apply the principle of single difference, we must make sure that there is really only a single difference between the instances that we bring into comparison. the air-pump was invented shortly before the foundation of the royal society, and its members made many experiments with this new means of isolating an agent and thus discovering its potentialities. for example, live animals were put into the receiver, and the air exhausted, with the result that they quickly died. the absence of the air being the sole difference, it was thus proved to be indispensable to life. but air is a composite agent, and when means were contrived of separating its components, the effects of oxygen alone and of carbonic acid alone were experimentally determined. a good example of the difficulty of excluding agencies other than those we are observing, of making sure that none such intrude, is found in the experiments that have been made in connexion with spontaneous generation. the question to be decided is whether life ever comes into existence without the antecedent presence of living germs. and the method of determining this is to exclude all germs rigorously from a compound of inorganic matter, and observe whether life ever appears. if we could make sure in any one case that no germs were antecedently present, we should have proved that in that case at least life was spontaneously generated. the difficulty here arises from the subtlety of the agent under observation. the notion that maggots are spontaneously generated in putrid meat, was comparatively easy to explode. it was found that when flies were excluded by fine wire-gauze, the maggots did not appear. but in the case of microscopic organisms proof is not so easy. the germs are invisible, and it is difficult to make certain of their exclusion. a french experimenter, pouchet, thought he had obtained indubitable cases of spontaneous generation. he took infusions of vegetable matter, boiled them to a pitch sufficient to destroy all germs of life, and hermetically sealed up the liquid in glass flasks. after an interval, micro-organisms appeared. doubts as to the conclusion that they had been spontaneously generated turned upon two questions: whether all germs in the liquid had been destroyed by the preliminary boiling, and whether germs could have found access in the course of the interval before life appeared. at a certain stage in pouchet's process he had occasion to dip the mouths of the flasks in mercury. it occurred to pasteur in repeating the experiments that germs might have found their way in from the atmospheric dust on the surface of this mercury. that this was so was rendered probable by his finding that when he carefully cleansed the surface of the mercury no life appeared afterwards in his flasks. the application of the principle in human affairs is rendered uncertain by the immense complication of the phenomena, the difficulty of experiment, and the special liability of our judgments to prejudice. that men and communities of men are influenced by circumstances is not to be denied, and the influence of circumstances, if it is to be traced at all, must be traced through observed facts. observation of the succession of phenomena must be part at least of any method of tracing cause and effect. we must watch what follows upon the addition of new agencies to a previously existing sum. but we can seldom or never get a decisive observation from one pair of instances, a clear case of difference of result preceded by a single difference in the antecedents. the simple method of experimental addition or subtraction is practically inapplicable. we can do nothing with a man analogous to putting him into a hermetically sealed retort. any man or any community that is the subject of our observations must be under manifold influences. each of them probably works some fraction of the total change observable, but how are they to be disentangled? consider, for example, how impossible it would be to prove in an individual case, on the strict principle of single difference, that evil communications corrupt good manners. moral deterioration may be observed following upon the introduction of an evil companion, but how can we make sure that no other degrading influence has operated, and that no original depravity has developed itself in the interval? yet such propositions of moral causation can be proved from experience with reasonable probability. only it must be by more extended observations than the strict method of difference takes into account. the method is to observe repeated coincidences between evil companionship and moral deterioration, and to account for this in accordance with still wider observations of the interaction of human personalities. for equally obvious reasons the simple method of difference is inapplicable to tracing cause and effect in communities. every new law or repeal of an old law is the introduction of a new agency, but the effects of it are intermixed with the effects of other agencies that operate at the same time. thus professor cairnes remarks, concerning the introduction of a high protective tariff into the united states in , that before its results could appear in the trade and manufacture of the states, there occurred ( ) the great civil war, attended with enormous destruction of capital; ( ) consequent upon this the creation of a huge national debt, and a great increase of taxation; ( ) the issue of an inconvertible paper currency, deranging prices and wages; ( ) the discovery of great mineral resources and oil-springs; ( ) a great extension of railway enterprise. obviously in such circumstances other methods than the method of difference must be brought into play before there can be any satisfactory reasoning on the facts observed. still what investigators aim at is the isolation of the results of single agencies. [footnote : prof. bain, who adopts mill's canon, silently drops the words within brackets. they seem to be an inadvertence. the "circumstance," in all the examples that mill gives, is an antecedent circumstance. herschel's statement, of which mill's is an adaptation, runs as follows: "if we can either find produced by nature, or produce designedly for ourselves, two instances which agree exactly in all but one particular and differ in that one, its influence in producing the phenomenon, if it have any, must thereby be rendered apparent".] chapter v. methods of observation.--elimination.--single agreement. i.--the principle of elimination. the essence of what mill calls the method of agreement is really the elimination[ ] of accidental, casual, or fortuitous antecedents. it is a method employed when we are given an effect and set to work to discover the cause. it is from the effect that we start and work back. we make a preliminary analysis of the antecedents; call the roll, as it were, of all circumstances present before the effect appeared. then we proceed to examine other instances of the same effect, and other instances of the occurrence of the various antecedents, and bring to bear the principle that any antecedent in the absence of which the effect has appeared or on the presence of which it has not appeared may be set aside as fortuitous, as being not an indispensable antecedent. this is really the guiding principle of the method as a method of observation. let the inquiry, for example, be into the cause of endemic goitre. instances of the disease have been collected from the medical observations of all countries over many years. why is it endemic in some localities and not in others? we proceed on the assumption that the cause, whatever it is, must be some circumstance common to all localities where it is endemic. if any such circumstance is obvious at once, we may conclude on the mere principle of repeated coincidence that there is causal connexion between it and the disease, and continue our inquiry into the nature of the connexion. but if no such circumstance is obvious, then in the course of our search for it we eliminate, as fortuitous, conditions that are present in some cases but absent in others. one of the earliest theories was that endemic goitre was connected with the altitude and configuration of the ground, some notorious centres of it being deeply cleft mountain valleys, with little air and wind and damp marshy soil. but wider observation found it in many valleys neither narrower nor deeper than others that were exempt, and also in wide exposed valleys such as the aar. was it due to the geological formation? this also had to be abandoned, for the disease is often incident within very narrow limits, occurring in some villages and sparing others though the geological formation is absolutely the same. was it due to the character of the drinking-water? especially to the presence of lime or magnesia? this theory was held strongly, and certain springs characterised as goitre-springs. but the springs in some goitre centres show not a trace of magnesia. the comparative immunity of coast regions suggested that it might be owing to a deficiency of iodine in the drinking-water and the air, and many instances were adduced in favour of this. but further inquiries made out the presence of iodine in considerable quantities, in the air, the water, and the vegetation of districts where goitre was widely prevalent; while in cuba it is said that not a trace of iodine is discoverable either in the air or the water, and yet it is quite free from goitre. after a huge multiplication of instances, resulting in the elimination of every local condition that had been suggested as a possible cause, hirsch came to the conclusion that the true cause must be a morbid poison, and that endemic goitre has to be reckoned among the infectious diseases.[ ] on this negative principle, that if a circumstance comes and goes without bringing the phenomenon in its train, the phenomenon is causally independent of it, common-sense is always at work disconnecting events that are occasionally coincident in time. a bird sings at our window, for example, and the clock ticks on the mantelpiece. but the clock does not begin to tick when the bird begins to sing, nor cease to tick when the bird flies away. accordingly, if the clock should stop at any time, and we wished to inquire into the cause, and anybody were to suggest that the stoppage of the clock was caused by the stoppage of a bird's song outside, we should dismiss the suggestion at once. we should eliminate this circumstance from our inquiry, on the ground that from other observations we knew it to be a casual or fortuitous concomitant. hotspur's retort to glendover (p. ) was based on this principle. when poetic sentiment or superstition rejects a verdict of common-sense or science, it is because it imagines a causal connexion to exist that is not open to observation, as in the case of the grandfather's clock which stopped short never to go again when the old man died. ii.--the principle of single agreement. the procedure in mill's "method of agreement" consists in thus eliminating fortuitous antecedents or concomitants till only one remains. we see the nature of the proof relied upon when we ask, how far must elimination be carried in order to attain proof of causal connexion? the answer is that we must go on till we have eliminated all but one. we must multiply instances of the phenomenon, till we have settled of each of the antecedents except one that it is not the cause. we must have taken account of all the antecedents, and we must have found in our observations that all but one have been only occasionally present. _when all the antecedents of an effect except one can be absent without the disappearance of the effect, that one is causally connected with the effect, due precautions being taken that no other circumstances have been present besides those taken account of._ mill's canon of the method of agreement is substantially identical with this:-- when two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon. herschel's statement, on which this canon is founded, runs as follows: "any circumstance in which all the facts without exception agree, may be the cause in question, or if not, at least a collateral effect of the same cause: if there be but one such point of agreement, the possibility becomes a certainty". all the instances examined must agree in one circumstance--hence the title method of agreement. but it is not in the agreement merely that the proof consists, but the agreement in one circumstance combined with difference in all the other circumstances, when we are certain that every circumstance has come within our observation. it is the singleness of the agreement that constitutes the proof just as it is the singleness of the difference in the method of difference.[ ] it has been said that mill's method of agreement amounts after all only to an uncontradicted _inductio per enumerationem simplicem_, which he himself stigmatised as induction improperly so called. but this is not strictly correct. it is a misunderstanding probably caused by calling the method that of agreement simply, instead of calling it the method of single agreement, so as to lay stress upon the process of elimination by which the singleness is established. it is true that in the course of our observations we do perform an induction by simple enumeration. in eliminating, we at the same time generalise. that is to say, in multiplying instances for the elimination of non-causes, we necessarily at the same time multiply instances where the true causal antecedent, if there is only one possible, is present. an antecedent containing the true cause must always be there when the phenomenon appears, and thus we may establish by our eliminating observations a uniformity of connexion between two facts. take, for example, roger bacon's inquiry into the cause of the colours of the rainbow. his first notion seems to have been to connect the phenomenon with the substance crystal, probably from his thinking of the crystal firmament then supposed to encircle the universe. he found the rainbow colours produced by the passage of light through hexagonal crystals. but on extending his observations, he found that the passage of light through other transparent mediums was also attended by the phenomenon. he found it in dewdrops, in the spray of waterfalls, in drops shaken from the oar in rowing. he thus eliminated the substance crystal, and at the same time established the empirical law that the passage of light through transparent mediums of a globular or prismatic shape was a causal antecedent of the rainbow colours.[ ] ascertainment of invariable antecedents may thus proceed side by side with that of variable antecedents, the use of the elimination being simply to narrow the scope of the inquiry. but the proof set forth in mill's canon does not depend merely on one antecedent or concomitant being invariably present, but also on the assumption that all the influential circumstances have been within our observation. then only can we be sure that the instances have _only one_ circumstance in common. the truth is that owing to the difficulty of fulfilling this condition, proof of causation in accordance with mill's canon is practically all but impossible. it is not attained in any of the examples commonly given. the want of conclusiveness is disguised by the fact that both elimination and positive observation of mere agreement or uniform concomitance are useful and suggestive in the search for causes, though they do not amount to complete proof such as the canon describes. thus in the inquiry into the cause of goitre, the elimination serves some purpose though the result is purely negative. when the inquirer is satisfied that goitre is not originated by any directly observable local conditions, altitude, temperature, climate, soil, water, social circumstances, habits of exertion, his search is profitably limited. and mere frequency, much more constancy of concomitance, raises a presumption of causal connexion, and looking out for it is valuable as a mode of reconnoitring. the first thing that an inquirer naturally asks when confronted by numerous instances of a phenomenon is, what have they in common? and if he finds that they have some one circumstance invariably or even frequently present, although he cannot prove that they have no other circumstance in common as the cannon of single agreement requires, the presumption of causal connexion is strong enough to furnish good ground for further inquiry. if an inquirer finds an illness with marked symptoms in a number of different households, and finds also that all the households get their milk supply from the same source, this is not conclusive proof of causation, but it is a sufficient presumption to warrant him in examining whether there is any virulent ingredient in the milk. thus varying the circumstances so as to bring out a common antecedent, though it does not end in exact proof, may indicate causal connexion though it does not prove what the nature of the connexion is. roger bacon's observations indicated that the production of rainbow colours was connected with the passage of light through a transparent globe or prism. it was reserved for newton to prove by other methods that white light was composed of rays, and that those rays were differently refracted in passing through the transparent medium. we have another example of how far mere agreement, revealed by varying the circumstances, carries us towards discovery of the cause, in wells's investigation of the cause of dew. comparing the numerous instances of dew appearing without visible fall of moisture, wells found that they all agreed in the comparative coldness of the surface dewed. this was all the agreement that he established by observation; he did not carry observation to the point of determining that there was absolutely no other common circumstance: when he had simply discovered dewed surfaces, he tried next to show by reasoning from other knows facts how the coldness of the surface affected the aqueous vapour of the neighbouring air. he did not establish his theory of dew by the method of agreement: but the observation of an agreement or common feature in a number of instances was a stage in the process by which he reached his theory. iii.--mill's "joint method of agreement and difference". after examining a variety of instances in which an effect appears, and finding that they all agree in the antecedent presence of some one circumstance, we may proceed to examine instances otherwise similar (_in pari materia_, as prof. fowler puts it) where the effect does not appear. if these all agree in the absence of the circumstance that is uniformly present with the effect, we have corroborative evidence that there is causal connexion between this circumstance and the effect. the principle of this method seems to have been suggested to mill by wells's investigations into dew. wells exposed a number of polished surfaces of various substances, and compared those in which there was a copious deposit of dew with those in which there was little or none. if he could have got two surfaces, one dewed and the other not, identical in every concomitant but one, he would have attained complete proof on the principle of single difference. but this being impracticable, he followed a course which approximated to the method of eliminating every circumstance but one from instances of dew, and every circumstance but one in the instances of no-dew. mill sums up as follows the results of his experiments: "it appears that the instances in which much dew is deposited, which are very various, agree in this, and, _so far as we are able to observe, in this only_, that they either radiate heat rapidly or conduct it slowly: qualities between which there is no other circumstance of agreement than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. the instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (_as far as we can observe_) _in nothing except_ in _not_ having this same property. we seem therefore to have detected the characteristic difference between the substances on which the dew is produced, and those on which it is not produced. and thus have been realised the requisitions of what we have termed the indirect method of difference, or the joint method of agreement and difference." the canon of this method is accordingly stated by mill as follows:-- if two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. in practice, however, this theoretical standard of proof is never attained. what investigators really proceed upon is the presumption afforded, to use prof. bain's terms, by agreement in presence combined with agreement in absence. when it is found that all substances which have a strong smell agree in being readily oxidisable, and that the marsh gas or carbonetted hydrogen which has no smell is not oxidisable at common temperatures, the presumption that oxidation is one of the causal circumstances in smell is strengthened, even though we have not succeeded in eliminating every circumstance but this one from either the positive or the negative instances. so in the following examples given by prof. fowler there is not really a compliance with the theoretical requirements of mill's method: there is only an increased presumption from the double agreement. "the joint method of agreement and difference (or the indirect method of difference, or, as i should prefer to call it, the double method of agreement) is being continually employed by us in the ordinary affairs of life. if when i take a particular kind of food, i find that i invariably suffer from some particular form of illness, whereas, when i leave it off, i cease to suffer, i entertain a double assurance that the food is the cause of my illness. i have observed that a certain plant is invariably plentiful on a particular soil; if, with a wide experience, i fail to find it growing on any other soil, i feel confirmed in my belief that there is in this particular soil some chemical constituent, or some peculiar combination of chemical constituents, which is highly favourable, if not essential, to the growth of the plant." [footnote : elimination, or setting aside as being of no concern, must not be confounded with the exclusion of agents practised in applying the method of difference. we use the word in its ordinary sense of putting outside the sphere of an argument. by a curious slip, professor bain follows mill in applying the word sometimes to the process of singling out or disentangling a causal circumstance. this is an inadvertent departure from the ordinary usage, according to which elimination means discarding from consideration as being non-essential.] [footnote : hirsch's _geographical and historical pathology_, creighton's translation, vol. ii. pp. - .] [footnote : the bare titles difference and agreement, though they have the advantage of simplicity, are apt to puzzle beginners inasmuch as in the method of difference the agreement among the instances is at a maximum, and the difference at a minimum, and _vice versâ_ in the method of agreement. in both methods it is really the isolation of the connexion between antecedent and sequent that constitutes the proof.] [footnote : that rainbows in the sky are produced by the passage of light through minute drops in the clouds was an inference from this observed uniformity.] chapter vi. methods of observation.--minor methods. i.--concomitant variations. _whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation._ this simple principle is constantly applied by us in connecting and disconnecting phenomena. if we hear a sound which waxes and wanes with the rise and fall of the wind, we at once connect the two phenomena. we may not know what the causal connexion is, but if they uniformly vary together, there is at once a presumption that the one is causally dependent on the other, or that both are effects of the same cause. this principle was employed by wells in his researches into dew. some bodies are worse conductors of heat than others, and rough surfaces radiate heat more rapidly than smooth. wells made observations on conductors and radiators of various degrees, and found that the amount of dew deposited was greater or less according as the objects conducted heat slowly or radiated heat rapidly. he thus established what herschel called a "scale of intensity" between the conducting and radiating properties of the bodies bedewed, and the amount of the dew deposit. the explanation was that in bad conductors the surface cools more quickly than in good conductors because heat is more slowly supplied from within. similarly in rough surfaces there is a more rapid cooling because heat is given off more quickly. but whatever the explanation might be, the mere concomitant variation of the dew deposit with these properties showed that there was some causal connexion between them. it must be remembered that the mere fact of concomitant variation is only an index that some causal connexion exists. the nature of the connexion must be ascertained by other means, and may remain a problem, one of the uses of such observed facts being indeed to suggest problems, for inquiry. thus a remarkable concomitance has been observed between spots on the sun, displays of aurora borealis, and magnetic storms. the probability is that they are causally connected, but science has not yet discovered how. similarly in the various sciences properties are arranged in scales of intensity, and any correspondence between two scales becomes a subject for investigation on the assumption that it points to a causal connexion. we shall see afterwards how in social investigations concomitant variations in averages furnish material for reasoning. when two variants can be precisely measured, the ratio of the variation may be ascertained by the method of single difference. we may change an antecedent in degree, and watch the corresponding change in the effect, taking care that no other agent influences the effect in the meantime. often when we cannot remove an agent altogether, we may remove it in a measurable amount, and observe the result. we cannot remove friction altogether, but the more it is diminished, the further will a body travel under the impulse of the same force. until a concomitant variation has been fully explained, it is merely an empirical law, and any inference that it extends at the same rate beyond the limits of observation must be made with due caution. "parallel variation," says professor bain, "is sometimes interrupted by critical points, as in the expansion of bodies by heat, which suffers a reverse near the point of cooling. again, the energy of a solution does not always follow the strength; very dilute solutions occasionally exercise a specific power not possessed in any degree by stronger. so, in the animal body, food and stimulants operate proportionally up to a certain point, at which their further operation is checked by the peculiarities in the structure of the living organs.... we cannot always reason from a few steps in a series to the whole series, partly because of the occurrence of critical points, and partly from the development at the extremes of new and unsuspected powers. sir john herschel remarks that until very recently 'the formulæ empirically deduced for the elasticity of steam, those for the resistance of fluids, and on other similar subjects, have almost invariably failed to support the theoretical structures that have been erected upon them'."[ ] ii.--single residue. _subduct from any phenomenon such part as previous induction has shown to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents._ "complicated phenomena, in which several causes concurring, opposing, or quite independent of each other, operate at once, so as to produce a compound effect, may be simplified by subducting the effect of all the known causes, as well as the nature of the case permits, either by deductive reasoning or by appeal to experience, and thus leaving as it were a _residual phenomenon_ to be explained. it is by this process, in fact, that science, in its present advanced state, is chiefly promoted. most of the phenomena which nature presents are very complicated; and when the effects of all known causes are estimated with exactness, and subducted, the residual facts are constantly appearing in the form of phenomena altogether new, and leading to the most important conclusions."[ ] it is obvious that this is not a primary method of observation, but a method that may be employed with great effect to guide observation when a considerable advance has been made in accurate knowledge of agents and their mode of operation. the greatest triumph of the method, the discovery of the planet neptune, was won some years after the above passage from herschel's discourse was written. certain perturbations were observed in the movements of the planet uranus: that is to say, its orbit was found not to correspond exactly with what it should be when calculated according to the known influences of the bodies then known to astronomers. these perturbations were a residual phenomenon. it was supposed that they might be due to the action of an unknown planet, and two astronomers, adams and le verrier, simultaneously calculated the position of a body such as would account for the observed deviations. when telescopes were directed to the spot thus indicated, the planet neptune was discovered. this was in september, : before its actual discovery, sir john herschel exulted in the prospect of it in language that strikingly expresses the power of the method. "we see it," he said, "as columbus saw america from the shores of spain. its movements have been felt, trembling along the far-reaching line of our analysis, with a certainty hardly inferior to that of ocular demonstration."[ ] many of the new elements in chemistry have been discovered in this way. for example, when distinctive spectrums had been observed for all known substances, then on the assumption that every substance has a distinctive spectrum, the appearance of lines not referable to any known substance indicated the existence of hitherto undiscovered substances and directed search for them. thus bunsen in discovered two new alkaline metals, cæsium and rubidium. he was examining alkalies left from the evaporation of a large quantity of mineral water from durkheim. on applying the spectroscope to the flame which this particular salt or mixture of salts gave off, he found that some bright lines were visible which he had never observed before, and which he knew were not produced either by potash or soda. he then set to work to analyse the mixture, and ultimately succeeded in separating two new alkaline substances. when he had succeeded in getting them separate, it was of course by the method of difference that he ascertained them to be capable of producing the lines that had excited his curiosity. [footnote : bain's _logic_, vol. ii. p. .] [footnote : herschel's _discourse_, § .] [footnote : de morgan's _budget of paradoxes_, p. .] chapter vii. the method of explanation. given perplexity as to the cause of any phenomenon, what is our natural first step? we may describe it as searching for a clue: we look carefully at the circumstances with a view to finding some means of assimilating what perplexes us to what is already within our knowledge. our next step is to make a guess, or conjecture, or, in scientific language, a hypothesis. we exercise our reason or _nous_, or imagination, or whatever we choose to call the faculty, and try to conceive some cause that strikes us as sufficient to account for the phenomenon. if it is not at once manifest that this cause has really operated, our third step is to consider what appearances ought to present themselves if it did operate. we then return to the facts in question, and observe whether those appearances do present themselves. if they do, and if there is no other way of accounting for the effect in all its circumstances, we conclude that our guess is correct, that our hypothesis is proved, that we have reached a satisfactory explanation. these four steps or stages may be distinguished in most protracted inquiries into cause. they correspond to the four stages of what mr. jevons calls the inductive method _par excellence_, preliminary observation, hypothesis, deduction and verification. seeing that the word induction is already an overloaded drudge, perhaps it would be better to call these four stages the method of explanation. the word induction, if we keep near its original and most established meaning, would apply strictly only to the fourth stage, the verification, the bringing in of the facts to confirm our hypothesis. we might call the method the newtonian method, for all four stages are marked in the prolonged process by which he made good his theory of gravitation. to give the name of inductive method simply to all the four stages of an orderly procedure from doubt to a sufficient explanation is to encourage a widespread misapprehension. there could be no greater error than to suppose that only the senses are used in scientific investigation. there is no error that men of science are so apt to resent in the mouths of the non-scientific. yet they have partly brought it on themselves by their loose use of the word induction, which they follow bacon in wresting from the traditional meaning of induction, using it to cover both induction or the bringing in of facts--an affair mainly of observation--and reasoning, the exercise of nous, the process of constructing satisfactory hypotheses. in reaction against the popular misconception which bacon encouraged, it is fashionable now to speak of the use of imagination in science. this is well enough polemically. imagination as commonly understood is akin to the constructive faculty in science, and it is legitimate warfare to employ the familiar word of high repute to force general recognition of the truth. but in common usage imagination is appropriated to creative genius in the fine arts, and to speak of imagination in science is to suggest that science deals in fictions, and has discarded newton's declaration _hypotheses non fingo_. in a fight for popular respect, men of science may be right to claim for themselves imagination; but in the interests of clear understanding, the logician must deplore that they should defend themselves from a charge due to their abuse of one word by making an equally unwarrantable and confusing extension of another. call it what we will, the faculty of likely guessing, of making probable hypotheses, of conceiving in all its circumstances the past situation or the latent and supramicroscopical situation out of which a phenomenon has emerged, is one of the most important of the scientific man's special gifts. it is by virtue of it that the greatest advancements of knowledge have been achieved, the cardinal discoveries in molar and molecular physics, biology, geology, and all departments of science. we must not push the idea of stages in explanatory method too far: the right explanation may be reached in a flash. the idea of stages is really useful mainly in trying to make clear the various difficulties in investigation, and the fact that different men of genius may show different powers in overcoming them. the right hypothesis may occur in a moment, as if by simple intuition, but it may be tedious to prove, and the gifts that tell in proof, such as newton's immense mathematical power in calculating what a hypothesis implies, darwin's patience in verifying, faraday's ingenuity in devising experiments, are all great gifts, and may be serviceable at different stages. but without originality and fertility in probable hypothesis, nothing can be done. the dispute between mill and whewell as to the place and value of hypotheses in science was in the main a dispute about words. mill did not really undervalue hypothesis, and he gave a most luminous and accurate account of the conditions of proof. but here and there he incautiously spoke of the "hypothetical method" (by which he meant what we have called the method of explanation) as if it were a defective kind of proof, a method resorted to by science when the "experimental methods" could not be applied. whether his language fairly bore this construction is not worth arguing, but this was manifestly the construction that whewell had in his mind when he retorted, as if in defence of hypotheses, that "the inductive process consists in framing successive hypotheses, the comparison of these with the ascertained facts of nature, and the introduction into them of such modifications as the comparison may render necessary". this is a very fair description of the whole method of explanation. there is nothing really inconsistent with it in mill's account of his "hypothetical method"; only he erred himself or was the cause of error in others in suggesting, intentionally or unintentionally, that the experimental methods were different methods of proof. the "hypothetical method," as he described it, consisting of induction, ratiocination, and verification, really comprehends the principles of all modes of observation, whether naturally or artificially experimental. we see this at once when we ask how the previous knowledge is got in accordance with which hypotheses are framed. the answer must be, by observation. however profound the calculations, it must be from observed laws, or supposed analogues of them, that we start. and it is always by observation that the results of these calculations are verified. both mill and whewell, however, confined themselves too exclusively to the great hypotheses of the sciences, such as gravitation and the undulatory theory of light. in the consideration of scientific method, it is a mistake to confine our attention to these great questions, which from the multitude of facts embraced can only be verified by prolonged and intricate inquiry. attempts at the explanation of the smallest phenomena proceed on the same plan, and the verification of conjectures about them is subject to the same conditions, and the methods of investigation and the conditions of verification can be studied most simply in the smaller cases. further, i venture to think it a mistake to confine ourselves to scientific inquiry in the narrow sense, meaning thereby inquiry conducted within the pale of the exact sciences. for not merely the exact sciences but all men in the ordinary affairs of life must follow the same methods or at least observe the same principles and conditions, in any satisfactory attempt to explain. tares appear among the wheat. good seed was sown: whence, then, come the tares? "an enemy has done this." if an enemy has actually been observed sowing the tares, his agency can be proved by descriptive testimony. but if he has not been seen in the act, we must resort to what is known in courts of law as circumstantial evidence. this is the "hypothetical method" of science. that the tares are the work of an enemy is a hypothesis: we examine all the circumstances of the case in order to prove, by inference from our knowledge of similar cases, that thus, and thus only, can those circumstances be accounted for. similarly, when a question is raised as to the authorship of an anonymous book. we first search for a clue by carefully noting the diction, the structure of the sentences, the character and sources of the illustration, the special tracks of thought. we proceed upon the knowledge that every author has characteristic turns of phrase and imagery and favourite veins of thought, and we look out for such internal evidence of authorship in the work before us. special knowledge and acumen may enable us to detect the authorship at once from the general resemblance to known work. but if we would have clear proof, we must show that the resemblance extends to all the details of phrase, structure and imagery: we must show that our hypothesis of the authorship of xyz explains all the circumstances. and even this is not sufficient, as many erroneous guesses from internal evidence may convince us. we must establish further that there is no other reasonable way of accounting for the matter and manner of the book; for example, that it is not the work of an imitator. an imitator may reproduce all the superficial peculiarities of an author with such fidelity that the imitation can hardly be distinguished from the original: thus few can distinguish between fenton's work and pope's in the translation of the odyssey. we must take such known facts into account in deciding a hypothesis of authorship. such hypotheses can seldom be decided on internal evidence alone: other circumstantial evidence--other circumstances that ought to be discoverable if the hypothesis is correct--must be searched for. the operation of causes that are manifest only in their effects must be proved by the same method as the operation of past causes that have left only their effects behind them. whether light is caused by a projection of particles from a luminous body or by an agitation communicated through an intervening medium cannot be directly observed. the only proof open is to calculate what should occur on either hypothesis, and observe whether this does occur. in such a case there is room for the utmost calculating power and experimental ingenuity. the mere making of the general hypothesis or guess is simple enough, both modes of transmitting influence, the projection of moving matter and the travelling of an undulation or wave movement, being familiar facts. but it is not so easy to calculate exactly how a given impulse would travel, and what phenomena of ray and shadow, of reflection, refraction and diffraction ought to be visible in its progress. still, no matter how intricate the calculation, its correspondence with what can be observed is the only legitimate proof of the hypothesis. ii.--obstacles to explanation.--plurality of causes and intermixture of effects. there are two main ways in which explanation may be baffled. there may exist more than one cause singly capable of producing the effect in question, and we may have no means of determining which of the equally sufficient causes has actually been at work. for all that appears the tares in our wheat may be the effect of accident or of malicious design: an anonymous book may be the work of an original author or of an imitator. again, an effect may be the joint result of several co-operating causes, and it may be impossible to determine their several potencies. the bitter article in the _quarterly_ may have helped to kill john keats, but it co-operated with an enfeebled constitution and a naturally over-sensitive temperament, and we cannot assign its exact weight to each of these coefficients. death may be the result of a combination of causes; organic disease co-operating with exposure, over-fatigue co-operating with the enfeeblement of the system by disease. the technical names for these difficulties, plurality of causes and intermixture of effects, are apt to confuse without some clearing up. in both kinds of difficulty more causes than one are involved: but in the one kind of case there is a plurality of possible or equally probable causes, and we are at a loss to decide which: in the other kind of case there is a plurality of co-operating causes; the effect is the result or product of several causes working conjointly, and we are unable to assign to each its due share. it is with a view to overcoming these difficulties that science endeavours to isolate agencies and ascertain what each is capable of singly. mill and bain treat plurality of causes and intermixture of effects in connexion with the experimental methods. it is better, perhaps, to regard them simply as obstacles to explanation, and the experimental methods as methods of overcoming those obstacles. the whole purpose of the experimental methods is to isolate agencies and effects: unless they can be isolated, the methods are inapplicable. in situations where the effects observable may be referred with equal probability to more than one cause, you cannot eliminate so as to obtain a single agreement. the method of agreement is frustrated. and an investigator can get no light from mixed effects, unless he knows enough of the causes at work to be able to apply the method of residues. if he does not, he must simply look out for or devise instances where the agencies are at work separately, and apply the principle of single difference. great, however, as the difficulties are, the theory of plurality and intermixture baldly stated makes them appear greater than they are in practice. there is a consideration that mitigates the complication, and renders the task of unravelling it not altogether hopeless. this is that different causes have distinctive ways of operating, and leave behind them marks of their presence by which their agency in a given case may be recognised. an explosion, for example, occurs. there are several explosive agencies, capable of causing as much destruction as meets the eye at the first glance. the agent in the case before us may be gunpowder or it may be dynamite. but the two agents are not so alike in their mode of operation as to produce results identical in every circumstance. the expert inquirer knows by previous observation that when gunpowder acts the objects in the neighbourhood are blackened; and that an explosion of dynamite tears and shatters in a way peculiar to itself. he is thus able to interpret the traces, to make and prove a hypothesis. a man's body is found dead in water. it may be a question whether death came by drowning or by previous violence. he may have been suffocated and afterwards thrown into the water. but the circumstances will tell the true story. death by drowning has distinctive symptoms. if drowning was the cause, water will be found in the stomach and froth in the trachea. thus, though there may be a plurality of possible causes, the causation in the given case may be brought home to one by distinctive accompaniments, and it is the business of the scientific inquirer to study these. what is known as the "ripple-mark" in sandstone surfaces may be produced in various ways. the most familiar way is by the action of the tides on the sand of the sea-shore, and the interpreter who knows this way only would ascribe the marks at once to this agency. but ripple-marks are produced also by the winds on drifting sands, by currents of water where no tidal influence is felt, and in fact by any body of water in a state of oscillation. is it, then, impossible to decide between these alternative possibilities of causation? no: wind-ripples and current-ripples and tidal-ripples have each their own special character and accompanying conditions, and the hypothesis of one rather than another may be made good by means of these. "in rock-formations," mr. page says,[ ] "there are many things which at first sight seem similar, and yet on more minute examination, differences are detected and conditions discovered which render it impossible that these appearances can have arisen from the same causation." the truth is that generally when we speak of plurality of causes, of alternative possibilities of causation, we are not thinking of the effect in its individual entirety, but only of some general or abstract aspect of it. when we say, _e.g._, that death may be produced by a great many different causes, poison, gunshot wounds, disease of this or that organ, we are thinking of death in the abstract, not of the particular case under consideration, which as an individual case, has characters so distinctive that only one combination of causes is possible. the effort of science is to become less and less abstract in this sense, by observing agencies or combinations of agencies apart and studying the special characters of their effects. that knowledge is then applied, on the assumption that where those characters are present, the agent or combination of agencies has been at work. given an effect to be explained, it is brought home to one out of several possible alternatives by _circumstantial evidence_. bacon's phrase, _instantia crucis_,[ ] or finger-post instance, might be conveniently appropriated as a technical name for a circumstance that is decisive between rival hypotheses. this was, in effect, proposed by sir john herschel,[ ] who drew attention to the importance of these crucial instances, and gave the following example: "a curious example is given by m. fresnel, as decisive, in his mind, of the question between the two great opinions on the nature of light, which, since the time of newton and huyghens, have divided philosophers. when two very clean glasses are laid one on the other, if they be not perfectly flat, but one or both in an almost imperceptible degree convex or prominent, beautiful and vivid colours will be seen between them; and if these be viewed through a red glass, their appearance will be that of alternate dark and bright stripes.... now, the coloured stripes thus produced are explicable on both theories, and are appealed to by both as strong confirmatory facts; but there is a difference in one circumstance according as one or the other theory is employed to explain them. in the case of the huyghenian doctrine, the intervals between the bright stripes ought to appear _absolutely black_; in the other, _half bright_, when viewed [in a particular manner] through a prism. this curious case of difference was tried as soon as the opposing consequences of the two theories were noted by m. fresnel, and the result is stated by him to be decisive in favour of that theory which makes light to consist in the vibrations of an elastic medium." iii.--the proof of a hypothesis. the completest proof of a hypothesis is when that which has been hypothetically assumed to exist as a means of accounting for certain phenomena is afterwards actually observed to exist or is proved by descriptive testimony to have existed. our argument, for example, from internal evidence that mill in writing his logic aimed at furnishing a method for social investigations is confirmed by a letter to miss caroline fox, in which he distinctly avowed that object. the most striking example of this crowning verification in science is the discovery of the planet neptune, in which case an agent hypothetically assumed was actually brought under the telescope as calculated. examples almost equally striking have occurred in the history of the evolution doctrine. hypothetical ancestors with certain peculiarities of structure have been assumed as links between living species, and in some cases their fossils have actually been found in the geological register. such triumphs of verification are necessarily rare. for the most part the hypothetical method is applied to cases where proof by actual observation is impossible, such as prehistoric conditions of the earth or of life upon the earth, or conditions in the ultimate constitution of matter that are beyond the reach of the strongest microscope. indeed, some would confine the word hypothesis to cases of this kind. this, in fact, was done by mill: hypothesis, as he defined it, was a conjecture not completely proved, but with a large amount of evidence in its favour. but seeing that the procedure of investigation is the same, namely, conjecture, calculation and comparison of facts with the calculated results, whether the agency assumed can be brought to the test of direct observation or not, it seems better not to restrict the word hypothesis to incompletely proved conjectures, but to apply it simply to a conjecture made at a certain stage in whatever way it may afterwards be verified. in the absence of direct verification, the proof of a hypothesis is exclusive sufficiency to explain the circumstances. the hypothesis must account for all the circumstances, and there must be no other way of accounting for them. another requirement was mentioned by newton in a phrase about the exact meaning of which there has been some contention. the first of his regulæ philosophandi laid down that the cause assumed must be a _vera causa_. "we are not," the rule runs, "to admit other causes of natural things than such as both are true, and suffice for explaining their phenomena."[ ] it has been argued that the requirement of "verity" is superfluous; that it is really included in the requirement of sufficiency; that if a cause is sufficient to explain the phenomena it must _ipso facto_ be the true cause. this may be technically arguable, given a sufficient latitude to the word sufficiency: nevertheless, it is convenient to distinguish between mere sufficiency to explain the phenomena in question, and the proof otherwise that the cause assigned really exists _in rerum natura_, or that it operated in the given case. the frequency with which the expression _vera causa_ has been used since newton's time shows that a need is felt for it, though it may be hard to define "verity" precisely as something apart from "sufficiency". if we examine the common usage of the expression we shall probably find that what is meant by insisting on a _vera causa_ is that we must have some evidence for the cause assigned outside the phenomena in question. in seeking for verification of a hypothesis we must extend our range beyond the limited facts that have engaged our curiosity and that demand explanation. there can be little doubt that newton himself aimed his rule at the cartesian hypothesis of vortices. this was an attempt to explain the solar system on the hypothesis that cosmic space is filled with a fluid in which the planets are carried round as chips of wood in a whirlpool, or leaves or dust in a whirlwind. now this is so far a _vera causa_ that the action of fluid vortices is a familiar one: we have only to stir a cup of tea with a bit of stalk in it to get an instance. the agency supposed is sufficient also to account for the revolution of a planet round the sun, given sufficient strength in the fluid to buoy up the planet. but if there were such a fluid in space there would be other phenomena: and in the absence of these other phenomena the hypothesis must be dismissed as imaginary. the fact that comets pass into and out of spaces where the vortices must be assumed to be in action without exhibiting any perturbation is an _instantia crucis_ against the hypothesis. if by the requirement of a _vera causa_ were meant that the cause assigned must be one directly open to observation, this would undoubtedly be too narrow a limit. it would exclude such causes as the ether which is assumed to fill interstellar space as a medium for the propagation of light. the only evidence for such a medium and its various properties is sufficiency to explain the phenomena. like suppositions as to the ultimate constitution of bodies, it is of the nature of what professor bain calls a "representative fiction": the only condition is that it must explain all the phenomena, and that there must be no other way of explaining all. when it is proved that light travels with a finite velocity, we are confined to two alternative ways of conceiving its transmission, a projection of matter from the luminous body and the transference of vibrations through an intervening medium. either hypothesis would explain many of the facts: our choice must rest with that which best explains all. but supposing that all the phenomena of light were explained by attributing certain properties to this intervening medium, it would probably be held that the hypothesis of an ether had not been fully verified till other phenomena than those of light had been shown to be incapable of explanation on any other hypothesis. if the properties ascribed to it to explain the phenomena of light sufficed at the same time to explain otherwise inexplicable phenomena connected with heat, electricity, or gravity, the evidence of its reality would be greatly strengthened. not only must the circumstances in hand be explained, but other circumstances must be found to be such as we should expect if the cause assigned really operated. take, for example, the case of erratic blocks or boulders, huge fragments of rock found at a distance from their parent strata. the lowlands of england, scotland, and ireland, and the great central plain of northern europe contain many such fragments. their composition shows indubitably that they once formed part of hills to the northward of their present site. they must somehow have been detached and transported to where we now find them. how? one old explanation is that they were carried by witches, or that they were themselves witches accidentally dropped and turned into stone. any such explanation by supernatural means can neither be proved nor disproved. some logicians would exclude such hypotheses altogether on the ground that they cannot be rendered either more or less probable by subsequent examination.[ ] the proper scientific limit, however, is not to the making of hypotheses, but to the proof of them. the more hypotheses the merrier: only if such an agency as witchcraft is suggested, we should expect to find other evidence of its existence in other phenomena that could not otherwise be explained. again, it has been suggested that the erratic boulders may have been transported by water. water is so far a _vera causa_ that currents are known to be capable of washing huge blocks to a great distance. but blocks transported in this way have the edges worn off by the friction of their passage: and, besides, currents strong enough to dislodge and force along for miles blocks as big as cottages must have left other marks of their presence. the explanation now received is that glaciers and icebergs were the means of transport. but this explanation was not accepted till multitudes of circumstances were examined all tending to show that glaciers had once been present in the regions where the erratic blocks are found. the minute habits of glaciers have been studied where they still exist: how they slowly move down carrying fragments of rock; how icebergs break off when they reach water, float off with their load, and drop it when they melt; how they grind and smooth the surfaces of rocks over which they pass or that are frozen into them: how they undercut and mark the faces of precipices past which they move; how moraines are formed at the melting ends of them, and so forth. when a district exhibits all the circumstances that are now observed to attend the action of glaciers the proof of the hypothesis that glaciers were once there is complete. [footnote : page's _philosophy of geology_, p. .] [footnote : crux in this phrase means a cross erected at the parting of ways, with arms to tell whither each way leads.] [footnote : _discourse_, § .] [footnote : causas rerum naturalium non plures admitti debere quam quæ et veriæ sint et carum phenomenis explicandis sufficiant.] [footnote : see prof. fowler on the conditions of hypotheses, _inductive logic_, pp. - .] chapter viii. supplementary methods of investigation. i.--the maintenance of averages.--supplement to the method of difference. a certain amount of law obtains among events that are usually spoken of as matters of chance or accident in the individual case. every kind of accident recurs with a certain uniformity. if we take a succession of periods, and divide the total number of any kind of event by the number of periods, we get what is called the average for that period: and it is observed that such averages are maintained from period to period. over a series of years there is a fixed proportion between good harvests and bad, between wet days and dry: every year nearly the same number of suicides takes place, the same number of crimes, of accidents to life and limb, even of suicides, crimes, or injuries by particular means: every year in a town nearly the same number of children stray from their parents and are restored by the police: every year nearly the same number of persons post letters without putting an address on them. this maintenance of averages is simple matter of observation, a datum of experience, an empirical law. once an average for any kind of event has been noted, we may count upon its continuance as we count upon the continuance of any other kind of observed uniformity. insurance companies proceed upon such empirical laws of average in length of life and immunity from injurious accidents by sea or land: their prosperity is a practical proof of the correctness and completeness of the observed facts and the soundness of their inference to the continuance of the average. the constancy of averages is thus a guide in practice. but in reasoning upon them in investigations of cause, we make a further assumption than continued uniformity. we assume that the maintenance of the average is due to the permanence of the producing causes. we regard the average as the result of the operation of a limited sum of forces and conditions, incalculable as regards their particular incidence, but always pressing into action, and thus likely to operate a certain number of times within a limited period. assuming the correctness of this explanation, it would follow that _any change in the average is due to some change in the producing conditions_; and this derivative law is applied as a help in the observation and explanation of social facts. statistics are collected and classified: averages are struck: and changes in the average are referred to changes in the concomitant conditions. with the help of this law, we may make a near approach to the precision of the method of difference. a multitude of unknown or unmeasured agents may be at work on a situation, but we may accept the average as the result of their joint operation. if then a new agency is introduced or one of the known agents is changed in degree, and this is at once followed by a change in the average, we may with fair probability refer the change in the result to the change in the antecedents. the difficulty is to find a situation where only one antecedent has been changed before the appearance of the effect. this difficulty may be diminished in practice by eliminating changes that we have reason to know could not have affected the circumstances in question. suppose, for example, our question is whether the education act of had an influence in the decrease of juvenile crime. such a decrease took place _post hoc_; was it _propter hoc_? we may at once eliminate or put out of account the abolition of purchase in the army or the extension of the franchise as not having possibly exercised any influence on juvenile crime. but with all such eliminations, there may still remain other possible influences, such as an improvement in the organisation of the police, or an expansion or contraction in employment. "can you tell me in the face of chronology," a leading statesman once asked, "that the crimes act of did not diminish disorder in ireland?" but chronological sequence alone is not a proof of causation as long as there are other contemporaneous changes of condition that may also have been influential. the great source of fallacy is our proneness to eliminate or isolate in accordance with our prejudices. this has led to the gibe that anything can be proved by statistics. undoubtedly statistics may be made to prove anything if you have a sufficiently low standard of proof and ignore the facts that make against your conclusion. but averages and variations in them are instructive enough if handled with due caution. the remedy for rash conclusions from statistics is not no statistics, but more of them and a sound knowledge of the conditions of reasonable proof. ii.--the presumption from extra-casual coincidence. we have seen that repeated coincidence raises a presumption of causal connexion between the coinciding events. if we find two events going repeatedly together, either abreast or in sequence, we infer that the two are somehow connected in the way of causation, that there is a reason for the coincidence in the manner of their production. it may not be that the one produces the other, or even that their causes are in any way connected: but at least, if they are independent one of the other, both are tied down to happen at the same place and time,--the coincidence of both with time and place is somehow fixed. but though this is true in the main, it is not true without qualification. we expect a certain amount of repeated coincidence without supposing causal connexion. if certain events are repeated very often within our experience, if they have great positive frequency, we may observe them happening together more than once without concluding that the coincidence is more than fortuitous. for example, if we live in a neighbourhood possessed of many black cats, and sally forth to our daily business in the morning, a misfortune in the course of the day might more than once follow upon our meeting a black cat as we went out without raising in our minds any presumption that the one event was the result of the other. certain planets are above the horizon at certain periods of the year and below the horizon at certain other periods. all through the year men and women are born who afterwards achieve distinction in various walks of life, in love, in war, in business, at the bar, in the pulpit. we perceive a certain number of coincidences between the ascendancy of certain planets and the birth of distinguished individuals without suspecting that planetary influence was concerned in their superiority. marriages take place on all days of the year: the sun shines on a good many days at the ordinary time for such ceremonies; some marriages are happy, some unhappy; but though in the case of many happy marriages the sun has shone upon the bride, we regard the coincidence as merely accidental. men often dream of calamities and often suffer calamities in real life: we should expect the coincidence of a dream of calamity followed by a reality to occur more than once as a result of chance. there are thousands of men of different nationalities in business in london, and many fortunes are made: we should expect more than one man of any nationality represented there to make a fortune without arguing any connexion between his nationality and his success. we allow, then, for a certain amount of repeated coincidence without presuming causal connexion: can any rule be laid down for determining the exact amount? prof. bain has formulated the following rule: "consider the positive frequency of the phenomena themselves, how great frequency of coincidence must follow from that, supposing there is neither connexion nor repugnance. if there be greater frequency, there is connexion; if less, repugnance." i do not know that we can go further definite in precept. the number of casual coincidences bears a certain proportion to the positive frequency of the coinciding phenomena: that proportion is to be determined by common-sense in each case. it may be possible, however, to bring out more clearly the principle on which common-sense proceeds in deciding what chance will and will not account for, although our exposition amounts only to making more clear what it is that we mean by chance as distinguished from assignable reason. i would suggest that in deciding what chance will not account for, we make regressive application of a principle which may be called the principle of equal and unequal alternatives, and which may be worded as follows:-- of a given number of possible alternatives, all equally possible, one of which is bound to occur at a given time, we expect each to have its turn an equal number of times in the long run. if several of the alternatives are of the same kind, we expect an alternative of that kind to recur with a frequency proportioned to their greater number. if any of the alternatives has an advantage, it will recur with a frequency proportioned to the strength of that advantage. situations in which alternatives are absolutely equal are rare in nature, but they are artificially created for games "of chance," as in tossing a coin, throwing dice, drawing lots, shuffling and dealing a pack of cards. the essence of all games of chance is to construct a number of equal alternatives, making them as nearly equal as possible, and to make no prearrangement which of the number shall come off. we then say that this is determined by chance. if we ask why we believe that when we go on bringing off one alternative at a time, each will have its turn, part of the answer undoubtedly is that given by de morgan, namely, that we know no reason why one should be chosen rather than another. this, however, is probably not the whole reason for our belief. the rational belief in the matter is that it is only in the long run or on the average that each of the equal alternatives will have its turn, and this is probably founded on the experience of actual trial. the mere equality of the alternatives, supposing them to be perfectly equal, would justify us as much in expecting that each would have its turn in a single revolution of the series, in one complete cycle of the alternatives. this, indeed, may be described as the natural and primitive expectation which is corrected by experience. put six balls in a wicker bottle, shake them up, and roll one out: return this one, and repeat the operation: at the end of six draws we might expect each ball to have had its turn of being drawn if we went merely on the abstract equality of the alternatives. but experience shows us that in six successive draws the same ball may come out twice or even three or four times, although when thousands of drawings are made each comes out nearly an equal number of times. so in tossing a coin, heads may turn up ten or twelve times in succession, though in thousands of tosses heads and tails are nearly equal. runs of luck are thus within the rational doctrine of chances: it is only in the long run that luck is equalised supposing that the events are pure matter of chance, that is, supposing the fundamental alternatives to be equal. if three out of six balls are of the same colour, we expect a ball of that colour to come out three times as often as any other colour on the average of a long succession of tries. this illustrates the second clause of our principle. the third is illustrated by a loaded coin or die. by making regressive application of the principle thus ascertained by experience, we often obtain a clue to special causal connexion. we are at least enabled to isolate a problem for investigation. if we find one of a number of alternatives recurring more frequently than the others, we are entitled to presume that they are not equally possible, that there is some inequality in their conditions. the inequality may simply lie in the greater possible frequency of one of the coinciding events, as when there are three black balls in a bottle of six. we must therefore discount the positive frequency before looking for any other cause. suppose, for example, we find that the ascendancy of jupiter coincides more frequently with the birth of men afterwards distinguished in business than with the birth of men otherwise distinguished, say in war, or at the bar, or in scholarship. we are not at liberty to conclude planetary influence till we have compared the positive frequency of the different modes of distinction. the explanation of the more frequently repeated coincidence may simply be that more men altogether are successful in business than in war or law or scholarship. if so, we say that chance accounts for the coincidence, that is to say, that the coincidence is casual as far as planetary influence is concerned. so in epidemics of fever, if we find on taking a long average that more cases occur in some streets of a town than in others, we are not warranted in concluding that the cause lies in the sanitary conditions of those streets or in any special liability to infection without first taking into account the number of families in the different streets. if one street showed on the average ten times as many cases as another, the coincidence might still be judged casual if there were ten times as many families in it. apart from the fallacy of overlooking the positive frequency, certain other fallacies or liabilities to error in applying this doctrine of chances may be specified. . we are apt, under the influence of prepossession or prejudice, to remember certain coincidences better than others, and so to imagine extra-casual coincidence where none exists. this bias works in confirming all kinds of established beliefs, superstitious and other, beliefs in dreams, omens, retributions, telepathic communications, and so forth. many people believe that nobody who thwarts them ever comes to good, and can produce numerous instances from experience in support of this belief. . we are apt, after proving that there is a residuum beyond what chance will account for on due allowance made for positive frequency, to take for granted that we have proved some particular cause for this residuum. now we have not really explained the residuum by the application of the principle of chances: we have only isolated a problem for explanation. there may be more than chance will account for: yet the cause may not be the cause that we assign off-hand. take, for example, the coincidence that has been remarked between race and different forms of christianity in europe. if the distribution of religious systems were entirely independent of race, it might be said that you would expect one system to coincide equally often with different races in proportion to the positive number of their communities. but the greek system is found almost solely among slavonic peoples, the roman among celtic, and the protestant among teutonic. the coincidence is greater than chance will account for. is the explanation then to be found in some special adaptability of the religious system to the character of the people? this may be the right explanation, but we have not proved it by merely discounting chance. to prove this we must show that there was no other cause at work, that character was the only operative condition in the choice of system, that political combinations, for example, had nothing to do with it. the presumption from extra-casual coincidence is only that there is a special cause: in determining what that is we must conform to the ordinary conditions of explanation. so coincidence between membership of the government and a classical education may be greater than chance would account for, and yet the circumstance of having been taught latin and greek at school may have had no special influence in qualifying the members for their duties. the proportion of classically educated in the government may be greater than the proportion of them in the house of commons, and yet their eminence may be in no way due to their education. men of a certain social position have an advantage in the competition for office, and all those men have been taught latin and greek as a matter of course. technically speaking, the coinciding phenomena may be independent effects of the same cause. . where the alternative possibilities are very numerous, we are apt not to make due allowance for the number, sometimes overrating it, sometimes underrating it. the fallacy of underrating the number is often seen in games of chance, where the object is to create a vast number of alternatives, all equally possible, equally open to the player, without his being able to affect the advent of one more than another. in whist, for example, there are some six billions of possible hands. yet it is a common impression that, one night with another, in the course of a year, a player will have dealt to him about an equal number of good and bad hands. this is a fallacy. a very much longer time is required to exhaust the possible combinations. suppose a player to have hands in the course of a year: this is only one "set," one combination, out of thousands of millions of such sets possible. among those millions of sets, if there is nothing but chance in the matter, there ought to be all proportions of good and bad, some sets all good, some all bad, as well as some equally divided between good and bad.[ ] sometimes, however, the number of possible alternatives is overrated. thus, visitors to london often remark that they never go there without meeting somebody from their own locality, and they are surprised at this as if they had the same chance of meeting their fellow-visitors and any other of the four millions of the metropolis. but really the possible alternatives of rencounter are far less numerous. the places frequented by visitors to london are filled by much more limited numbers: the possible rencounters are to be counted by thousands rather than by millions. [footnote : see de morgan's _essay on probabilities_, c. vi., "on common notions of probability".] chapter ix. probable inference to particulars--the measurement of probability. undoubtedly there are degrees of probability. not only do we expect some events with more confidence than others: we may do so, and our confidence may be misplaced: but we have reason to expect some with more confidence than others. there are different degrees of rational expectation. can those degrees be measured numerically? the question has come into logic from the mathematicians. the calculation of probabilities is a branch of mathematics. we have seen how it may be applied to guide investigation by eliminating what is due to chance, and it has been vaguely conceived by logicians that what is called the calculus of probabilities might be found useful also in determining by exact numerical measurement the probability of single events. dr. venn, who has written a separate treatise on the logic of chance, mentions "accurate quantitative apportionment of our belief" as one of the goals which logic should strive to attain. the following passage will show his drift.[ ] a man in good health would doubtless like to know whether he will be alive this time next year. the fact will be settled one way or the other in due time, if he can afford to wait, but if he wants a present decision, statistics and the theory of probability can alone give him any information. he learns that the odds are, say five to one that he will survive, and this is an answer to his question as far as any answer can be given. statisticians are gradually accumulating a vast mass of data of this general character. what they may be said to aim at is to place us in the position of being able to say, in any given time or place, what are the odds for or against any at present indeterminable fact which belongs to a class admitting of statistical treatment. again, outside the regions of statistics proper--which deal, broadly speaking, with events which can be numbered or measured, and which occur with some frequency--there is still a large field as to which some better approach to a reasoned intensity of belief can be acquired. what will be the issue of a coming war? which party will win in the next election? will a patient in the crisis of a given disease recover or not? that statistics are lying here in the background, and are thus indirectly efficient in producing and graduating our belief, i fully hold; but there is such a large intermediate process of estimating, and such scope for the exercise of a practised judgment, that no direct appeal to statistics in the common sense can directly help us. in sketching out therefore the claims of an ideal condition of knowledge, we ought clearly to include a due apportionment of belief to every event of such a class as this. it is an obvious defect that one man should regard as almost certain what another man regards as almost impossible. short, therefore, of certain prevision of the future, we want complete agreement as to the degree of probability of every future event: and for that matter of every past event as well. technically speaking, if we extend the name modality (see p. ) to any qualification of the certainty of a statement of belief, what dr. venn here desiderates, as he has himself suggested, is a more exact measurement of the modality of propositions. we speak of things as being certain, possible, impossible, probable, extremely probable, faintly probable, and so forth: taking certainty as the highest degree of probability[ ] shading gradually down to the zero of the impossible, can we obtain an exact numerical measure for the gradations of assurance? to examine the principles of all the cases in which chances for and against an occurrence have been calculated from real or hypothetical data, would be to trespass into the province of mathematics, but a few simple cases will serve to show what it is that the calculus attempts to measure, and what is the practical value of the measurement as applied to the probability of a single event. suppose there are balls in a box, white and black, all being alike except in respect of colour, we say that the chances of drawing a black ball as against a white are as to , and the probability of drawing black is measured by the fraction / . in believing this we proceed on the principle already explained (p. ) of proportional chances. we do not know for certain whether black or white will emerge, but knowing the antecedent situation we expect black rather than white with a degree of assurance corresponding to the proportions of the two in the box. it is our degree of rational assurance that we measure by this fraction, and the rationality of it depends on the objective condition of the facts, and is the same for all men, however much their actual degree of confidence may vary with individual temperament. that black will be drawn seven times out of every ten on an average if we go on drawing to infinity, is as certain as any empirical law: it is the probability of a single draw that we measure by the fraction / . when we build expectations of single events on statistics of observed proportions of events of that kind, it is ultimately on the same principle that rational expectation rests. that the proportion will obtain on the average we regard as certain: the ratio of favourable cases to the whole number of possible alternatives is the measure of rational expectation or probability in regard to a particular occurrence. if every year five per cent. of the children of a town stray from their guardians, the probability of this or that child's going astray is / . the ratio is a correct measure only on the assumption that the average is maintained from year to year. without going into the combination of probabilities, we are now in a position to see the practical value of such a calculus as applied to particular cases. there has been some misunderstanding among logicians on the point. mr. jevons rebuked mill for speaking disrespectfully of the calculus, eulogised it as one of the noblest creations of the human intellect, and quoted butler's saying that "probability is the guide of life". but when butler uttered this famous saying he was probably not thinking of the mathematical calculus of probabilities as applied to particular cases, and it was this special application to which mill attached comparatively little value. the truth is that we seldom calculate or have any occasion to calculate individual chances except as a matter of curiosity. it is true that insurance offices calculate probabilities, but it is not the probability of this or that man dying at a particular age. the precise shade of probability for the individual, in so far as this depends on vital statistics, is a matter of indifference to the company as long as the average is maintained. our expectations about any individual life cannot be measured by a calculation of the chances because a variety of other elements affect those expectations. we form beliefs about individual cases, but we try to get surer grounds for them than the chances as calculable from statistical data. suppose a person were to institute a home for lost dogs, he would doubtless try to ascertain how many dogs were likely to go astray, and in so doing would be guided by statistics. but in judging of the probability of the straying of a particular dog, he would pay little heed to statistics as determining the chances, but would proceed upon empirical knowledge of the character of the dog and his master. even in betting on the field against a particular horse, the bookmaker does not calculate from numerical data such as the number of horses entered or the number of times the favourite has been beaten: he tries to get at the pedigree and previous performances of the various horses in the running. we proceed by calculation of chances only when we cannot do better. [footnote : _empirical logic_, p. .] [footnote : mr. jevons held that all inference is merely probable and that no inference is certain. but this is a purposeless repudiation of common meaning, which he cannot himself consistently adhere to. we find him saying that if a penny is tossed into the air it will _certainly_ come down on one side or the other, on which side being a matter of probability. in common speech probability is applied to a degree of belief short of certainty, but to say that certainty is the highest degree of probability does no violence to the common meaning.] chapter x. inference from analogy. the word analogy was appropriated by mill, in accordance with the usage of the eighteenth century, to designate a ground of inference distinct from that on which we proceed in extending a law, empirical or scientific, to a new case. but it is used in various other senses, more or less similar, and in order to make clear the exact logical sense, it is well to specify some of these. the original word [greek: analogia], as employed by aristotle, corresponds to the word proportion in arithmetic: it signified an equality of ratios, [greek: isotês logôn]: two compared with four is analogous to four compared with eight. there is something of the same meaning in the technical use of the word in physiology, where it is used to signify similarity of function as distinguished from similarity of structure, which is called homology: thus the tail of a whale is analogous to the tail of a fish, inasmuch as it is similarly used for motion, but it is homologous with the hind legs of a quadruped; a man's arms are homologous with a horse's fore legs, but they are not analogous inasmuch as they are not used for progression. apart from these technical employments, the word is loosely used in common speech for any kind of resemblance. thus de quincey speaks of the "analogical" power in memory, meaning thereby the power of recalling things by their inherent likeness as distinguished from their casual connexions or their order in a series. but even in common speech, there is a trace of the original meaning: generally when we speak of analogy we have in our minds more than one pair of things, and what we call the analogy is some resemblance between the different pairs. this is probably what whately had in view when he defined analogy as "resemblance of relations". in a strict logical sense, however, as defined by mill, sanctioned by the previous usage of butler and kant, analogy means more than a resemblance of relations. it means a preponderating resemblance between two things such as to warrant us in inferring that the resemblance extends further. this is a species of argument distinct from the extension of an empirical law. in the extension of an empirical law, the ground of inference is a coincidence frequently repeated within our experience, and the inference is that it has occurred or will occur beyond that experience: in the argument from analogy, the ground of inference is the resemblance between two individual objects or kinds of objects in a certain number of points, and the inference is that they resemble one another in some other point, known to belong to the one, but not known to belong to the other. "two things go together in many cases, therefore in all, including this one," is the argument in extending a generalisation: "two things agree in many respects, therefore in this other," is the argument from analogy. the example given by reid in his _intellectual powers_ has become the standard illustration of the peculiar argument from analogy. we may observe a very great similitude between this earth which we inhabit, and the other planets, saturn, jupiter, mars, venus and mercury. they all revolve round the sun, as the earth does, although at different distances and in different periods. they borrow all their light from the sun, as the earth does. several of them are known to revolve round their axis like the earth, and by that means have like succession of day and night. some of them have moons, that serve to give them light in the absence of the sun, as our moon does to us. they are all, in their motions, subject to the same law of gravitation as the earth is. from all this similitude it is not unreasonable to think that these planets may, like our earth, be the habitation of various orders of living creatures. there is some probability in this conclusion from analogy.[ ] the argument from analogy is sometimes said to range through all degrees of probability from certainty to zero. but this is true only if we take the word analogy in its loosest sense for any kind of resemblance. if we do this, we may call any kind of argument an argument from analogy, for all inferences turn upon resemblance. i believe that if i throw my pen in the air it will come down again, because it is like other ponderable bodies. but if we use the word in its limited logical sense, the degree of probability is much nearer zero than certainty. this is apparent from the conditions that logicians have formulated of a strict argument from analogy. . the resemblance must be preponderating. in estimating the value of an argument from analogy, we must reckon the points of difference as counting against the conclusion, and also the points in regard to which we do not know whether the two objects agree or differ. the numerical measure of value is the ratio of the points of resemblance to the points of difference _plus_ the unknown points. thus, in the argument that the planets are inhabited because they resemble the earth in some respects and the earth is inhabited, the force of the analogy is weakened by the fact that we know very little about the surface of the planets. . in a numerical estimate all circumstances that hang together as effects of one cause must be reckoned as one. otherwise, we might make a fallaciously imposing array of points of resemblance. thus in reid's enumeration of the agreements between the earth and the planets, their revolution round the sun and their obedience to the law of gravitation should count as one point of resemblance. if two objects agree in _a_, _b_, _c_, _d_, _e_, but _b_ follows from _a_, and _d_ and _e_ from _c_, the five points count only as two. . if the object to which we infer is known to possess some property incompatible with the property inferred, the general resemblance counts for nothing. the moon has no atmosphere, and we know that air is an indispensable condition of life. hence, however much the moon may resemble the earth, we are debarred from concluding that there are living creatures on the moon such as we know to exist on the earth. we know also that life such as it is on the earth is possible only within certain limits of temperature, and that mercury is too hot for life, and saturn too cold, no matter how great the resemblance to the earth in other respects. . if the property inferred is known or presumed to be a concomitant of one or more of the points of resemblance, any argument from analogy is superfluous. this is, in effect, to say that we have no occasion to argue from general resemblance when we have reason to believe that a property follows from something that an object is known to possess. if we knew that any one of the planets possessed all the conditions, positive and negative, of life, we should not require to reckon up all the respects in which it resembles the earth in order to create a presumption that it is inhabited. we should be able to draw the conclusion on other grounds than those of analogy. newton's famous inference that the diamond is combustible is sometimes quoted as an argument from analogy. but, technically speaking, it was rather, as professor bain has pointed out, of the nature of an extended generalisation. comparing bodies in respect of their densities and refracting powers, he observed that combustible bodies refract more than others of the same density; and observing the exceptionally high refracting power of the diamond, he inferred from this that it was combustible, an inference afterwards confirmed by experiment. "the concurrence of high refracting power with inflammability was an empirical law; and newton, perceiving the law, extended it to the adjacent case of the diamond. the remark is made by brewster that had newton known the refractive powers of the minerals _greenockite_ and _octohedrite_, he would have extended the inference to them, and would have been mistaken."[ ] from these conditions it will be seen that we cannot conclude with any high degree of probability from analogy alone. this is not to deny, as mr. jevons seems to suppose, that analogies, in the sense of general resemblances, are often useful in directing investigation. when we find two things very much alike, and ascertain that one of them possesses a certain property, the presumption that the other has the same is strong enough to make it worth while trying whether as a matter of fact it has. it is said that a general resemblance of the hills near ballarat in australia to the californian hills where gold had been found suggested the idea of digging for gold at ballarat. this was a lucky issue to an argument from analogy, but doubtless many have dug for gold on similar general resemblances without finding that the resemblance extended to that particular. similarly, many of the extensions of the pharmacopeia have proceeded upon general resemblances, the fact that one drug resembles another in certain properties being a sufficient reason for trying whether the resemblance goes further. the lucky guesses of what is known as natural sagacity are often analogical. a man of wide experience in any subject-matter such as the weather, or the conduct of men in war, in business, or in politics, may conclude to the case in hand from some previous case that bears a general resemblance to it, and very often his conclusions may be perfectly sound though he has not made a numerical estimate of the data. the chief source of fallacy in analogical argument is ignoring the number of points of difference. it often happens that an amount of resemblance only sufficient for a rhetorical simile is made to do duty as a solid argument. thus the resemblance between a living body and the body politic is sometimes used to support inferences from successful therapeutic treatment to state policy. the advocates of annual parliaments in the time of the commonwealth based their case on the serpent's habit of annually casting its skin. wisest of beasts the serpent see, just emblem of eternity, and of a state's duration; each year an annual skin he takes, and with fresh life and vigour wakes at every renovation. britain! that serpent imitate. thy commons house, that skin of state, by annual choice restore; so choosing thou shall live secure, and freedom to thy sons inure, till time shall be no more. carlyle's saying that a ship could never be taken round cape horn if the crew were consulted every time the captain proposed to alter the course, if taken seriously as an analogical argument against representative government, is open to the objection that the differences between a ship and a state are too great for any argument from one to the other to be of value. it was such fallacious analogies as these that heine had in view in his humorous prayer, "heaven defend us from the evil one and from metaphors". [footnote : hamilton's _reid_, p. .] [footnote : bain's _logic_, ii. .] printed at the edinburgh press, and young street * * * * * transcriber's note: page : 'aneo symplokês' corrected to 'aneu symplokês' brett fishburne the game of logic by lewis carroll --------------------- | | | | | | | -----x------ | | | | | | | | | | | |---y-----m------y'---| | | | | | | | | | | | -----x'----- | | | | | | | --------------------- colours for ------------- counters | | | ___ | x | | | | see the sun is overhead, |--y-------y'-| shining on us, full and | | | red! | x' | | | | now the sun is gone away, ------------- and the empty sky is grey! ___ the game of logic by lewis carrol to my child-friend. i charm in vain; for never again, all keenly as my glance i bend, will memory, goddess coy, embody for my joy departed days, nor let me gaze on thee, my fairy friend! yet could thy face, in mystic grace, a moment smile on me, 'twould send far-darting rays of light from heaven athwart the night, by which to read in very deed thy spirit, sweetest friend! so may the stream of life's long dream flow gently onward to its end, with many a floweret gay, adown its willowy way: may no sigh vex, no care perplex, my loving little friend! nota bene. with each copy of this book is given an envelope, containing a diagram (similar to the frontispiece) on card, and nine counters, four red and five grey. the envelope, &c. can be had separately, at d. each. the author will be very grateful for suggestions, especially from beginners in logic, of any alterations, or further explanations, that may seem desirable. letters should be addressed to him at " , bedford street, covent garden, london." preface "there foam'd rebellious logic, gagg'd and bound." this game requires nine counters--four of one colour and five of another: say four red and five grey. besides the nine counters, it also requires one player, at least. i am not aware of any game that can be played with less than this number: while there are several that require more: take cricket, for instance, which requires twenty-two. how much easier it is, when you want to play a game, to find one player than twenty-two. at the same time, though one player is enough, a good deal more amusement may be got by two working at it together, and correcting each other's mistakes. a second advantage, possessed by this game, is that, besides being an endless source of amusement (the number of arguments, that may be worked by it, being infinite), it will give the players a little instruction as well. but is there any great harm in that, so long as you get plenty of amusement? contents. chapter page i. new lamps for old. . propositions . . . . . . . . syllogisms . . . . . . . . . fallacies . . . . . . . . ii. cross questions. . elementary . . . . . . . . . half of smaller diagram. propositions to be represented . . . . . . do. symbols to be interpreted. . . smaller diagram. propositions to be represented . . . . . . . . do. symbols to be interpreted. . . larger diagram. propositions to be represented . . . . . . . . both diagrams to be employed . . iii. crooked answers. . elementary . . . . . . . . . half of smaller diagram. propositions represented . . . . . . . . do. symbols interpreted . . . . smaller diagram. propositions represented. . do. symbols interpreted . . . . larger diagram. propositions represented. . both diagrams employed . . . . iv. hit or miss . . . . . . . . . chapter i. new lamps for old. "light come, light go." _________ . propositions. "some new cakes are nice." "no new cakes are nice." "all new cakes are nice." there are three 'propositions' for you--the only three kinds we are going to use in this game: and the first thing to be done is to learn how to express them on the board. let us begin with "some new cakes are nice." but before doing so, a remark has to be made--one that is rather important, and by no means easy to understand all in a moment: so please to read this very carefully. the world contains many things (such as "buns", "babies", "beetles". "battledores". &c.); and these things possess many attributes (such as "baked", "beautiful", "black", "broken", &c.: in fact, whatever can be "attributed to", that is "said to belong to", any thing, is an attribute). whenever we wish to mention a thing, we use a substantive: when we wish to mention an attribute, we use an adjective. people have asked the question "can a thing exist without any attributes belonging to it?" it is a very puzzling question, and i'm not going to try to answer it: let us turn up our noses, and treat it with contemptuous silence, as if it really wasn't worth noticing. but, if they put it the other way, and ask "can an attribute exist without any thing for it to belong to?", we may say at once "no: no more than a baby could go a railway-journey with no one to take care of it!" you never saw "beautiful" floating about in the air, or littered about on the floor, without any thing to be beautiful, now did you? and now what am i driving at, in all this long rigmarole? it is this. you may put "is" or "are" between names of two things (for example, "some pigs are fat animals"), or between the names of two attributes (for example, "pink is light-red"), and in each case it will make good sense. but, if you put "is" or "are" between the name of a thing and the name of an attribute (for example, "some pigs are pink"), you do not make good sense (for how can a thing be an attribute?) unless you have an understanding with the person to whom you are speaking. and the simplest understanding would, i think, be this--that the substantive shall be supposed to be repeated at the end of the sentence, so that the sentence, if written out in full, would be "some pigs are pink (pigs)". and now the word "are" makes quite good sense. thus, in order to make good sense of the proposition "some new cakes are nice", we must suppose it to be written out in full, in the form "some new cakes are nice (cakes)". now this contains two 'terms'--"new cakes" being one of them, and "nice (cakes)" the other. "new cakes," being the one we are talking about, is called the 'subject' of the proposition, and "nice (cakes)" the 'predicate'. also this proposition is said to be a 'particular' one, since it does not speak of the whole of its subject, but only of a part of it. the other two kinds are said to be 'universal', because they speak of the whole of their subjects--the one denying niceness, and the other asserting it, of the whole class of "new cakes". lastly, if you would like to have a definition of the word 'proposition' itself, you may take this:--"a sentence stating that some, or none, or all, of the things belonging to a certain class, called its 'subject', are also things belonging to a certain other class, called its 'predicate'". you will find these seven words--proposition, attribute, term, subject, predicate, particular, universal--charmingly useful, if any friend should happen to ask if you have ever studied logic. mind you bring all seven words into your answer, and you friend will go away deeply impressed--'a sadder and a wiser man'. now please to look at the smaller diagram on the board, and suppose it to be a cupboard, intended for all the cakes in the world (it would have to be a good large one, of course). and let us suppose all the new ones to be put into the upper half (marked 'x'), and all the rest (that is, the not-new ones) into the lower half (marked 'x''). thus the lower half would contain elderly cakes, aged cakes, ante-diluvian cakes--if there are any: i haven't seen many, myself--and so on. let us also suppose all the nice cakes to be put into the left-hand half (marked 'y'), and all the rest (that is, the not-nice ones) into the right-hand half (marked 'y''). at present, then, we must understand x to mean "new", x' "not-new", y "nice", and y' "not-nice." and now what kind of cakes would you expect to find in compartment no. ? it is part of the upper half, you see; so that, if it has any cakes in it, they must be new: and it is part of the left-hand half; so that they must be nice. hence if there are any cakes in this compartment, they must have the double 'attribute' "new and nice": or, if we use letters, the must be "x y." observe that the letters x, y are written on two of the edges of this compartment. this you will find a very convenient rule for knowing what attributes belong to the things in any compartment. take no. , for instance. if there are any cakes there, they must be "x' y", that is, they must be "not-new and nice." now let us make another agreement--that a red counter in a compartment shall mean that it is 'occupied', that is, that there are some cakes in it. (the word 'some,' in logic, means 'one or more' so that a single cake in a compartment would be quite enough reason for saying "there are some cakes here"). also let us agree that a grey counter in a compartment shall mean that it is 'empty', that is that there are no cakes in it. in the following diagrams, i shall put ' ' (meaning 'one or more') where you are to put a red counter, and ' ' (meaning 'none') where you are to put a grey one. as the subject of our proposition is to be "new cakes", we are only concerned, at present, with the upper half of the cupboard, where all the cakes have the attribute x, that is, "new." now, fixing our attention on this upper half, suppose we found it marked like this, ----------- | | | | | | | | | ----------- that is, with a red counter in no. . what would this tell us, with regard to the class of "new cakes"? would it not tell us that there are some of them in the x y-compartment? that is, that some of them (besides having the attribute x, which belongs to both compartments) have the attribute y (that is, "nice"). this we might express by saying "some x-cakes are y-(cakes)", or, putting words instead of letters, "some new cakes are nice (cakes)", or, in a shorter form, "some new cakes are nice". at last we have found out how to represent the first proposition of this section. if you have not clearly understood all i have said, go no further, but read it over and over again, till you do understand it. after that is once mastered, you will find all the rest quite easy. it will save a little trouble, in doing the other propositions, if we agree to leave out the word "cakes" altogether. i find it convenient to call the whole class of things, for which the cupboard is intended, the 'universe.' thus we might have begun this business by saying "let us take a universe of cakes." (sounds nice, doesn't it?) of course any other things would have done just as well as cakes. we might make propositions about "a universe of lizards", or even "a universe of hornets". (wouldn't that be a charming universe to live in?) so far, then, we have learned that ----------- | | | | | | | | | ----------- means "some x and y," i.e. "some new are nice." i think you will see without further explanation, that ----------- | | | | | | | | | ----------- means "some x are y'," i.e. "some new are not-nice." now let us put a grey counter into no. , and ask ourselves the meaning of ----------- | | | | | | | | | ----------- this tells us that the x y-compartment is empty, which we may express by "no x are y", or, "no new cakes are nice". this is the second of the three propositions at the head of this section. in the same way, ----------- | | | | | | | | | ----------- would mean "no x are y'," or, "no new cakes are not-nice." what would you make of this, i wonder? ----------- | | | | | | | | | ----------- i hope you will not have much trouble in making out that this represents a double proposition: namely, "some x are y, and some are y'," i.e. "some new are nice, and some are not-nice." the following is a little harder, perhaps: ----------- | | | | | | | | | ----------- this means "no x are y, and none are y'," i.e. "no new are nice, and none are not-nice": which leads to the rather curious result that "no new exist," i.e. "no cakes are new." this is because "nice" and "not-nice" make what we call an 'exhaustive' division of the class "new cakes": i.e. between them, they exhaust the whole class, so that all the new cakes, that exist, must be found in one or the other of them. and now suppose you had to represent, with counters the contradictory to "no cakes are new", which would be "some cakes are new", or, putting letters for words, "some cakes are x", how would you do it? this will puzzle you a little, i expect. evidently you must put a red counter somewhere in the x-half of the cupboard, since you know there are some new cakes. but you must not put it into the left-hand compartment, since you do not know them to be nice: nor may you put it into the right-hand one, since you do not know them to be not-nice. what, then, are you to do? i think the best way out of the difficulty is to place the red counter on the division-line between the xy-compartment and the xy'-compartment. this i shall represent (as i always put ' ' where you are to put a red counter) by the diagram ----------- | | | | - - | | | | ----------- our ingenious american cousins have invented a phrase to express the position of a man who wants to join one or the other of two parties--such as their two parties 'democrats' and 'republicans'--but can't make up his mind which. such a man is said to be "sitting on the fence." now that is exactly the position of the red counter you have just placed on the division-line. he likes the look of no. , and he likes the look of no. , and he doesn't know which to jump down into. so there he sits astride, silly fellow, dangling his legs, one on each side of the fence! now i am going to give you a much harder one to make out. what does this mean? ----------- | | | | | | | | | ----------- this is clearly a double proposition. it tells us not only that "some x are y," but also the "no x are not y." hence the result is "all x are y," i.e. "all new cakes are nice", which is the last of the three propositions at the head of this section. we see, then, that the universal proposition "all new cakes are nice" consists of two propositions taken together, namely, "some new cakes are nice," and "no new cakes are not-nice." in the same way ----------- | | | | | | | | | ----------- would mean "all x are y' ", that is, "all new cakes are not-nice." now what would you make of such a proposition as "the cake you have given me is nice"? is it particular or universal? "particular, of course," you readily reply. "one single cake is hardly worth calling 'some,' even." no, my dear impulsive reader, it is 'universal'. remember that, few as they are (and i grant you they couldn't well be fewer), they are (or rather 'it is') all that you have given me! thus, if (leaving 'red' out of the question) i divide my universe of cakes into two classes--the cakes you have given me (to which i assign the upper half of the cupboard), and those you haven't given me (which are to go below)--i find the lower half fairly full, and the upper one as nearly as possible empty. and then, when i am told to put an upright division into each half, keeping the nice cakes to the left, and the not-nice ones to the right, i begin by carefully collecting all the cakes you have given me (saying to myself, from time to time, "generous creature! how shall i ever repay such kindness?"), and piling them up in the left-hand compartment. and it doesn't take long to do it! here is another universal proposition for you. "barzillai beckalegg is an honest man." that means "all the barzillai beckaleggs, that i am now considering, are honest men." (you think i invented that name, now don't you? but i didn't. it's on a carrier's cart, somewhere down in cornwall.) this kind of universal proposition (where the subject is a single thing) is called an 'individual' proposition. now let us take "nice cakes" as the subject of proposition: that is, let us fix our thoughts on the left-hand half of the cupboard, where all the cakes have attribute y, that is, "nice." ----- suppose we find it marked like this:-- | | | | what would that tell us? | | ----- | | | | | | ----- i hope that it is not necessary, after explaining the horizontal oblong so fully, to spend much time over the upright one. i hope you will see, for yourself, that this means "some y are x", that is, "some nice cakes are new." "but," you will say, "we have had this case before. you put a red counter into no. , and you told us it meant 'some new cakes are nice'; and now you tell us that it means 'some nice cakes are new'! can it mean both?" the question is a very thoughtful one, and does you great credit, dear reader! it does mean both. if you choose to take x (that is, "new cakes") as your subject, and to regard no. as part of a horizontal oblong, you may read it "some x are y", that is, "some new cakes are nice": but, if you choose to take y (that is, "nice cake") as your subject, and to regard no. as part of an upright oblong, then you may read it "some y are x", that is, "some nice cakes are new". they are merely two different ways of expressing the very same truth. without more words, i will simply set down the other ways in which this upright oblong might be marked, adding the meaning in each case. by comparing them with the various cases of the horizontal oblong, you will, i hope, be able to understand them clearly. you will find it a good plan to examine yourself on this table, by covering up first one column and then the other, and 'dodging about', as the children say. also you will do well to write out for yourself two other tables--one for the lower half of the cupboard, and the other for its right-hand half. and now i think we have said all we need to say about the smaller diagram, and may go on to the larger one. _________________________________________________ | symbols. | meanings. _______________|_________________________________ ----- | | | | | | | some y are x'; | | | i.e. some nice are not-new. ----- | | | | | | | | | | ----- | | ----- | | | | no y are x; | | | i.e. no nice are new. | | | ----- | [observe that this is merely another way of | | | expressing "no new are nice."] | | | | | | ----- | | ----- | | | | | | | no y are x'; | | | i.e. no nice are not-new. ----- | | | | | | | | | | ----- | | ----- | | | | | | | some y are x, and some are x'; | | | i.e. some nice are new, and some are ----- | not-new. | | | | | | | | | ----- | | ----- | | | | | | | no y are x, and none are x'; i.e. no y | | | exist; ----- | i.e. no cakes are nice. | | | | | | | | | ----- | | ----- | | | | | | | all y are x; | | | i.e. all nice are new. ----- | | | | | | | | | | ----- | | ----- | | | | | | | all y are x'; | | | i.e. all nice are not-new. ----- | | | | | | | | | | ----- | _______________|_________________________________ this may be taken to be a cupboard divided in the same way as the last, but also divided into two portions, for the attribute m. let us give to m the meaning "wholesome": and let us suppose that all wholesome cakes are placed inside the central square, and all the unwholesome ones outside it, that is, in one or other of the four queer-shaped outer compartments. we see that, just as, in the smaller diagram, the cakes in each compartment had two attributes, so, here, the cakes in each compartment have three attributes: and, just as the letters, representing the two attributes, were written on the edges of the compartment, so, here, they are written at the corners. (observe that m' is supposed to be written at each of the four outer corners.) so that we can tell in a moment, by looking at a compartment, what three attributes belong to the things in it. for instance, take no. . here we find x, y', m, at the corners: so we know that the cakes in it, if there are any, have the triple attribute, 'xy'm', that is, "new, not-nice, and wholesome." again, take no. . here we find, at the corners, x', y', m': so the cakes in it are "not-new, not-nice, and unwholesome." (remarkably untempting cakes!) it would take far too long to go through all the propositions, containing x and y, x and m, and y and m which can be represented on this diagram (there are ninety-six altogether, so i am sure you will excuse me!) and i must content myself with doing two or three, as specimens. you will do well to work out a lot more for yourself. taking the upper half by itself, so that our subject is "new cakes", how are we to represent "no new cakes are wholesome"? this is, writing letters for words, "no x are m." now this tells us that none of the cakes, belonging to the upper half of the cupboard, are to be found inside the central square: that is, the two compartments, no. and no. , are empty. and this, of course, is represented by ------------------- | | | | _____|_____ | | | | | | | | | | | | | | | | ------------------- and now how are we to represent the contradictory proposition "some x are m"? this is a difficulty i have already considered. i think the best way is to place a red counter on the division-line between no. and no. , and to understand this to mean that one of the two compartments is 'occupied,' but that we do not at present know which. this i shall represent thus:-- ------------------- | | | | _____|_____ | | | | | | | | - - | | | | | | | ------------------- now let us express "all x are m." this consists, we know, of two propositions, "some x are m," and "no x are m'." let us express the negative part first. this tells us that none of the cakes, belonging to the upper half of the cupboard, are to be found outside the central square: that is, the two compartments, no. and no. , are empty. this, of course, is represented by ------------------- | | | | _____|_____ | | | | | | | | | | | | | | | | ------------------- but we have yet to represent "some x are m." this tells us that there are some cakes in the oblong consisting of no. and no. : so we place our red counter, as in the previous example, on the division-line between no. and no. , and the result is ------------------- | | | | _____|_____ | | | | | | | | - - | | | | | | | ------------------- now let us try one or two interpretations. what are we to make of this, with regard to x and y? ------------------- | | | | _____|_____ | | | | | | | | | | | | | | | | ------------------- this tells us, with regard to the xy'-square, that it is wholly 'empty', since both compartments are so marked. with regard to the xy-square, it tells us that it is 'occupied'. true, it is only one compartment of it that is so marked; but that is quite enough, whether the other be 'occupied' or 'empty', to settle the fact that there is something in the square. if, then, we transfer our marks to the smaller diagram, so as to get rid of the m-subdivisions, we have a right to mark it ----------- | | | | | | | | | ----------- which means, you know, "all x are y." the result would have been exactly the same, if the given oblong had been marked thus:-- ------------------- | | | | _____|_____ | | | | | | | | | | | | | | | | ------------------- once more: how shall we interpret this, with regard to x and y? ------------------- | | | | _____|_____ | | | | | | | | | | | | | | | | ------------------- this tells us, as to the xy-square, that one of its compartments is 'empty'. but this information is quite useless, as there is no mark in the other compartment. if the other compartment happened to be 'empty' too, the square would be 'empty': and, if it happened to be 'occupied', the square would be 'occupied'. so, as we do not know which is the case, we can say nothing about this square. the other square, the xy'-square, we know (as in the previous example) to be 'occupied'. if, then, we transfer our marks to the smaller diagram, we get merely this:-- ----------- | | | | | | | | | ----------- which means, you know, "some x are y'." these principles may be applied to all the other oblongs. for instance, to represent "all y' are m'" we should mark the ------- right-hand upright oblong (the one | | that has the attribute y') thus:-- |--- | | | | |---|- -| | | | |--- | | | ------- and, if we were told to interpret the lower half of the cupboard, marked as follows, with regard to x and y, ------------------- | | | | | | | | | | | | | | | | -----|----- | | | | ------------------- we should transfer it to the smaller diagram thus, ----------- | | | | | | | | | ----------- and read it "all x' are y." two more remarks about propositions need to be made. one is that, in every proposition beginning with "some" or "all", the actual existence of the 'subject' is asserted. if, for instance, i say "all misers are selfish," i mean that misers actually exist. if i wished to avoid making this assertion, and merely to state the law that miserliness necessarily involves selfishness, i should say "no misers are unselfish" which does not assert that any misers exist at all, but merely that, if any did exist, they would be selfish. the other is that, when a proposition begins with "some" or "no", and contains more that two attributes, these attributes may be re-arranged, and shifted from one term to the other, "ad libitum." for example, "some abc are def" may be re-arranged as "some bf are acde," each being equivalent to "some things are abcdef". again "no wise old men are rash and reckless gamblers" may be re-arranged as "no rash old gamblers are wise and reckless," each being equivalent to "no men are wise old rash reckless gamblers." . syllogisms now suppose we divide our universe of things in three ways, with regard to three different attributes. out of these three attributes, we may make up three different couples (for instance, if they were a, b, c, we might make up the three couples ab, ac, bc). also suppose we have two propositions given us, containing two of these three couples, and that from them we can prove a third proposition containing the third couple. (for example, if we divide our universe for m, x, and y; and if we have the two propositions given us, "no m are x'" and "all m' are y", containing the two couples mx and my, it might be possible to prove from them a third proposition, containing x and y.) in such a case we call the given propositions 'the premisses', the third one 'the conclusion' and the whole set 'a syllogism'. evidently, one of the attributes must occur in both premisses; or else one must occur in one premiss, and its contradictory in the other. in the first case (when, for example, the premisses are "some m are x" and "no m are y'") the term, which occurs twice, is called 'the middle term', because it serves as a sort of link between the other two terms. in the second case (when, for example, the premisses are "no m are x'" and "all m' are y") the two terms, which contain these contradictory attributes, may be called 'the middle terms'. thus, in the first case, the class of "m-things" is the middle term; and, in the second case, the two classes of "m-things" and "m'-things" are the middle terms. the attribute, which occurs in the middle term or terms, disappears in the conclusion, and is said to be "eliminated", which literally means "turned out of doors". now let us try to draw a conclusion from the two premisses-- "some new cakes are unwholesome; no nice cakes are unwholesome." in order to express them with counters, we need to divide cakes in three different ways, with regard to newness, to niceness, and to wholesomeness. for this we must use the larger diagram, making x mean "new", y "nice", and m "wholesome". (everything inside the central square is supposed to have the attribute m, and everything outside it the attribute m', i.e. "not-m".) you had better adopt the rule to make m mean the attribute which occurs in the middle term or terms. (i have chosen m as the symbol, because 'middle' begins with 'm'.) now, in representing the two premisses, i prefer to begin with the negative one (the one beginning with "no"), because grey counters can always be placed with certainty, and will then help to fix the position of the red counters, which are sometimes a little uncertain where they will be most welcome. let us express, the "no nice cakes are unwholesome (cakes)", i.e. "no y-cakes are m'-(cakes)". this tells us that none of the cakes belonging to the y-half of the cupboard are in its m'-compartments (i.e. the ones outside the central square). hence the two compartments, no. and no. , are both 'empty'; and we must place a grey counter in each of them, thus:-- ----------- | | | | --|-- | | | | | | |--|-----|--| | | | | | | --|-- | | | | ----------- we have now to express the other premiss, namely, "some new cakes are unwholesome (cakes)", i.e. "some x-cakes are m'-(cakes)". this tells us that some of the cakes in the x-half of the cupboard are in its m'-compartments. hence one of the two compartments, no. and no. , is 'occupied': and, as we are not told in which of these two compartments to place the red counter, the usual rule would be to lay it on the division-line between them: but, in this case, the other premiss has settled the matter for us, by declaring no. to be empty. hence the red counter has no choice, and must go into no. , thus:-- ----------- | | | | --|-- | | | | | | |--|-----|--| | | | | | | --|-- | | | | ----------- and now what counters will this information enable us to place in the smaller diagram, so as to get some proposition involving x and y only, leaving out m? let us take its four compartments, one by one. first, no. . all we know about this is that its outer portion is empty: but we know nothing about its inner portion. thus the square may be empty, or it may have something in it. who can tell? so we dare not place any counter in this square. secondly, what of no. ? here we are a little better off. we know that there is something in it, for there is a red counter in its outer portion. it is true we do not know whether its inner portion is empty or occupied: but what does that matter? one solitary cake, in one corner of the square, is quite sufficient excuse for saying "this square is occupied", and for marking it with a red counter. as to no. , we are in the same condition as with no. --we find it partly 'empty', but we do not know whether the other part is empty or occupied: so we dare not mark this square. and as to no. , we have simply no information at all. the result is ------- | | | |---|---| | | | ------- our 'conclusion', then, must be got out of the rather meager piece of information that there is a red counter in the xy'-square. hence our conclusion is "some x are y' ", i.e. "some new cakes are not-nice (cakes)": or, if you prefer to take y' as your subject, "some not-nice cakes are new (cakes)"; but the other looks neatest. we will now write out the whole syllogism, putting the symbol &there [*] for "therefore", and omitting "cakes", for the sake of brevity, at the end of each proposition. [*][note from brett: the use of "&there " is a rather arbitrary selection. there is no font available in general practice which renders the "therefore" symbol correction (three dots in a triangular formation). this can be done, however, in html, so if this document is read in a browser, then the symbol will be properly recognized. this is a poor man's excuse.] "some new cakes are unwholesome; no nice cakes are unwholesome &there some new cakes are not-nice." and you have now worked out, successfully, your first 'syllogism'. permit me to congratulate you, and to express the hope that it is but the beginning of a long and glorious series of similar victories! we will work out one other syllogism--a rather harder one than the last--and then, i think, you may be safely left to play the game by yourself, or (better) with any friend whom you can find, that is able and willing to take a share in the sport. let us see what we can make of the two premisses-- "all dragons are uncanny; all scotchmen are canny." remember, i don't guarantee the premisses to be facts. in the first place, i never even saw a dragon: and, in the second place, it isn't of the slightest consequence to us, as logicians, whether our premisses are true or false: all we have to do is to make out whether they lead logically to the conclusion, so that, if they were true, it would be true also. you see, we must give up the "cakes" now, or our cupboard will be of no use to us. we must take, as our 'universe', some class of things which will include dragons and scotchmen: shall we say 'animals'? and, as "canny" is evidently the attribute belonging to the 'middle terms', we will let m stand for "canny", x for "dragons", and y for "scotchmen". so that our two premisses are, in full, "all dragon-animals are uncanny (animals); all scotchman-animals are canny (animals)." and these may be expressed, using letters for words, thus:-- "all x are m'; all y are m." the first premiss consists, as you already know, of two parts:-- "some x are m'," and "no x are m." and the second also consists of two parts:-- "some y are m," and "no y are m'." let us take the negative portions first. we have, then, to mark, on the larger diagram, first, "no x are m", and secondly, "no y are m'". i think you will see, without further explanation, that the two results, separately, are ----------- ----------- | | | | | | | --|-- | | --|-- | | | | | | | | | | | |--|--|--|--| |--|--|--|--| | | | | | | | | | | | --|-- | | --|-- | | | | | | | ----------- ----------- and that these two, when combined, give us ----------- | | | | --|-- | | | | | | |--|--|--|--| | | | | | | --|-- | | | | ----------- we have now to mark the two positive portions, "some x are m'" and "some y are m". the only two compartments, available for things which are xm', are no. and no. . of these, no. is already marked as 'empty'; so our red counter must go into no. . similarly, the only two, available for ym, are no. and no. . of these, no. is already marked as 'empty'; so our red counter must go into no. . the final result is ----------- | | | | --|-- | | | | | | |--|--|--|--| | | | | | | --|-- | | | | ----------- and now how much of this information can usefully be transferred to the smaller diagram? let us take its four compartments, one by one. as to no. ? this, we see, is wholly 'empty'. (so mark it with a grey counter.) as to no. ? this, we see, is 'occupied'. (so mark it with a red counter.) as to no. ? ditto, ditto. as to no. ? no information. the smaller diagram is now pretty liberally marked:-- ------- | | | |---|---| | | | ------- and now what conclusion can we read off from this? well, it is impossible to pack such abundant information into one proposition: we shall have to indulge in two, this time. first, by taking x as subject, we get "all x are y'", that is, "all dragons are not-scotchmen": secondly, by taking y as subject, we get "all y are x'", that is, "all scotchmen are not-dragons". let us now write out, all together, our two premisses and our brace of conclusions. "all dragons are uncanny; all scotchmen are canny. &there all dragons are not-scotchmen; all scotchmen are not-dragons." let me mention, in conclusion, that you may perhaps meet with logical treatises in which it is not assumed that any thing exists at all, by "some x are y" is understood to mean "the attributes x, y are compatible, so that a thing can have both at once", and "no x are y" to mean "the attributes x, y are incompatible, so that nothing can have both at once". in such treatises, propositions have quite different meanings from what they have in our 'game of logic', and it will be well to understand exactly what the difference is. first take "some x are y". here we understand "are" to mean "are, as an actual fact"--which of course implies that some x-things exist. but they (the writers of these other treatises) only understand "are" to mean "can be", which does not at all imply that any exist. so they mean less than we do: our meaning includes theirs (for of course "some x are y" includes "some x can be y"), but theirs does not include ours. for example, "some welsh hippopotami are heavy" would be true, according to these writers (since the attributes "welsh" and "heavy" are quite compatible in a hippopotamus), but it would be false in our game (since there are no welsh hippopotami to be heavy). secondly, take "no x are y". here we only understand "are" to mean "are, as an actual fact"--which does not at all imply that no x can be y. but they understand the proposition to mean, not only that none are y, but that none can possibly be y. so they mean more than we do: their meaning includes ours (for of course "no x can be y" includes "no x are y"), but ours does not include theirs. for example, "no policemen are eight feet high" would be true in our game (since, as an actual fact, no such splendid specimens are ever found), but it would be false, according to these writers (since the attributes "belonging to the police force" and "eight feet high" are quite compatible: there is nothing to prevent a policeman from growing to that height, if sufficiently rubbed with rowland's macassar oil--which said to make hair grow, when rubbed on hair, and so of course will make a policeman grow, when rubbed on a policeman). thirdly, take "all x are y", which consists of the two partial propositions "some x are y" and "no x are y'". here, of course, the treatises mean less than we do in the first part, and more than we do in the second. but the two operations don't balance each other--any more than you can console a man, for having knocked down one of his chimneys, by giving him an extra door-step. if you meet with syllogisms of this kind, you may work them, quite easily, by the system i have given you: you have only to make 'are' mean 'are capable of being', and all will go smoothly. for "some x are y" will become "some x are capable of being y", that is, "the attributes x, y are compatible". and "no x are y" will become "no x are capable of being y", that is, "the attributes x, y are incompatible". and, of course, "all x are y" will become "some x are capable of being y, and none are capable of being y'", that is, "the attributes x, y are compatible, and the attributes x, y' are incompatible." in using the diagrams for this system, you must understand a red counter to mean "there may possibly be something in this compartment," and a grey one to mean "there cannot possibly be anything in this compartment." . fallacies. and so you think, do you, that the chief use of logic, in real life, is to deduce conclusions from workable premisses, and to satisfy yourself that the conclusions, deduced by other people, are correct? i only wish it were! society would be much less liable to panics and other delusions, and political life, especially, would be a totally different thing, if even a majority of the arguments, that scattered broadcast over the world, were correct! but it is all the other way, i fear. for one workable pair of premisses (i mean a pair that lead to a logical conclusion) that you meet with in reading your newspaper or magazine, you will probably find five that lead to no conclusion at all: and, even when the premisses are workable, for one instance, where the writer draws a correct conclusion, there are probably ten where he draws an incorrect one. in the first case, you may say "the premisses are fallacious": in the second, "the conclusion is fallacious." the chief use you will find, in such logical skill as this game may teach you, will be in detecting 'fallacies' of these two kinds. the first kind of fallacy--'fallacious premisses'--you will detect when, after marking them on the larger diagram, you try to transfer the marks to the smaller. you will take its four compartments, one by one, and ask, for each in turn, "what mark can i place here?"; and in every one the answer will be "no information!", showing that there is no conclusion at all. for instance, "all soldiers are brave; some englishmen are brave. &there some englishmen are soldiers." looks uncommonly like a syllogism, and might easily take in a less experienced logician. but you are not to be caught by such a trick! you would simply set out the premisses, and would then calmly remark "fallacious premisses!": you wouldn't condescend to ask what conclusion the writer professed to draw--knowing that, whatever it is, it must be wrong. you would be just as safe as that wise mother was, who said "mary, just go up to the nursery, and see what baby's doing, and tell him not to do it!" the other kind of fallacy--'fallacious conclusion'--you will not detect till you have marked both diagrams, and have read off the correct conclusion, and have compared it with the conclusion which the writer has drawn. but mind, you mustn't say "fallacious conclusion," simply because it is not identical with the correct one: it may be a part of the correct conclusion, and so be quite correct, as far as it goes. in this case you would merely remark, with a pitying smile, "defective conclusion!" suppose, of example, you were to meet with this syllogism:-- "all unselfish people are generous; no misers are generous. &there no misers are unselfish." the premisses of which might be thus expressed in letters:-- "all x' are m; no y are m." here the correct conclusion would be "all x' are y'" (that is, "all unselfish people are not misers"), while the conclusion, drawn by the writer, is "no y are x'," (which is the same as "no x' are y," and so is part of "all x' are y'.") here you would simply say "defective conclusion!" the same thing would happen, if you were in a confectioner's shop, and if a little boy were to come in, put down twopence, and march off triumphantly with a single penny-bun. you would shake your head mournfully, and would remark "defective conclusion! poor little chap!" and perhaps you would ask the young lady behind the counter whether she would let you eat the bun, which the little boy had paid for and left behind him: and perhaps she would reply "sha'n't!" but if, in the above example, the writer had drawn the conclusion "all misers are selfish" (that is, "all y are x"), this would be going beyond his legitimate rights (since it would assert the existence of y, which is not contained in the premisses), and you would very properly say "fallacious conclusion!" now, when you read other treatises on logic, you will meet with various kinds of (so-called) 'fallacies' which are by no means always so. for example, if you were to put before one of these logicians the pair of premisses "no honest men cheat; no dishonest men are trustworthy." and were to ask him what conclusion followed, he would probably say "none at all! your premisses offend against two distinct rules, and are as fallacious as they can well be!" then suppose you were bold enough to say "the conclusion is 'no men who cheat are trustworthy'," i fear your logical friend would turn away hastily--perhaps angry, perhaps only scornful: in any case, the result would be unpleasant. i advise you not to try the experiment! "but why is this?" you will say. "do you mean to tell us that all these logicians are wrong?" far from it, dear reader! from their point of view, they are perfectly right. but they do not include, in their system, anything like all the possible forms of syllogisms. they have a sort of nervous dread of attributes beginning with a negative particle. for example, such propositions as "all not-x are y," "no x are not-y," are quite outside their system. and thus, having (from sheer nervousness) excluded a quantity of very useful forms, they have made rules which, though quite applicable to the few forms which they allow of, are no use at all when you consider all possible forms. let us not quarrel with them, dear reader! there is room enough in the world for both of us. let us quietly take our broader system: and, if they choose to shut their eyes to all these useful forms, and to say "they are not syllogisms at all!" we can but stand aside, and let them rush upon their fate! there is scarcely anything of yours, upon which it is so dangerous to rush, as your fate. you may rush upon your potato-beds, or your strawberry-beds, without doing much harm: you may even rush upon your balcony (unless it is a new house, built by contract, and with no clerk of the works) and may survive the foolhardy enterprise: but if you once rush upon your fate--why, you must take the consequences! chapter ii. cross questions. "the man in the wilderness asked of me 'how many strawberries grow in the sea?'" __________ . elementary. . what is an 'attribute'? give examples. . when is it good sense to put "is" or "are" between two names? give examples. . when is it not good sense? give examples. . when it is not good sense, what is the simplest agreement to make, in order to make good sense? . explain 'proposition', 'term', 'subject', and 'predicate'. give examples. . what are 'particular' and 'universal' propositions? give examples. . give a rule for knowing, when we look at the smaller diagram, what attributes belong to the things in each compartment. . what does "some" mean in logic? [see pp. , ] . in what sense do we use the word 'universe' in this game? . what is a 'double' proposition? give examples. . when is a class of things said to be 'exhaustively' divided? give examples. . explain the phrase "sitting on the fence." . what two partial propositions make up, when taken together, "all x are y"? . what are 'individual' propositions? give examples. . what kinds of propositions imply, in this game, the existence of their subjects? . when a proposition contains more than two attributes, these attributes may in some cases be re-arranged, and shifted from one term to the other. in what cases may this be done? give examples. __________ break up each of the following into two partial propositions: . all tigers are fierce. . all hard-boiled eggs are unwholesome. . i am happy. . john is not at home. __________ [see pp. , ] . give a rule for knowing, when we look at the larger diagram, what attributes belong to the things contained in each compartment. . explain 'premisses', 'conclusion', and 'syllogism'. give examples. . explain the phrases 'middle term' and 'middle terms'. . in marking a pair of premisses on the larger diagram, why is it best to mark negative propositions before affirmative ones? . why is it of no consequence to us, as logicians, whether the premisses are true or false? . how can we work syllogisms in which we are told that "some x are y" is to be understood to mean "the attribute x, y are compatible", and "no x are y" to mean "the attributes x, y are incompatible"? . what are the two kinds of 'fallacies'? . how may we detect 'fallacious premisses'? . how may we detect a 'fallacious conclusion'? . sometimes the conclusion, offered to us, is not identical with the correct conclusion, and yet cannot be fairly called 'fallacious'. when does this happen? and what name may we give to such a conclusion? [see pp. - ] . half of smaller diagram. propositions to be represented. ----------- | | | | x | | | | --y-----y'- __________ . some x are not-y. . all x are not-y. . some x are y, and some are not-y. . no x exist. . some x exist. . no x are not-y. . some x are not-y, and some x exist. __________ taking x="judges"; y="just"; . no judges are just. . some judges are unjust. . all judges are just. __________ taking x="plums"; y="wholesome"; . some plums are wholesome. . there are no wholesome plums. . plums are some of them wholesome, and some not. . all plums are unwholesome. [see pp. , ] ----- | | | x | | |--y--| | | | x' | | ----- __________ taking y="diligent students"; x="successful"; . no diligent students are unsuccessful. . all diligent students are successful. . no students are diligent. . there are some diligent, but unsuccessful, students. . some students are diligent. [see pp. , ] . half of smaller diagram. symbols to be interpreted. __________ ----------- | | | | x | | | | --y-----y'- __________ ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- ------- ------- | | | | | | . | - | . | | | | | | | | | ------- ------- __________ taking x="good riddles"; y="hard"; ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- __________ [see pp. , ] taking x="lobster"; y="selfish"; ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- __________ ----- | | x | | | |--y'-| | | x' | | | ----- taking y="healthy people"; x="happy"; --- --- --- --- | | | | | | | | . |---| . |- -| . |---| . |---| | | | | | | | | --- --- --- --- [see p. ] . smaller diagram. propositions to be represented. ----------- | | | | x | |--y--|--y'-| | x' | | | | ----------- __________ . all y are x. . some y are not-x. . no not-x are not-y. . some x are not-y. . some not-y are x. . no not-x are y. . some not-x are not-y. . all not-x are not-y. . some not-y exist. . no not-x exist. . some y are x, and some are not-x. . all x are y, and all not-y are not-x. [see pp. , ] taking "nations" as universe; x="civilised"; y="warlike"; . no uncivilised nation is warlike. . all unwarlike nations are uncivilised. . some nations are unwarlike. . all warlike nations are civilised, and all civilised nations are warlike. . no nation is uncivilised. __________ taking "crocodiles" as universe; x="hungry"; and y="amiable"; . all hungry crocodiles are unamiable. . no crocodiles are amiable when hungry. . some crocodiles, when not hungry, are amiable; but some are not. . no crocodiles are amiable, and some are hungry. . all crocodiles, when not hungry, are amiable; and all unamiable crocodiles are hungry. . some hungry crocodiles are amiable, and some that are not hungry are unamiable. [see pp. , ] . smaller diagram. symbols to be interpreted. __________ ----------- | | | | x | |--y--|--y'-| | x' | | | | ----------- __________ ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- __________ taking "houses" as universe; x="built of brick"; and y="two-storied"; interpret ------- ------- | | | | | | . |---|---| . |---|---| | | | | - | ------- ---|--- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- [see p. ] taking "boys" as universe; x="fat"; and y="active"; interpret ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- __________ taking "cats" as universe; x="green-eyed"; and y="good-tempered"; interpret ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- [see pp. , ] . larger diagram. propositions to be represented. __________ ----------- | | | | --x-- | | | | | | |--y--m--y'-| | | | | | | --x'- | | | | ----------- __________ . no x are m. . some y are m'. . all m are x'. . no m' are y'. . no m are x; all y are m. . some x are m; no y are m. . all m are x'; no m are y. . no x' are m; no y' are m'. [see pp. , ] taking "rabbits" as universe; m="greedy"; x="old"; and y="black"; represent . no old rabbits are greedy. . some not-greedy rabbits are black. . all white rabbits are free from greediness. . all greedy rabbits are young. . no old rabbits are greedy; all black rabbits are greedy. . all rabbits, that are not greedy, are black; no old rabbits are free from greediness. __________ taking "birds" as universe; m="that sing loud"; x="well-fed"; and y="happy"; represent . all well-fed birds sing loud; no birds, that sing loud, are unhappy. . all birds, that do not sing loud, are unhappy; no well-fed birds fail to sing loud. __________ taking "persons" as universe; m="in the house"; x="john"; and y="having a tooth-ache"; represent . john is in the house; everybody in the house is suffering from tooth-ache. . there is no one in the house but john; nobody, out of the house, has a tooth-ache. __________ [see pp. - ] taking "persons" as universe; m="i"; x="that has taken a walk"; y="that feels better"; represent . i have been out for a walk; i feel much better. __________ choosing your own 'universe' &c., represent . i sent him to bring me a kitten; he brought me a kettle by mistake. [see pp. , ] . both diagrams to be employed. __________ ----------- | | | ----------- | --x-- | | | | | | | | | | x | |--y--m--y'-| |--y--|--y'-| | | | | | | x' | | --x'- | | | | | | | ----------- ----------- __________ n.b. in each question, a small diagram should be drawn, for x and y only, and marked in accordance with the given large diagram: and then as many propositions as possible, for x and y, should be read off from this small diagram. ----------- ----------- | | | | | | | --|-- | | --|-- | | | | | | | | | | | . |--|--|--|--| . |--|--|--|--| | | | | | | | | | | | --|-- | | --|-- | | | | | | | ----------- ----------- [see p. ] ----------- ----------- | | | | | | | --|-- | | --|-- | | | | | | | | | | | . |--|--|--|--| . |--|--|--|--| | | | | | | | | | | | --|-- | | --|-- | | | | | | | ----------- ----------- __________ mark, in a large diagram, the following pairs of propositions from the preceding section: then mark a small diagram in accordance with it, &c. . no. . [see p. ] . no. . . no. . . no. . . no. . . no. . [see p. ] . no. . . no. . __________ mark, on a large diagram, the following pairs of propositions: then mark a small diagram, &c. these are, in fact, pairs of premisses for syllogisms: and the results, read off from the small diagram, are the conclusions. . no exciting books suit feverish patients; unexciting books make one drowsy. . some, who deserve the fair, get their deserts; none but the brave deserve the fair. . no children are patient; no impatient person can sit still. [see pp. - ] . all pigs are fat; no skeletons are fat. . no monkeys are soldiers; all monkeys are mischievous. . none of my cousins are just; no judges are unjust. . some days are rainy; rainy days are tiresome. . all medicine is nasty; senna is a medicine. . some jews are rich; all patagonians are gentiles. . all teetotalers like sugar; no nightingale drinks wine. . no muffins are wholesome; all buns are unwholesome. . no fat creatures run well; some greyhounds run well. . all soldiers march; some youths are not soldiers. . sugar is sweet; salt is not sweet. . some eggs are hard-boiled; no eggs are uncrackable. . there are no jews in the house; there are no gentiles in the garden. [see pp. - ] . all battles are noisy; what makes no noise may escape notice. . no jews are mad; all rabbis are jews. . there are no fish that cannot swim; some skates are fish. . all passionate people are unreasonable; some orators are passionate. [see pp. - ] chapter iii. crooked answers. "i answered him, as i thought good, 'as many as red-herrings grow in the wood'." __________ . elementary. . whatever can be "attributed to", that is "said to belong to", a thing, is called an 'attribute'. for example, "baked", which can (frequently) be attributed to "buns", and "beautiful", which can (seldom) be attributed to "babies". . when they are the names of two things (for example, "these pigs are fat animals"), or of two attributes (for example, "pink is light red"). . when one is the name of a thing, and the other the name of an attribute (for example, "these pigs are pink"), since a thing cannot actually be an attribute. . that the substantive shall be supposed to be repeated at the end of the sentence (for example, "these pigs are pink (pigs)"). . a 'proposition' is a sentence stating that some, or none, or all, of the things belonging to a certain class, called the 'subject', are also things belonging to a certain other class, called the 'predicate'. for example, "some new cakes are not nice", that is (written in full) "some new cakes are not nice cakes"; where the class "new cakes" is the subject, and the class "not-nice cakes" is the predicate. . a proposition, stating that some of the things belonging to its subject are so-and-so, is called 'particular'. for example, "some new cakes are nice", "some new cakes are not nice." a proposition, stating that none of the things belonging to its subject, or that all of them, are so-and-so, is called 'universal'. for example, "no new cakes are nice", "all new cakes are not nice". . the things in each compartment possess two attributes, whose symbols will be found written on two of the edges of that compartment. . "one or more." . as a name of the class of things to which the whole diagram is assigned. . a proposition containing two statements. for example, "some new cakes are nice and some are not-nice." . when the whole class, thus divided, is "exhausted" among the sets into which it is divided, there being no member of it which does not belong to some one of them. for example, the class "new cakes" is "exhaustively" divided into "nice" and "not-nice" since every new cake must be one or the other. . when a man cannot make up his mind which of two parties he will join, he is said to be "sitting on the fence"--not being able to decide on which side he will jump down. . "some x are y" and "no x are y'". . a proposition, whose subject is a single thing, is called 'individual'. for example, "i am happy", "john is not at home". these are universal propositions, being the same as "all the i's that exist are happy", "all the johns, that i am now considering, are not at home". . propositions beginning with "some" or "all". . when they begin with "some" or "no". for example, "some abc are def" may be re-arranged as "some bf are acde", each being equivalent to "some abcdef exist". . some tigers are fierce, no tigers are not-fierce. . some hard-boiled eggs are unwholesome, no hard-boiled eggs are wholesome. . some i's are happy, no i's are unhappy. . some johns are not at home, no johns are at home. . the things, in each compartment of the larger diagram, possess three attributes, whose symbols will be found written at three of the corners of the compartment (except in the case of m', which is not actually inserted in the diagram, but is supposed to stand at each of its four outer corners). . if the universe of things be divided with regard to three different attributes; and if two propositions be given, containing two different couples of these attributes; and if from these we can prove a third proposition, containing the two attributes that have not yet occurred together; the given propositions are called 'the premisses', the third one 'the conclusion', and the whole set 'a syllogism'. for example, the premisses might be "no m are x'" and "all m' are y"; and it might be possible to prove from them a conclusion containing x and y. . if an attribute occurs in both premisses, the term containing it is called 'the middle term'. for example, if the premisses are "some m are x" and "no m are y'", the class of "m-things" is 'the middle term.' if an attribute occurs in one premiss, and its contradictory in the other, the terms containing them may be called 'the middle terms'. for example, if the premisses are "no m are x'" and "all m' are y", the two classes of "m-things" and "m'-things" may be called 'the middle terms'. . because they can be marked with certainty: whereas affirmative propositions (that is, those that begin with "some" or "all") sometimes require us to place a red counter 'sitting on a fence'. . because the only question we are concerned with is whether the conclusion follows logically from the premisses, so that, if they were true, it also would be true. . by understanding a red counter to mean "this compartment can be occupied", and a grey one to mean "this compartment cannot be occupied" or "this compartment must be empty". . 'fallacious premisses' and 'fallacious conclusion'. . by finding, when we try to transfer marks from the larger diagram to the smaller, that there is 'no information' for any of its four compartments. . by finding the correct conclusion, and then observing that the conclusion, offered to us, is neither identical with it nor a part of it. . when the offered conclusion is part of the correct conclusion. in this case, we may call it a 'defective conclusion'. . half of smaller diagram. propositions represented. __________ ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- ------- ------- | | | | | | . | | | . | | | | | | | | | ------- ------- ------- ------- | | | | | | . | | . | | | | | | | | | ------- ------- ------- | | | . | | | it might be thought that the proper | | | ------- ------- | | | diagram would be | |, in order to express "some | | | ------- x exist": but this is really contained in "some x are y'." to put a red counter on the division-line would only tell us "one of the compartments is occupied", which we know already, in knowing that one is occupied. ------- | | | . no x are y. i.e. | | | | | | ------- ------- | | | . some x are y'. i.e. | | | | | | ------- ------- | | | . all x are y. i.e. | | | | | | ------- ------- | | | . some x are y. i.e. | | | | | | ------- ------- | | | . no x are y. i.e. | | | | | | ------- ------- | | | . some x are y, and some are y'. i.e. | | | | | | ------- ------- | | | . all x are y'. i.e. | | | | | | ------- --- | | . no y are x'. i.e. |---| | | --- --- | | . all y are x. i.e. |---| | | --- --- | | . no y exist. i.e. |---| | | --- --- | | . some y are x'. i.e. |---| | | --- --- | | . some y exist. i.e. |- -| | | --- . half of smaller diagram. symbols interpreted. __________ . no x are y'. . no x exist. . some x exist. . all x are y'. . some x are y. i.e. some good riddles are hard. . all x are y. i.e. all good riddles are hard. . no x exist. i.e. no riddles are good. . no x are y. i.e. no good riddles are hard. . some x are y'. i.e. some lobsters are unselfish. . no x are y. i.e. no lobsters are selfish. . all x are y'. i.e. all lobsters are unselfish. . some x are y, and some are y'. i.e. some lobsters are selfish, and some are unselfish. . all y' are x'. i.e. all invalids are unhappy. . some y' exist. i.e. some people are unhealthy. . some y' are x, and some are x'. i.e. some invalids are happy, and some are unhappy. . no y' exist. i.e. nobody is unhealthy. . smaller diagram. propositions represented. __________ ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|- -| . |---|---| | | | | | | ------- ------- ------- ------- | | | | | | . |---|---| . |---|---| | | | | | | ------- ------- ------- | | | . no x' are y. i.e. |---|---| | | | ------- ------- | | | . all y' are x'. i.e. |---|---| | | | ------- ------- | | | . some y' exist. i.e. |---|- -| | | | ------- ------- | | | . all y are x, and all x are y. i.e. |---|---| | | | ------- ------- | | | . no x' exist. i.e. |---|---| | | | ------- ------- | | | . all x are y'. i.e. |---|---| | | | ------- ------- | | | . no x are y. i.e. |---|---| | | | ------- ------- | | | . some x' are y, and some are y'. i.e. |---|---| | | | ------- ------- | | | . no y exist, and some x exist. i.e. |---|---| | | | ------- ------- | | | . all x' are y, and all y' are x. i.e. |---|---| | | | ------- ------- | | | . some x are y, and some x' are y'. i.e. |---|---| | | | ------- . smaller diagram. symbols interpreted. __________ . some y are not-x, or, some not-x are y. . no not-x are not-y, or, no not-y are not-x. . no not-y are x. . no not-x exist. i.e. no things are not-x. . no y exist. i.e. no houses are two-storied. . some x' exist. i.e. some houses are not built of brick. . no x are y'. or, no y' are x. i.e. no houses, built of brick, are other than two-storied. or, no houses, that are not two-storied, are built of brick. . all x' are y'. i.e. all houses, that are not built of brick, are not two-storied. . some x are y, and some are y'. i.e. some fat boys are active, and some are not. . all y' are x'. i.e. all lazy boys are thin. . all x are y', and all y' are x. i.e. all fat boys are lazy, and all lazy ones are fat. . all y are x, and all x' are y. i.e. all active boys are fat, and all thin ones are lazy. . no x exist, and no y' exist. i.e. no cats have green eyes, and none have bad tempers. . some x are y', and some x' are y. or some y are x', and some y' are x. i.e. some green-eyed cats are bad-tempered, and some, that have not green eyes, are good-tempered. or, some good-tempered cats have not green eyes, and some bad-tempered ones have green eyes. . some x are y, and no x' are y'. or, some y are x, and no y' are x'. i.e. some green-eyed cats are good-tempered, and none, that are not green-eyed, are bad-tempered. or, some good-tempered cats have green eyes, and none, that are bad-tempered, have not green eyes. . all x are y', and all x' are y. or, all y are x', and all y' are x. i.e. all green-eyed cats are bad-tempered and all, that have not green eyes, are good-tempered. or, all good-tempered ones have eyes that are not green, and all bad-tempered ones have green eyes. . larger diagram. propositions represented. __________ --------------- --------------- | | | | | | | ---|--- | | ---|--- | | | | | | | | | | | . |---|---|---|---| . |- -|---|---|---| | | | | | | | | | | | ---|--- | | ---|--- | | | | | | | --------------- --------------- --------------- --------------- | | | | | | | ---|--- | | ---|--- | | | | | | | | | | | . |---|---|---|---| . |---|---|---|---| | | - | | | | | | | | ---|--- | | ---|--- | | | | | | | --------------- --------------- --------------- --------------- | | | | | | | ---|--- | | ---|--- | | | | | | | | | | | . |---|---|---|---| . |---|---|---|---| | | | | | | | | | | | ---|--- | | ---|--- | | | | | | | --------------- --------------- --------------- --------------- | | | | | | | ---|--- | | ---|--- | | | | | | | | | | | . |---|---|---|---| . |---|---|---|---| | | | | | | | | | | | ---|--- | | ---|--- | | | | | | | --------------- --------------- --------------- | | | | ---|--- | | | | | | . no x are m. i.e. |---|---|---|---| | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . some m' are y. i.e. |- -|---|---|---| | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all y' are m'. i.e. |---|---|---|- -| | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all m are x'. i.e. |---|---|---|---| | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . no x are m; i.e. |---|---|---|---| all y are m. | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all m' are y; i.e. |---|---|---|---| no x are m'. | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all x are m; i.e. |---|---|---|---| no m are y'. | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all m' are y'; i.e. |---|---|---|---| no x are m'. | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all x are m; i.e. |---|---|---|---| all m are y. | | | | | | ---|--- | [see remarks on no. , p. .] | | | --------------- --------------- | | | | ---|--- | | | | | | . no x' are m; i.e. |---|---|---|---| no m' are y. | | | | | | ---|--- | | | | --------------- --------------- | | | | ---|--- | | | | | | . all m are x; i.e. |---|---|---|---| all m are y. | | | | | | ---|--- | | | | --------------- . we had better take "persons" as universe. we may choose "myself" as 'middle term', in which case the premisses will take the form i am a-person-who-sent-him-to-bring-a-kitten; i am a-person-to-whom-he-brought-a-kettle-by-mistake. or we may choose "he" as 'middle term', in which case the premisses will take the form he is a-person-whom-i-sent-to-bring-me-a-kitten; he is a-person-who-brought-me-a-kettle-by-mistake. the latter form seems best, as the interest of the anecdote clearly depends on his stupidity--not on what happened to me. let us then make m = "he"; x = "persons whom i sent, &c."; and y = "persons who brought, &c." hence, all m are x; all m are y. and the required diagram is --------------- | | | | ---|--- | | | | | | |---|---|---|---| | | | | | | ---|--- | | | | --------------- . both diagrams employed. ------- | | | . |---|---| i.e. all y are x'. | | | ------- ------- | | | . |---|---| i.e. some x are y'; or, some y' are x. | | | ------- ------- | | | . |---|---| i.e. some y are x'; or, some x' are y. | | | ------- ------- | | | . |---|---| i.e. no x' are y'; or, no y' are x'. | | | ------- ------- | | | . |---|---| i.e. all y are x'. i.e. all black rabbits | | | are young. ------- ------- | | | . |---|---| i.e. some y are x'. i.e. some black | | | rabbits are young. ------- ------- | | | . |---|---| i.e. all x are y. i.e. all well-fed birds | | | are happy. ------- ------- | | | i.e. some x' are y'. i.e. some birds, . |---|---| that are not well-fed, are unhappy; | | | or, some unhappy birds are not ------- well-fed. ------- | | | . |---|---| i.e. all x are y. i.e. john has got a | | | tooth-ache. ------- ------- | | | . |---|---| i.e. no x' are y. i.e. no one, but john, | | | has got a tooth-ache. ------- ------- | | | . |---|---| i.e. some x are y. i.e. some one, who | | | has taken a walk, feels better. ------- ------- | | | i.e. some x are y. i.e. some one, . |---|---| whom i sent to bring me a kitten, | | | brought me a kettle by mistake. ------- --------------- | | | | ---|--- | | | | | | . |- -|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "books" be universe; m="exciting", x="that suit feverish patients"; y="that make one drowsy". no m are x; &there no y' are x. all m' are y. i.e. no books suit feverish patients, except such as make one drowsy. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="that deserve the fair"; x="that get their deserts"; y="brave". some m are x; &there some y are x. no y' are m. i.e. some brave persons get their deserts. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="patient"; x="children"; y="that can sit still". no x are m; &there no x are y. no m' are y. i.e. no children can sit still. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "things" be universe; m="fat"; x="pigs"; y="skeletons". all x are m; &there all x are y'. no y are m. i.e. all pigs are not-skeletons. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "creatures" be universe; m="monkeys"; x="soldiers"; y="mischievous". no m are x; &there some y are x'. all m are y. i.e. some mischievous creatures are not soldiers. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="just"; x="my cousins"; y="judges". no x are m; &there no x are y. no y are m'. i.e. none of my cousins are judges. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "periods" be universe; m="days"; x="rainy"; y="tiresome". some m are x; &there some x are y. all xm are y. i.e. some rainy periods are tiresome. n.b. these are not legitimate premisses, since the conclusion is really part of the second premiss, so that the first premiss is superfluous. this may be shown, in letters, thus:-- "all xm are y" contains "some xm are y", which contains "some x are y". or, in words, "all rainy days are tiresome" contains "some rainy days are tiresome", which contains "some rainy periods are tiresome". moreover, the first premiss, besides being superfluous, is actually contained in the second; since it is equivalent to "some rainy days exist", which, as we know, is implied in the proposition "all rainy days are tiresome". altogether, a most unsatisfactory pair of premisses! --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "things" be universe; m="medicine"; x="nasty"; y="senna". all m are x; &there all y are x. all y are m. i.e. senna is nasty. [see remarks on no. , p .] --------------- | | | | ---|--- | | | | | | . |- -|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="jews"; x="rich"; y="patagonians". some m are x; &there some x are y'. all y are m'. i.e. some rich persons are not patagonians. --------------- | | | | ---|--- | | | - | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "creatures" be universe; m="teetotalers"; x="that like sugar"; y="nightingales". all m are x; &there no y are x'. no y are m'. i.e. no nightingales dislike sugar. --------------- | | | | ---|--- | | | | | | . |- -|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "food" be universe; m="wholesome"; x="muffins"; y="buns". no x are m; all y are m. there is 'no information' for the smaller diagram; so no conclusion can be drawn. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "creatures" be universe; m="that run well"; x="fat"; y="greyhounds". no x are m; &there some y are x'. some y are m. i.e. some greyhounds are not fat. --------------- | | | | ---|--- | | | - | | . |- -|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="soldiers"; x="that march"; y="youths". all m are x; some y are m'. there is 'no information' for the smaller diagram; so no conclusion can be drawn. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "food" be universe; m="sweet"; x="sugar"; y="salt". all x are m; &there all x are y'. all y are m'. all y are x'. i.e. sugar is not salt. salt is not sugar. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "things" be universe; m="eggs"; x="hard-boiled"; y="crackable". some m are x; &there some x are y. no m are y'. i.e. some hard-boiled things can be cracked. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="jews"; x="that are in the house"; y="that are in the garden". no m are x; &there no x are y. no m' are y. i.e. no persons, that are in the house, are also in the garden. --------------- | | | | ---|--- | | | - | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "things" be universe; m="noisy"; x="battles"; y="that may escape notice". all x are m; &there some x' are y. all m' are y. i.e. some things, that are not battles, may escape notice. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "persons" be universe; m="jews"; x="mad"; y="rabbis". no m are x; &there all y are x'. all y are m. i.e. all rabbis are sane. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "things" be universe; m="fish"; x="that can swim"; y="skates". no m are x'; &there some y are x. some y are m. i.e. some skates can swim. --------------- | | | | ---|--- | | | | | | . |---|---|---|---| ------- | | | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- let "people" be universe; m="passionate"; x="reasonable"; y="orators". all m are x'; &there some y are x'. some y are m. i.e. some orators are unreasonable. [see remarks on no. , p. .] chapter iv. hit or miss. "thou canst not hit it, hit it, hit it, thou canst not hit it, my good man." __________ . pain is wearisome; no pain is eagerly wished for. . no bald person needs a hair-brush; no lizards have hair. . all thoughtless people do mischief; no thoughtful person forgets a promise. . i do not like john; some of my friends like john. . no potatoes are pine-apples; all pine-apples are nice. . no pins are ambitious; no needles are pins. . all my friends have colds; no one can sing who has a cold. . all these dishes are well-cooked; some dishes are unwholesome if not well-cooked. . no medicine is nice; senna is a medicine. . some oysters are silent; no silent creatures are amusing. . all wise men walk on their feet; all unwise men walk on their hands. . "mind your own business; this quarrel is no business of yours." . no bridges are made of sugar; some bridges are picturesque. . no riddles interest me that can be solved; all these riddles are insoluble. . john is industrious; all industrious people are happy. . no frogs write books; some people use ink in writing books. . no pokers are soft; all pillows are soft. . no antelope is ungraceful; graceful animals delight the eye. . some uncles are ungenerous; all merchants are generous. . no unhappy people chuckle; no happy people groan. . audible music causes vibration in the air; inaudible music is not worth paying for. . he gave me five pounds; i was delighted. . no old jews are fat millers; all my friends are old millers. . flour is good for food; oatmeal is a kind of flour. . some dreams are terrible; no lambs are terrible. . no rich man begs in the street; all who are not rich should keep accounts. . no thieves are honest; some dishonest people are found out. . all wasps are unfriendly; all puppies are friendly. . all improbable stories are doubted; none of these stories are probable. . "he told me you had gone away." "he never says one word of truth." . his songs never last an hour; a song, that lasts an hour, is tedious. . no bride-cakes are wholesome; unwholesome food should be avoided. . no old misers are cheerful; some old misers are thin. . all ducks waddle; nothing that waddles is graceful. . no professors are ignorant; some ignorant people are conceited. . toothache is never pleasant; warmth is never unpleasant. . bores are terrible; you are a bore. . some mountains are insurmountable; all stiles can be surmounted. . no frenchmen like plumpudding; all englishmen like plumpudding. . no idlers win fame; some painters are not idle. . no lobsters are unreasonable; no reasonable creatures expect impossibilities. . no kind deed is unlawful; what is lawful may be done without fear. . no fossils can be crossed in love; any oyster may be crossed in love. . "this is beyond endurance!" "well, nothing beyond endurance has ever happened to me." . all uneducated men are shallow; all these students are educated. . all my cousins are unjust; no judges are unjust. . no country, that has been explored, is infested by dragons; unexplored countries are fascinating. . no misers are generous; some old men are not generous. . a prudent man shuns hyaenas; no banker is imprudent. . some poetry is original; no original work is producible at will. . no misers are unselfish; none but misers save egg-shells. . all pale people are phlegmatic; no one, who is not pale, looks poetical. . all spiders spin webs; some creatures, that do not spin webs, are savage. . none of my cousins are just; all judges are just. . john is industrious; no industrious people are unhappy. . umbrellas are useful on a journey; what is useless on a journey should be left behind. . some pillows are soft; no pokers are soft. . i am old and lame; no old merchant is a lame gambler. . no eventful journey is ever forgotten; uneventful journeys are not worth writing a book about. . sugar is sweet; some sweet things are liked by children. . richard is out of temper; no one but richard can ride that horse. . all jokes are meant to amuse; no act of parliament is a joke. . "i saw it in a newspaper." "all newspapers tell lies." . no nightmare is pleasant; unpleasant experiences are not anxiously desired. . prudent travellers carry plenty of small change; imprudent travellers lose their luggage. . all wasps are unfriendly; no puppies are unfriendly. . he called here yesterday; he is no friend of mine. . no quadrupeds can whistle; some cats are quadrupeds. . no cooked meat is sold by butchers; no uncooked meat is served at dinner. . gold is heavy; nothing but gold will silence him. . some pigs are wild; there are no pigs that are not fat. . no emperors are dentists; all dentists are dreaded by children. . all, who are not old, like walking; neither you nor i are old. . all blades are sharp; some grasses are blades. . no dictatorial person is popular; she is dictatorial. . some sweet things are unwholesome; no muffins are sweet. . no military men write poetry; no generals are civilians. . bores are dreaded; a bore is never begged to prolong his visit. . all owls are satisfactory; some excuses are unsatisfactory. . all my cousins are unjust; all judges are just. . some buns are rich; all buns are nice. . no medicine is nice; no pills are unmedicinal. . some lessons are difficult; what is difficult needs attention. . no unexpected pleasure annoys me; your visit is an unexpected pleasure. . caterpillars are not eloquent; jones is eloquent. . some bald people wear wigs; all your children have hair. . all wasps are unfriendly; unfriendly creatures are always unwelcome. . no bankrupts are rich; some merchants are not bankrupts. . weasels sometimes sleep; all animals sometimes sleep. . ill-managed concerns are unprofitable; railways are never ill-managed. . everybody has seen a pig; nobody admires a pig. ______________ extract a pair of premisses out of each of the following: and deduce the conclusion, if there is one:-- . "the lion, as any one can tell you who has been chased by them as often as i have, is a very savage animal: and there are certain individuals among them, though i will not guarantee it as a general law, who do not drink coffee." . "it was most absurd of you to offer it! you might have known, if you had had any sense, that no old sailors ever like gruel!" "but i thought, as he was an uncle of yours--" "an uncle of mine, indeed! stuff!" "you may call it stuff, if you like. all i know is, my uncles are all old men: and they like gruel like anything!" "well, then your uncles are--" . "do come away! i can't stand this squeezing any more. no crowded shops are comfortable, you know very well." "well, who expects to be comfortable, out shopping?" "why, i do, of course! and i'm sure there are some shops, further down the street, that are not crowded. so--" . "they say no doctors are metaphysical organists: and that lets me into a little fact about you, you know." "why, how do you make that out? you never heard me play the organ." "no, doctor, but i've heard you talk about browning's poetry: and that showed me that you're metaphysical, at any rate. so--" ___________________ extract a syllogism out of each of the following: and test its correctness:-- . "don't talk to me! i've known more rich merchants than you have: and i can tell you not one of them was ever an old miser since the world began!" "and what has that got to do with old mr. brown?" "why, isn't he very rich?" "yes, of course he is. and what then?" "why, don't you see that it's absurd to call him a miserly merchant? either he's not a merchant, or he's not a miser!" . "it is so kind of you to enquire! i'm really feeling a great deal better to-day." "and is it nature, or art, that is to have the credit of this happy change?" "art, i think. the doctor has given me some of that patent medicine of his." "well, i'll never call him a humbug again. there's somebody, at any rate, that feels better after taking his medicine!" . "no, i don't like you one bit. and i'll go and play with my doll. dolls are never unkind." "so you like a doll better than a cousin? oh you little silly!" "of course i do! cousins are never kind--at least no cousins i've ever seen." "well, and what does that prove, i'd like to know! if you mean that cousins aren't dolls, who ever said they were?" . "what are you talking about geraniums for? you can't tell one flower from another, at this distance! i grant you they're all red flowers: it doesn't need a telescope to know that." "well, some geraniums are red, aren't they?" "i don't deny it. and what then? i suppose you'll be telling me some of those flowers are geraniums!" "of course that's what i should tell you, if you'd the sense to follow an argument! but what's the good of proving anything to you, i should like to know?" . "boys, you've passed a fairly good examination, all things considered. now let me give you a word of advice before i go. remember that all, who are really anxious to learn, work hard." "i thank you, sir, in the name of my scholars! and proud am i to think there are some of them, at least, that are really anxious to learn." "very glad to hear it: and how do you make it out to be so?" "why, sir, i know how hard they work--some of them, that is. who should know better?" ___________________ extract from the following speech a series of syllogisms, or arguments having the form of syllogisms: and test their correctness. it is supposed to be spoken by a fond mother, in answer to a friend's cautious suggestion that she is perhaps a little overdoing it, in the way of lessons, with her children. . "well, they've got their own way to make in the world. we can't leave them a fortune apiece. and money's not to be had, as you know, without money's worth: they must work if they want to live. and how are they to work, if they don't know anything? take my word for it, there's no place for ignorance in these times! and all authorities agree that the time to learn is when you're young. one's got no memory afterwards, worth speaking of. a child will learn more in an hour than a grown man in five. so those, that have to learn, must learn when they're young, if ever they're to learn at all. of course that doesn't do unless children are healthy: i quite allow that. well, the doctor tells me no children are healthy unless they've got a good colour in their cheeks. and only just look at my darlings! why, their cheeks bloom like peonies! well, now, they tell me that, to keep children in health, you should never give them more than six hours altogether at lessons in the day, and at least two half-holidays in the week. and that's exactly our plan i can assure you! we never go beyond six hours, and every wednesday and saturday, as ever is, not one syllable of lessons do they do after their one o'clock dinner! so how you can imagine i'm running any risk in the education of my precious pets is more than i can understand, i promise you!" the end. [transcriber's note: in this plain-text rendering, .'. means therefore [alpha], [beta], ..., [alpha], [beta], ... for greek symbols] deductive logic by st. george stock, m.a. pembroke college, oxford preface. one critic, who was kind enough to look at this book in manuscript, recommended me to abandon the design of publishing it, on the ground that my logic was too like all other logics; another suggested to me to cut out a considerable amount of new matter. the latter advice i have followed; the former has encouraged me to hope that i shall not be considered guilty of wanton innovation. the few novelties which i have ventured to retain will, i trust, be regarded as legitimate extensions of received lines of teaching. my object has been to produce a work which should be as thoroughly representative of the present state of the logic of the oxford schools as any of the text-books of the past. the qualities which i have aimed at before all others have been clearness and consistency. for the task which i have taken upon myself i may claim one qualification--that of experience; since more than seventeen years have now elapsed since i took my first pupil in logic for the honour school of moderations, and during that time i have been pretty continuously engaged in studying and teaching the subject. in acknowledging my obligations to previous writers i must begin with archbishop whately, whose writings first gave me an interest in the subject. the works of mill and hamilton have of course been freely drawn upon. i have not followed either of those two great writers exclusively, but have endeavoured to assimilate what seemed best in both. to professor fowler i am under a special debt. i had not the privilege of personal teaching from him in logic,--as i had in some other subjects; but his book fell into my hands at an early period in my mental training, and was so thoroughly studied as to have become a permanent part of the furniture of my mind. much the same may be said of my relation to the late professor jevons's elementary lessons in logic. two other books, which i feel bound to mention with special emphasis, are hansel's edition of aldrich and mccosh's laws of discursive thought. if there be added to the foregoing watts's logic, thomson's outlines of the laws of thought, bain's deductive logic, jevons's studies in deductive logic and principles of science, bradley's principles of logic, abbott's elements of logic, walker's edition of murray, ray's text-book of deductive logic, and weatherley's rudiments of logic, i think the list will be exhausted of modern works from which i am conscious of having borrowed. but, not to forget the sun, while thanking the manufacturers of lamps and candles, i should add that i have studied the works of aristotle according to the measure of my time and ability. this work has had the great advantage of having been revised, while still in manuscript, by mr. alfred robinson, fellow of new college, to whom i cannot sufficiently express my obligation. i have availed myself to the full of the series of criticisms which he was kind enough to send me. as some additions have been made since then, he cannot be held in anyway responsible for the faults which less kindly critics may detect. for the examples at the end i am mainly indebted to others, and to a large extent to my ingenious friend, the rev. w. j. priest of merton college. my thanks are due also to my friend and former pupil, mr. gilbert grindle, scholar of corpus, who has been at the pains to compose an index, and to revise the proofs as they passed through the press. and last, but not least, i must set on record my gratitude to commander r. a. stock, r.n., one of her majesty's knights of windsor, without whose brotherly aid this work might never have been written, and would certainly not have assumed exactly its present shape. oxford, _october_ , . contents. preface. introduction, §§ - . part i. of terms, §§ - . chap. i. of the term as distinguished from other words, §§ - . ii. of the division of things, §§ - . iii. of the divisions of terms, §§ - . iv. of the law of inverse variation of extension and intension, §§ - . part ii. of propositions, §§ - . chap. i. of the proposition as distinguished from other sentences, §§ - . ii. of the copula, §§ - . iii. of the divisions of propositions, §§ - . iv. of the distribution of terms, §§ - . v. of the quantification of the predicate, §§ - . vi. of the heads of predicables, §§ - . vii. of definition, §§ - . viii. of division, §§ - . part iii. of inferences, §§ - . chap. i. of inferences in general, §§ - . ii. of deductive inferences, §§ - . iii. of opposition, §§ - . iv. of conversion, §§ - . v. of permutation, §§ - . vi. of compound forms of immediate inference, §§ - . vii. of other forms of immediate inference, §§ - . viii. of mediate inferences or syllogisms, §§ - . ix. of mood and figure, §§ - . x. of the canon of reasoning, §§ - . xi. of the general rules of syllogism, §§ - . xii. of the determination of the legitimate moods of syllogism, §§ - . xiii. of the special rules of the four figures, §§ - . xiv. of the determination of the moods that are valid in the four figures, §§ - . xv. of the special canons of the four figures, §§ - . xvi. of the special uses of the four figures, §§ - . xvii. of the syllogism with three figures, §§ - . xviii. of reduction, §§ - . xix. of immediate inference as applied to complex propositions, §§ - . xx. of complex syllogisms, §§ - . xxi. of the reduction of the partly conjunctive syllogism, §§ - . xxii. of the partly conjunctive syllogism regarded as all immediate inference, §§ - . xxiii. of the disjunctive syllogism, §§ - . xxiv. of the reduction of the disjunctive syllogism, §§ - . xxv. of the disjunctive syllogism regarded as an immediate inference, §§ - . xxvi. of the mixed form of complex syllogism, §§ - . xxvii. of the reduction of the dilemma, §§ - . xxviii. of the dilemma regarded as an immediate inference, §§ , . xxix. of trains of reasoning, §§ - . xxx. of fallacies, §§ - . exercises. index. introduction. § . logic is divided into two branches, namely-- ( ) inductive, ( ) deductive. § . the problem of inductive logic is to determine the actual truth or falsity of propositions: the problem of deductive logic is to determine their relative truth or falsity, that is to say, given such and such propositions as true, what others will follow from them. § . hence in the natural order of treatment inductive logic precedes deductive, since it is induction which supplies us with the general truths, from which we reason down in our deductive inferences. § . it is not, however, with logic as a whole that we are here concerned, but only with deductive logic, which may be defined as the science of the formal laws of thought. § . in order fully to understand this definition we must know exactly what is meant by 'thought,' by a 'law of thought,' by the term 'formal,' and by 'science.' § . thought, as here used, is confined to the faculty of comparison. all thought involves comparison, that is to say, a recognition of likeness or unlikeness. § . the laws of thought are the conditions of correct thinking. the term 'law,' however, is so ambiguous that it will be well to determine more precisely in what sense it is here used. § . we talk of the 'laws of the land' and of the 'laws of nature,' and it is evident that we mean very different things by these expressions. by a law in the political sense is meant a command imposed by a superior upon an inferior and sanctioned by a penalty for disobedience. but by the 'laws of nature' are meant merely certain uniformities among natural phenomena; for instance, the 'law of gravitation' means that every particle of matter does invariably attract every other particle of matter in the universe. § . the word 'law' is transferred by a metaphor from one of these senses to the other. the effect of such a command as that described above is to produce a certain amount of uniformity in the conduct of men, and so, where we observe uniformity in nature, we assume that it is the result of such a command, whereas the only thing really known to us is the fact of uniformity itself. § . now in which of these two senses are we using the term 'laws of thought'? the laws of the land, it is plain, are often violated, whereas the laws of nature never can be so [footnote: there is a sense in which people frequently speak of the laws of nature being violated, as when one says that intemperance or celibacy is a violation of the laws of nature, but here by 'nature' is meant an ideal perfection in the conditions of existence.]. can the laws of thought be violated in like manner with the laws of the land? or are they inviolable like the laws of nature? § . in appearance they can be, and manifestly often are violated-for how else could error be possible? but in reality they can not. no man ever accepts a contradiction when it presents itself to the mind as such: but when reasoning is at all complicated what does really involve a contradiction is not seen to do so; and this sort of error is further assisted by the infinite perplexities of language. § . the laws of thought then in their ultimate expression are certain uniformities which invariably hold among mental phenomena, and so far they resemble the laws of nature: but in their complex applications they may be violated owing to error, as the laws of the land may be violated by crime. § . we have now to determine the meaning of the expression 'formal laws of thought.' § . the distinction between form and matter is one which pervades all nature. we are familiar with it in the case of concrete things. a cup, for instance, with precisely the same form, may be composed of very different matter-gold, silver, pewter, horn or what not? § . similarly in every act of thought we may distinguish two things-- ( ) the object thought about, ( ) the way in which the mind thinks of it. the first is called the matter; the second the form of thought. § . now formal, which is another name for deductive logic, is concerned only with the way in which the mind thinks, and has nothing to do with the particular objects thought about. § . since the form may be the same, whilst the matter is different, we may say that formal logic is concerned with the essential and necessary elements of thought as opposed to such as are accidental and contingent. by 'contingent' is meant what holds true in some cases, but not in others. for instance, in the particular case of equilateral triangles it is true to say, not only that 'all equilateral triangles are equiangular,' but also that 'all equiangular triangles are equilateral.' but the evidence for these two propositions is independent. the one is not a formal consequence of the other. if it were, we should be able to apply the same inference to all matter, and assert generally that if all a is b, all b is a, which it is notorious that we cannot do. § . it remains now for the full elucidation of our definition to determine what is meant by 'science.' § . the question has often been discussed whether logic is a science or an art. the answer to it must depend upon the meaning we assign to these terms. § . broadly speaking, there is the same difference between science and art as there is between knowing and doing. science is systematized knowledge; art is systematized action. science is acquired by study; art is acquired by practice. § . now logic is manifestly a branch of knowledge, and does not necessarily confer any practical skill. it is only the right use of its rules in thinking which can make men think better. it is therefore, in the broad sense of the terms, wholly a science and not at all an art. § . but this word 'art,' like most others, is ambiguous, and is often used, not for skill displayed in practice, but for the knowledge necessary thereto. this meaning is better conveyed by the term 'practical science.' § . science is either speculative or practical. in the first case we study merely that we may know; in the latter that we may do. anatomy is a speculative science; surgery is a practical science. in the first case we study the human frame in order that we may understand its structure; in the second that we may assist its needs. whether logic is a speculative or a practical science depends entirely upon the way in which it is treated. if we study the laws of thought merely that we may know what they are, we are making it a speculative science; if we study the same laws with a view to deducing rules for the guidance of thought, we are making it a practical science. § . hence logic may be declared to be both the science and the art of thinking. it is the art of thinking in the same sense in which grammar is the art of speaking. grammar is not in itself the right use of words, but a knowledge of it enables men to use words correctly. in the same way a knowledge of logic enables men to think correctly, or at least to avoid incorrect thoughts. as an art logic may be called the navigation of the sea of thought. § . the laws of thought are all reducible to the three following axioms, which are known as the three fundamental laws of thought. ( ) the law of identity-- whatever is, is; or, in a more precise form, every a is a. ( ) the law of contradiction-- nothing can both be and not be; nothing can be a and not a. ( ) the law of excluded middle-- everything must either be or not be; everything is either a or not a. § . each of these principles is independent and self-evident. § . if it were possible for the law of identity to be violated, no violation of the law of contradiction would necessarily ensue: for a thing might then be something else, without being itself at the same time, which latter is what the law of contradiction militates against. neither would the law of excluded middle be infringed. for, on the supposition, a thing would be something else, whereas all that the law of excluded middle demands is that it should either be itself or not. a would in this case adopt the alternative of being not a. § . again, the violation of the law of contradiction does not involve any violation of the law of identity: for a thing might in that case be still itself, so that the law of identity would be observed, even though, owing to the law of contradiction not holding, it were not itself at the same time. neither would the law of excluded middle be infringed. for a thing would, on the supposition, be both itself and not itself, which is the very reverse of being neither. § . lastly, the law of excluded middle might be violated without a violation of the law of contradiction: for we should then have a thing which was neither a nor not a, but not a thing which was both at the same time. neither would the law of identity be infringed. for we should in this case have a thing which neither was nor was not, so that the conditions of the law of identity could not exist to be broken. that law postulates that whatever is, is: here we have a thing which never was to begin with. § . these principles are of so simple a character that the discussion of them is apt to be regarded as puerile. especially is this the case with regard to the law of identity. this principle in fact is one of those things which are more honoured in the breach than in the observance. suppose for a moment that this law did not hold--then what would become of all our reasoning? where would be the use of establishing conclusions about things, if they were liable to evade us by a protean change of identity? § . the remaining two laws supplement each other in the following way. the law of contradiction enables us to affirm of two exhaustive and mutually exclusive alternatives, that it is impossible for both to be true; the law of excluded middle entitles us to add, that it is equally impossible for both to be false. or, to put the same thing in a different form, the law of contradiction lays down that one of two such alternatives must be false; the law of excluded middle adds that one must be true. § . there are three processes of thought ( ) conception. ( ) judgement. ( ) inference or reasoning. § . conception, which is otherwise known as simple apprehension, is the act of forming in the mind the idea of anything, e.g. when we form in the mind the idea of a cup, we are performing the process of conception. § . judgement, in the sense in which it is here used [footnote: sometimes the term 'judgement' is extended to the comparison of nameless sense-impressions, which underlies the formation of concepts. but this amounts to identifying judgement with thought in general.] may be resolved into putting two ideas together in the mind, and pronouncing as to their agreement or disagreement, e.g. we have in our minds the idea of a cup and the idea of a thing made of porcelain, and we combine them in the judgement--'this cup is made of porcelain.' § . inference, or reasoning, is the passage of the mind from one or more judgements to another, e.g. from the two judgements 'whatever is made of porcelain is brittle,' and 'this cup is made of porcelain,' we elicit a third judgement, 'this cup is brittle.' § . corresponding to these three processes there are three products of thought, viz. ( ) the concept. ( ) the judgement. ( ) the inference. § . since our language has a tendency to confuse the distinction between processes and products, [footnote: e.g. we have to speak quite indiscriminately of sensation, imagination, reflexion, sight, thought, division, definition, and so on, whether we mean in any case a process or a product.] it is the more necessary to keep them distinct in thought. strictly we ought to speak of conceiving, judging and inferring on the one hand, and, on the other, of the concept, the judgement and the inference. the direct object of logic is the study of the products rather than of the processes of thought. but, at the same time, in studying the products we are studying the processes in the only way in which it is possible to do so. for the human mind cannot be both actor and spectator at once; we must wait until a thought is formed in our minds before we can examine it. thought must be already dead in order to be dissected: there is no vivisection of consciousness. thus we can never know more of the processes of thought than what is revealed to us in their products. § . when the three products of thought are expressed in language, they are called respectively ( ) the term. ( ) the proposition. ( ) the inference. § . such is the ambiguity of language that we have already used the term 'inference' in three different senses--first, for the act or process of inferring; secondly, for the result of that act as it exists in the mind; and, thirdly, for the same thing as expressed in language. later on we shall have to notice a further ambiguity in its use. § . it has been declared that thought in general is the faculty of comparison, and we have now seen that there are three products of thought. it follows that each of these products of thought must be the result of a comparison of some kind or other. the concept is the result of comparing attributes. the judgement is the result of comparing concepts. the inference is the result of comparing judgements. § . in what follows we shall, for convenience, adopt the phraseology which regards the products of thought as clothed in language in preference to that which regards the same products as they exist in the mind of the individual. for although the object of logic is to examine thought pure and simple, it is obviously impossible to discuss it except as clothed in language. accordingly the three statements above made may be expressed as follows-- the term is the result of comparing attributes. the proposition is the result of comparing terms. the inference is the result of comparing propositions. § . there is an advantage attending the change of language in the fact that the word 'concept' is not an adequate expression for the first of the three products of thought, whereas the word 'term' is. by a concept is meant a general notion, or the idea of a class, which corresponds only to a common term. now not only are common terms the results of comparison, but singular terms, or the names of individuals, are so too. § . the earliest result of thought is the recognition of an individual object as such, that is to say as distinguished and marked off from the mass of its surroundings. no doubt the first impression produced upon the nascent intelligence of an infant is that of a confused whole. it requires much exercise of thought to distinguish this whole into its parts. the completeness of the recognition of an individual object is announced by attaching a name to it. hence even an individual name, or singular term, implies thought or comparison. before the _child_ can attach a meaning to the word '_mother_,' which to it is a singular term, it must have distinguished between the set of impressions produced in it by one object from those which are produced in it by others. thus, when vergil says incipe, parve puer, risu cognoscere matrem, he is exhorting the beatific infant to the exercise of the faculty of comparison. § . that a common term implies comparison does not need to be insisted upon. it is because things resemble each other in certain of their attributes that we call them by a common name, and this resemblance could not be ascertained except by comparison, at some time and by some one. thus a common term, or concept, is the compressed result of an indefinite number of comparisons, which lie wrapped up in it like so many fossils, witnessing to prior ages of thought. § . in the next product of thought, namely, the proposition, we have the result of a single act of comparison between two terms; and this is why the proposition is called the unit of thought, as being the simplest and most direct result of comparison. § . in the third product of thought, namely, the inference, we have a comparison of propositions either directly or by means of a third. this will be explained later on. for the present we return to the first product of thought. § . the nature of singular terms has not given rise to much dispute; but the nature of common terms has been the great battle-ground of logicians. what corresponds to a singular term is easy to determine, for the thing of which it is a name is there to point to: but the meaning of a common term, like 'man' or 'horse,' is not so obvious as people are apt to think on first hearing of the question. § . a common term or class-name was known to mediæval logicians under the title of a universal; and it was on the question 'what is a universal ' that they split into the three schools of realists, nominalists, and conceptualists. here are the answers of the three schools to this question in their most exaggerated form-- § . universals, said the realists, are substances having an independent existence in nature. § . universals, said the nominalists, are a mere matter of words, the members of what we call a class having nothing in common but the name. § . universals, said the conceptualists, exist in the mind alone, they are the conceptions under which the mind regards external objects. § . the origin of pure realism is due to plato and his doctrine of 'ideas'; for idealism, in this sense, is not opposed to realism, but identical with it. plato seems to have imagined that, as there was a really existing thing corresponding to a singular term, such as socrates, so there must be a really existing thing corresponding to the common term 'man.' but when once the existence of these general objects is admitted, they swamp all other existences. for individual men are fleeting and transitory--subject to growth, decay and death--whereas the idea of man is imperishable and eternal. it is only by partaking in the nature of these ideas that individual objects exist at all. § . pure nominalism was the swing of the pendulum of thought to the very opposite extreme; while conceptualism was an attempt to hit the happy mean between the two. § . roughly it may be said that the realists sought for the answer to the question 'what is a universal?' in the matter of thought, the conceptualists in the form, and the nominalists in the expression. § . a full answer to the question 'what is a universal?' will bring in something of the three views above given, while avoiding the exaggeration of each. a universal is a number of things that are called by the same name; but they would not be called by the same name unless they fell under the same conception in the mind; nor would they fall under the same conception in the mind unless there actually existed similar attributes in the several members of a class, causing us to regard them under the same conception and to give them the same name. universals therefore do exist in nature, and not merely in the mind of man: but their existence is dependent upon individual objects, instead of individual objects depending for their existence upon them. aristotle saw this very clearly, and marked the distinction between the objects corresponding to the singular and to the common term by calling the former primary and the latter secondary existences. rosinante and excalibur are primary, but 'horse' and 'sword' secondary existences. § . we have seen that the three products of thought are each one stage in advance of the other, the inference being built upon the proposition, as the proposition is built upon the term. logic therefore naturally divides itself into three parts. the first part of logic deals with the term; the second part deals with the proposition; the third part deals with the inference. part i.--of terms. chapter . _of the term as distinguished from other words._ § . the word 'term' means a boundary. § . the subject and predicate are the two terms, or boundaries, of a proposition. in a proposition we start from a subject and end in a predicate (§§ - ), there being nothing intermediate between the two except the act of pronouncing as to their agreement or disagreement, which is registered externally under the sign of the copula. thus the subject is the 'terminus a quo,' and the predicate is the 'terminus ad quem.' § . hence it appears that the term by its very name indicates that it is arrived at by an analysis of the proposition. it is the judgement or proposition that is the true unit of thought and speech. the proposition as a whole is prior in conception to the terms which are its parts: but the parts must come before the whole in the synthetic order of treatment. § . a term is the same thing as a name or noun. § . a name is a word, or collection of words, which serves as a mark to recall or transmit the idea of a thing, either in itself or through some of its attributes. § . nouns, or names, are either substantive or adjective. a noun substantive is the name of a thing in itself, that is to say, without reference to any special attribute. § . a noun adjective is a name which we are entitled to add to a thing, when we know it to possess a given attribute. § . the verb, as such, is not recognised by logic, but is resolved into predicate and copula, that is to say, into a noun which is affirmed or denied of another, plus the sign of that affirmation or denial. 'the kettle boils' is logically equivalent to 'the kettle is boiling,' though it is by no means necessary to express the proposition in the latter shape. here we see that 'boils' is equivalent to the noun 'boiling' together with the copula 'is,' which declares its agreement with the noun 'kettle.' 'boiling' here is a noun adjective, which we are entitled to add to 'kettle,' in virtue of certain knowledge which we have about the latter. being a verbal noun, it is called in grammar a participle, rather than a mere adjective. the word 'attributive' in logic embraces both the adjective and participle of grammar. § . in grammar every noun is a separate word: but to logic, which is concerned with the thought rather than with the expression, it is indifferent whether a noun, or term, consists of one word or many. the latter are known as 'many-worded names.' in the following passage, taken at random from butler's analogy--'these several observations, concerning the active principle of virtue and obedience to god's commands, are applicable to passive submission or resignation to his will'--we find the subject consisting of fourteen words, and the predicate of nine. it is the exception rather than the rule to find a predicate which consists of a single word. many-worded names in english often consist of clauses introduced by the conjunction 'that,' as 'that letters should be written in strict conformity with nature is true': often also of a grammatical subject with one or more dependent clauses attached to it, as 'he who fights and runs away, will live to fight another day.' § . every term then is not a word, since a term may consist of a collection of words. neither is every word a term. 'over,' for instance, and 'swiftly,' and, generally, what are called particles in grammar, do not by themselves constitute terms, though they may be employed along with other words to make up a term. § . the notions with which thought deals involve many subtle relations and require many nice modifications. language has instruments, more or less perfect, whereby such relations and modifications may be expressed. but these subsidiary aids to expression do not form a notion which can either have something asserted of it or be asserted itself of something else. § . hence words are divided into three classes-- ( ) categorematic; ( ) syncategorematic; ( ) acategorematic. § . a categorematic word is one which can be used by itself as a term. § . a syncategorematic word is one which can help to form a term. § . an acategorematic word is one which can neither form, nor help to form, a term [footnote: comparatively few of the parts of speech are categorematic. nouns, whether substantive or adjective, including of course pronouns and participles, are so, but only in their nominative cases, except when an oblique case is so used as to be equivalent to an attributive. verbs also are categorematic, but only in three of their moods, the indicative, the infinitive, and the potential. the imperative and optative moods clearly do not convey assertions at all, while the subjunctive can only figure as a subordinate member of some assertion. we may notice, too, that the relative pronoun, unlike the rest, is necessarily syncategorematic, for the same reason as the subjunctive mood. of the remaining parts of speech the article, adverb, preposition, and conjunction can never be anything but syncategorematic, while the interjection is acategorematic, like the vocative case of nouns and the imperative and optative moods of verbs, which do not enter at all into the form of sentence known as the proposition.]. § . categorematic literally means 'predicable.' 'horse,' 'swift,' 'galloping' are categorematic. thus we can say, 'the horse is swift,' or 'the horse is galloping.' each of these words forms a term by itself, but 'over' and 'swiftly' can only help to form a term, as in the proposition, 'the horse is galloping swiftly over the plain.' § . a term then may be said to be a categorematic word or collection of words, that is to say, one which can be used by itself as a predicate. § . to entitle a word or collection of words to be called a term, it is not necessary that it should be capable of standing by itself as a subject. many terms which can be used as predicates are incapable of being used as subjects: but every term which can be used as a subject (with the doubtful exception of proper names) can be used also as a predicate. the attributives 'swift' and 'galloping' are terms, quite as much as the subject 'horse,' but they cannot themselves be used as subjects. § . when an attributive appears to be used as a subject, it is owing to a grammatical ellipse. thus in latin we say 'boni sapientes sunt,' and in english 'the good are wise,' because it is sufficiently declared by the inflexional form in the one case, and by the usage of the language in the other, that men are signified. it is an accident of language how far adjectives can be used as subjects. they cease to be logical attributives the moment they are so used. § . there is a sense in which every word may become categorematic, namely, when it is used simply as a word, to the neglect of its proper meaning. thus we can say--'"swiftly" is an adverb.' 'swiftly' in this sense is really no more than the proper name for a particular word. this sense is technically known as the 'suppositio materialis' of a word. chapter ii. _of the division of things._ § . before entering on the divisions of terms it is necessary to advert for a moment to a division of the things whereof they are names. § . by a 'thing' is meant simply an object of thought--whatever one can think about. § . things are either substances or attributes. attributes may be sub-divided into qualities and relations. thing _______________|_______________ | | substance attribute _____________|____________ | | quality relation § . a substance is a thing which can be conceived to exist by itself. all bodies are material substances. the soul, as a thinking subject, is an immaterial substance. § . an attribute is a thing which depends for its existence upon a substance, e.g. greenness, hardness, weight, which cannot be conceived to exist apart from green, hard, and heavy substances. § . a quality is an attribute which does not require more than one substance for its existence. the attributes just mentioned are qualities. there might be greenness, hardness, and weight, if there were only one green, hard and heavy substance in the universe. § . a relation is an attribute which requires two or more substances for its existence, e.g. nearness, fatherhood, introduction. § . when we say that a substance can be conceived to exist by itself, what is meant is that it can be conceived to exist independently of other substances. we do not mean that substances can be conceived to exist independently of attributes, nor yet out of relation to a mind perceiving them. substances, so far as we can know them, are only collections of attributes. when therefore we say that substances can be conceived to exist by themselves, whereas attributes are dependent for their existence upon substances, the real meaning of the assertion reduces itself to this, that it is only certain collections of attributes which can be conceived to exist independently; whereas single attributes depend for their existence upon others. the colour, smoothness or solidity of a table cannot be conceived apart from the extension, whereas the whole cluster of attributes which constitutes the table can be conceived to exist altogether independently of other 'such clusters. we can imagine a table to exist, if the whole material universe were annihilated, and but one mind left to perceive it. apart from mind, however, we cannot imagine it: since what we call the attributes of a material substance are no more than the various modes in which we find our minds affected. § . the above division of things belongs rather to the domain of metaphysics than of logic: but it is the indispensable basis of the division of terms, to which we now proceed. chapter iii. _of the division of terms._ § . the following scheme presents to the eye the chief divisions of terms. term division of terms according to their place in thought. subject-term attributive according to the kind of thing signified. abstract concrete according to quantity in extension. singular common according to quality. positive privative negative according to number of meanings. univocal equivocal according to number of things involved in the name. absolute relative according to number of quantities. connotative non-connotative _subject-term and attributive._ § . by a subject-term is meant any term which is capable of standing by itself as a subject, e.g. 'ribbon,' 'horse.' § . attributives can only be used as predicates, not as subjects, e.g. 'cherry-coloured,' 'galloping.' these can only be used in conjunction with other words (syncategorematically) to make up a subject. thus we can say 'a cherry-coloured ribbon is becoming,' or 'a galloping horse is dangerous.' § . attributives are contrivances of language whereby we indicate that a subject has a certain attribute. thus, when we say 'this paper is white,' we indicate that the subject 'paper' possesses the attribute whiteness. logic, however, also recognises as attributives terms which signify the non-possession of attributes. 'not-white' is an attributive equally with 'white.' § . an attributive then may be defined as a term which signifies the possession, or non-possession, of an attribute by a subject. § . it must be carefully noticed that attributives are not names of attributes, but names of the things which possess the attributes, in virtue of our knowledge that they possess them. thus 'white' is the name of all the things which possess the attribute whiteness, and 'virtuous' is a name; not of the abstract quality, virtue, itself, but of the men and actions which possess it. it is clear that a term can only properly be said to be a name of those things whereof it can be predicated. now, we cannot intelligibly predicate an attributive of the abstract quality, or qualities, the possession of which it implies. we cannot, for instance, predicate the term 'learned' of the abstract quality of learning: but we may predicate it of the individuals, varro and vergil. attributives, then, are to be regarded as names, not of the attributes which they imply, but of the things in which those attributes are found. § . attributives, however, are names of things in a less direct way than that in which subject-terms may be the names of the same things. attributives are names of things only in predication, whereas subject-terms are names of things in or out of predication. the terms 'horse' and 'bucephalus' are names of certain things, in this case animals, whether we make any statement about them or not: but the terms 'swift' and 'fiery' only become names of the same things in virtue of being predicable of them. when we say 'horses are swift' or 'bucephalus was fiery,' the terms 'swift' and 'fiery' become names respectively of the same things as 'horse' and 'bucephalus.' this function of attributives as names in a secondary sense is exactly expressed by the grammatical term 'noun adjective.' an attributive is not directly the name of anything. it is a name added on in virtue of the possession by a given thing of a certain attribute, or, in some cases, the non-possession. § . although attributives cannot be used as subjects, there is nothing to prevent a subject-term from being used as a predicate, and so assuming for the time being the functions of an attributive. when we say 'socrates was a man,' we convey to the mind the idea of the same attributes which are implied by the attributive 'human.' but those terms only are called attributives which can never be used except as predicates. § . this division into subject-terms and attributives may be regarded as a division of terms according to their place in thought. attributives, as we have seen, are essentially predicates, and can only be thought of in relation to the subject, whereas the subject is thought of for its own sake. _abstract and concrete terms_. § . an abstract term is the name of an attribute, e.g. whiteness [footnote: since things cannot be spoken of except by their names, there is a constantly recurring source of confusion between the thing itself and the name of it. take for instance 'whiteness.' the attribute whiteness is a thing, the word 'whiteness' is a term.], multiplication, act, purpose, explosion. § . a concrete term is the name of a substance, e.g. a man, this chair, the soul, god. § . abstract terms are so called as being arrived at by a process of abstraction. what is meant by abstraction will be clear from a single instance. the mind, in contemplating a number of substances, may draw off, or abstract, its attention from all their other characteristics, and fix it only on some point, or points, which they have in common. thus, in contemplating a number of three-cornered objects, we may draw away our attention from all their other qualities, and fix it exclusively upon their three-corneredness, thus constituting the abstract notion of 'triangle.' abstraction may be performed equally well in the case of a single object: but the mind would not originally have known on what points to fix its attention except by a comparison of individuals. § . abstraction too may be performed upon attributes as well as substances. thus, having by abstraction already arrived at the notion of triangle, square, and so on, we may fix our attention upon what these have in common, and so rise to the higher abstraction of 'figure.' as thought becomes more complex, we may have abstraction on abstraction and attributes of attributes. but, however many steps may intervene, attributes may always be traced back to substances at last. for attributes of attributes can mean at bottom nothing but the co-existence of attributes in, or in connection with, the same substances. § . we have said that abstract terms are so called, as being arrived at by abstraction: but it must not be inferred from this statement that all terms which are arrived at by abstraction are abstract. if this were so, all names would be abstract except proper names of individual substances. all common terms, including attributives, are arrived at by abstraction, but they are not therefore abstract terms. those terms only are called abstract, which cannot be applied to substances at all. the terms 'man' and 'human' are names of the same substance of which socrates is a name. humanity is a name only of certain attributes of that substance, namely those which are shared by others. all names of concrete things then are concrete, whether they denote them individually or according to classes, and whether directly and in themselves, or indirectly, as possessing some given attribute. § . by a 'concrete thing' is meant an individual substance conceived of with all its attributes about it. the term is not confined to material substances. a spirit conceived of under personal attributes is as concrete as plum-pudding. § . since things are divided exhaustively into substances and attributes, it follows that any term which is not the name of a thing capable of being conceived to exist by itself, must be an abstract term. individual substances can alone be conceived to exist by themselves: all their qualities, actions, passions, and inter-relations, all their states, and all events with regard to them, presuppose the existence of these individual substances. all names therefore of such things as those just enumerated are abstract terms. the term 'action,' for instance, is an abstract term. for how could there be action without an agent? the term 'act' also is equally abstract for the same reason. the difference between 'action' and 'act' is not the difference between abstract and concrete, but the difference between the name of a process and the name of the corresponding product. unless acts can be conceived to exist without agents they are as abstract as the action from which they result. § . since every term must be either abstract or concrete, it may be asked--are attributives abstract or concrete? the answer of course depends upon whether they are names of substances or names of attributes. but attributives, it must be remembered, are never directly names of anything, in the way that subject-terms are; they are only names of things in virtue of being predicated of them. whether an attributive is abstract or concrete, depends on the nature of the subject of which it is asserted or denied. when we say 'this man is noble,' the term 'noble' is concrete, as being the name of a substance: but when we say 'this act is noble,' the term 'noble' is abstract, as being the name of an attribute. § . the division of terms into abstract and concrete is based upon the kind of thing signified. it involves no reference to actual existence. there are imaginary as well as real substances. logically a centaur is as much a substance as a horse. _terms._ § . a singular term is a name which can be applied, in the same sense, to one thing only, e.g. 'john,' 'paris,' 'the capital of france,' 'this pen.' § . a common term is a name which can be applied, in the same sense, to a class of things, e.g. 'man,' 'metropolis,' 'pen.' in order that a term may be applied in the same sense to a number of things, it is evident that it must indicate attributes which are common to all of them. the term 'john' is applicable to a number of things, but not in the same sense, as it does not indicate attributes. § . common terms are formed, as we have seen already (§ ), by abstraction, i. e. by withdrawing the attention from the attributes in which individuals differ, and concentrating it upon those which they have in common. § . a class need not necessarily consist of more than two things. if the sun and moon were the only heavenly bodies in the universe, the word 'heavenly body' would still be a common term, as indicating the attributes which are possessed alike by each. § . this being so, it follows that the division of terms into singular and common is as exhaustive as the preceding ones, since a singular term is the name of one thing and a common term of more than one. it is indifferent whether the thing in question be a substance or an attribute; nor does it matter how complex it may be, so long as it is regarded by the mind as one. § . since every term must thus be either singular or common, the members of the preceding divisions must find their place under one or both heads of this one. subject-terms may plainly fall under either head of singular or common: but attributives are essentially common terms. such names as 'green,' 'gentle,' 'incongruous' are applicable, strictly in the same sense, to all the things which possess the attributes which they imply. § . are abstract terms then, it may be asked, singular or common? to this question we reply--that depends upon how they are used. the term 'virtue,' for instance, in one sense, namely, as signifying moral excellence in general, without distinction of kind, is strictly a singular term, as being the name of one attribute: but as applied to different varieties of moral excellence--justice, generosity, gentleness and so on--it is a common term, as being a name which is applicable, in the same sense, to a class of attributes. similarly the term 'colour,' in a certain sense, signifies one unvarying attribute possessed by bodies, namely, the power of affecting the eye, and in this sense it is a singular term: but as applied to the various ways in which the eye may be affected, it is evidently a common term, being equally applicable to red, blue, green, and every other colour. as soon as we begin to abstract from attributes, the higher notion becomes a common term in reference to the lower. by a 'higher notion' is meant one which is formed by a further process of abstraction. the terms 'red,' 'blue,' 'green,' etc., are arrived at by abstraction from physical objects; 'colour' is arrived at by abstraction from them, and contains nothing, but what is common to all. it therefore applies in the same sense to each, and is a common term in relation to them. § . a practical test as to whether an abstract term, in any given case, is being used as a singular or common term, is to try whether the indefinite article or the sign of the plural can be attached to it. the term 'number,' as the name of a single attribute of things, admits of neither of these adjuncts: but to talk of 'a number' or 'the numbers, two, three, four,' etc., at once marks it as a common term. similarly the term 'unity' denotes a single attribute, admitting of no shades of distinction: but when a writer begins to speak of 'the unities' he is evidently using the word for a class of things of some kind or other, namely, certain dramatical proprieties of composition. proper _names_ and _designations_. § . singular terms may be subdivided into proper names and designations. § . a proper name is a permanent singular term applicable to a thing in itself; a designation is a singular term devised for the occasion, or applicable to a thing only in so far as it possesses some attribute. § . 'homer' is a proper name; 'this man,' 'the author of the iliad' are designations. § . the number of things, it is clear, is infinite. for, granting that the physical universe consists of a definite number of atoms--neither one more nor one less--still we are far from having exhausted the possible number of things. all the manifold material objects, which are made up by the various combinations of these atoms, constitute separate objects of thought, or things, and the mind has further an indefinite power of conjoining and dividing these objects, so as to furnish itself with materials of thought, and also of fixing its attention by abstraction upon attributes, so as to regard them as things, apart from the substances to which they belong. § . this being so, it is only a very small number of things, which are constantly obtruding themselves upon the mind, that have singular terms permanently set apart to denote them. human beings, some domestic animals, and divisions of time and place, have proper names assigned to them in most languages, e.g. 'john,' 'mary,' 'grip,' 'january,' 'easter,' 'belgium,' 'brussels,' 'the thames,' 'ben-nevis.' besides these, all abstract terms, when used without reference to lower notions, are of the nature of proper names, being permanently set apart to denote certain special attributes, e.g. 'benevolence,' 'veracity,' 'imagination,' 'indigestibility, 'retrenchment.' § . but the needs of language often require a singular term to denote some thing which has not had a proper name assigned to it. this is effected by taking a common term, and so limiting it as to make it applicable, under the given circumstances, to one thing only. such a limitation may be effected in english by prefixing a demonstrative or the definite article, or by appending a description, e.g. 'this pen,' 'the sofa,' 'the last rose of summer.' when a proper name is unknown, or for some reason, unavailable, recourse may be had to a designation, e.g. 'the honourable member who spoke last but one.' _collective terms_. § . the division of terms into singular and common being, like those which have preceded it, fundamental and exhaustive, there is evidently no room in it for a third class of collective terms. nor is there any distinct class of terms to which that name can be given. the same term may be used collectively or distributively in different relations. thus the term 'library,' when used of the books which compose a library, is collective; when used of various collections of books, as the bodleian, queen's library, and so on, it is distributive, which, in this case, is the same thing as being a common term. § , the distinction between the collective and distributive use of a term is of importance, because the confusion of the two is a favourite source of fallacy. when it is said 'the plays of shakspeare cannot be read in a day,' the proposition meets with a very different measure of acceptance according as its subject is understood collectively or distributively. the word 'all' is perfectly ambiguous in this respect. it may mean all together or each separately--two senses which are distinguished in latin by 'totus' or 'cunctus,' for the collective, and 'omnis' for the distributive use. § . what is usually meant however when people speak of a collective term is a particular kind of singular term. § . from this point of view singular terms may be subdivided into individual and collective, by an individual term being meant the name of one object, by a collective term the name of several considered as one. 'this key' is an individual term; 'my bunch of keys' is a collective term. § . a collective term is quite as much the name of one thing as an individual term is, though the thing in question happens to be a group. a group is one thing, if we choose to think of it as one. for the mind, as we have already seen, has an unlimited power of forming its own things, or objects of thought. thus a particular peak in a mountain chain is as much one thing as the chain itself, though, physically speaking, it is inseparable from it, just as the chain itself is inseparable from the earth's surface. in the same way a necklace is as much one thing as the individual beads which compose it. § . we have just seen that a collective term is the name of a group regarded as one thing: but every term which is the name of such a group is not necessarily a collective term. 'london,' for instance, is the name of a group of objects considered as one thing. but 'london' is not a collective term, whereas 'flock,' 'regiment,' and 'senate' are. wherein then lies the difference? it lies in this--that flock, regiment and senate are groups composed of objects which are, to a certain extent, similar, whereas london is a group made up of the most dissimilar objects--streets and squares and squalid slums, fine carriages and dirty faces, and so on. in the case of a true collective term all the members of the group will come under some one common name. thus all the members of the group, flock of sheep, come under the common name 'sheep,' all the members of the group 'regiment' under the common name, 'soldier,' and so on. § . the subdivision of singular terms into individual and collective need not be confined to the names of concrete things. an abstract term like 'scarlet,' which is the name of one definite attribute, may be reckoned 'individual,' while a term like 'human nature,' which is the name of a whole group of attributes, would more fitly be regarded as collective. § . the main division of terms, which we have been discussing, into singular and collective, is based upon their quantity in extension. this phrase will be explained presently. § . we come now to a threefold division of terms into positive, privative and negative. it is based upon an implied two-fold division into positive and non-positive, the latter member being subdivided into privative and negative. term _______________|_______________ | | positive non-positive _____________|____________ | | privative negative if this division be extended, as it sometimes is, to terms in general, a positive term must be taken to mean only the definite, or comparatively definite, member of an exhaustive division in accordance with the law of excluded middle (§ ). thus 'socrates' and 'man' are positive, as opposed to 'not-socrates' and 'not-man.' § . the chief value of the division, however, and especially of the distinction drawn between privative and negative terms, is in relation to attributives. from this point of view we may define the three classes of terms as follows: a positive term signifies the presence of an attribute, e.g.: 'wise,' 'full.' a negative term signifies merely the absence of an attribute, e.g. 'not-wise,' 'not-full.' a privative term signifies the absence of an attribute in a subject capable of possessing it, e.g. 'unwise,' 'empty'. [footnote: a privative term is usually defined to mean one which signifies the absence of an attribute where it was once possessed, or might have been expected to be present, e.g. 'blind.' the utility of the slight extension of meaning here assigned to the expression will, it is hoped, prove its justification.] § . thus a privative term stands midway in meaning between the other two, being partly positive and partly negative--negative in so far as it indicates the absence of a certain attribute, positive in so far as it implies that the thing which is declared to lack that attribute is of such a nature as to be capable of possessing it. a purely negative term conveys to the mind no positive information at all about the nature of the thing of which it is predicated, but leaves us to seek for it among the universe of things which fail to exhibit a given attribute. a privative term, on the other hand, restricts us within a definite sphere. the term 'empty' restricts us within the sphere of things which are capable of fulness, that is, if the term be taken in its literal sense, things which possess extension in three dimensions. § . a positive and a negative term, which have the same matter, must exhaust the universe between them, e.g. 'white' and 'not-white,' since, according to the law of excluded middle, everything must be either one or the other. to say, however, that a thing is 'not-white' is merely to say that the term 'white' is inapplicable to it. 'not-white' may be predicated of things which do not possess extension as well as of those which do. such a pair of terms as 'white' and 'not-white,' in their relation to one another, are called contradictories. § . contrary terms must be distinguished from contradictory. contrary terms are those which are most opposed under the same head. thus 'white' and 'black' are contrary terms, being the most opposed under the same head of colour. 'virtuous' and 'vicious' again are contraries, being the most opposed under the same head of moral quality. § . a positive and a privative term in the same matter will always be contraries, e.g. 'wise' and 'unwise,' 'safe' and 'unsafe': but contraries do not always assume the shape of positive and privative terms, but may both be positive in form, e.g. 'wise' and 'foolish,' 'safe' and 'dangerous.' § . words which are positive in form are often privative in meaning, and vice versâ. this is the case, for instance, with the word 'safe,' which connotes nothing more than the absence of danger. we talk of a thing involving 'positive danger' and of its being 'positively unsafe' to do so and so. 'unhappy,' on the other hand, signifies the presence of actual misery. similarly in latin 'inutilis' signifies not merely that there is no benefit to be derived from a thing, but that it is _positively injurious_. all such questions, however, are for the grammarian or lexicographer, and not for the logician. for the latter it is sufficient to know that corresponding to every term which signifies the presence of some attribute there may be imagined another which indicates the absence of the same attribute, where it might be possessed, and a third which indicates its absence, whether it might be possessed or not. § . negative terms proper are formed by the prefix 'not-' or 'non-,' and are mere figments of logic. we do not in practice require to speak of the whole universe of objects minus those which possess a given attribute or collection of attributes. we have often occasion to speak of things which might be wise and are not, but seldom, if ever, of all things other than wise. § . every privative attributive has, or may have, a corresponding abstract term, and the same is the case with negatives: for the absence of an attribute, is itself an attribute. corresponding to 'empty,' there is 'emptiness'; corresponding to 'not-full' there may be imagined the term 'not-fulness.' § . the contrary of a given term always involves the contradictory, but it involves positive elements as well. thus 'black' is 'not-white,' but it is something more besides. terms which, without being directly contrary, involve a latent contradiction, are called repugnant, e.g. 'red' and 'blue.' all terms whatever which signify attributes that exclude one another may be called incompatible. § . the preceding division is based on what is known as the quality of terms, a positive term being said to differ in quality from a non-positive one. _univocal and equivocal terms_. § . a term is said to be univocal, when it has one and the same meaning wherever it occurs. a term which has more than one meaning is called equivocal. 'jam-pot,' 'hydrogen' are examples of univocal terms; 'pipe' and 'suit' of equivocal. § . this division does not properly come within the scope of logic, since it is a question of language, not of thought. from the logician's point of view an equivocal term is two or more different terms, for the definition in each sense would be different. § . sometimes a third member is added to the same division under the head of analogous terms. the word 'sweet,' for instance, is applied by analogy to things so different in their own nature as a lump of sugar, a young lady, a tune, a poem, and so on. again, because the head is the highest part of man, the highest part of a stream is called by analogy 'the head.' it is plainly inappropriate to make a separate class of analogous terms. rather, terms become equivocal by being extended by analogy from one thing to another. _absolute and relative terms_. § . an absolute term is a name given to a thing without reference to anything else. § . a relative term is a name given to a thing with direct reference to some other thing. § . 'hodge' and 'man' are absolute terms. 'husband' 'father,' 'shepherd' are relative terms. 'husband' conveys a direct reference to 'wife,' 'father' to 'child,' 'shepherd' to 'sheep.' given one term of a relation, the other is called the correlative, e.g. 'subject' is the correlative of 'ruler,' and conversely 'ruler' of 'subject.' the two terms are also spoken of as a pair of correlatives. § . the distinction between relative and absolute applies to attributives as well as subject-terms. 'greater,' 'near, 'like,' are instances of attributives which everyone would recognise as relative. § . a relation, it will be remembered, is a kind of attribute, differing from a quality in that it necessarily involves more substances than one. every relation is at bottom a fact, or series of facts, in which two or more substances play a part. a relative term connotes this fact or facts from the point of view of one of the substances, its correlative from that of the other. thus 'ruler' and 'subject' imply the same set of facts, looked at from opposite points of view. the series of facts itself, regarded from either side, is denoted by the corresponding abstract terms, 'rule 'and 'subjection.' § . it is a nice question whether the abstract names of relations should themselves be considered relative terms. difficulties will perhaps be avoided by confining the expression 'relative _term_' to names of concrete things. 'absolute,' it must be remembered, is a mere negative of 'relative,' and covers everything to which the definition of the latter does not strictly apply. now it can hardly be said that 'rule' is a name given to a certain abstract thing with direct reference to some other thing, namely, subjection. rather 'rule' and 'subjection' are two names for identically the same series of facts, according to the side from which we look at them. 'ruler' and 'subject,' on the other hand, are names of two distinct substances, but each involving a reference to the other. § . this division then may be said to be based on the number of things involved in the name. _connotative and non-connotative terms._ § . before explaining this division, it is necessary to treat of what is called the quantity of terms. _quantity of terms._ § . a term is possessed of quantity in two ways-- ( ) in extension; ( ) in intension. § . the extension of a term is the number of things to which it applies. § . the intension of a term is the number of attributes which it implies. § . it will simplify matters to bear in mind that the intension of a term is the same thing as its meaning. to take an example, the term 'man' applies to certain things, namely, all the members of the human race that have been, are, or ever will be: this is its quantity in extension. but the term 'man' has also a certain meaning, and implies certain attributes--rationality, animality, and a definite bodily shape: the sum of these attributes constitutes its quantity in intension. § . the distinction between the two kinds of quantity possessed by a term is also conveyed by a variety of expressions which are here appended. extension = breadth = compass = application = denotation. intension = depth = comprehension = implication = connotation. of these various expressions, 'application' and 'implication' have the advantage of most clearly conveying their own meaning. 'extension' and 'intension,' however, are more usual; and neither 'implication' nor 'connotation' is quite exact as a synonym for 'intension.' (§ .) § . we now return to the division of terms into connotative and non-connotative. § . a term is said to connote attributes, when it implies certain attributes at the same time that it applies to certain things distinct therefrom. [footnote: originally 'connotative' was used in the same sense in which we have used 'attributive,' for a word which directly signifies the presence of an attribute and indirectly applies to a subject. in this, its original sense, it was the subject which was said to be connoted, and not the attribute.] § . a term which possesses both extension and intension, distinct from one another, is connotative. § . a term which possesses no intension (if that be possible) or in which extension and intension coincide is non-connotative. § . the subject-term, 'man,' and its corresponding attributive, 'human,' have both extension and intension, distinct from one another. they are therefore connotative. but the abstract term, 'humanity,' denotes the very collection of attributes, which was before connoted by the concrete terms, 'man' and 'human.' in this case, therefore, extension and intension coincide, and the term is non-connotative. § . the above remark must be understood to be limited to abstract terms in their singular sense. when employed as common terms, abstract terms possess both extension and intension distinct from one another. thus the term 'colour' applies to red, blue, and yellow, and at the same time implies (i.e. connotes), the power of affecting the eye. § . since all terms are names of things, whether substances or attributes, it is clear that all terms must possess extension, though the extension of singular terms is the narrowest possible, as being confined to one thing. § . are there then any terms which possess no intension? to ask this, is to ask--are there any terms which have absolutely no meaning? it is often said that proper names are devoid of meaning, and the remark is, in a certain sense, true. when we call a being by the name 'man,' we do so because that being possesses human attributes, but when we call the same being by the name, 'john,' we do not mean to indicate the presence of any johannine attributes. we simply wish to distinguish that being, in thought and language, from other beings of the same kind. roughly speaking, therefore, proper names are devoid of meaning or intension. but no name can be entirely devoid of meaning. for, even setting aside the fact, which is not universally true, that proper names indicate the sex of the owner, the mere act of giving a name to a thing implies at least that the thing exists, whether in fact or thought; it implies what we may call 'thinghood': so that every term must carry with it some small amount of intension. § . from another point of view, however, proper names possess more intension than any other terms. for when we know a person, his name calls up to our minds all the individual attributes with which we are familiar, and these must be far more numerous than the attributes which are conveyed by any common term which can be applied to him. thus the name 'john' means more to a person who knows him than 'attorney,' 'conservative,' 'scamp,' of 'vestry-man,' or any other term which may happen to apply to him. this, however, is the acquired intension of a term, and must be distinguished from the original intension. the name 'john' was never meant to indicate the attributes which its owner has, as a matter of fact, developed. he would be john all the same, if he were none of these. § . hitherto we have been speaking only of christening-names, but it is evident that family names have a certain amount of connotation from the first. for when we dub john with the additional appellation of smith, we do not give this second name as a mere individual mark, but intend thereby to indicate a relationship to other persons. the amount of connotation that can be conveyed by proper names is very noticeable in the latin language. let us take for an example the full name of a distinguished roman--publius cornelius scipio Æmilianus africanus minor. here it is only the prænomen, publius, that can be said to be a mere individual mark, and even this distinctly indicates the sex of the owner. the nomen proper, cornelius, declares the wearer of it to belong to the illustrious gens cornelia. the cognomen, scipio, further specifies him as a member of a distinguished family in that gens. the agnomen adoptivum indicates his transference by adoption from one gens to another. the second agnomen recalls the fact of his victory over the carthaginians, while the addition of the word 'minor' distinguishes him from the former wearer of the same title. the name, instead of being devoid of meaning, is a chapter of history in itself. homeric epithets, such as 'the cloud-compeller,' 'the earth-shaker' are instances of intensive proper names. many of our own family names are obviously connotative in their origin, implying either some personal peculiarity, e.g. armstrong, cruikshank, courteney; or the employment, trade or calling of the original bearer of the name, smith, carpenter, baker, clark, leach, archer, and so on; or else his abode, domain or nationality, as de caen, de montmorency, french, langley; or simply the fact of descent from some presumably more noteworthy parent, as jackson, thomson, fitzgerald, o'connor, macdonald, apjohn, price, davids, etc. the question, however, whether a term is connotative or not, has to be decided, not by its origin, but by its use. we have seen that there are some proper names which, in a rough sense, may be said to possess no intension. § . the other kind of singular terms, namely, designations (§ ) are obviously connotative. we cannot employ even the simplest of them without conveying more or less information about the qualities of the thing which they are used to denote. when, for instance, we say 'this table,' 'this book,' we indicate the proximity to the speaker of the object in question. other designations have a higher degree of intension, as when we say 'the present prime minister of england,' 'the honourable member who brought forward this motion to-night.' such terms have a good deal of significance in themselves, apart from any knowledge we may happen to possess of the individuals they denote. § . we have seen that, speaking quite strictly, there are no terms which are non-connotative: but, for practical purposes, we may apply the expression to proper names, on the ground that they possess no intension, and to singular abstract terms on the ground that their extension and intension coincide. in the latter case it is indifferent whether we call the quantity extension or intension. only we cannot call it 'connotation,' because that implies two quantities distinct from one another. a term must already denote a subject before it can be said to connote its attributes. § . the division of terms into connotative and non-connotative is based on their possession of one quantity or two. chapter iv. _of the law of inverse variation of extension and intension._ § . in a series of terms which fall under one another, as the extension decreases, the intension increases, and vice versâ. take for instance the following series-- thing | substance | matter | organism | animal | vertebrate | mammal | ruminant | sheep | this sheep. here the term at the top possesses the widest possible extension, since it applies to everything. but at the same time it possesses the least possible amount of intension, implying nothing more than mere existence, whether in fact or thought. on the other hand, the term at the bottom possesses the greatest amount of intension, since it implies all the attributes of, an individual superadded to those of the class to which it belongs: but its extension is the narrowest possible, being limited to one thing. § . at each step in the descent from the term at the top, which is called the 'summum genus,' to the individual, we decrease the extension by increasing the intension. thus by adding on to the bare notion of a thing the idea of independent existence, we descend to the term 'substance,' this process is known as determination, or specialisation. § . again, by withdrawing our attention from the individual characteristics of a particular sheep, and fixing it upon those which are common to it with other animals of the same kind, we arrive at the common term, 'sheep.' here we have increased the extension by decreasing the intension. this process is known as generalisation. § . generalisation implies abstraction, but we may have abstraction without generalisation. § . the following example is useful, as illustrating to the eye how a decrease of extension is accompanied by an increase of intension. at each step of the descent here we visibly tack on a fresh attribute. [footnote: this example is borrowed from professor jevons.] ship | steam-ship | screw steam-ship | iron screw steam-ship | british iron screw steam-ship. could we see the classes denoted by the names the pyramid would be exactly inverted. § . the law of inverse variation of extension and intension must of course be confined to the inter-relations of a series of terms of which each can be predicated of the other until we arrive at the bottom of the scale. it is not meant to apply to the extension and intension of the same term. the increase of population does not add to the meaning of 'baby.' part ii.--of propositions. chapter i. _of the proposition as distinguished from other sentences_. § . as in considering the term, we found occasion to distinguish it from words generally, so now, in considering the proposition, it will be well to begin by distinguishing it from other sentences. § . every proposition is a sentence, but every sentence is not a proposition. § . the field of logic is far from being conterminous with that of language. language is the mirror of man's whole nature, whereas logic deals with language only so far as it gives clothing to the products of thought in the narrow sense which we have assigned to that term. language has materials of every sort lying strewn about, among which the logician has to seek for his proper implements. § . sentences may be employed for a variety of purposes-- ( ) to ask a question; ( ) to give an order; ( ) to express a feeling; ( ) to make a statement. these various uses give rise respectively to ( ) the interrogative sentence; ( ) the imperative sentence; ( ) the exclamatory sentence; ( ) the enunciative sentence; indicative potential. it is with the last of these only that logic is concerned. § . the proposition, therefore, corresponds to the indicative and potential, or conditional, sentences of grammar. for it must be borne in mind that logic recognises no difference between a statement of fact and a supposition. 'it may rain to-morrow' is as much a proposition as 'it is raining now.' § . leaving the grammatical aspect of the proposition, we must now consider it from the purely logical point of view. § . a proposition is a judgement expressed in words; and a judgement is a direct comparison between two concepts. § . the same thing may be expressed more briefly by saying that a proposition is a direct comparison between two terms. § . we say 'direct comparison,' because the syllogism also may be described as a comparison between two terms: but in the syllogism the two terms are compared indirectly, or by means of a third term. § . a proposition may be analysed into two terms and a copula, which is nothing more than the sign of agreement or disagreement between them. § . the two terms are called the subject and the predicate (§ ). § . the subject is that of which something is stated. § . the predicate is that which is stated of the subject. § . hence the subject is thought of for its own sake, and the predicate for the sake of the subject. chapter ii. of _the copula_. § . there are two kinds of copula, one for affirmative and one for negative statements. § . materially the copula is expressed by some part of the verb 'to be,' with or without the negative, or else is wrapped up in some inflexional form of a verb. § . the material form of the copula is an accident of language, and a matter of indifference to logic. 'the kettle boils' is as logical a form of expression as 'the kettle is boiling.' for it must be remembered that the word 'is' here is a mere sign of agreement between the two terms, and conveys no notion of actual existence. we may use it indeed with equal propriety to express non-existence, as when we say 'an idol is nothing.' § . when the verb 'to be' expresses existence in fact it is known in grammar as 'the substantive verb.' in this use it is predicate as well as copula, as when we say 'god is,' which may be analysed, if we please, into 'god is existent.' § . we have laid down above that there are two kinds of copula, affirmative and negative: but some logicians have maintained that the copula is always affirmative. § . what then, it may be asked, on this view, is the meaning of negative propositions! to which the answer is, that a negative proposition asserts an agreement between the subject and a negative term. when, for instance, we say 'the whale is not a fish,' this would be interpreted to mean 'the whale is a not-fish.' § . undoubtedly any negative proposition may be exhibited in an affirmative form, since, by the law of excluded middle, given a pair of contradictory terms, wherever the one can be asserted, the other can be denied, and vice versâ. we shall find later on that this principle gives rise to one of the forms of immediate inference. the only question then can be, which is the more natural and legitimate form of expression. it seems simpler to suppose that we assert the agreement of 'whale' with 'not-fish' by implication only, and that what we directly do is to predicate a disagreement between 'whale' and the positive attributes connoted by 'fish.' for since 'not-fish' must apply to every conceivable object of thought except those which fall under the positive term 'fish,' to say that a whale is a 'not-fish,' is to say that we have still to search for 'whale' throughout the whole universe of being, minus a limited portion; which is only a more clumsy way of saying that it is not to be found in that portion. § . again, the term 'not-fish' must be understood either in its intension or in its extension. if it be understood in its intension, what it connotes is simply the absence of the positive qualities which constitute a fish, a meaning which is equally conveyed by the negative form of proposition. we gain nothing in simplicity by thus confounding assertion with denial. if, on the other hand, it is to be taken in extension, this involves the awkwardness of supposing that the predicative power of a term resides in its extensive capacity. § . we therefore recognise predication as being of two kinds--affirmation and negation--corresponding to which there are two forms of copula. § . on the other hand, other logicians have maintained that there are many kinds of copula, since the copula must vary according to the various degrees of probability with which we can assert or deny a predicate of a subject. this view is technically known as the doctrine of _the modality of the copula._ § . it may plausibly be maintained that the division of propositions into affirmative and negative is not an exhaustive one, since the result of an act of judgement is not always to lead the mind to a clear assertion or a clear denial, but to leave it in more or less doubt as to whether the predicate applies to the subject or not. instead of saying simply a is b, or a is not b, we may be led to one of the following forms of proposition-- a is possibly b. a is probably b. a is certainly b. the adverbial expression which thus appears to qualify the copula is known as 'the mode.' § . when we say 'the accused may be guilty' we have a proposition of very different force from 'the accused is guilty,' and yet the terms appear to be the same. wherein then does the difference lie? 'in the copula' would seem to be the obvious reply. we seem therefore driven to admit that there are as many different kinds of copula as there are different degrees of assurance with which a statement may be made. § . but there is another way in which modal propositions may be regarded. instead of the mode being attached to the copula, it may be considered as itself constituting the predicate, so that the above propositions would be analysed thus-- that a is b, is possible. that a is b, is probable. that a is b, is certain. § . the subject here is itself a proposition of which we predicate various degrees of probability. in this way the division of propositions into affirmative and negative is rendered exhaustive. for wherever before we had a doubtful assertion, we have now an assertion of doubtfulness. § . if degrees of probability can thus be eliminated from the copula, much more so can expressions of time, which may always be regarded as forming part of the predicate. 'the sun will rise to-morrow' may be analysed into 'the sun is going to rise to-morrow.' in either case the tense belongs equally to the predicate. it is often an awkward task so to analyse propositions relative to past or future time as to bring out the copula under the form 'is' or 'is not': but fortunately there is no necessity for so doing, since, as has been said before (§ ), the material form of the copula is a matter of indifference to logic. indeed in affirmative propositions the mere juxtaposition of the subject and predicate is often sufficient to indicate their agreement, e.g. 'most haste, worst speed,' chalepha tha kala. it is because all propositions are not affirmative that we require a copula at all. moreover the awkwardness of expression just alluded to is a mere accident of language. in latin we may say with equal propriety 'sol orietur cras' or 'sol est oriturus cras'; while past time may also be expressed in the analytic form in the case of deponent verbs, as 'caesar est in galliam profectus'--'caesar is gone into gaul.' § . the copula then may always be regarded as pure, that is, as indicating mere agreement or disagreement between the two terms of the proposition. chapter iii. _of the divisions of propositions_. § . the most obvious and the most important division of propositions is into true and false, but with this we are not concerned. formal logic can recognise no difference between true and false propositions. the one is represented by the same symbols as the other. § . we may notice, however, in passing, that truth and falsehood are attributes of propositions and of propositions only. for something must be predicated, i.e. asserted or denied, before we can have either truth or falsehood. neither concepts or terms, on the one hand, nor reasonings, on the other, can properly be said to be true or false. in the mere notion of a centaur or of a black swan there is neither truth nor falsehood; it is not until we make some statement about these things, such as that 'black swans are found in australia,' or 'i met a centaur in the high street yesterday,' that the question of truth or falsehood comes in. in such expressions as a 'true friend' or 'a false patriot' there is a tacit reference to propositions. we mean persons of whom the terms 'friend' and 'patriot' are truly or falsely predicated. neither can we with any propriety talk of true or false reasoning. reasoning is either valid or invalid: it is only the premisses of our reasonings, which are propositions, that can be true or false. we may have a perfectly valid process of reasoning which starts from a false assumption and lands us in a false conclusion. § . all truth and falsehood then are contained in propositions; and propositions are divided according to the quality of the matter into true and false. but the consideration of the matter is outside the sphere of formal or deductive logic. it is the problem of inductive logic to establish, if possible, a criterion of evidence whereby the truth or falsehood of propositions may be judged (§ ). § . another usual division of propositions is into pure and modal, the latter being those in which the copula is modified by some degree of probability. this division is excluded by the view which has just been taken of the copula, as being always simply affirmative or simply negative. § . we are left then with the following divisions of propositions-- proposition according to form simple complex conjunctive 	disjunctive universal singular 	general according to matter verbal real according to quantity universal singular 	general particular indefinite 	(strictly) particular according to quality affirmative negative _simple and complex propositions_. § . a simple proposition is one in which a predicate is directly affirmed or denied of a subject, e.g. 'rain is falling.' § . a simple proposition is otherwise known as categorical. § . a complex proposition is one in which a statement is made subject to some condition, e.g. 'if the wind drops, rain will fall.' § . hence the complex proposition is also known as conditional. § . every complex proposition consists of two parts-- ( ) antecedent; ( ) consequent. § . the antecedent is the condition on which another statement is made to depend. it precedes the other in the order of thought, but may either precede or follow it in the order of language. thus we may say indifferently--'if the wind drops, we shall have rain' or 'we shall have rain, if the wind drops.' § . the consequent is the statement which is made subject to some condition. § . the complex proposition assumes two forms, ( ) if a is b, c is d. this is known as the conjunctive or hypothetical proposition. ( ) either a is b or c is d. this is known as the disjunctive proposition. § . the disjunctive proposition may also appear in the form a is either b or c, which is equivalent to saying either a is b or a is c; or again in the form either a or b is c, which is equivalent to saying either a is c or b is c. § . as the double nomenclature may cause some confusion, a scheme is appended. proposition ____________|_____________ | | simple complex (categorical) (conditional) ___________|__________ | | conjunctive disjunctive. (hypothetical) § . the first set of names is preferable. 'categorical' properly means 'predicable' and 'hypothetical' is a mere synonym for 'conditional.' § . let us examine now what is the real nature of the statement which is made in the complex form of proposition. when, for instance, we say 'if the sky falls, we shall catch larks,' what is it that we really mean to assert? not that the sky will fall, and not that we shall catch larks, but a certain connection between the two, namely, that the truth of the antecedent involves the truth of the consequent. this is why this form of proposition is called 'conjunctive,' because in it the truth of the consequent is conjoined to the truth of the antecedent. § . again, when we say 'jones is either a knave or a fool,' what is really meant to be asserted is--'if you do not find jones to be a knave, you may be sure that he is a fool.' here it is the falsity of the antecedent which involves the truth of the consequent; and the proposition is known as 'disjunctive,' because the truth of the consequent is disjoined from the truth of the antecedent. § . complex propositions then turn out to be propositions about propositions, that is, of which the subject and predicate are themselves propositions. but the nature of a proposition never varies in thought. ultimately every proposition must assume the form 'a is, or is not, b.' 'if the sky falls, we shall catch larks' may be compressed into 'sky-falling is lark-catching.' § . hence this division turns upon the form of expression, and may be said to be founded on the simplicity or complexity of the terms employed in a proposition. § . in the complex proposition there appears to be more than one subject or predicate or both, but in reality there is only a single statement; and this statement refers, as we have seen, to a certain connection between two propositions. § . if there were logically, and not merely grammatically, more than one subject or predicate, there would be more than one proposition. thus when we say 'the jews and carthaginians were semitic peoples and spoke a semitic language,' we have four propositions compressed into a single sentence for the sake of brevity. § . on the other hand when we say 'either the carthaginians were of semitic origin or argument from language is of no value in ethnology,' we have two propositions only in appearance. § . the complex proposition then must be distinguished from those contrivances of language for abbreviating expression in which several distinct statements are combined into a single sentence. _verbal and real propositions_. § . a verbal proposition is one which states nothing more about the subject than is contained in its definition, e.g. 'man is an animal'; 'men are rational beings.' § . a real proposition states some fact not contained in the definition of the subject, e.g. 'some animals have four feet.' § . it will be seen that the distinction between verbal and real propositions assumes a knowledge of the precise meaning of terms, that is to say, a knowledge of definitions. § . to a person who does not know the meaning of terms a verbal proposition will convey as much information as a real one. to say 'the sun is in mid-heaven at noon,' though a merely verbal proposition, will convey information to a person who is being taught to attach a meaning to the word 'noon.' we use so many terms without knowing their meaning, that a merely verbal proposition appears a revelation to many minds. thus there are people who are surprised to hear that the lion is a cat, though in its definition 'lion' is referred to the class 'cat.' the reason of this is that we know material objects far better in their extension than in their intension, that is to say, we know what things a name applies to without knowing the attributes which those things possess in common. § . there is nothing in the mere look of a proposition to inform us whether it is verbal or real; the difference is wholly relative to, and constituted by, the definition of the subject. when we have accepted as the definition of a triangle that it is 'a figure contained by three sides,' the statement of the further fact that it has three angles becomes a real proposition. again the proposition 'man is progressive' is a real proposition. for though his progressiveness is a consequence of his rationality, still there is no actual reference to progressiveness contained in the usually accepted definition, 'man is a rational animal.' § . if we were to admit, under the term 'verbal proposition,' all statements which, though not actually contained in the definition of the subject, are implied by it, the whole body of necessary truth would have to be pronounced merely verbal, and the most penetrating conclusions of mathematicians set down as only another way of stating the simplest axioms from which they started. for the propositions of which necessary truth is composed are so linked together that, given one, the rest can always follow. but necessary truth, which is arrived at 'a priori,' that is, by the mind's own working, is quite as real as contingent truth, which is arrived at 'a posteriori,' or by the teachings of experience, in other words, through our own senses or those of others. § . the process by which real truth, which is other than deductive, is arrived at 'a priori' is known as intuition. e.g. the mind sees that what has three sides cannot but have three angles. § . only such propositions then must be considered verbal as state facts expressly mentioned in the definition. § . strictly speaking, the division of propositions into verbal and real is extraneous to our subject: since it is not the province of logic to acquaint us with the content of definitions. § , the same distinction as between verbal and real proposition, is conveyed by the expressions 'analytical' and 'synthetical,' or 'explicative' and 'ampliative' judgements. § . a verbal proposition is called analytical, as breaking up the subject into its component notions. § . a real proposition is called synthetical, as attaching some new notion to the subject. § . among the scholastic logicians verbal propositions were known as 'essential,' because what was stated in the definition was considered to be of the essence of the subject, while real propositions were known as 'accidental.' _universal and particular propositions_. § . a universal proposition is one in which it is evident from the form that the predicate applies to the subject in its whole extent. § . when the predicate does not apply to the subject in its whole extent, or when it is not clear that it does so, the proposition is called particular. § . to say that a predicate applies to a subject in its whole extent, is to say that it is asserted or denied of all the things of which the subject is a name. § . 'all men are mortal' is a universal proposition. § . 'some men are black' is a particular proposition. so also is 'men are fallible;' for here it is not clear from the form whether 'all' or only 'some' is meant. § . the latter kind of proposition is known as indefinite, and must be distinguished from the particular proposition strictly so called, in which the predicate applies to part only of the subject. § . the division into universal and particular is founded on the quantity of propositions. § . the quantity of a proposition is determined by the quantity in extension of its subject. § . very often the matter of an indefinite proposition is such as clearly to indicate to us its quantity. when, for instance, we say 'metals are elements,' we are understood to be referring to all metals; and the same thing holds true of scientific statements in general. formal logic, however, cannot take account of the matter of propositions; and is therefore obliged to set down all indefinite propositions as particular, since it is not evident from the form that they are universal. § . particular propositions, therefore, are sub-divided into such as are indefinite and such as are particular, in the strict sense of the term. § . we must now examine the sub-division of universal propositions into singular and general. § . a singular proposition is one which has a singular term for its subject, e.g. 'virtue is beautiful.' § . a general proposition is one which has for its subject a common term taken in its whole extent. § . now when we say 'john is a man' or 'this table is oblong,' the proposition is quite as universal, in the sense of the predicate applying to the whole of the subject, as when we say 'all men are mortal.' for since a singular term applies only to one thing, we cannot avoid using it in its whole extent, if we use it at all. § . the most usual signs of generality in a proposition are the words 'all,' 'every,' 'each,' in affirmative, and the words 'no,' 'none,' 'not one,' &c. in negative propositions. § . the terminology of the division of propositions according to quantity is unsatisfactory. not only has the indefinite proposition to be set down as particular, even when the sense manifestly declares it to be universal; but the proposition which is expressed in a particular form has also to be construed as indefinite, _so_ that an unnatural meaning is imparted to the word 'some,' as used in logic. if in common conversation we were to say 'some cows chew the cud,' the person whom we were addressing would doubtless imagine us to suppose that there were some cows which did not possess this attribute. but in logic the word 'some' is not held to express more than 'some at least, if not all.' hence we find not only that an indefinite proposition may, as a matter of fact, be strictly particular, but that a proposition which appears to be strictly particular may be indefinite. so a proposition expressed in precisely the same form 'some a is b' may be either strictly particular, if some be taken to exclude all, or indefinite, if the word 'some' does not exclude the possibility of the statement being true of all. it is evident that the term 'particular' has become distorted from its original meaning. it would naturally lead us to infer that a statement is limited to part of the subject, whereas, by its being opposed to universal, in the sense in which that term has been defined, it can only mean that we have nothing to show us whether part or the whole is spoken of. § . this awkwardness of expression is due to the indefinite proposition having been displaced from its proper position. formerly propositions were divided under three heads-- ( ) universal, ( ) particular, ( ) indefinite. but logicians anxious for simplification asked, whether a predicate in any given case must not either apply to the whole of the subject or not? and whether, therefore, the third head of indefinite propositions were not as superfluous as the so-called 'common gender' of nouns in grammar? § . it is quite true that, as a matter of fact, any given predicate must either apply to the whole of the subject or not, so that in the nature of things there is no middle course between universal and particular. but the important point is that we may not know whether the predicate applies to the whole of the subject or not. the primary division then should be into propositions whose quantity is known and propositions whose quantity is unknown. those propositions whose quantity is known may be sub-divided into 'definitely universal' and 'definitely particular,' while all those whose quantity is unknown are classed together under the term 'indefinite.' hence the proper division is as follows-- proposition __________|____________ | | definite indefinite _____|_______ | | universal particular. § . another very obvious defeat of terminology is that the word 'universal' is naturally opposed to 'singular,' whereas it is here so used as to include it; while, on the other hand, there is no obvious difference between universal and general, though in the division the latter is distinguished from the former as species from genus. _affirmative and negative propositions._ § . this division rests upon the quality of propositions. § . it is the quality of the form to be affirmative or negative: the quality of the matter, as we saw before (§ ), is to be true or false. but since formal logic takes no account of the matter of thought, when we speak of 'quality' we are understood to mean the quality of the form. § . by combining the division of propositions according to quantity with the division according to quality, we obtain four kinds of proposition, namely-- ( ) universal affirmative (a). ( ) universal negative (e). ( ) particular affirmative (i). ( ) particular negative (o). § . this is an exhaustive classification of propositions, and any proposition, no matter what its form may be, must fall under one or other of these four heads. for every proposition must be either universal or particular, in the sense that the subject must either be known to be used in its whole extent or not; and any proposition, whether universal or particular, must be either affirmative or negative, for by denying modality to the copula we have excluded everything intermediate between downright assertion and denial. this classification therefore may be regarded as a procrustes' bed, into which every proposition is bound to fit at its proper peril. § . these four kinds of propositions are represented respectively by the symbols a, e, i, o. § . the vowels a and i, which denote the two affirmatives, occur in the latin words 'affirmo' and 'aio;' e and o, which denote the two negatives, occur in the latin word 'nego.' _extensive and intensive propositions._ § . it is important to notice the difference between extensive and intensive propositions; but this is not a division of propositions, but a distinction as to our way of regarding them. propositions may be read either in extension or intension. thus when we say 'all cows are ruminants,' we may mean that the class, cow, is contained in the larger class, ruminant. this is reading the proposition in extension. or we may mean that the attribute of chewing the cud is contained in, or accompanies, the attributes which make up our idea of 'cow.' this is reading the proposition in intension. what, as a matter of fact, we do mean, is a mixture of the two, namely, that the class, cow, has the attribute of chewing the cud. for in the ordinary and natural form of proposition the subject is used in extension, and the predicate in intension, that is to say, when we use a subject, we are thinking of certain objects, whereas when we use a predicate, we indicate the possession of certain attributes. the predicate, however, need not always be used in intension, e.g. in the proposition 'his name is john' the predicate is not intended to convey the idea of any attributes at all. what is meant to be asserted is that the name of the person in question is that particular name, john, and not zacharias or abinadab or any other name that might be given him. § . let it be noticed that when a proposition is read in extension, the predicate contains the subject, whereas, when it is read in intension, the subject contains the predicate. _exclusive propositions._ § . an exclusive proposition is so called because in it all but a given subject is excluded from participation in a given predicate, e.g. 'the good alone are happy,' 'none but the brave deserve the fair,' 'no one except yourself would have done this.' § . by the above forms of expression the predicate is declared to apply to a given subject and to that subject only. hence an exclusive proposition is really equivalent to two propositions, one affirmative and one negative. the first of the above propositions, for instance, means that some of the good are happy, and that no one else is so. it does not necessarily mean that all the good are happy, but asserts that among the good will be found all the happy. it is therefore equivalent to saying that all the happy are good, only that it puts prominently forward in addition what is otherwise a latent consequence of that assertion, namely, that some at least of the good are happy. § . logically expressed the exclusive proposition when universal assumes the form of an e proposition, with a negative term for its subject no not-a is b. § . under the head of exclusive comes the strictly particular proposition, 'some a is b,' which implies at the same time that 'some a is not b.' here 'some' is understood to mean 'some only,' which is the meaning that it usually bears in common language. when, for instance, we say 'some of the gates into the park are closed at nightfall,' we are understood to mean 'some are left open.' _exceptive propositions._ § . an exceptive proposition is so called as affirming the predicate of the whole of the subject, with the exception of a certain part, e.g. 'all the jury, except two, condemned the prisoner.' § . this form of proposition again involves two distinct statements, one negative and one affirmative, being equivalent to 'two of the jury did not condemn the prisoner; and all the rest did.' § . the exceptive proposition is merely an affirmative way of stating the exclusive-- no not-a is b = all not-a is not-b. no one but the sage is sane = all except the sage are mad. _tautologous or identical propositions_ § . a tautologous or identical proposition affirms the subject of itself, e.g. 'a man's a man,' 'what i have written, i have written,' 'whatever is, is.' the second of these instances amounts formally to saying 'the thing that i have written is the thing that i have written,' though of course the implication is that the writing will not be altered. chapter iv. _of the distribution of terms._ § . the treatment of this subject falls under the second part of logic, since distribution is not an attribute of terms in themselves, but one which they acquire in predication. § . a term is said to be distributed when it is known to be used in its whole extent, that is, with reference to all the things of which it is a name. when it is not so used, or is not known to be so used, it is called undistributed. § . when we say 'all men are mortal,' the subject is distributed, since it is apparent from the form of the expression that it is used in its whole extent. but when we say 'men are miserable' or 'some men are black,' the subject is undistributed. § . there is the same ambiguity attaching to the term 'undistributed' which we found to underlie the use of the term 'particular.' 'undistributed' is applied both to a term whose quantity is undefined, and to one whose quantity is definitely limited to a part of its possible extent. § . this awkwardness arises from not inquiring first whether the quantity of a term is determined or undetermined, and afterwards proceeding to inquire, whether it is determined as a whole or part of its possible extent. as it is, to say that a term is distributed, involves two distinct statements-- ( ) that its quantity is known; ( ) that its quantity is the greatest possible. the term 'undistributed' serves sometimes to contradict one of these statements and sometimes to contradict the other. § . with regard to the quantity of the subject of a proposition no difficulty can arise. the use of the words 'all' or 'some,' or of a variety of equivalent expressions, mark the subject as being distributed or undistributed respectively, while, if there be nothing to mark the quantity, the subject is for that reason reckoned undistributed. § . with regard to the predicate more difficulty may arise. § . it has been laid down already that, in the ordinary form of proposition, the subject is used in extension and the predicate in intension. let us illustrate the meaning of this by an example. if someone were to say 'cows are ruminants,' you would have a right to ask him whether he meant 'all cows' or only 'some.' you would not by so doing be asking for fresh information, but merely for a more distinct explanation of the statement already made. the subject being used in extension naturally assumes the form of the whole or part of a class. but, if you were to ask the same person 'do you mean that cows are all the ruminants that there are, or only some of them?' he would have a right to complain of the question, and might fairly reply, 'i did not mean either one or the other; i was not thinking of ruminants as a class. i wished merely to assert an attribute of cows; in fact, i meant no more than that cows chew the cud.' § . since therefore a predicate is not used in extension at all, it cannot possibly be known whether it is used in its whole extent or not. § . it would appear then that every predicate is necessarily undistributed; and this consequence does follow in the case of affirmative propositions. § . in a negative proposition, however, the predicate, though still used in intension, must be regarded as distributed. this arises from the nature of a negative proposition. for we must remember that in any proposition, although the predicate be not meant in extension, it always admits of being so read. now we cannot exclude one class from another without at the same time wholly excluding that other from the former. to take an example, when we say 'no horses are ruminants,' the meaning we really wish to convey is that no member of the class, horse, has a particular attribute, namely, that of chewing the cud. but the proposition admits of being read in another form, namely, 'that no member of the class, horse, is a member of the class, ruminant.' for by excluding a class from the possession of a given attribute, we inevitably exclude at the same time any class of things which possess that attribute from the former class. § . the difference between the use of a predicate in an affirmative and in a negative proposition may be illustrated to the eye as follows. to say 'all a is b' may mean either that a is included in b or that a and b are exactly co-extensive. [illustration] § . as we cannot be sure which of these two relations of a to b is meant, the predicate b has to be reckoned undistributed, since a term is held to be distributed only when we know that it is used in its whole extent. § . to say 'no a is b,' however, is to say that a falls wholly outside of b, which involves the consequence that b falls wholly outside of a. [illustration] § . let us now apply the same mode of illustration to the particular forms of proposition. § . if i be taken in the strictly particular sense, there are, from the point of view of extension, two things which may be meant when we say 'some a is b'-- ( ) that a and b are two classes which overlap one another, that is to say, have some members in common, e.g. 'some cats are black.' [illustration] ( ) that b is wholly contained in a, which is an inverted way of saying that all b is a, e.g. 'some animals are men.' [illustration] § . since we cannot be sure which of these two is meant, the predicate is again reckoned undistributed. § . if on the other hand be taken in an indefinite sense, so as to admit the possibility of the universal being true, then the two diagrams which have already been used for a must be extended to , in addition to its own, together with the remarks which we made in connection with them (§§ - ). § . again, when we say 'some a is not b,' we mean that some, if not the whole of a, is excluded from the possession of the attribute b. in either case the things which possess the attribute b are wholly excluded either from a particular part or from the whole of a. the predicate therefore is distributed. [illustration] from the above considerations we elicit the following-- § . four rules for the distribution of terms. ( ) all universal propositions distribute their subject. ( ) no particular propositions distribute their subject, ( ) all negative propositions distribute their predicate. ( ) no affirmative propositions distribute their predicate. § . the question of the distribution or non-distribution of the subject turns upon the quantity of the proposition, whether universal or particular; the question of the distribution or non-distribution of the predicate turns upon the quality of the proposition, whether affirmative or negative. chapter v. _of the quantification of the predicate._ § . the rules that have been given for the distribution of terms, together with the fourfold division of propositions into a, e, , , are based on the assumption that it is the distribution or non-distribution of the subject only that needs to be taken into account in estimating the quantity of a proposition. § . but some logicians have maintained that the predicate, though seldom quantified in expression, must always be quantified in thought--in other words, that when we say, for instance, 'all a is b,' we must mean either that 'all a is all b' or only that 'all a is some b.' § . if this were so, it is plain that the number of possible propositions would be exactly doubled, and that, instead of four forms, we should now have to recognise eight, which may be expressed as follows-- . all a is all b. ([upsilon]). . all a is some b. ([lambda]). . no a is any b. ([epsilon]). . no a is some b. ([eta]). . some a is all b. ([upsilon]). . some a is some b. ([iota]). . some a is not any b. ([omega]). . some a is not some b. ([omega]). § . it is evident that it is the second of the above propositions which represents the original a, in accordance with the rule that 'no affirmative propositions distribute their predicate' (§ ). § . the third represents the original e, in accordance with the rule that 'all negative propositions distribute their predicate.' § . the sixth represents the original i, in accordance with the rule that 'no affirmative propositions distribute their predicate.' § . the seventh represents the original o, in accordance with the rule that 'all negative propositions distribute their predicate.' § . four new symbols are required, if the quantity of the predicate as well as that of the subject be taken into account in the classification of propositions. these have been supplied, somewhat fancifully, as follows-- § . the first, 'all a is all b,' which distributes both subject and predicate, has been called [upsilon], to mark its extreme universality. § . the fourth, 'no a is some b,' is contained in e, and has therefore been denoted by the symbol [eta], to show its connection with e. § . the fifth, 'some a is all b,' is the exact converse of the second, 'all a is some b,' and has therefore been denoted by the symbol [upsilon], which resembles an inverted a. § . the eighth is contained in o, as part in whole, and has therefore had assigned to it the symbol [omega], § . the attempt to take the predicate in extension, instead of, as it should naturally be taken, in intension, leads to some curious results. let us take, for instance, the u proposition. either the sign of quantity 'all' must be understood as forming part of the predicate or not. if it is not, then the u proposition 'all a is all b' seems to contain within itself, not one proposition, but two, namely, 'all a is b' and 'all b is a.' but if on the other hand 'all' is understood to form part of the predicate, then u is not really a general but a singular proposition. when we say, 'all men are rational animals,' we have a true general proposition, because the predicate applies to the subject distributively, and not collectively. what we mean is that 'rational animal' may be affirmed of every individual in the class, man. but when we say 'all men are all rational animals,' the predicate no longer applies to the subject distributively, but only collectively. for it is obvious that 'all rational animals' cannot be affirmed of every individual in the class, man. what the proposition means is that the class, man, is co-extensive with the class, rational animal. the same meaning may be expressed intensively by saying that the one class has the attribute of co-extension with the other. § . under the head o u come all propositions in which both subject and predicate are singular terms, e.g. 'homer was the author of the iliad,' 'virtue is the way to happiness.' § . the proposition [eta] conveys very little information to the mind. 'no a is some b' is compatible with the a proposition in the same matter. 'no men are some animals' may be true, while at the same time it is true that 'all men are animals.' no men, for instance, are the particular animals known as kangaroos. § . the [omega] proposition conveys still less information than the [eta]. for [omega] is compatible, not only with a, but with [upsilon]. even though 'all men are all rational animals,' it is still true that 'some men are not some rational animals': for no given human being is the same rational animal as any other. § . nay, even when the [upsilon] is an identical proposition, [omega] will still hold in the same matter. 'all rational animals are all rational animals': but, for all that, 'some rational animals are not some others.' this last form of proposition therefore is almost wholly devoid of meaning. § . the chief advantage claimed for the quantification of the predicate is that it reduces every affirmative proposition to an exact equation between its subject and predicate. as a consequence every proposition would admit of simple conversion, that is to say, of having the subject and predicate transposed without any further change in the proposition. the forms also of reduction (a term which will be explained later on) would be simplified; and generally the introduction of the quantified predicate into logic might be attended with certain mechanical advantages. the object of the logician, however, is not to invent an ingenious system, but to arrive at a true analysis of thought. now, if it be admitted that in the ordinary form of proposition the subject is used in extension and the predicate in intension, the ground for the doctrine is at once cut away. for, if the predicate be not used in its extensive capacity at all, we plainly cannot be called upon to determine whether it is used in its whole extent or not. chapter vi. _of the heads of predicables_. § . a predicate is something which is stated of a subject. § . a predicable is something which can be stated of a subject. § . the heads of predicables are a classification of the various things which can be stated of a subject, viewed in their relation to it. § . the treatment of this topic, therefore, as it involves the relation of a predicate to a subject, manifestly falls under the second part of logic, which deals with the proposition. it is sometimes treated under the first part of logic, as though the heads of predicables were a classification of universal notions, i.e. common terms, in relation to one another, without reference to their place in the proposition. § . the heads of predicables are commonly reckoned as five, namely, ( ) genus. ( ) species. ( ) difference. ( ) property. ( ) accident. § . we will first define these terms in the sense in which they are now used, and afterwards examine the principle on which the classification is founded and the sense in which they were originally intended. ( ) a genus is a larger class containing under it smaller classes. animal is a genus in relation to man and brute. ( ) a species is a smaller class contained under a larger one. man is a species in relation to animal. ( ) difference is the attribute, or attributes, which distinguish one species from others contained under the same genus. rationality is the attribute which distinguishes the species, man, from the species, brute. n.b. the genus and the difference together make up the definition of a class-name, or common term. ( ) a property is an attribute which is not contained in the definition of a term, but which flows from it. a generic property is one which flows from the genus. a specific property is one which flows from the difference. it is a generic property of man that he is mortal, which is a consequence of his animality. it is a specific property of man that he is progressive, which is a consequence of his rationality. ( ) an accident is an attribute, which is neither contained in the definition, nor flows from it. § . accidents are either separable or inseparable. a separable accident is one which belongs only to some members of a class. an inseparable accident is one which belongs to all the members of a class. blackness is a separable accident of man, an inseparable accident of coals. § . the attributes which belong to anything may be distinguished broadly under the two heads of essential and non-essential, or accidental. by the essential attributes of anything are meant those which are contained in, or which flow from, the definition. now it may be questioned whether there can, in the nature of things, be such a thing as an inseparable accident. for if an attribute were found to belong invariably to all the members of a class, we should suspect that there was some causal connection between it and the attributes which constitute the definition, that is, we should suspect the attribute in question to be essential and not accidental. nevertheless the term 'inseparable accident' may be retained as a cloak for our ignorance, whenever it is found that an attribute does, as a matter of fact, belong to all the members of a class, without there being any apparent reason why it should do so. it has been observed that animals which have horns chew the cud. as no one can adduce any reason why animals that have horns should chew the cud any more than animals which have not, we may call the fact of chewing the cud an inseparable accident of horned animals. § . the distinction between separable and inseparable accidents is sometimes extended from classes to individuals. an inseparable accident of an individual is one which belongs to him at all times. a separable accident of an individual is one which belongs to him at one time and not at another. § . it is an inseparable accident of an individual that he was born at a certain place and on a certain date. it is a separable accident of an individual that he resides at a certain place and is of a certain age. § . there are some remarks which it may be well to make about the above five terms before we pass on to investigate the principle upon which the division is based. § . in the first place, it must of course be borne in mind that genus and species are relative terms. no class in itself can be either a genus or a species; it only becomes so in reference to some other class, as standing to it in the relation of containing or contained. § . again, the distinction between genus and difference on the one hand and property on the other is wholly relative to an assumed definition. when we say 'man is an animal,' 'man is rational,' 'man is progressive,' there is nothing in the nature of these statements themselves to tell us that the predicate is genus, difference, or property respectively. it is only by a tacit reference to the accepted definition of man that this becomes evident to us, similarly, we cannot know beforehand that the fact of a triangle having three sides is its difference, and the fact of its having three angles a property. it is only when we assume the definition of a triangle as a three-sided figure that the fact of its having three angles sinks into a property. had we chosen to define it, in accordance with its etymological meaning, as a figure with three angles, its three-sidedness would then have been a mere property, instead of being the difference; for these two attributes are so connected together that, whichever is postulated, the other will necessarily follow. § . lastly, it must be noticed that we have not really defined the term 'accident,' not having stated what it is, but only what it is not. it has in fact been reserved as a residual head to cover any attribute which is neither a difference nor a property. § . if the five heads of predicables above given were offered to us as an exhaustive classification of the possible relations in which the predicate can stand to the subject in a proposition, the first thing that would strike us is that they do not cover the case in which the predicate is a singular term. in such a proposition as 'this man is john,' we have neither a predication of genus or species nor of attribute: but merely the identification of one term with another, as applying to the same object. such criticism as this, however, would be entirely erroneous, since no singular term was regarded as a predicate. a predicable was another name for a universal, the common term being called a predicable in one relation and a universal in another-a predicable, extensively, in so far as it was applicable to several different things, a universal, intensively, in so far as the attributes indicated were implied in several other notions, as the attributes indicated by 'animal' are implied in 'horse,' 'sheep,' 'goat,' &c. § . it would be less irrelevant to point out how the classification breaks down in relation to the singular term as subject. when, for instance, we say 'socrates is an animal,' 'socrates is a man,' there is nothing in the proposition to show us whether the predicate is a genus or a species: for we have not here the relation of class to class, which gives us genus or species according to their relative extension, but the relation of a class to an individual. § . again, when we say ( ) some animals are men, ( ) some men are black, what is there to tell us that the predicate is to be regarded in the one case as a species and in the other as an accident of the subject? nothing plainly but the assumption of a definition already known. § . but if this assumption be granted, the classification seems to admit of a more or less complete defense by logic. for, given any subject, we can predicate of it either a class or an attribute. when the predicate is a class, the term predicated is called a genus, if the subject itself be a class, or a species, if it be an individual. when, on the other hand, the predicate is an attribute, the attribute predicated may be either the very attribute which distinguishes the subject from other members of the same class, in which case it is called the difference, or it may be some attribute connected with the definition, i.e. property, or not connected with it, i.e. accident. § . these results may be exhibited in the following scheme-- predicate ________________|_________________ | | class attribute ______|_______ __________|________ | | | | (subject a (subject a (the (not the common singular distinguishing distinguishing term) term) attribute) attribute) genus species difference |___________________ | | (connected (not connected with the with the definition) definition) property accident § . the distinction which underlies this division between predicating a class and predicating an attribute (in quid or in quale) is a perfectly intelligible one, corresponding as it does to the grammatical distinction between the predicate being a noun substantive or a noun adjective. nevertheless it is a somewhat arbitrary one, since, even when the predicate is a class-name, what we are concerned to convey to the mind, is the fact that the subject possesses the attributes which are connoted by that class-name. we have not here the difference between extensive and intensive predication, since, as we have already seen (§ ), that is not a difference between one proposition and another, but a distinction in our mode of interpreting any and every proposition. whatever proposition we like to take may be read either in extension or in intension, according as we fix our minds on the fact of inclusion in a class or the fact of the possession of attributes. § . it will be seen that the term 'species,' as it appears in the scheme, has a wholly different meaning from the current acceptation in which it was defined above. species, in its now accepted meaning, signifies the relation of a smaller class to a larger one: as it was originally intended in the heads of predicables it signifies a class in reference to individuals. § . another point which requires to be noticed with regard to this five-fold list of heads of predicables, if its object be to classify the relations of a predicate to a subject, is that it takes no account of those forms of predication in which class and attribute are combined. under which of the five heads would the predicates in the following propositions fall? ( ) man is a rational animal. ( ) man is a featherless biped. in the one case we have a combination of genus and difference; in the other we have a genus combined with an accident. § . the list of heads of predicables which we have been discussing is not derived from aristotle, but from the 'introduction' of porphyry, a greek commentator who lived more than six centuries later. _aristotle's heads of predicables_. § . aristotle himself, by adopting a different basis of division, has allowed room in his classification for the mixed forms of predication above alluded to. his list contains only four heads, namely, genus ([greek: génos]) definition ([greek: òrismós]) proprium ([greek: îdion]) accident ([greek: sumbebekós]) § . genus here is not distinguished from difference. whether we say 'man is an animal' or 'man is rational,' we are equally understood to be predicating a genus. § . there is no account taken of species, which, when predicated, resolves itself either into genus or accident. when predicated of an individual, it is regarded as a genus, e.g. 'socrates is a man'; when predicated of a class, it is regarded as an accident, e.g. 'some animals are men.' § . aristotle's classification may easily be seen to be exhaustive. for every predicate must either be coextensive with its subject or not, i.e. predicable of the same things. and if the two terms coincide in extension, the predicate must either coincide also in intension with the subject or not. a predicate which coincides both in extension and intension with its subject is exactly what is meant by a definition. one which coincides in extension without coinciding in intension, that is, which applies to the same things without expressing the whole meaning, of the subject, is what is known as a proprium or peculiar property. if, on the other hand, the two terms are not co-extensive, the predicate must either partially coincide in intension with the subject or not. [footnote: the case could not arise of a predicate which was entirely coincided in intension with a subject with which it was not co-extensive. for, if the extension of the predicate were greater than that of the subject, its intension would be less, and if less, greater, in accordance with the law of inverse variation of the two quantities (§ ).] this is equivalent to saying that it must either state part of the definition of the subject or not. now the definition is made up of genus and difference, either of which may form the predicate: but as the two are indistinguishable in relation to a single subject, they are lumped together for the present purpose under the one head, genus. when the predicate, not being co-extensive, is not even partially co-intensive with its subject, it is called an accident. § . proprium, it will be seen, differs from property. a proprium is an attribute which is possessed by all the members of a class, and by them alone, e.g. 'men are the only religious animals.' § . under the head of definition must be included all propositions in which the predicate is a mere synonym of the subject, e.g. 'naso is ovid,' 'a hebrew is a jew,' 'the skipper is the captain.' in such propositions the predicate coincides in extension with the subject, and may be considered to coincide in intension where the intension of both subject and predicate is at zero, as in the case of two proper names. § . designations and descriptions will fall under the head of 'proprium' or peculiar property, e.g. 'lord salisbury is the present prime minister of england,' 'man is a mammal with hands and without hair.' for here, while the terms are coincident in extension, they are far from being so in intension. § . the term 'genus' must be understood to include not only genus in the accepted sense, but difference and generic property as well. § . these results may be exhibited in the following scheme-- predicate ___________________|______________ | | coextensive with not the subject coextensive ________|_________ _____|________ | | | | co-intensive not partially not at all with the subject cointensive cointensive [greek: sumbubekós] [greek: òrismós] [greek: îdion] [greek: génos] accident ______|_____ ______|_____________ |________________ | | | | | | | | defini- synonym designa- descrip- peculiar genus differ- generic tion tion tion property ence property § . thus aristotle's four heads of predicables may be split up, if we please, into nine-- . definition \ > [greek: òrismós]. . synonym / . designation \ | . description > [greek: îdion]. | . peculiar property/ . genus	 \ | . difference	 > [greek: génos]. | . generic property/ . accident--[greek: sumbebekós]. § . we now pass on to the two subjects of definition and division, the discussion of which will complete our treatment of the second part of logic. definition and division correspond respectively to the two kinds of quantity possessed by terms. definition is unfolding the quantity of a term in intension. division is unfolding the quantity of a term in extension. chapter vii. _of definition._ § . to define a term is to unfold its intension, i.e. to explain its meaning. § . from this it follows that any term which possesses no intension cannot be defined. § . hence proper names do not admit of definition, except just in so far as they do possess some slight degree of intension: thus we can define the term 'john' only so far as to say that 'john' is the name of a male person. this is said with regard to the original intension of proper names; their acquired intension will be considered later. § . again, since definition is unfolding the intension of a term, it follows that those terms will not admit of being defined whose intension is already so simple that it cannot be unfolded further. of this nature are names of simple attributes, such as greenness, sweetness, pleasure, existence. we know what these things are, but we cannot define them. to a man who has never enjoyed sight, no language can convey an idea of the greenness of the grass or the blueness of the sky; and if a person were unaware of the meaning of the term 'sweetness,' no form of words could convey to him an idea of it. we might put a lump of sugar into his mouth, but that would not be a logical definition. § . thus we see that, for a thing to admit of definition, the idea of it must be complex. simple ideas baffle definition, but at the same time do not require it. in defining we lay out the simpler ideas which are combined in our notion of something, and so explain that complex notion. we have defined 'triangle,' when we analyse it into 'figure' and 'contained by three lines.' similarly we have defined 'substance' when we analyse it into 'thing' and 'which can be conceived to exist by itself.' § . but when we get to 'thing' we have reached a limit. the summum genus, or highest class under which all things fall, cannot be defined any more than a simple attribute; and for the very good reason that it connotes nothing but pure being, which is the simplest of all attributes. to say that a thing is an 'object of thought' is not really to define it, but to explain its etymology, and to reclaim a philosophical term from its abuse by popular language, in which it is limited to the concrete and the lifeless. again, to define it negatively and to say that a thing is 'that which is not nothing' does not carry us any further than we were before. the law of contradiction warrants us in saying as much as that. § . definition is confined to subject-terms, and does not properly extend to attributives. for definition is of things through names, and an attributive out of predication is not the name of anything. the attributive is defined, so far as it can be, through the corresponding abstract term. § . common terms, other than attributives, ought always to admit of definition. for things are distributed by the mind into classes owing to their possessing certain attributes in common, and the definition of the class-name can be effected by detailing these attributes, or at least a sufficient number of them. § . it is different with singular terms. singular terms, when abstract, admit of definition, in so far as they are not names of attributes so simple as to evade analysis. when singular terms are concrete, we have to distinguish between the two cases of proper names and designations. designations are connotative singular terms. they are formed by limiting a common term to the 'case in hand.' whatever definition therefore fits the common term will fit also the designation which is formed from it, if we add the attributes implied by the limitations. thus whatever definition fits the common term 'prime minister' will fit also the singular term 'the present prime minister of england' by the addition to it of the attributes of place and time which are indicated by the expression. such terms as this have a definite amount of intension, which can therefore be seized upon and expounded by a definition. § . but proper names, having no original intension of their own, cannot be defined at all; whereas, if we look upon them from the point of view of their acquired intension, they defy definition by reason of the very complexity of their meaning. we cannot say exactly what 'john' and 'mary' mean, because those names, to us who know the particular persons denoted by them, suggest all the most trifling accidents of the individual as well as the essential attributes of the genus. § . definition serves the practical purpose of enabling us mentally to distinguish, or, as the name implies, 'mark off' the thing defined from all other things whatsoever. this may seem at first an endless task, but there is a short cut by which the goal may be reached. for, if we distinguish the thing in hand from the things which it is most like, we shall, 'a fortiori,' have distinguished it from things to which it bears a less resemblance. § . hence the first thing to do in seeking for a definition is to fix upon the class into which the thing to be defined most naturally falls, and then to distinguish the thing in question from the other members of that class. if we were asked to define a triangle, we would not begin by distinguishing it from a hawser, but from a square and other figures with which it is more possible to confound it. the class into which a thing falls is called its genus, and the attribute or attributes which distinguish it from other members of that class are called its difference. § . if definition thus consists in referring a thing to a class, we see a further reason why the summum genus of all things cannot be defined. § . we have said that definition is useful in enabling us to distinguish things from one another in our minds: but this must not be regarded as the direct object of the process. for this object may be accomplished without giving a definition at all, by means of what is called a description. by a description is meant an enumeration of accidents with or without the mention of some class-name. it is as applicable to proper names as to common terms. when we say 'john smith lives next door on the right-hand side and passes by to his office every morning at nine o'clock,' we have, in all probability, effectually distinguished john smith from other people: but living next, &c., cannot be part of the intension of john smith, since john smith may change his residence or abandon his occupation without ceasing to be called by his name. indirectly then definition serves the purpose of distinguishing things in the mind, but its direct object is to unfold the intension of terms, and so impart precision to our thoughts by setting plainly before us the meaning of the words we are using. § . but when we say that definition is unfolding the intension of terms, it must not be imagined that we are bound in defining to unfold completely the intension of terms. this would be a tedious, and often an endless, task. a term may mean, or convey to the mind, a good many more attributes than those which are stated in its definition. there is no limit indeed to the meaning which a term may legitimately convey, except the common attributes of the things denoted by it. who shall say, for instance, that a triangle means a figure with three sides, and does not mean a figure with three angles, or the surface of the perpendicular bisection of a cone? or again, that man means a rational, and does not mean a speaking, a religious, or an aesthetic animal, or a biped with two eyes, a nose, and a mouth? the only attributes of which it can safely be asserted that they can form no part of the intension of a term are those which are not common to all the things to which the name applies. thus a particular complexion, colour, height, creed, nationality cannot form any part of the intension of the term 'man.' but among the attributes common to a class we cannot distinguish between essential and unessential, except by the aid of definition itself. formal logic cannot recognise any order of priority between the attributes common to all the members of a class, such as to necessitate our recognising some as genera and differentiae and relegating others to the place of properties or inseparable accidents. § . the art of giving a good definition is to seize upon the salient characteristics of the thing defined and those wherefrom the largest number of other attributes can be deduced as consequences. to do this well requires a special knowledge of the thing in question, and is not the province of the formal logician. § . we have seen already, in treating of the heads of predicables (§ ), that the difference between genus and difference on the one hand and property on the other is wholly relative to some assumed definition. now definitions are always to a certain extent arbitrary, and will vary with the point of view from which we consider the thing required to be defined. thus 'man' is usually contrasted with 'brute,' and from this point of view it is held a sufficient definition of him to say that he is 'a rational animal,' but a theologian might be more anxious to contrast man with supposed incorporeal intelligences, and from this point of view man would be defined as an 'embodied spirit.' § . in the two definitions just given it will be noticed that we have really employed exactly the same attributes, only their place as genus and difference has been reversed. it is man's rational, or spiritual, nature which distinguishes him from the brutes: but this is just what he is supposed to have in common with incorporeal intelligences, from whom he is differentiated by his animal nature. [illustration] this illustration is sufficient to show us that, while there is no absolute definition of anything, in the sense of a fixed genus and difference, there may at the same time be certain attributes which permanently distinguish the members of a given class from those of all other classes. § . the above remarks will have made it clear that the intension of a term is often much too wide to be conveyed by any definition; and that what a definition generally does is to select certain attributes from the whole intension, which are regarded as being more typical of the thing than the remainder. no definition can be expected to exhaust the whole intension of a term, and there will always be room for varying definitions of the same thing, according to the different points of view from which it is approached. § . names of attributes lend themselves to definition far more easily than names of substances. the reason of this is that names of attributes are primarily intensive in force, whereas substances are known to us in extension before they become known to us in intension. there is no difficulty in defining a term like 'triangle' or 'monarchy,' because these terms were expressly invented to cover certain attributes; but the case is different with such terms as 'dog,' 'tree,' 'plant,' 'metal,' and other names of concrete things. we none of us have any difficulty in recognising a dog or tree, when we see them, or in distinguishing them from other animals or plants respectively. we are therefore led to imagine that we know the meaning of these terms. it is not until we are called upon for a definition that we discover how superficial our knowledge really is of the common attributes possessed by the things which these names denote. § . it might be imagined that a common name would never be given to things except in virtue of our knowledge of their common attributes. but as a matter of fact, the common name was first given from a confused notion of resemblance, and we had afterwards to detect the common attributes, when sometimes the name had been so extended from one thing to another like it, that there were hardly any definite attributes possessed in common by the earlier and later members of the class. § . this is especially the case where the meaning of terms has been extended by analogy, e.g. head, foot, arm, post, pole, pipe, &c. § . but in the progress of thought we come to form terms in which the intensive capacity is everything. of this kind notably are mathematical conceptions. terms of this kind, as we said before, lend themselves readily to definition. § . we may lay down then roughly that words are easy or difficult of definition according as their intensive or extensive capacity predominates. § . there is a marked distinction to be observed between the classes made by the mind of man and the classes made by nature, which are known as 'real kinds.' in the former there is generally little or nothing in common except the particular attribute which is selected as the ground of classification, as in the case of red and white things, which are alike only in their redness or whiteness; or else their attributes are all necessarily connected, as in the case of circle, square and triangle. but the members of nature's classes agree in innumerable attributes which have no discoverable connection with one another, and which must therefore, provisionally at least, be regarded as standing in the relation of inseparable accidents to any particular attributes which we may select for the purposes of definition. there is no assignable reason why a rational animal should have hair on its head or a nose on its face, and yet man, as a matter of fact, has both; and generally the particular bodily configuration of man can only be regarded as an inseparable accident of his nature as a rational animal. § . 'real kinds' belong to the class of words mentioned above in which the extension predominates over the intension. we know well enough the things denoted by them, while most of us have only a dim idea of the points of resemblance between these things. nature's classes moreover shade off into one another by such imperceptible degrees that it is often impossible to fix the boundary line between one class and another. a still greater source of perplexity in dealing with real kinds is that it is sometimes almost impossible to fix upon any attribute which is common to every individual member of the class without exception. all that we can do in such cases is to lay down a type of the class in its perfect form, and judge of individual instances by the degree of their approximation to it. again, real kinds being known to us primarily in extension, the intension which we attach to the names is hable to be affected by the advance of knowledge. in dealing therefore with such terms we must be content with provisional definitions, which adequately express our knowledge of the things denoted by them, at the time, though a further study of their attributes may induce us subsequently to alter the definition. thus the old definition of animal as a sentient organism has been rendered inadequate by the discovery that so many of the phenomena of sensation can be exhibited by plants, § . but terms in which intension is the predominant idea are more capable of being defined once for all. aristotle's definitions of 'wealth' and 'monarchy' are as applicable now as in his own day, and no subsequent discoveries of the properties of figures will render euclid's definitions unavailable. § . we may distinguish therefore between two kinds of definition, namely, ( ) final. ( ) provisional. § . a distinction is also observed between real and nominal definitions. both of these explain the meaning of a term: but a real definition further assumes the actual existence of the thing defined. thus the explanation of the term 'centaur' would be a nominal, that of 'horse' a real definition. it is useless to assert, as is often done, that a nominal definition explains the meaning of a term and a real definition the nature of a thing; for, as we have seen already, the meaning of a term is whatever we know of the nature of a thing. § . it now remains to lay down certain rules for correct definition. § . the first rule that is commonly given is that a definition should state the essential attributes of the thing defined. but this amounts merely to saying that a definition should be a definition; since it is only by the aid of definition that we can distinguish between essential and non-essential among the common attributes exhibited by a class of things. the rule however may be retained as a material test of the soundness of a definition, in the sense that he who seeks to define anything should fix upon its most important attributes. to define man as a mammiferous animal having two hands, or as a featherless biped, we feel to be absurd and incongruous, since there is no reference to the most salient characteristic of man, namely, his rationality. nevertheless we cannot quarrel with these definitions on formal, but only on material grounds. again, if anyone chose to define logic as the art of thinking, all we could say is that we differ from him in opinion, as we think logic is more properly to be regarded as the science of the laws of thought. but here also it is on material grounds that we dissent from the definition. § . confining ourselves therefore to the sphere with which we are properly concerned, we lay down the following _rules for definition._ ( ) a definition must be co-extensive with the term defined. ( ) a definition must not state attributes which imply one another. ( ) a definition must not contain the name defined, either directly or by implication. ( ) a definition must be clearer than the term defined. ( ) a definition must not be negative, if it can be affirmative. briefly, a definition must be adequate ( ), terse ( ), clear ( ); and must not be tautologous ( ), or, if it can be avoided, negative ( ). § . it is worth while to notice a slight ambiguity in the term 'definition' itself. sometimes it is applied to the whole proposition which expounds the meaning of the term; at other times it is confined to the predicate of this proposition. thus in stating the first four rules we have used the term in the latter sense, and in stating the fifth in the former. § . we will now illustrate the force of the above rules by giving examples of their violation. rule . violations. a triangle is a figure with three equal sides. a square is a four-sided figure having all its sides equal. in the first instance the definition is less extensive than the term defined, since it applies only to equilateral triangles. this fault may be amended by decreasing the intension, which we do by eliminating the reference to the equality of the sides. in the second instance the definition is more extensive than the term defined. we must accordingly increase the intension by adding a new attribute 'and all its angles right angles.' rule . violation. a triangle is a figure with three sides and three angles. one of the chief merits of a definition is to be terse, and this definition is redundant, since what has three sides cannot but have three angles. rule . violations. a citizen is a person both of whose parents were citizens. man is a human being. rule . violations. a net is a reticulated fabric, decussated at regular intervals. life is the definite combination of heterogeneous changes, both simultaneous and successive, in correspondence with external co-existences and sequences. rule . violations. a mineral is that which is neither animal nor vegetable. virtue is the absence of vice. § . the object of definition being to explain what a thing is, this object is evidently defeated, if we confine ourselves to saying what it is not. but sometimes this is impossible to be avoided. for there are many terms which, though positive in form, are privative in force. these terms serve as a kind of residual heads under which to throw everything within a given sphere, which does not exhibit certain positive attributes. of this unavoidably negative nature was the definition which we give of 'accident,' which amounted merely to saying that it was any attribute which was neither a difference nor a property. § . the violation of rule , which guards against defining a thing by itself, is technically known as 'circulus in definiendo,' or defining in a circle. this rule is often apparently violated, without being really so. thus euclid defines an acute-angled triangle as one which has three acute angles. this seems a glaring violation of the rule, but is perfectly correct in its context; for it has already been explained what is meant by the terms 'triangle' and 'acute angle,' and all that is now required is to distinguish the acute-angled triangle from its cognate species. he might have said that an acute-angled triangle is one which has neither a right angle nor an obtuse angle: but rightly preferred to throw the same statement into a positive form. § . the violation of rule is known as 'ignotum per ignotius' or 'per aeque ignotum.' this rule also may seemingly be violated when it is not really so. for a definition may be correct enough from a special point of view, which, apart from that particular context, would appear ridiculous. from the point of view of conic sections, it is correct enough to define a triangle as that section of a cone which is formed by a plane passing through the vertex perpendicularly to the base, but this could not be expected to make things clearer to a person who was inquiring for the first time into the meaning of the word triangle. but a real violation of the fourth rule may arise, not only from obscurity, but from the employment of ambiguous language or metaphor. to say that 'temperance is a harmony of the soul' or that 'bread is the staff of life,' throws no real light upon the nature of the definiend. § . the material correctness of a definition is, as we have already seen, a matter extraneous to formal logic. an acquaintance with the attributes which terms imply involves material knowledge quite as much as an acquaintance with the things they apply to; knowledge of the intension and of the extension of terms is alike acquired by experience. no names are such that their meaning is rendered evident by the very constitution of our mental faculties; yet nothing short of this would suffice to bring the material content of definition within the province of formal logic. chapter viii. _of division._ § . to divide a term is to unfold its extension, that is, to set forth the things of which it is a name. § . but as in definition we need not completely unfold the intension of a term, so in division we must not completely unfold its extension. § . completely to unfold the extension of a term would involve stating all the individual objects to which the name applies, a thing which would be impossible in the case of most common terms. when it is done, it is called enumeration. to reckon up all the months of the year from january to december would be an enumeration, and not a division, of the term 'month.' § . logical division always stops short at classes. it may be defined as the statement of the various classes of things that can be called by a common name. technically we may say that it consists in breaking up a genus into its component species. § . since division thus starts with a class and ends with classes, it is clear that it is only common terms which admit of division, and also that the members of the division must themselves be common terms. § . an 'individual' is so called as not admitting of logical division. we may divide the term 'cow' into classes, as jersey, devonshire, &c., to which the name 'cow' will still be applicable, but the parts of an individual cow are no longer called by the name of the whole, but are known as beefsteaks, briskets, &c. § . in dividing a term the first requisite is to fix upon some point wherein certain members of the class differ from others. the point thus selected is called the fundamentum divisionis or basis of the division. § . the basis of the division will of course differ according to the purpose in hand, and the same term will admit of being divided on a number of different principles. thus we may divide the term 'man,' on the basis of colour, into white, black, brown, red, and yellow; or, on the basis of locality, into europeans, asiatics, africans, americans, australians, new zealanders, and polynesians; or again, on a very different principle, into men of nervous, sanguine, bilious, lymphatic and mixed temperaments. § . the term required to be divided is known as the totum divisum or divided whole. it might also be called the dividend. § . the classes into which the dividend is split up are called the membra dividentia, or dividing members. § . only two rules need be given for division-- ( ) the division must be conducted on a single basis. ( ) the dividing members must be coextensive with the divided whole. § . more briefly, we may put the same thing thus--there must be no cross-division ( ) and the division must be exhaustive ( ). § . the rule, which is commonly given, that each dividing member must be a common term, is already provided for under our definition of the process. § . the rule that the dividend must be predicable of each of the dividing members is contained in our second rule; since, if there were any term of which the dividend were not predicable, it would be impossible for the dividing members to be exactly coextensive with it. it would not do, for instance, to introduce mules and donkeys into a division of the term horse. § . another rule, which is sometimes given, namely, that the constituent species must exclude one another, is a consequence of our first; for, if the division be conducted on a single principle, the constituent species must exclude one another. the converse, however, does not hold true. we may have a division consisting of mutually exclusive members, which yet involves a mixture of different bases, e.g. if we were to divide triangle into scalene, isosceles and equiangular. this happens because two distinct attributes may be found in invariable conjunction. § . there is no better test, however, of the soundness of a division than to try whether the species overlap, that is to say, whether there are any individuals that would fall into two or more of the classes. when this is found to be the case, we may be sure that we have mixed two or more different fundamenta divisionis. if man, for instance, were to be divided into european, american, aryan, and semitic, the species would overlap; for both europe and america contain inhabitants of aryan and semitic origin. we have here members of a division based on locality mixed up with members of another division, which is based on race as indicated by language. § . the classes which are arrived at by an act of division may themselves be divided into smaller classes. this further process is called subdivision. § . let it be noticed that rule applies only to a single act of division. the moment that we begin to subdivide we not only may, but must, adopt a new basis of division; since the old one has, 'ex hypothesi,' been exhausted. thus, having divided men according to the colour of their skins, if we wish to subdivide any of the classes, we must look out for some fresh attribute wherein some men of the same complexion differ from others, e.g. we might divide black men into woolly-haired blacks, such as the negroes, and straight-haired blacks, like the natives of australia. § . we will now take an instance of division and subdivision, with a view to illustrating some of the technical terms which are used in connection with the process. keeping closely to our proper subject, we will select as an instance a division of the products of thought, which it is the province of logic to investigate. product of thought _______________|____________________________ | | | term proposition inference ____|___ ______|_____ _____|______ | | | | | | singular common universal particular immediate mediate ___|___ ___|___ | | | | a e i o here we have first a threefold division of the products of thought based on their comparative complexity. the first two of these, namely, the term and the proposition, are then subdivided on the basis of their respective quantities. in the case of inference the basis of the division is again the degree of complexity. the subdivision of the proposition is carried a step further than that of the others. having exhausted our old basis of quantity, we take a new attribute, namely, quality, on which to found the next step of subdivision. § . now in such a scheme of division and subdivision as the foregoing, the highest class taken is known as the summum genus. thus the summum genus is the same thing as the divided whole, viewed in a different relation. the term which is called the divided whole with reference to a single act of division, is called the summum genus whenever subdivision has taken place. § . the classes at which the division stops, that is, any which are not subdivided, are known as the infimae species. § . all classes intermediate between the summum genus and the infimae species are called subaltern genera or subaltern species, according to the way they are looked at, being genera in relation to the classes below them and species in relation to the classes above them. § . any classes which fall immediately under the same genus are called cognate species, e.g. singular and common terms are cognate species of term. § . the classes under which any lower class successively falls are called cognate genera. the relation of cognate species to one another is like that of children of the same parents, whereas cognate genera resemble a line of ancestry. § . the specific difference of anything is the attribute or attributes which distinguish it from its cognate species. thus the specific difference of a universal proposition is that the predicate is known to apply to the whole of the subject. a specific difference is said to constitute the species. § . the specific difference of a higher class becomes a generic difference with respect to the class below it. a generic difference then may be said to be the distinguishing attribute of the whole class to which a given species belongs. the generic difference is common to species that are cognate to one another, whereas the specific difference is peculiar to each. it is the generic difference of an a proposition that it is universal, the specific difference that it is affirmative. § . the same distinction is observed between the specific and generic properties of a thing. a specific property is an attribute which flows from the difference of a thing itself; a generic property is an attribute which flows from the difference of the genus to which the thing belongs. it is a specific property of an e proposition that its predicate is distributed, a generic property that its contrary cannot be true along with it (§ ); for this last characteristic flows from the nature of the universal proposition generally. § . it now remains to say a few words as to the place in logic of the process of division. since the attributes in which members of the same class differ from one another cannot possibly be indicated by their common name, they must be sought for by the aid of experience; or, to put the same thing in other words, since all the infimae species are alike contained under the summum genus, their distinctive attributes can be no more than separable accidents when viewed in relation to the summum genus. hence division, being always founded on the possession or non-possession of accidental attributes, seems to lie wholly outside the sphere of formal logic. this however is not quite the case, for, in virtue of the law of excluded middle, there is always open to us, independently of experience, a hypothetical division by dichotomy. by dichotomy is meant a division into two classes by a pair of contradictory terms, e.g. a division of the class, man, into white and not-white. now we cannot know, independently of experience, that any members of the class, man, possess whiteness; but we may be quite sure, independently of all experience, that men are either white or not. hence division by dichotomy comes strictly within the province of formal logic. only it must be noticed that both sides of the division must be hypothetical. for experience alone can tell us, on the one hand, that there are any men that are white, and on the other, that there are any but white men. § . what we call a division on a single basis is in reality the compressed result of a scheme of division and subdivision by dichotomy, in which a fresh principle has been introduced at every step. thus when we divide men, on the basis of colour, into white, black, brown, red and yellow, we may be held to have first divided men into white and not-white, and then to have subdivided the men that are not-white into black and not-black, and so on. from the strictly formal point of view this division can only be represented as follows-- men ___________________|_____ | | white (if any) not-white (if any) _________________|_____ | | black (if any) not-black (if any) __________________|____ | | brown (if any) not-brown (if any) ____________________|____ | | red (if any) not-red (if any). § . formal correctness requires that the last term in such a series should be negative. we have here to keep the term 'not-red' open, to cover any blue or green men that might turn up. it is only experience that enables us to substitute the positive term 'yellow' for 'not-red,' since we know as a matter of fact that there are no men but those of the five colours given in the original division. § . any correct logical division always admits of being arrived at by the longer process of division and subdivision by dichotomy. for instance, the term quadrilateral, or four-sided rectilinear figure, is correctly divided into square, oblong, rhombus, rhomboid and trapezium. the steps of which this division consists are as follows-- quadrilateral __________|_________ | | parallelogram trapezium _____|_____________________ | | rectangle non-rectangle ___|___ _____|_____ | | | | square oblong rhombus rhomboid. § . in reckoning up the infimae species in such a scheme, we must of course be careful not to include any class which has been already subdivided; but no harm is done by mixing an undivided class, like trapezium, with the subdivisions of its cognate species. § . the two processes of definition and division are intimately connected with one another. every definition suggests a division by dichotomy, and every division supplies us at once with a complete definition of all its members. § . definition itself, so far as concerns its content, is, as we have already seen, extraneous to formal logic: but when once we have elicited a genus and difference out of the material elements of thought, we are enabled, without any further appeal to experience, to base thereon a division by dichotomy. thus when man has been defined as a rational animal, we have at once suggested to us a division of animal into rational and irrational. § . again, the addition of the attributes, rational and irrational respectively, to the common genus, animal, ipso facto supplies us with definitions of the species, man and brute. similarly, when we subdivided rectangle into square and oblong on the basis of the equality or inequality of the adjacent sides, we were by so doing supplied with a definition both of square and oblong--'a square is a rectangle having all its sides equal,' and 'an oblong is a rectangle which has only its opposite sides equal.' § . the definition of a square just given amounts to the same thing as euclid's definition, but it complies with a rule which has value as a matter of method, namely, that the definition should state the proximate genus of the thing defined. § . since definition and division are concerned with the intension and extension of terms, they are commonly treated of under the first part of logic: but as the treatment of the subject implies a familiarity with the heads of predicables, which in their turn imply the proposition, it seems more desirable to deal with them under the second. § . we have already had occasion to distinguish division from enumeration. the latter is the statement of the individual things to which a name applies. in enumeration, as in division, the wider term is predicable of each of the narrower ones. § . partition is the mapping out of a physical whole into its component parts, as when we say that a tree consists of roots, stem, and branches. in a partition the name of the whole is not predicable of each of the parts. § . distinction is the separation from one another of the various meanings of an equivocal term. the term distinguished is predicable indeed of each of the members, but of each in a different sense. an equivocal term is in fact not one but several terms, as would quickly appear, if we were to use definitions in place of names. § . we have seen that a logical whole is a genus viewed in relation to its underlying species. from this must be distinguished a metaphysical whole, which is a substance viewed in relation to its attributes, or a class regarded in the same way. logically, man is a part of the class, animal; metaphysically, animal is contained in man. thus a logical whole is a whole in extension, while a metaphysical whole is a whole in intension. from the former point of view species is contained in genus; from the latter genus is contained in species. part iii.--of inferences. chapter i. _of inferences in general_. § . to infer is to arrive at some truth, not by direct experience, but as a consequence of some truth or truths already known. if we see a charred circle on the grass, we infer that somebody has been lighting a fire there, though we have not seen anyone do it. this conclusion is arrived at in consequence of our previous experience of the effects of fire. § . the term inference is used both for a process and for a product of thought. as a process inference may be defined as the passage of the mind from one or more propositions to another. as a product of thought inference may be loosely declared to be the result of comparing propositions. § . every inference consists of two parts-- ( ) the truth or truths already known; ( ) the truth which we arrive at therefrom. the former is called the antecedent, the latter the consequent. but this use of the terms 'antecedent' and 'consequent' must be carefully distinguished from the use to which they were put previously, to denote the two parts of a complex proposition. § . strictly speaking, the term inference, as applied to a product of thought, includes both the antecedent and consequent: but it is often used for the consequent to the exclusion of the antecedent. thus, when we have stated our premisses, we say quite naturally, 'and the inference i draw is so and so.' § . inferences are either inductive or deductive. in induction we proceed from the less to the more general; in deduction from the more to the less general, or, at all events, to a truth of not greater generality than the one from which we started. in the former we work up to general principles; in the latter we work down from them, and elicit the particulars which they contain. § . hence induction is a real process from the known to the unknown, whereas deduction is no more than the application of previously existing knowledge; or, to put the same thing more technically, in an inductive inference the consequent is not contained in the antecedent, in a deductive inference it is. § . when, after observing that gold, silver, lead, and other metals, are capable of being reduced to a liquid state by the application of heat, the mind leaps to the conclusion that the same will hold true of some other metal, as platinum, or of all metals, we have then an inductive inference, in which the conclusion, or consequent, is a new proposition, which was not contained in those that went before. we are led to this conclusion, not by reason, but by an instinct which teaches us to expect like results, under like circumstances. experience can tell us only of the past: but we allow it to affect our notions of the future through a blind belief that 'the thing that hath been, it is that which shall be; and that which is done is that which shall be done; and there is no new thing under the sun.' take away this conviction, and the bridge is cut which connects the known with the unknown, the past with the future. the commonest acts of daily life would fail to be performed, were it not for this assumption, which is itself no product of the reason. thus man's intellect, like his faculties generally, rests upon a basis of instinct. he walks by faith, not by sight. § . it is a mistake to talk of inductive reasoning, as though it were a distinct species from deductive. the fact is that inductive inferences are either wholly instinctive, and so unsusceptible of logical vindication, or else they may be exhibited under the form of deductive inferences. we cannot be justified in inferring that platinum will be melted by heat, except where we have equal reason for asserting the same thing of copper or any other metal. in fact we are justified in drawing an individual inference only when we can lay down the universal proposition, 'every metal can be melted by heat.' but the moment this universal proposition is stated, the truth of the proposition in the individual instance flows from it by way of deductive inference. take away the universal, and we have no logical warrant for arguing from one individual case to another. we do so, as was said before, only in virtue of that vague instinct which leads us to anticipate like results from like appearances. § . inductive inferences are wholly extraneous to the science of formal logic, which deals only with formal, or necessary, inferences, that is to say with deductive inferences, whether immediate or mediate. these are called formal, because the truth of the consequent is apparent from the mere form of the antecedent, whatever be the nature of the matter, that is, whatever be the terms employed in the proposition or pair of propositions which constitutes the antecedent. in deductive inference we never do more than vary the form of the truth from which we started. when from the proposition 'brutus was the founder of the roman republic,' we elicit the consequence 'the founder of the roman republic was brutus,' we certainly have nothing more in the consequent than was already contained in the antecedent; yet all deductive inferences may be reduced to identities as palpable as this, the only difference being that in more complicated cases the consequent is contained in the antecedent along with a number of other things, whereas in this case the consequent is absolutely all that the antecedent contains. § . on the other hand, it is of the very essence of induction that there should be a process from the known to the unknown. widely different as these two operations of the mind are, they are yet both included under the definition which we have given of inference, as the passage of the mind from one or more propositions to another. it is necessary to point this out, because some logicians maintain that all inference must be from the known to the unknown, whereas others confine it to 'the carrying out into the last proposition of what was virtually contained in the antecedent judgements.' § . another point of difference that has to be noticed between induction and deduction is that no inductive inference can ever attain more than a high degree of probability, whereas a deductive inference is certain, but its certainty is purely hypothetical. § . without touching now on the metaphysical difficulty as to how we pass at all from the known to the unknown, let us grant that there is no fact better attested by experience than this--'that where the circumstances are precisely alike, like results follow.' but then we never can be absolutely sure that the circumstances in any two cases are precisely alike. all the experience of all past ages in favour of the daily rising of the sun is not enough to render us theoretically certain that the sun will rise tomorrow we shall act indeed with a perfect reliance upon the assumption of the coming day-break; but, for all that, the time may arrive when the conditions of the universe shall have changed, and the sun will rise no more. § . on the other hand a deductive inference has all the certainty that can be imparted to it by the laws of thought, or, in other words, by the structure of our mental faculties; but this certainty is purely hypothetical. we may feel assured that if the premisses are true, the conclusion is true also. but for the truth of our premisses we have to fall back upon induction or upon intuition. it is not the province of deductive logic to discuss the material truth or falsity of the propositions upon which our reasonings are based. this task is left to inductive logic, the aim of which is to establish, if possible, a test of material truth and falsity. § . thus while deduction is concerned only with the relative truth or falsity of propositions, induction is concerned with their actual truth or falsity. for this reason deductive logic has been termed the logic of consistency, not of truth. § . it is not quite accurate to say that in deduction we proceed from the more to the less general, still less to say, as is often said, that we proceed from the universal to the particular. for it may happen that the consequent is of precisely the same amount of generality as the antecedent. this is so, not only in most forms of immediate inference, but also in a syllogism which consists of singular propositions only, e.g. the tallest man in oxford is under eight feet. so and so is the tallest man in oxford. .'. so and so is under eight feet. this form of inference has been named traduction; but there is no essential difference between its laws and those of deduction. § . subjoined is a classification of inferences, which will serve as a map of the country we are now about to explore. inference ________________________|__________ | | inductive deductive _________________|_______________ | | immediate mediate ___________|__________ ______|______ | | | | simple compound simple complex ______|________________ | ______|_____________|_ | | | | | | | opposition conversion permutation | conjunctive disjunctive dilemma | _________|________ | | conversion conversion by by negation position chapter ii. _of deductive inferences._ $ . deductive inferences are of two kinds--immediate and mediate. § . an immediate inference is so called because it is effected without the intervention of a middle term, which is required in mediate inference. § . but the distinction between the two might be conveyed with at least equal aptness in this way-- an immediate inference is the comparison of two propositions directly. a mediate inference is the comparison of two propositions by means of a third. § . in that sense of the term inference in which it is confined to the consequent, it may be said that-- an immediate inference is one derived from a single proposition. a mediate inference is one derived from two propositions conjointly. § . there are never more than two propositions in the antecedent of a deductive inference. wherever we have a conclusion following from more than two propositions, there will be found to be more than one inference. § . there are three simple forms of immediate inference, namely opposition, conversion and permutation. § . besides these there are certain compound forms, in which permutation is combined with conversion. chapter iii. _of opposition._ § . opposition is an immediate inference grounded on the relation between propositions which have the same terms, but differ in quantity or in quality or in both. § . in order that there should be any formal opposition between two propositions, it is necessary that their terms should be the same. there can be no opposition between two such propositions as these-- ( ) all angels have wings. ( ) no cows are carnivorous. § . if we are given a pair of terms, say a for subject and b for predicate, and allowed to affix such quantity and quality as we please, we can of course make up the four kinds of proposition recognised by logic, namely, a. all a is b. e. no a is b. i. some a is b. o. some a is not b. § . now the problem of opposition is this: given the truth or falsity of any one of the four propositions a, e, i, o, what can be ascertained with regard to the truth or falsity of the rest, the matter of them being supposed to be the same? § . the relations to one another of these four propositions are usually exhibited in the following scheme-- a . . . . contrary . . . . e . . . . . . . . . . . . . . . . . . . . . . . . subaltern contradictory subaltern . . . . . . . . . . . . . . . . . . . . . . . . i . . . sub-contrary . . . o § . contrary opposition is between two universals which differ in quality. § . sub-contrary opposition is between two particulars which differ in quality. § . subaltern opposition is between two propositions which differ only in quantity. § . contradictory opposition is between two propositions which differ both in quantity and in quality. § . subaltern opposition is also known as subalternation, and of the two propositions involved the universal is called the subalternant and the particular the subalternate. both together are called subalterns, and similarly in the other forms of opposition the two propositions involved are known respectively as contraries, sub-contraries and contradictories. § . for the sake of convenience some relations are classed under the head of opposition in which there is, strictly speaking, no opposition at all between the two propositions involved. § . between sub-contraries there is an apparent, but not a real opposition, since what is affirmed of one part of a term may often with truth be denied of another. thus there is no incompatibility between the two statements. ( ) some islands are inhabited. ( ) some islands are not inhabited. § . in the case of subaltern opposition the truth of the universal not only may, but must, be compatible with that of the particular. § . immediate inference by relation would be a more appropriate name than opposition; and relation might then be subdivided into compatible and incompatible relation. by 'compatible' is here meant that there is no conflict between the _truth_ of the two propositions. subaltern and sub-contrary opposition would thus fall under the head of compatible relation; contrary and contradictory relation under that of incompatible relation. relation ______________|_____________ | | compatible incompatible ______|_____ _____|_______ | | | | subaltern sub-contrary contrary contradictory. § . it should be noticed that the inference in the case of opposition is from the truth or falsity of one of the opposed propositions to the truth or falsity of the other. § . we will now lay down the accepted laws of inference with regard to the various kinds of opposition. § . contrary propositions may both be false, but cannot both be true. hence if one be true, the other is false, but not vice versâ. § . sub-contrary propositions may both be true, but cannot both be false. hence if one be false, the other is true, but not vice versâ. § . in the case of subaltern propositions, if the universal be true, the particular is true; and if the particular be false, the universal is false; but from the truth of the particular or the falsity of the universal no conclusion can be drawn. § . contradictory propositions cannot be either true or false together. hence if one be true, the other is false, and vice versâ. § . by applying these laws of inference we obtain the following results-- if a be true, e is false, o false, i true. if a be false, e is unknown, o true, i unknown. if e be true, o is true, i false, a false. if e be false, o is unknown, i true, a unknown. if o be true, i is unknown, a false, e unknown. if o be false, i is true, a true, e false. if i be true, a is unknown, e false, o unknown. if i be false, a is false, e true, o true. § . it will be seen from the above that we derive more information from deriving a particular than from denying a universal. should this seem surprising, the paradox will immediately disappear, if we reflect that to deny a universal is merely to assert the contradictory particular, whereas to deny a particular is to assert the contradictory universal. it is no wonder that we should obtain more information from asserting a universal than from asserting a particular. § . we have laid down above the received doctrine with regard to opposition: but it is necessary to point out a flaw in it. when we say that of two sub-contrary propositions, if one be false, the other is true, we are not taking the propositions i and o in their now accepted logical meaning as indefinite (§ ), but rather in their popular sense as 'strict particular' propositions. for if i and o were taken as indefinite propositions, meaning 'some, if not all,' the truth of i would not exclude the possibility of the truth of a, and, similarly, the truth of o would not exclude the possibility of the truth of e. now a and e may both be false. therefore i and o, being possibly equivalent to them, may both be false also. in that case the doctrine of contradiction breaks down as well. for i and o may, on this showing, be false, without their contradictories e and a being thereby rendered true. this illustrates the awkwardness, which we have previously had occasion to allude to, which ensures from dividing propositions primarily into universal and particular, instead of first dividing them into definite and indefinite, and particular (§ ). § . to be suddenly thrown back upon the strictly particular view of i and o in the special case of opposition, after having been accustomed to regard them as indefinite propositions, is a manifest inconvenience. but the received doctrine of opposition does not even adhere consistently to this view. for if i and o be taken as strictly particular propositions, which exclude the possibility of the universal of the same quality being true along with them, we ought not merely to say that i and o may both be true, but that if one be true the other must also be true. for i being true, a is false, and therefore o is true; and we may argue similarly from the truth of o to the truth of i, through the falsity of e. or--to put the same thing in a less abstract form--since the strictly particular proposition means 'some, but not all,' it follows that the truth of one sub-contrary necessarily carries with it the truth of the other, if we lay down that some islands only are inhabited, it evidently follows, or rather is stated simultaneously, that there are some islands also which are not inhabited. for the strictly particular form of proposition 'some a only is b' is of the nature of an exclusive proposition, and is really equivalent to two propositions, one affirmative and one negative. § . it is evident from the above considerations that the doctrine of opposition requires to be amended in one or other of two ways. either we must face the consequences which follow from regarding i and o as indefinite, and lay down that sub-contraries may both be false, accepting the awkward corollary of the collapse of the doctrine of contradiction; or we must be consistent with ourselves in regarding i and o, for the particular purposes of opposition, as being strictly particular, and lay down that it is always possible to argue from the truth of one sub-contrary to the truth of the other. the latter is undoubtedly the better course, as the admission of i and o as indefinite in this connection confuses the theory of opposition altogether. § . of the several forms of opposition contradictory opposition is logically the strongest. for this three reasons may be given-- ( ) contradictory opposites differ both in quantity and in quality, whereas others differ only in one or the other. ( ) contradictory opposites are incompatible both as to truth and falsity, whereas in other cases it is only the truth _or_ falsity of the two that is incompatible. ( ) contradictory opposition is the safest form to adopt in argument. for the contradictory opposite refutes the adversary's proposition as effectually as the contrary, and is not so hable to a counter-refutation. § . at first sight indeed contrary opposition appears stronger, because it gives a more sweeping denial to the adversary's assertion. if, for instance, some person with whom we were arguing were to lay down that 'all poets are bad logicians,' we might be tempted in the heat of controversy to maintain against him the contrary proposition 'no poets are bad logicians.' this would certainly be a more emphatic contradiction, but, logically considered, it would not be as sound a one as the less obtrusive contradictory, 'some poets are not bad logicians,' which it would be very difficult to refute. § . the phrase 'diametrically opposed to one another' seems to be one of the many expressions which have crept into common language from the technical usage of logic. the propositions a and o and e and i respectively are diametrically opposed to one another in the sense that the straight lines connecting them constitute the diagonals of the parallelogram in the scheme of opposition. § . it must be noticed that in the case of a singular proposition there is only one mode of contradiction possible. since the quantity of such a proposition is at the minimum, the contrary and contradictory are necessarily merged into one. there is no way of denying the proposition 'this house is haunted,' save by maintaining the proposition which differs from it only in quality, namely, 'this house is not haunted.' . a kind of generality might indeed he imparted even to a singular proposition by expressing it in the form 'a is always b.' thus we may say, 'this man is always idle'--a proposition which admits of being contradicted under the form 'this man is sometimes not idle.' chapter iv. _of conversion._ § . conversion is an immediate inference grounded on the transposition of the subject and predicate of a proposition. § . in this form of inference the antecedent is technically known as the convertend, i.e. the proposition to be converted, and the consequent as the converse, i.e. the proposition which has been converted. § . in a loose sense of the term we may be said to have converted a proposition when we have merely transposed the subject and predicate, when, for instance, we turn the proposition 'all a is b' into 'all b is a' or 'some a is not b' into 'some b is not a.' but these propositions plainly do not follow from the former ones, and it is only with conversion as a form of inference--with illative conversion as it is called--that logic is concerned. § . for conversion as a form of inference two rules have been laid down-- ( ) no term must be distributed in the converse which was not distributed in the convertend. ( ) the quality of the converse must be the same as that of the convertend. § . the first of these rules is founded on the nature of things. a violation of it involves the fallacy of arguing from part of a term to the whole. § . the second rule is merely a conventional one. we may make a valid inference in defiance of it: but such an inference will be seen presently to involve something more than mere conversion. § . there are two kinds of conversion-- ( ) simple. ( ) per accidens or by limitation. § . we are said to have simply converted a proposition when the quantity remains the same as before. § . we are said to have converted a proposition per accidens, or by limitation, when the rules for the distribution of terms necessitate a reduction in the original quantity of the proposition. § . a can only be converted per accidens. e and i can be converted simply. o cannot be converted at all. § . the reason why a can only be converted per accidens is that, being affirmative, its predicate is undistributed (§ ). since 'all a is b' does not mean more than 'all a is some b,' its proper converse is 'some b is a.' for, if we endeavoured to elicit the inference, 'all b is a,' we should be distributing the term b in the converse, which was not distributed in the convertend. hence we should be involved in the fallacy of arguing from the part to the whole. because 'all doctors are men' it by no means follows that 'all men are doctors.' § . e and i admit of simple conversion, because the quantity of the subject and predicate is alike in each, both subject and predicate being distributed in e and undistributed in i. / no a is b. e < \ .'. no b is a. / some a is b. i < \ .'. some b is a. § . the reason why o cannot be converted at all is that its subject is undistributed and that the proposition is negative. now, when the proposition is converted, what was the subject becomes the predicate, and, as the proposition must still be negative, the former subject would now be distributed, since every negative proposition distributes its predicate. hence we should necessarily have a term distributed in the converse which was not distributed in the convertend. from 'some men are not doctors,' it plainly does not follow that 'some doctors are not men'; and, generally from 'some a is not b' it cannot be inferred that 'some b is not a,' since the proposition 'some a is not b' admits of the interpretation that b is wholly contained in a. [illustration] § . it may often happen as a matter of fact that in some given matter a proposition of the form 'all b is a' is true simultaneously with 'all a is b.' thus it is as true to say that 'all equiangular triangles are equilateral' as that 'all equilateral triangles are equiangular.' nevertheless we are not logically warranted in inferring the one from the other. each has to be established on its separate evidence. § . on the theory of the quantified predicate the difference between simple conversion and conversion by limitation disappears. for the quantity of a proposition is then no longer determined solely by reference to the quantity of its subject. 'all a is some b' is of no greater quantity than 'some b is all a,' if both subject and predicate have an equal claim to be considered. § . some propositions occur in ordinary language in which the quantity of the predicate is determined. this is especially the case when the subject is a singular term. such propositions admit of conversion by a mere transposition of their subject and predicate, even though they fall under the form of the a proposition, e.g. virtue is the condition of happiness. .'. the condition of happiness is virtue. and again, virtue is a condition of happiness. .'. a condition of happiness is virtue. in the one case the quantity of the predicate is determined by the form of the expression as distributed, in the other as undistributed. § . conversion offers a good illustration of the principle on which we have before insisted, namely, that in the ordinary form of proposition the subject is used in extension and the predicate in intension. for when by conversion we change the predicate into the subject, we are often obliged to attach a noun substantive to the predicate, in order that it may be taken in extension, instead of, as before, in intension, e.g. some mothers are unkind. .'. some unkind persons are mothers. again, virtue is conducive to happiness. .'. one of the things which are conducive to happiness is virtue. chapter v. _of permutation._ § . permutation [footnote: called by some writers obversion.] is an immediate inference grounded on a change of quality in a proposition and a change of the predicate into its contradictory-term. § . in less technical language we may say that permutation is expressing negatively what was expressed affirmatively and vice versâ. § . permutation is equally applicable to all the four forms of proposition. (a) all a is b. .'. no a is not-b (e). (e) no a is b. .'. all a is not-b (a). (i) some a is b. .'. some a is not not-b (o). (o) some a is not b. .'. some a is not-b (i). § , or, to take concrete examples-- (a) all men are fallible. .'. no men are not-fallible (e). (e) no men are perfect. .'. all men are not-perfect (a). (i) some poets are logical. .'. some poets are not not-logical (o). (o) some islands are not inhabited. .'. some islands are not-inhabited (i). § . the validity of permutation rests on the principle of excluded middle, namely--that one or other of a pair of contradictory terms must be applicable to a given subject, so that, when one may be predicated affirmatively, the other may be predicated negatively, and vice versâ (§ ). § . merely to alter the quality of a proposition would of course affect its meaning; but when the predicate is at the same time changed into its contradictory term, the original meaning of the proposition is retained, whilst the form alone is altered. hence we may lay down the following practical rule for permutation-- change the quality of the proposition and change the predicate into its contradictory term. § . the law of excluded middle holds only with regard to contradictories. it is not true of a pair of positive and privative terms, that one or other of them must be applicable to any given subject. for the subject may happen to fall wholly outside the sphere to which such a pair of terms is limited. but since the fact of a term being applied is a sufficient indication of its applicability, and since within a given sphere positive and privative terms are as mutually destructive as contradictories, we may in all cases substitute the privative for the negative term in immediate inference by permutation, which will bring the inferred proposition more into conformity with the ordinary usage of language. thus the concrete instances given above will appear as follows-- (a) all men are fallible. .'. no men are infallible (e). (e) no men are perfect. .'. all men are imperfect (a). (i) some poets are logical. .'. some poets are not illogical (o). (o) some islands are not inhabited. .'. some islands are uninhabited (i). chapter vi. _of compound forms of immediate inference._ § . having now treated of the three simple forms of immediate inference, we go on to speak of the compound forms, and first of _conversion by negation._ § . when a and o have been permuted, they become respectively e and i, and, in this form, admit of simple conversion. we have here two steps of inference: but the process may be performed at a single stroke, and is then known as conversion by negation. thus from 'all a is b' we may infer 'no not-b is a,' and again from 'some a is not b' we may infer 'some not-b is a.' the nature of these inferences will be seen better in concrete examples. § . (a) all poets are imaginative. .'. no unimaginative persons are poets (e). (o) some parsons are not clerical. .'. some unclerical persons are parsons (i). § . the above inferences, when analysed, will be found to resolve themselves into two steps, namely, ( ) permutation. ( ) simple conversion. (a) all a is b. .'. no a is not-b (by permutation). .'. no not-b is a (by simple conversion). (o) some a is not b. .'. some a is not-b (by permutation). .'. some not-b is a (by simple conversion). § . the term conversion by negation has been arbitrarily limited to the exact inferential procedure of permutation followed by simple conversion. hence it necessarily applies only to a and propositions, since these when permuted become e and , which admit of simple conversion; whereas e and themselves are permuted into a and , which do not. there seems to be no good reason, however, why the term 'conversion by negation' should be thus restricted in its meaning; instead of being extended to the combination of permutation with conversion, no matter in what order the two processes may be performed. if this is not done, inferences quite as legitimate as those which pass under the title of conversion by negation are left without a name. § . from e and inferences may be elicited as follows-- (e) no a is b. .'. all b is not-a (a). (i) some a is b. .'. some b is not not-a (o). (e) no good actions are unbecoming. .'. all unbecoming actions are not-good (a). (i) some poetical persons are logicians. .'. some logicians are not unpoetical (o). or, taking a privative term for our subject, some unpractical persons are statesmen. .'. some statesmen are not practical. § . when the inferences just given are analysed, it will be found that the process of simple conversion precedes that of permutation. § . in the case of the e proposition a compound inference can be drawn even in the original order of the processes, no a is b. .'. some not-b is a. no one who employs bribery is honest. .'. some dishonest men employ bribery. the inference here, it must be remembered, does not refer to matter of fact, but means that one of the possible forms of dishonesty among men is that of employing bribery. § . if we analyse the preceding, we find that the second step is conversion by limitation. no a is b. .'. all a is not-b (by permutation). .'. some not-b is a (by conversion per accidens). § . from a again an inference can be drawn in the reverse order of conversion per accidens followed by permutation-- all a is b. .'. some b is not not-a. all ingenuous persons are agreeable. .'. some agreeable persons are not disingenuous. § . the intermediate link between the above two propositions is the converse per accidens of the first--'some b is a.' this inference, however, coincides with that from (§ ), as the similar inference from e (§ ) coincides with that from (§ ). § . all these inferences agree in the essential feature of combining permutation with conversion, and should therefore be classed under a common name. § . adopting then this slight extension of the term, we define conversion by negation as--a form of conversion in which the converse differs in quality from the convertend, and has the contradictory of one of the original terms. § . a still more complex form of immediate inference is known as _conversion by contraposition._ this mode of inference assumes the following form-- all a is b. .'. all not-b is not-a. all human beings are fallible. .'. all infallible beings are not-human. § . this will be found to resolve itself on analysis into three steps of inference in the following order-- ( ) permutation. ( ) simple conversion. ( ) permutation. § . let us verify this statement by performing the three steps. all a is b. .'. no a is not-b (by permutation). .'. no not-b is a (by simple conversion). .'. all not-b is not-a (by permutation). all englishmen are aryans. .'. no englishmen are non-aryans. .'. no non-aryans are englishmen. .'. all non-aryans are non-englishmen. § . conversion by contraposition may be complicated in appearance by the occurrence of a negative term in the subject or predicate or both, e.g. all not-a is b. .'. all not-b is a. again, all a is not-b. .'. all b is not-a. lastly, all not-a is not-b. .'. all b is a. § . the following practical rule will be found of use for the right performing of the process-- transpose the subject and predicate, and substitute for each its contradictory term. § . as concrete illustrations of the above forms of inference we may take the following-- all the men on this board that are not white are red. .'. all the men on this board that are not red are white. again, all compulsory labour is inefficient. .'. all efficient labour is free (=non-compulsory). lastly, all inexpedient acts are unjust. .'. all just acts are expedient. § . conversion by contraposition may be said to rest on the following principle-- if one class be wholly contained in another, whatever is external to the containing class is external also to the class contained. [illustration] § . the same principle may be expressed intensively as follows:-- if an attribute belongs to the whole of a subject, whatever fails to exhibit that attribute does not come under the subject. § . this statement contemplates conversion by contraposition only in reference to the a proposition, to which the process has hitherto been confined. logicians seem to have overlooked the fact that conversion by contraposition is as applicable to the o as to the a proposition, though, when expressed in symbols, it presents a more clumsy appearance. some a is not b. .'. some not-b is not not-a. some wholesome things are not pleasant. .'. some unpleasant things are not unwholesome. § . the above admits of analysis in exactly the same way as the same process when applied to the a proposition. some a is not b. .'. some a is not-b (by permutation). .'. some not-b is a (by simple conversion). .'. some not-b is not not-a (by permutation). the result, as in the case of the a proposition, is the converse by negation of the original proposition permuted. § . contraposition may also be applied to the e proposition by the use of conversion per accidens in the place of simple conversion. but, owing to the limitation of quantity thus effected, the result arrived at is the same as in the case of the o proposition. thus from 'no wholesome things are pleasant' we could draw the same inference as before. here is the process in symbols, when expanded. no a is b. .'. all a is not-b (by permutation). .'. some not-b is a (by conversion per accidens). .'. some not-b is not not-a (by permutation). § . in its unanalysed form conversion by contraposition may be defined generally as--a form of conversion in which both subject and predicate are replaced by their contradictories. § . conversion by contraposition differs in several respects from conversion by negation. ( ) in conversion by negation the converse differs in quality from the convertend: whereas in conversion by contraposition the quality of the two is the same. ( ) in conversion by negation we employ the contradictory either of the subject or predicate, but in conversion by contraposition we employ the contradictory of both. ( ) conversion by negation involves only two steps of immediate inference: conversion by contraposition three. § . conversion by contraposition cannot be applied to the ordinary e proposition except by limitation (§ ). from 'no a is b' we cannot infer 'no not-b is not-a.' for, if we could, the contradictory of the latter, namely, 'some not-b is not-a' would be false. but it is manifest that this is not necessarily false. for when one term is excluded from another, there must be numerous individuals which fall under neither of them, unless it should so happen that one of the terms is the direct contradictory of the other, which is clearly not conveyed by the form of the expression 'no a is b. 'no a is not-a' stands alone among e propositions in admitting of full conversion by contraposition, and the form of that is the same after it as before. § . nor can conversion by contraposition be applied at all to i. [illustration] from 'some a is b' we cannot infer that 'some not-b is not-a.' for though the proposition holds true as a matter of fact, when a and b are in part mutually exclusive, yet this is not conveyed by the form of the expression. it may so happen that b is wholly contained under a, while a itself contains everything. in this case it will be true that 'no not-b is not-a,' which contradicts the attempted inference. thus from the proposition 'some things are substances' it cannot be inferred that 'some not-substances are not-things,' for in this case the contradictory is true that 'no not-substances are not-things'; and unless an inference is valid in every case, it is not formally valid at all. § . it should be noticed that in the case of the [nu] proposition immediate inferences are possible by mere contraposition without conversion. all a is all b. .'. all not-a is not-b. for example, if all the equilateral triangles are all the equiangular, we know at once that all non-equilateral triangles are also non-equiangular. § . the principle upon which this last kind of inference rests is that when two terms are co-extensive, whatever is excluded from the one is excluded also from the other. chapter vii. _of other forms of immediate inference._ § . having treated of the main forms of immediate inference, whether simple or compound, we will now close this subject with a brief allusion to some other forms which have been recognised by logicians. § . every statement of a relation may furnish us with ail immediate inference in which the same fact is presented from the opposite side. thus from 'john hit james' we infer 'james was hit by john'; from 'dick is the grandson of tom' we infer 'tom is the grandfather of dick'; from 'bicester is north-east of oxford' we infer 'oxford is south-west of bicester'; from 'so and so visited the academy the day after he arrived in london' we infer 'so and so arrived in london the day before he visited the academy'; from 'a is greater than b' we infer 'b is less than a'; and so on without limit. such inferences as these are material, not formal. no law can be laid down for them except the universal postulate, that 'whatever is true in one form of words is true in every other form of words which conveys the same meaning.' § . there is a sort of inference which goes under the title of immediate inference by added determinants, in which from some proposition already made another is inferred, in which the same attribute is attached both to the subject and the predicate, e.g., a horse is a quadruped. .'. a white horse is a white quadruped. § . such inferences are very deceptive. the attributes added must be definite qualities, like whiteness, and must in no way involve a comparison. from 'a horse is a quadruped' it may seem at first sight to follow that 'a swift horse is a swift quadruped.' but we need not go far to discover how little formal validity there is about such an inference. from 'a horse is a quadruped' it by no means follows that 'a slow horse is a slow quadruped'; for even a slow horse is swift compared with most quadrupeds. all that really follows here is that 'a slow horse is a quadruped which is slow for a horse.' similarly, from 'a bushman is a man' it does not follow that 'a tall bushman is a tall man,' but only that 'a tall bushman is a man who is tall for a bushman'; and so on generally. § . very similar to the preceding is the process known as immediate inference by complex conception, e.g. a horse is a quadruped. .'. the head of a horse is the head of a quadruped. § . this inference, like that by added determinants, from which it differs in name rather than in nature, may be explained on the principle of substitution. starting from the identical proposition, 'the head of a quadruped is the head of a quadruped,' and being given that 'a horse is a quadruped,' so that whatever is true of 'quadruped' generally we know to be true of 'horse,' we are entitled to substitute the narrower for the wider term, and in this manner we arrive at the proposition, the head of a horse is the head of a quadruped. § . such an inference is valid enough, if the same caution be observed as in the case of added determinants, that is, if no difference be allowed to intervene in the relation of the fresh conception to the generic and the specific terms. chapter viii. _of mediate inferences or syllogisms._ § . a mediate inference, or syllogism, consists of two propositions, which are called the premisses, and a third proposition known as the conclusion, which flows from the two conjointly. § . in every syllogism two terms are compared with one another by means of a third, which is called the middle term. in the premisses each of the two terms is compared separately with the middle term; and in the conclusion they are compared with one another. § . hence every syllogism consists of three terms, one of which occurs twice in the premisses and does not appear at all in the conclusion. this term is called the middle term. the predicate of the conclusion is called the major term and its subject the minor term. § . the major and minor terms are called the extremes, as opposed to the mean or middle term. § . the premiss in which the major term is compared with the middle is called the major premiss. § . the other premiss, in which the minor term is compared with the middle, is called the minor premiss. § . the order in which the premisses occur in a syllogism is indifferent, but it is usual, for convenience, to place the major premiss first. § . the following will serve as a typical instance of a syllogism-- middle term major term \ major premiss. all mammals are warm-blooded | antecedent > or minor term middle term | premisses minor premiss. all whales are mammals / minor term major term \ consequent or .'. all whales are warm-blooded > conclusion. § . the reason why the names 'major, 'middle' and 'minor' terms were originally employed is that in an affirmative syllogism such as the above, which was regarded as the perfect type of syllogism, these names express the relative quantity in extension of the three terms. [illustration] § . it must be noticed however that, though the middle term cannot be of larger extent than the major nor of smaller extent than the minor, if the latter be distributed, there is nothing to prevent all three, or any two of them, from being coextensive. § . further, when the minor term is undistributed, we either have a case of the intersection of two classes, from which it cannot be told which of them is the larger, or the minor term is actually larger than the middle, when it stands to it in the relation of genus to species, as in the following syllogism-- all negroes have woolly hair. some africans are negroes. .'. some africans have woolly hair. [illustration] § . hence the names are not applied with strict accuracy even in the case of the affirmative syllogism; and when the syllogism is negative, they are not applicable at all: since in negative propositions we have no means of comparing the relative extension of the terms employed. had we said in the major premiss of our typical syllogism, 'no mammals are cold-blooded,' and drawn the conclusion 'no whales are cold-blooded,' we could not have compared the relative extent of the terms 'mammal' and 'cold-blooded,' since one has been simply excluded from the other. [illustration] § . so far we have rather described than defined the syllogism. all the products of thought, it will be remembered, are the results of comparison. the syllogism, which is one of them, may be so regarded in two ways-- ( ) as the comparison of two propositions by means of a third. ( ) as the comparison of two terms by means of a third or middle term. § . the two propositions which are compared with one another are the major premiss and the conclusion, which are brought into connection by means of the minor premiss. thus in the syllogism above given we compare the conclusion 'all whales are warm-blooded' with the major premiss 'all mammals are warm-blooded,' and find that the former is contained under the latter, as soon as we become acquainted with the intermediate proposition 'all whales are mammals.' § . the two terms which are compared with one another are of course the major and minor. § . the syllogism is merely a form into which our deductive inferences may be thrown for the sake of exhibiting their conclusiveness. it is not the form which they naturally assume in speech or writing. practically the conclusion is generally stated first and the premisses introduced by some causative particle as 'because,' 'since,' 'for,' &c. we start with our conclusion, and then give the reason for it by supplying the premisses. § . the conclusion, as thus stated first, was called by logicians the problema or quaestio, being regarded as a problem or question, to which a solution or answer was to be found by supplying the premisses. § . in common discourse and writing the syllogism is usually stated defectively, one of the premisses or, in some cases, the conclusion itself being omitted. thus instead of arguing at full length all men are fallible, the pope is a man, .'. the pope is fallible, we content ourselves with saying 'the pope is fallible, for he is a man,' or 'the pope is fallible, because all men are so'; or perhaps we should merely say 'all men are fallible, and the pope is a man,' leaving it to the sagacity of our hearers to supply the desired conclusion. a syllogism, as thus elliptically stated, is commonly, though incorrectly, called an enthymeme. when the major premiss is omitted, it is called an enthymeme of the first order; when the minor is omitted, an enthymeme of the second order; and when the conclusion is omitted an enthymeme of the third order. chapter ix. _of mood and figure._ § . syllogisms may differ in two ways-- ( ) in mood; ( ) in figure. § . mood depends upon the kind of propositions employed. thus a syllogism consisting of three universal affirmatives, aaa, would be said to differ in mood from one consisting of such propositions as eio or any other combination that might be made. the syllogism previously given to prove the fallibility of the pope belongs to the mood aaa. had we drawn only a particular conclusion, 'some popes are fallible,' it would have fallen into the mood aai. § . figure depends upon the arrangement of the terms in the propositions. thus a difference of figure is internal to a difference of mood, that is to say, the same mood can be in any figure. § . we will now show how many possible varieties there are of mood and figure, irrespective of their logical validity. § . and first as to mood. since every syllogism consists of three propositions, and each of these propositions may be either a, e, i, or o, it is clear that there will be as many possible moods as there can be combinations of four things, taken three together, with no restrictions as to repetition. it will be seen that there are just sixty-four of such combinations. for a may be followed either by itself or by e, i, or o. let us suppose it to be followed by itself. then this pair of premisses, aa, may have for its conclusion either a, e, i, or o, thus giving four combinations which commence with aa. in like manner there will be four commencing with ae, four with ai, and four with ao, giving a total of sixteen combinations which commence with a. similarly there will be sixteen commencing with e, sixteen with i, sixteen with o--in all sixty-four. it is very few, however, of these possible combinations that will be found legitimate, when tested by the rules of syllogism. § . next as to figure. there are four possible varieties of figure in a syllogism, as may be seen by considering the positions that can be occupied by the middle term in the premisses. for as there are only two terms in each premiss, the position occupied by the middle term necessarily determines that of the others. it is clear that the middle term must either occupy the same position in both premisses or not, that is, it must either be subject in both or predicate in both, or else subject in one and predicate in the other. now, if we are not acquainted with the conclusion of our syllogism, we do not know which is the major and which the minor term, and have therefore no means of distinguishing between one premiss and another; consequently we must stop here, and say that there are only three different arrangements possible. but, if the conclusion also be assumed as known, then we are able to distinguish one premiss as the major and the other as the minor; and so we can go further, and lay down that, if the middle term does not hold the same position in both premisses, it must either be subject in the major and predicate in the minor, or else predicate in the major and subject in the minor. § . hence there result _the four figures._ when the middle term is subject in the major and predicate in the minor, we are said to have the first figure. when the middle term is predicate in both premisses, we are said to have the second figure. when the middle term is subject in both premisses, we are said to have the third figure. when the middle term is predicate in the major premiss and subject in the minor, we are said to have the fourth figure. § . let a be the major term; b the middle. c the minor. figure i. figure ii. figure iii. figure iv. b--a a--b b--a a--b c--b c--b b--c b--c c--a c--a c--a c--a all these figures are legitimate, though the fourth is comparatively valueless. § . it will be well to explain by an instance the meaning of the assertion previously made, that a difference of figure is internal to a difference of mood. we will take the mood eio, and by varying the position of the terms, construct a syllogism in it in each of the four figures. i. e no wicked man is happy. i some prosperous men are wicked. o .'. some prosperous men are not happy. ii. e no happy man is wicked. i some prosperous men are wicked. o .'. some prosperous men are not happy. iii. e no wicked man is happy. i some wicked men are prosperous. o .'. some prosperous men are not happy. iv. e no happy man is wicked. i some wicked men are prosperous. o .'. some prosperous men are not happy. § . in the mood we have selected, owing to the peculiar nature of the premisses, both of which admit of simple conversion, it happens that the resulting syllogisms are all valid. but in the great majority of moods no syllogism would be valid at all, and in many moods a syllogism would be valid in one figure and invalid in another. as yet however we are only concerned with the conceivable combinations, apart from the question of their legitimacy. § . now since there are four different figures and sixty-four different moods, we obtain in all possible ways of arranging three terms in three propositions, that is, possible forms of syllogism. chapter x. _of the canon of reasoning._ & . the first figure was regarded by logicians as the only perfect type of syllogism, because the validity of moods in this figure may be tested directly by their complying, or failing to comply, with a certain axiom, the truth of which is self-evident. this axiom is known as the dictum de omni et nullo. it may be expressed as follows-- whatever may be affirmed or denied of a whole class may be affirmed or denied of everything contained in that class. § . this mode of stating the axiom contemplates predication as being made in extension, whereas it is more naturally to be regarded as being made in intension. § . the same principle may be expressed intensively as follows-- whatever has certain attributes has also the attributes which invariably accompany them .[footnote: nota notae est nota rei ipsius. 'whatever has any mark has that which it is a mark of.' mill, vol. i, p. ,] § . by aristotle himself the principle was expressed in a neutral form thus-- 'whatever is stated of the predicate will be stated also of the subject [footnote: [greek: osa katà toû kategorouménou légetai pánta kaì katà toû hypokeiménou rhaetésetai]. cat. , § i].' this way of putting it, however, is too loose. § . the principle precisely stated is as follows-- whatever may be affirmed or denied universally of the predicate of an affirmative proposition, may be affirmed or denied also of the subject. § . thus, given an affirmative proposition 'whales are mammals,' if we can affirm anything universally of the predicate 'mammals,' as, for instance, that 'all mammals are warm-blooded,' we shall be able to affirm the same of the subject 'whales'; and, if we can deny anything universally of the predicate, as that 'no mammals are oviparous,' we shall be able to deny the same of the subject. § . in whatever way the supposed canon of reasoning may be stated, it has the defect of applying only to a single figure, namely, the first. the characteristic of the reasoning in that figure is that some general rule is maintained to hold good in a particular case. the major premiss lays down some general principle, whether affirmative or negative; the minor premiss asserts that a particular case falls under this principle; and the conclusion applies the general principle to the particular case. but though all syllogistic reasoning may be tortured into conformity with this type, some of it finds expression more naturally in other ways. § . modern logicians therefore prefer to abandon the dictum de omni et nullo in any shape, and to substitute for it the following three axioms, which apply to all figures alike. _three axioms of mediale inference._ ( ) if two terms agree with the same third term, they agree with one another. ( ) if one term agrees, and another disagrees, with the same third term, they disagree with one another. ( ) if two terms disagree with the same third term, they may or may not agree with one another. § . the first of these axioms is the principle of all affirmative, the second of all negative, syllogisms; the third points out the conditions under which no conclusion can be drawn. if there is any agreement at all between the two terms and the third, as in the cases contemplated in the first and second axioms, then we have a conclusion of some kind: if it is otherwise, we have none. § . it must be understood with regard to these axioms that, when we speak of terms agreeing or disagreeing with the same third term, we mean that they agree or disagree with the same part of it. § . hence in applying these axioms it is necessary to bear in mind the rules for the distinction of terms. thus from all b is a, no c is b, the only inference which can be drawn is that some a is not c (which alters the figure from the first to the fourth). for it was only part of a which was known to agree with b. on the theory of the quantified predicate we could draw the inference no c is some a. § . it is of course possible for terms to agree with different parts of the same third term, and yet to have no connection with one another. thus all birds fly. all bats fly. but we do not infer therefrom that bats are birds or vice versâ. § . on the other hand, had we said,-- all birds lay eggs, no bats lay eggs, we might confidently have drawn the conclusion no bats are birds for the term 'bats,' being excluded from the whole of the term 'lay eggs,' is thereby necessarily excluded from that part of it which coincides with 'birds.' [illustration] chapter xi. _of the generad rules of syllogism._ § . we now proceed to lay down certain general rules to which all valid syllogisms must conform. these are divided into primary and derivative. i. _primary_. ( ) a syllogism must consist of three propositions only. ( ) a syllogism must consist of three terms only. ( ) the middle term must be distributed at least once in the premisses. ( ) no term must be distributed in the conclusion which was not distributed in the premisses. ( ) two negative premisses prove nothing. ( ) if one premiss be negative, the conclusion must be negative. ( ) if the conclusion be negative, one of the premisses must be negative: but if the conclusion be affirmative, both premisses must be affirmative. ii. _derivative_. ( ) two particular premisses prove nothing. ( ) if one premiss be particular, the conclusion must be particular. § . the first two of these rules are involved in the definition of the syllogism with which we started. we said it might be regarded either as the comparison of two propositions by means of a third or as the comparison of two terms by means of a third. to violate either of these rules therefore would be inconsistent with the fundamental conception of the syllogism. the first of our two definitions indeed (§ ) applies directly only to the syllogisms in the first figure; but since all syllogisms may be expressed, as we shall presently see, in the first figure, it applies indirectly to all. when any process of mediate inference appears to have more than two premisses, it will always be found that there is more than one syllogism. if there are less than three propositions, as in the fallacy of 'begging the question,' in which the conclusion simply reiterates one of the premisses, there is no syllogism at all. with regard to the second rule, it is plain that any attempted syllogism which has more than three terms cannot conform to the conditions of any of the axioms of mediate inference. § . the next two rules guard against the two fallacies which are fatal to most syllogisms whose constitution is unsound. § . the violation of rule is known as the fallacy of undistributed middle. the reason for this rule is not far to seek. for if the middle term is not used in either premiss in its whole extent, we may be referring to one part of it in one premiss and to quite another part of it in another, so that there will be really no middle term at all. from such premisses as these-- all pigs are omnivorous, all men are omnivorous, it is plain that nothing follows. or again, take these premisses-- some men are fallible, all popes are men. here it is possible that 'all popes' may agree with precisely that part of the term 'man,' of which it is not known whether it agrees with 'fallible' or not. § . the violation of rule is known as the fallacy of illicit process. if the major term is distributed in the conclusion, not having been distributed in the premiss, we have what is called illicit process of the major; if the same is the case with the minor term, we have illicit process of the minor. § . the reason for this rule is that if a term be used in its whole extent in the conclusion, which was not so used in the premiss in which it occurred, we would be arguing from the part to the whole. it is the same sort of fallacy which we found to underlie the simple conversion of an a proposition. § . take for instance the following-- all learned men go mad. john is not a learned man. .'. john will not go mad. in the conclusion 'john' is excluded from the whole class of persons who go mad, whereas in the premisses, granting that all learned men go mad, it has not been said that they are all the men who do so. we have here an illicit process of the major term. § . or again take the following-- all radicals are covetous. all radicals are poor. .'. all poor men are covetous. the conclusion here is certainly not warranted by our premisses. for in them we spoke only of some poor men, since the predicate of an affirmative proposition is undistributed. § . rule is simply another way of stating the third axiom of mediate inference. to know that two terms disagree with the same third term gives us no ground for any inference as to whether they agree or disagree with one another, e.g. ruminants are not oviparous. sheep are not oviparous. for ought that can be inferred from the premisses, sheep may or may not be ruminants. § . this rule may sometimes be violated in appearance, though not in reality. for instance, the following is perfectly legitimate reasoning. no remedy for corruption is effectual that does not render it useless. nothing but the ballot renders corruption useless. .'. nothing but the ballot is an effectual remedy for corruption. but on looking into this we find that there are four terms-- no not-a is b. no not-c is a. .'. no not-c is b. the violation of rule is here rendered possible by the additional violation of rule . in order to have the middle term the same in both premisses we are obliged to make the minor affirmative, thus no not-a is b. all not-c is not-a. .'. no not-c is b. no remedy that fails to render corruption useless is effectual. all but the ballot fails to render corruption useless. .'. nothing but the ballot is effectual. § . rule declares that, if one premiss be negative, the conclusion must be negative. now in compliance with rule , if one premiss be negative, the other must be affirmative. we have therefore the case contemplated in the second axiom, namely, of one term agreeing and the other disagreeing with the same third term; and we know that this can only give ground for a judgement of disagreement between the two terms themselves--in other words, to a negative conclusion. § . rule declares that, if the conclusion be negative, one of the premisses must be negative; but, if the conclusion be affirmative, both premisses must be affirmative. it is plain from the axioms that a judgement of disagreement can only be elicited from a judgement of agreement combined with a judgement of disagreement, and that a judgement of agreement can result only from two prior judgements of agreement. § . the seven rules already treated of are evident by their own light, being of the nature of definitions and axioms: but the two remaining rules, which deal with particular premisses, admit of being proved from their predecessors. § . proof of rule .--_that two particular premisses prove nothing_. we know by rule that both premisses cannot be negative. hence they must be either both affirmative, ii, or one affirmative and one negative, io or oi. now ii premisses do not distribute any term at all, and therefore the middle term cannot be distributed, which would violate rule . again in io or oi premisses there is only one term distributed, namely, the predicate of the o proposition. but rule requires that this one term should be the middle term. therefore the major term must be undistributed in the major premiss. but since one of the premisses is negative, the conclusion must be negative, by rule . and every negative proposition distributes its predicate. therefore the major term must be distributed where it occurs as predicate of the conclusion. but it was not distributed in the major premiss. therefore in drawing any conclusion we violate rule by an illicit process of the major term. § . proof of rule .--_that_, _if_ one _premiss be particular_, _the conclusion must be particular_. two negative premisses being excluded by rule , and two particular by rule , the only pairs of premisses we can have are-- ai, ao, ei. of course the particular premiss may precede the universal, but the order of the premisses will not affect the reasoning. ai premisses between them distribute one term only. this must be the middle term by rule . therefore the conclusion must be particular, as its subject cannot be distributed, ao and ei premisses each distribute two terms, one of which must be the middle term by rule : so that there is only one term left which may be distributed in the conclusion. but the conclusion must be negative by rule . therefore its predicate must be distributed. hence its subject cannot be so. therefore the conclusion must be particular. § . rules and are often lumped together in a single expression--'the conclusion must follow the weaker part,' negative being considered weaker than affirmative, and particular than universal. § . the most important rules of syllogism are summed up in the following mnemonic lines, which appear to have been perfected, though not invented, by a mediæval logician known as petrus hispanus, who was afterwards raised to the papal chair under the title of pope john xxi, and who died in -- distribuas medium, nec quartus terminus adsit; utraque nec praemissa negans, nec particularis; sectetur partem conclusio deteriorem, et non distribuat, nisi cum praemissa, negetve. chapter xii. _of the determination of the legitimate moods of syllogism._ § . it will be remembered that there were found to be possible moods, each of which might occur in any of the four figures, giving us altogether possible varieties of syllogism. the task now before us is to determine how many of these combinations of mood and figure are legitimate. § . by the application of the preceding rules we are enabled to reduce the possible moods to valid ones. this may be done by a longer or a shorter method. the longer method, which is perhaps easier of comprehension, is to write down the possible moods, and then strike out such as violate any of the rules of syllogism. aaa -aea- -aia- -aoa- -aae- aee -aie- -aoe- aai -aei- aii -aoi- -aao- aeo -aio- aoo -eaa- -eea- -eia- -eoa- eae -eee- -eie- -eoe- -eai- -eei- -eii- -eoi- eao -eeo- eio -eoo- [illustration] § . the batches which are crossed are those in which the premisses can yield no conclusion at all, owing to their violating rule or ; in the rest the premises are legitimate, but a wrong conclusion is drawn from each of them as are translineated. § . ieo stands alone, as violating rule . this may require a little explanation. since the conclusion is negative, the major term, which is its predicate, must be distributed. but the major premiss, being , does not distribute either subject or predicate. hence ieo must always involve an illicit process of the major. § . the ii moods which have been left valid, after being tested by the syllogistic rules, are as follows-- aaa. aai. aee. aeo. aii. aoo. eae. eao. eio. iai. oao. § . we will now arrive at the same result by a shorter and more scientific method. this method consists in first determining what pairs of premisses are valid in accordance with rules and g, and then examining what conclusions may be legitimately inferred from them in accordance with the other rules of syllogism. § . the major premiss may be either a, e, i or o. if it is a, the minor also may be either a, e, i or o. if it is e, the minor can only be a or i. if it is i, the minor can only be a or e. if it is o, the minor can only be a. hence there result valid pairs of premisses. aa. ae. ai. ao. ea. ei. ia. ie. oa. three of these pairs, namely aa, ae, ea, yield two conclusions apiece, one universal and one particular, which do not violate any of the rules of syllogism; one of them, ie, yields no conclusion at all; the remaining five have their conclusion limited to a single proposition, on the principle that the conclusion must follow the weaker part. hence we arrive at the same result as before, of ii legitimate moods-- aaa. aai. aee. aeo. eae. eao. aii. aoo. eio. iai. oao. chapter xiii. _of the special rules of the four figures_. § . our next task must be to determine how far the moods which we arrived at in the last chapter are valid in the four figures. but before this can be done, we must lay down the _special rules of the four figures_. figure . rule , the minor premiss must be affirmative. rule . the major premiss must be universal. figure ii. rule . one or other premiss must be negative. rule . the conclusion must be negative. rule . the major premiss must be universal. figure iii. rule . the minor premiss must be affirmative. rule . the conclusion must be particular. figure iv. rule . when the major premiss is affirmative, the minor must be universal. rule . when the minor premiss is particular, the major must be negative. rule , when the minor premiss is affirmative, the conclusion must be particular. rule . when the conclusion is negative, the major premiss must be universal. rule . the conclusion cannot be a universal affirmative. rule . neither of the premisses can be a particular negative. § . the special rules of the first figure are merely a reassertion in another form of the dictum de omni et nullo. for if the major premiss were particular, we should not have anything affirmed or denied of a whole class; and if the minor premiss were negative, we should not have anything declared to be contained in that class. nevertheless these rules, like the rest, admit of being proved from the position of the terms in the figure, combined with the rules for the distribution of terms (§ ). _proof of the special rules of the four figures._ figure . § . proof of rule .--_the minor premiss must be affirmative_. b--a c--b c--a if possible, let the minor premiss be negative. then the major must be affirmative (by rule ), [footnote: this refers to the general rules of syllogism.] and the conclusion must be negative (by rule ). but the major being affirmative, its predicate is undistributed; and the conclusion being negative, its predicate is distributed. now the major term is in this figure predicate both in the major premiss and in the conclusion. hence there results illicit process of the major term. therefore the minor premiss must be affirmative. § . proof of rule .--_the major premiss must be universal._ since the minor premiss is affirmative, the middle term, which is its predicate, is undistributed there. therefore it must be distributed in the major premiss, where it is subject. therefore the major premiss must be universal. figure ii. § . proof of rule ,--_one or other premiss must be negative_. a--b c--b c--a the middle term being predicate in both premisses, one or other must be negative; else there would be undistributed middle. § . proof of rule .--_the conclusion must be negative._ since one of the premisses is negative, it follows that the conclusion also must be so (by rule ). § . proof of rule .--_the major premiss must be universal._ the conclusion being negative, the major term will there be distributed. but the major term is subject in the major premiss. therefore the major premiss must be universal (by rule ). figure iii. § . proof of rule .--_the minor premiss must be affirmative._ b--a b--c c--a the proof of this rule is the same as in the first figure, the two figures being alike so far as the major term is concerned. § . proof of rule .--_the conclusion must be particular_. the minor premiss being affirmative, the minor term, which is its predicate, will be undistributed there. hence it must be undistributed in the conclusion (by rule ). therefore the conclusion must be particular. figure iv. § . proof of rule i.--_when the major premiss is affirmative, the minor must be universal_. if the minor were particular, there would be undistributed middle. [footnote: shorter proofs are employed in this figure, as the student is by this time familiar with the method of procedure.] § . proof of rule .--_when the minor premiss is particular, the major must be negative._ a--b b--c c--a this rule is the converse of the preceding, and depends upon the same principle. § . proof of rule .--_when the minor premiss is affirmative, the conclusion must be particular._ if the conclusion were universal, there would be illicit process of the minor. § . proof of rule .--_when the conclusion is negative, the major premiss must_ be universal. if the major premiss were particular, there would be illicit process of the major. § . proof of rule .--_the conclusion cannot be a universal affirmative_. the conclusion being affirmative, the premisses must be so too (by rule ). therefore the minor term is undistributed in the minor premiss, where it is predicate. hence it cannot be distributed in the conclusion (by rule ). therefore the affirmative conclusion must be particular. § . proof of rule .--_neither of the premisses can lie a, particular negative_. if the major premiss were a particular negative, the conclusion would be negative. therefore the major term would be distributed in the conclusion. but the major premiss being particular, the major term could not be distributed there. therefore we should have an illicit process of the major term. if the minor premiss were a particular negative, then, since the major must be affirmative (by rule ), we should have undistributed middle. chapter xiv _of the determination of the moods that are valid in the four figures._ § . by applying the special rules just given we shall be able to determine how many of the eleven legitimate moods are valid in the four figures. $ . these eleven legitimate moods were found to be aaa. aai. aee. aeo. aii. aoo. eae. eao. eio. iai. oao. figure . § . the rule that the major premiss must be universal excludes the last two moods, iai, oao. the rule that the minor premiss must be affirmative excludes three more, namely, aee, aeo, aoo. thus we are left with six moods which are valid in the first figure, namely, aaa. eae. aii. eio. aai. eao. figure ii. § . the rule that one premiss must be negative excludes four moods, namely, aaa, aai, aii, iai. the rule that the major must be universal excludes oao. thus we are left with six moods which are valid in the second figure, namely, eae. aee. eio. aoo. eao. aeo. figure iii. § . the rule that the conclusion must be particular confines us to eight moods, two of which, namely aee and aoo, are excluded by the rule that the minor premiss must be affirmative. thus we are left with six moods which are valid in the third figure, namely, aai. iai. aii. eao. oao. eio. figure iv. § . the first of the eleven moods, aaa, is excluded by the rule that the conclusion cannot be a universal affirmative. two more moods, namely aoo and oao, are excluded by the rule that neither of the premisses can be a particular negative. aii violates the rule that when the major premiss is affirmative, the minor must be universal. eae violates the rule that, when the minor premiss is affirmative, the conclusion must be particular. thus we are left with six moods which are valid in the fourth figure, namely, aai. aee. iai. eao. eio. aeo. § . thus the possible forms of syllogism have been reduced to two dozen legitimate combinations of mood and figure, six moods being valid in each of the four figures. figure i. aaa. eae. aii. eio. (aai. eao.) figure ii. eae. aee. eio. ago. (eao. aeo.) figure iii. aai. iai. aii. eao. oao. eio. figure iv. aai. aee. iai. eao. eio. (aeo.) § . the five moods enclosed in brackets, though valid, are useless. for the conclusion drawn is less than is warranted by the premisses. these are called subaltern moods, because their conclusions might be inferred by subalternation from the universal conclusions which can justly be drawn from the same premisses. thus aai is subaltern to aaa, eao to eae, and so on with the rest. § . the remaining combinations of mood and figure, which are loosely called 'moods,' though in strictness they should be called 'figured moods,' are generally spoken of under the names supplied by the following mnemonics-- barbara, celarent, darii, ferioque prioris; cesare, camestres, festino, baroko secundæ; tertia darapti, disamis, datisi, felapton, bokardo, ferison habet; quarta insuper addit bramantip, camenes, dimaris, fesapo, fresison: quinque subalterni, totidem generalibus orti, nomen habent nullum, nee, si bene colligis, usum. § . the vowels in these lines indicate the letters of the mood. all the special rules of the four figures can be gathered from an inspection of them. the following points should be specially noted. the first figure proves any kind of conclusion, and is the only one which can prove a. the second figure proves only negatives. the third figure proves only particulars. the fourth figure proves any conclusion except a. § . the first figure is called the perfect, and the rest the imperfect figures. the claim of the first to be regarded as the perfect figure may be rested on these grounds-- . it alone conforms directly to the dictum de omni et nullo. . it suffices to prove every kind of conclusion, and is the only figure in which a universal affirmative proposition can be established. . it is only in a mood of this figure that the major, middle and minor terms are to be found standing in their relative order of extension. § . the reason why a universal affirmative, which is of course infinitely the most important form of proposition, can only be proved in the first figure may be seen as follows. _proof that a can only be established in figure i._ an a conclusion necessitates both premisses being a propositions (by rule ). but the minor term is distributed in the conclusion, as being the subject of an a proposition, and must therefore be distributed in the minor premiss, in order to which it must be the subject. therefore the middle term must be the predicate and is consequently undistributed. in order therefore that the middle term may be distributed, it must be subject in the major premiss, since that also is an a proposition. but when the middle term is subject in the major and predicate in the minor premiss, we have what is called the first figure. chapter xv. _of the special canons of the four figures._ § . so far we have given only a negative test of legitimacy, having shown what moods are not invalidated by running counter to any of the special rules of the four figures. we will now lay down special canons for the four figures, conformity to which will serve as a positive test of the validity of a given mood in a given figure. the special canon of the first figure--will of course be practically equivalent to the dictum de omni et nullo. all of them will be expressed in terms of extension, for the sake of perspicuity. _special canons of the four figures._ figure . § . canon. if one term wholly includes or excludes another, which wholly or partly includes a third, the first term wholly or partly includes or excludes the third. here four cases arise-- [illustration] ( ) total inclusion (barbara). all b is a. all c is b. .'. all c is a. [illustration] ( ) partial inclusion (darii). all b is a. some c is b. .'. some c is a. [illustration] ( ) total exclusion (celarent). no b is a. all c is b. .'. no c is a. [illustration] ( ) partial exclusion (ferio). no b is a. some c is b. .'. some c is not a. figure ii. § . canon. if one term is excluded from another, which wholly or partly includes a third, or is included in another from which a third is wholly or partly excluded, the first is excluded from the whole or part of the third. here we have four cases, all of exclusion-- ( ) total exclusion on the ground of inclusion in an excluded term (cesare). [illustration] no a is b. all c is b. .'. no c is a. ( ) partial exclusion on the ground of a similar partial inclusion (festino). [illustration] no a is b. some c is b. .'. some c is not a. ( ) total exclusion on the ground of exclusion from an including term (camestres). [illustration] all a is b. no c is b. .'. no c is a. ( ) partial exclusion on the ground of a similar partial exclusion (baroko). [illustration] all a is b. some c is not b. .'. some c is not a. figure iii. § . canon. if two terms include another term in common, or if the first includes the whole and the second a part of the same term, or vice versâ, the first of these two terms partly includes the second; and if the first is excluded from the whole of a term which is wholly or in part included in the second, or is excluded from part of a term which is wholly included in the second, the first is excluded from part of the second. here it is evident from the statement that six cases arise-- ( ) total inclusion of the same term in two others (darapti). [illustration] all b is a. all b is c. .'. some c is a. ( ) total inclusion in the first and partial inclusion in the second (datisi). [illustration] all b is a. some b is c. .'. some c is a. ( ) partial inclusion in the first and total inclusion in the second (disamis). [illustration] some b is a. all b is c. .'. some c is a. ( ) total exclusion of the first from a term which is wholly included in the second (felapton). [illustration] no b is a. all b is c. .'. some c is not a. ( ) total exclusion of the first from a term which is partly included in the second (ferison). [illustration] no b is a. some b is c. .'. some c is not a. ( ) exclusion of the first from part of a term which is wholly included in the second (bokardo). [illustration] some b is not a. all b is c. .'. some c is not a. figure iv. § . canon. if one term is wholly or partly included in another which is wholly included in or excluded from a third, the third term wholly or partly includes the first, or, in the case of total inclusion, is wholly excluded from it; and if a term is excluded from another which is wholly or partly included in a third, the third is partly excluded from the first. here we have five cases-- ( ) of the inclusion of a whole term (bramsntip). [illustration] all a is b. all b is c. .'. some c is (all) a. ( ) of the inclusion of part of a term (dimaris). [illustration] some a is b. all b is c. .'. some c is (some) a, ( ) of the exclusion of a whole term (camenes). [illustration] all a is b. no b is c. .'. no c is a. ( ) partial exclusion on the ground of including the whole of an excluded term (fesapo). [illustration] no a is b. all b is c. .'. some c is not a. ( ) partial exclusion on the ground of including part of an excluded term (fresison). [illustration] no a is b. some b is c. .'. some c is not a. § . it is evident from the diagrams that in the subaltern moods the conclusion is not drawn directly from the premisses, but is an immediate inference from the natural conclusion. take for instance aai in the first figure. the natural conclusion from these premisses is that the minor term c is wholly contained in the major term a. but instead of drawing this conclusion we go on to infer that something which is contained in c, namely some c, is contained in a. [illustration] all b is a. all c is b. .'. all c is a. .'. some c is a. similarly in eao in figure , instead of arguing that the whole of c is excluded from a, we draw a conclusion which really involves a further inference, namely that part of c is excluded from a. [illustration] no b is a. all c is b. .'. no c is a. .'. some c is not a. § . the reason why the canons have been expressed in so cumbrous a form is to render the validity of all the moods in each figure at once apparent from the statement. for purposes of general convenience they admit of a much more compendious mode of expression. § . the canon of the first figure is known as the dictum de omni et nullo-- what is true (distributively) of a whole term is true of all that it includes. § . the canon of the second figure is known as the dictum de diverse-- if one term is contained in, and another excluded from a third term, they are mutually excluded. § . the canon of the third figure is known as the dictum de exemplo et de excepto-- two terms which contain a common part partly agree, or, if one contains a part which the other does not, they partly differ. § . the canon of the fourth figure has had no name assigned to it, and does not seem to admit of any simple expression. another mode of formulating it is as follows:-- whatever is affirmed of a whole term may have partially affirmed of it whatever is included in that term (bramantip, dimaris), and partially denied of it whatever is excluded (fesapo); whatever is affirmed of part of a term may have partially denied of it whatever is wholly excluded from that term (fresison); and whatever is denied of a whole term may have wholly denied of it whatever is wholly included in that term (camenes). § . from the point of view of intension the canons of the first three figures may be expressed as follows. § . canon of the first figure. dictum de omni et nullo-- an attribute of an attribute of anything is an attribute of the thing itself. § . canon of the second figure. dictum de diverso-- if a subject has an attribute which a class has not, or vice versa, the subject does not belong to the class. § . canon of the third figure. . dictum de exemplo-- if a certain attribute can be affirmed of any portion of the members of a class, it is not incompatible with the distinctive attributes of that class. . dictum de excepto-- if a certain attribute can be denied of any portion of the members of a class, it is not inseparable from the distinctive attributes of that class. chapter xvi. _of the special uses of the four figures._ § . the first figure is useful for proving the properties of a thing. § . the second figure is useful for proving distinctions between things. § . the third figure is useful for proving instances or exceptions. § . the fourth figure is useful for proving the species of a genus. figure . § . b is or is not a. c is b. .'. c is or is not a. we prove that c has or has not the property a by predicating of it b, which we know to possess or not to possess that property. luminous objects are material. comets are luminous. .'. comets are material. no moths are butterflies. the death's head is a moth. .'. the death's head is not a butterfly. figure ii. § . a is b. a is not b. c is not b. c is b. .'. c is not a. .'. c is not a. we establish the distinction between c and a by showing that a has an attribute which c is devoid of, or is devoid of an attribute which c has. all fishes are cold-blooded. a whale is not cold-blooded. .'. a whale is not a fish. no fishes give milk. a whale gives milk. .'. a whale is not a fish. figure iii. § . b is a. b is not a. b is c. b is c. .'. some c is a. .'. some c is not a. we produce instances of c being a by showing that c and a meet, at all events partially, in b. thus if we wish to produce an instance of the compatibility of great learning with original powers of thought, we might say sir william hamilton was an original thinker. sir william hamilton was a man of great learning. .'. some men of great learning are original thinkers. or we might urge an exception to the supposed rule about scotchmen being deficient in humour under the same figure, thus-- sir walter scott was not deficient in humour. sir walter scott was a scotchman. .'. some scotchmen are not deficient in humour. figure iv. § . all a is b, no a is b. all b is c. all b is c. .'. some c is a .'.some c is not a. we show here that a is or is not a species of c by showing that a falls, or does not fall, under the class b, which itself falls under c. thus-- all whales are mammals. all mammals are warm-blooded. .'. some warm-blooded animals are whales. no whales are fishes. all fishes are cold-blooded. .'. some cold-blooded animals are not whales. chapter xvii. _of the syllogism with three figures._ § . it will be remembered that in beginning to treat of figure (§ ) we pointed out that there were either four or three ligures possible according as the conclusion was assumed to be known or not. for, if the conclusion be not known, we cannot distinguish between the major and the minor term, nor, consequently, between one premiss and another. on this view the first and the fourth figures are the same, being that arrangement of the syllogism in which the middle term occupies a different position in one premiss from what it does in the other. we will now proceed to constitute the legitimate moods and figures of the syllogism irrespective of the conclusion. § . when the conclusion is set out of sight, the number of possible moods is the same as the number of combinations that can be made of the four things, a, e, i, o, taken two together, without restriction as to repetition. these are the following :-- aa ea ia oa ae -ee- ie -oe- ai ei -ii- -oi- ao -eo- -io- -oo- of which seven may be neglected as violating the general rules of the syllogism, thus leaving us with nine valid moods-- aa. ae. ai. ao. ea. ei. ia. ie. oa. § . we will now put these nine moods successively into the three figures. by so doing it will become apparent how far they are valid in each. § . let it be premised that when the extreme in the premiss that stands first is predicate in the conclusion, we are said to have a direct mood; when the extreme in the premiss that stands second is predicate in the conclusion, we are said to have an indirect mood. § . figure . _mood aa._ all b is a. all c is b. .'. all c is a, or some a is c, (barbara & bramantip). _mood ae._ all b is a. no c is b. .'. illicit process, or some a is not c, (fesapo). _mood ai._ all b is a. some c is b. .'. some c is a, or some a is c. (darii & disamis). _mood ao._ all b is a. some c is not b. .'. illicit process, (ferio). _mood ea._ no b is a. all c is b. .'. no c is a, or no a is c, (celarent & camenes). _mood ei._ no b is a. some c is b. .'. some c is not a, or illicit process. _mood ia._ some b is a. all c is b. .'. undistributed middle. _mood ie._ some b is c. some b is not a. no a is b. all c is b. .'. illicit process, or some c is not a, (fresison). _mood oa._ some b is not a. all c is b. .'. undistributed middle. § . thus we are left with six valid moods, which yield four direct conclusions and five indirect ones, corresponding to the four moods of the original first figure and the five moods of the original fourth, which appear now as indirect moods of the first figure. § . but why, it maybe asked, should not the moods of the first figure equally well be regarded as indirect moods of the fourth? for this reason-that all the moods of the fourth figure can be elicited out of premisses in which the terms stand in the order of the first, whereas the converse is not the case. if, while retaining the quantity and quality of the above premisses, i. e. the mood, we were in each case to transpose the terms, we should find that we were left with five valid moods instead of six, since ai in the reverse order of the terms involves undistributed middle; and, though we should have celarent indirect to camenes, and darii to dimaris, we should never arrive at the conclusion of barbara or have anything exactly equivalent to ferio. in place of barbara, bramantip would yield as an indirect mood only the subaltern aai in the first figure. both fesapo and fresison would result in an illicit process, if we attempted to extract the conclusion of ferio from them as an indirect mood. the nearest approach we could make to ferio would be the mood eao in the first figure, which may be elicited indirectly from the premisses of camenes, being subaltern to celarent. for these reasons the moods of the fourth figure are rightly to be regarded as indirect moods of the first, and not vice versâ. $ . figure ii. _mood aa._ all a is b. all c is b. .'. undistributed middle. _mood ae._ all a is b. no c is b. .'. no c is a, or no a is c, (camestres & cesare). _mood ai._ all a is b. some c is b. .'. undistributed middle. _mood ao._ all a is b. some c is not b. .'. some c is not a, (baroko), or illicit process. _mood ea._ no a is b. all c is b. .'. no c is a, or no a is c, (cesare & carnestres). _mood ei_ no a is b. some c is b. .'. some c is not a, (festino), or illicit process. _mood ia._ some a is b. all c is b. .'. undistributed middle. _mood ie._ some a is b. no c is b. .'. illicit process, or some a is not c, (festino). _mood oa._ some a is not b. all c is b. .'. illicit process, or some a is not c, (baroko). § . here again we have six valid moods, which yield four direct conclusions corresponding to cesare, carnestres, festino and baroko. the same four are repeated in the indirect moods. § . figure iii. _mood aa._ all b is a. all b is c. .'. some c is a, or some a is c, (darapti). _mood ae._ all b is a. no b is c. .'. illicit process, or some a is not c, (felapton). _mood ai._ all b is a, some b is c. .'. some c is a, or some a is c, (datisi & disamis). _mood ao._ all b is a. some b is not c. .'. illicit process, or some a is not c, (bokardo). _mood ea._ no b is a. all b is c. .'. some c is not a, (felapton), or illicit process. _mood ei._ no b is a. some b is c. .'. some c is not a, (ferison), or illicit process. _mood ia._ some b is a. all b is c. .'. some c is a, or some a is c, (disamis & datisi). _mood ie._ some b is a. no b is c. .'. illicit process, or some a is not c, (ferison). _mood qa._ some b is not a. all b is c. .'. some c is not a, (bokardo), or illicit process. § . in this figure every mood is valid, either directly or indirectly. we have six direct moods, answering to darapti, disamis, datisi, felapton, bokardo and ferison, which are simply repeated by the indirect moods, except in the case of darapti, which yields a conclusion not provided for in the mnemonic lines. darapti, though going under one name, has as much right to be considered two moods as disamis and datisi. chapter xviii. _of reduction._ § . we revert now to the standpoint of the old logicians, who regarded the dictum de omni et nullo as the principle of all syllogistic reasoning. from this point of view the essence of mediate inference consists in showing that a special case, or class of cases, comes under a general rule. but a great deal of our ordinary reasoning does not conform to this type. it was therefore judged necessary to show that it might by a little manipulation be brought into conformity with it. this process is called reduction. § . reduction is of two kinds-- ( ) direct or ostensive. ( ) indirect or ad impossibile. § . the problem of direct, or ostensive, reduction is this-- given any mood in one of the imperfect figures (ii, iii and iv) how to alter the form of the premisses so as to arrive at the same conclusion in the perfect figure, or at one from which it can be immediately inferred. the alteration of the premisses is effected by means of immediate inference and, where necessary, of transposition. § . the problem of indirect reduction, or reductio (per deductionem) ad impossibile, is this--given any mood in one of the imperfect figures, to show by means of a syllogism in the perfect figure that its conclusion cannot be false. § . the object of reduction is to extend the sanction of the dictum de omni et nullo to the imperfect figures, which do not obviously conform to it. § . the mood required to be reduced is called the reducend; that to which it conforms, when reduced, is called the reduct. _direct or ostensive reduction._ § . in the ordinary form of direct reduction, the only kind of immediate inference employed is conversion, either simple or by limitation; but the aid of permutation and of conversion by negation and by contraposition may also be resorted to. § . there are two moods, baroko and bokardo, which cannot be reduced ostensively except by the employment of some of the means last mentioned. accordingly, before the introduction of permutation into the scheme of logic, it was necessary to have recourse to some other expedient, in order to demonstrate the validity of these two moods. indirect reduction was therefore devised with a special view to the requirements of baroko and bokardo: but the method, as will be seen, is equally applicable to all the moods of the imperfect figures. § . the mnemonic lines, 'barbara, celarent, etc., provide complete directions for the ostensive reduction of all the moods of the second, third, and fourth figures to the first, with the exception of baroko and bokardo. the application of them is a mere mechanical trick, which will best be learned by seeing the process performed. § . let it be understood that the initial consonant of each name of a figured mood indicates that the reduct will be that mood which begins with the same letter. thus the b of bramantip indicates that bramantip, when reduced, will become barbara. § . where m appears in the name of a reducend, me shall have to take as major that premiss which before was minor, and vice versa-in other words, to transpose the premisses, m stands for mutatio or metathesis. § . s, when it follows one of the premisses of a reducend, indicates that the premiss in question must be simply converted; when it follows the conclusion, as in disamis, it indicates that the conclusion arrived at in the first figure is not identical in form with the original conclusion, but capable of being inferred from it by simple conversion. hence s in the middle of a name indicates something to be done to the original premiss, while s at the end indicates something to be done to the new conclusion. § . p indicates conversion per accidens, and what has just been said of s applies, mutatis mutandis, to p. § . k may be taken for the present to indicate that baroko and bokardo cannot be reduced ostensively. § . figure ii. cesare. \ / celarent. no a is b. \ = / no b is a. all c is b. / \ all c is b. .'. no c is a. / \ .'. no c is a. camestres. \ / celarent. all a is b. \ = / no b is c. no c is b. / \ all a is b. .'. no c is a. / \ .'. no a is c. .'. no c is a. festino. ferio. no a is b. \ / no b is a. some c is b. | = | some c is b. .'. some c is not a./ \ .'. some c is not a. [baroko] § . figure iii. darapti. \ / darii. all b is a. \ = / all b is a. all b is c. / \ some c is b. .'. some c is a. / \ some c is a. disamis. \ / darii. some b is a. \ = / all b is c. all b is c. / \ some a is b. .'. some c is a. / \ .'. some a is c. .'. some c is a. datisi. \ / darii. all b is a. \ = / all b is a. some b is c. / \ some c is b. .'. some c is a. / \ .'. some c is a. felapton. \ / ferio. no b is a. \ = / no b is a. all b is c. / \ some c is b. .'. some c is not-a. / \ .'. some c is not-a. [bokardo]. ferison. \ / ferio. no b is a. \ = / no b is a. some b is c. / \ some c is b .'. some c is not a. / \ .'. some c is not a. § . figure iv. bramantip. \ / barbara. all a is b. \ = / all b is c. all b is c. / \ all a is b. .. some c is a. / \ .. all a is c. .'. some c is a. camenes celarent all a is b \ / no b is c. no b is c. | = | all a is b. .. no c is a./ \ .'. no a is c. .'. no c is a. dimaris. darii. some a is b. \ / all b is c. all b is c. | = | some a is b. .'. some c is a./ \ .'. some a is c. .'. some c is a. fesapo. ferio. no a is b. \ / no b is a. all b is c. | = | some c is b. .'. some c is not a./ \ .'. some c is not a. fresison. ferio. no a is b. \ / no b is a. some b is c. | = | some c is b. .'. some c is not a./ \ .'. some c is not a. § . the reason why baroko and bokardo cannot be reduced ostensively by the aid of mere conversion becomes plain on an inspection of them. in both it is necessary, if we are to obtain the first figure, that the position of the middle term should be changed in one premiss. but the premisses of both consist of a and propositions, of which a admits only of conversion by limitation, the effect of which would be to produce two particular premisses, while does not admit of conversion at all, it is clear then that the proposition must cease to be before we can get any further. here permutation comes to our aid; while conversion by negation enables us to convert the a proposition, without loss of quantity, and to elicit the precise conclusion we require out of the reduct of boltardo. (baroko) fanoao. ferio. all a is b. \ / no not-b is a. some c is not-b. | = | some c is not-b. .'. some c is not-a./ \ .'. some c is not-a. (bokardo) donamon. darii. some b is not-a. \ / all b is c. all b is c. | = | some not-a is b .'. some c is not-a./ \ .'. some not-a is c. .'. some c is not-a. § . in the new symbols, fanoao and donamon, [pi] has been adopted as a symbol for permutation; n signifies conversion by negation. in donamon the first n stands for a process which resolves itself into permutation followed by simple conversion, the second for one which resolves itself into simple conversion followed by permutation, according to the extended meaning which we have given to the term 'conversion by negation.' if it be thought desirable to distinguish these two processes, the ugly symbol do[pi]samos[pi] may be adopted in place of donamon. § . the foregoing method, which may be called reduction by negation, is no less applicable to the other moods of the second figure than to baroko. the symbols which result from providing for its application would make the second of the mnemonic lines run thus-- benare[pi], cane[pi]e, denilo[pi], fano[pi]o secundae. § . the only other combination of mood and figure in which it will be found available is camenes, whose name it changes to canene. § . (cesare) benarea. barbara. no a is b. \ / all b is not-a. all c is b. | = | all c is b. .'. no c is a. / \ .'. all c is not-a. .'. no c is a. (camestres) cane[pi]e. celarent. all a is b. \ / no not-b is a. no c is b. | = | all c is not-b. .'. no c is a. / \ .'. no c is a. (festino) denilo[pi]. darii. no a is b. \ / all b is not-a. some c is b. | = | some c is b. .'. some c is not a./ \ .'. some c is not-a. .'. some c is not a. (camenes) canene. celarent. all a is b. \ / no not-b is a. no b is c. | = | all c is not-b. .'. no c is a. / \ .'. no c is a. § . the following will serve as a concrete instance of cane[pi]e reduced to the first figure. all things of which we have a perfect idea are perceptions. a substance is not a perception. .'. a substance is not a thing of which we have a perfect idea. when brought into celarent this becomes-- no not-perception is a thing of which we have a perfect idea. a substance is a not-perception. .'. no substance is a thing of which we have a perfect idea. § . we may also bring it, if we please, into barbara, by permuting the major premiss once more, so as to obtain the contrapositive of the original-- all not-perceptions are things of which we have an imperfect idea. all substances are not-perceptions. .'. all substances are things of which we have an imperfect idea. _indirect reduction._ § . we will apply this method to baroko. all a is b. all fishes are oviparous. some c is not b. some marine animals are not oviparous. .'. some c is not a. .'. some marine animals are not fishes. § . the reasoning in such a syllogism is evidently conclusive: but it does not conform, as it stands, to the first figure, nor (permutation apart) can its premisses be twisted into conformity with it. but though we cannot prove the conclusion true in the first figure, we can employ that figure to prove that it cannot be false, by showing that the supposition of its falsity would involve a contradiction of one of the original premisses, which are true ex hypothesi. § . if possible, let the conclusion 'some c is not a' be false. then its contradictory 'all c is a' must be true. combining this as minor with the original major, we obtain premisses in the first figure, all a is b, all fishes are oviparous, all c is a, all marine animals are fishes, which lead to the conclusion all c is b, all marine animals are oviparous. but this conclusion conflicts with the original minor, 'some c is not b,' being its contradictory. but the original minor is ex hypothesi true. therefore the new conclusion is false. therefore it must either be wrongly drawn or else one or both of its premisses must be false. but it is not wrongly drawn; since it is drawn in the first figure, to which the dictum de omni et nullo applies. therefore the fault must lie in the premisses. but the major premiss, being the same with that of the original syllogism, is ex hypothesi true. therefore the minor premiss, 'all c is a,' is false. but this being false, its contradictory must be true. now its contradictory is the original conclusion, 'some c is not a,' which is therefore proved to be true, since it cannot be false. § . it is convenient to represent the two syllogisms in juxtaposition thus-- baroko. barbara. all a is b. all a is b. some c is not b. \/ all c is a. .'. some c is not a. /\ all c is b. § . the lines indicate the propositions which conflict with one another. the initial consonant of the names baroko and eokardo indicates that the indirect reduct will be barbara. the k indicates that the o proposition, which it follows, is to be dropped out in the new syllogism, and its place supplied by the contradictory of the old conclusion. § . in bokardo the two syllogisms will stand thus-- bokardo. barbara. some b is not a. \ / all c is a. all b is c. x all b is c. .'. some c is not a./ \ .'. all b is a. § . the method of indirect reduction, though invented with a special view to baroko and bokardo, is applicable to all the moods of the imperfect figures. the following modification of the mnemonic lines contains directions for performing the process in every case:--barbara, celarent, darii, ferioque prioris; felake, dareke, celiko, baroko secundae; tertia cakaci, cikari, fakini, bekaco, bokardo, dekilon habet; quarta insuper addit cakapi, daseke, cikasi, cepako, cesïkon. § . the c which appears in two moods of the third figure, cakaci and bekaco, signifies that the new conclusion is the contrary, instead of, as usual, the contradictory of the discarded premiss. § . the letters s and p, which appear only in the fourth figure, signify that the new conclusion does not conflict directly with the discarded premiss, but with its converse, either simple or per accidens, as the case may be. § . l, n and r are meaningless, as in the original lines. chapter xix. _of immediate inference as applied to complex propositions._ § . so far we have treated of inference, or reasoning, whether mediate or immediate, solely as applied to simple propositions. but it will be remembered that we divided propositions into simple and complex. i t becomes incumbent upon us therefore to consider the laws of inference as applied to complex propositions. inasmuch however as every complex proposition is reducible to a simple one, it is evident that the same laws of inference must apply to both. § . we must first make good this initial statement as to the essential identity underlying the difference of form between simple and complex propositions. § . complex propositions are either conjunctive or disjunctive (§ ). § . conjunctive propositions may assume any of the four forms, a, e, i, o, as follows-- (a) if a is b, c is always d. (e) if a is b, c is never d. (i) if a is b, c is sometimes d. (o) if a is b, c is sometimes not d. § . these admit of being read in the form of simple propositions, thus-- (a) if a is b, c is always d = all cases of a being b are cases of c being d. (every ab is a cd.) (e) if a is b, c is never d = no cases of a being b are cases of c being d. (no ab is a cd.) (i) if a is b, c is sometimes d = some cases of a being b are cases of c being d. (some ab's are cd's.) (o) if a is b, c is sometimes not d = some cases of a being b are not cases of c being d. (some ab's are not cd's.) § . or, to take concrete examples, (a) if kings are ambitious, their subjects always suffer. = all cases of ambitious kings are cases of subjects suffering. (e) if the wind is in the south, the river never freezes. = no cases of wind in the south are cases of the river freezing. (i) if a man plays recklessly, the luck sometimes goes against him. = some cases of reckless playing are cases of going against one. (o) if a novel has merit, the public sometimes do not buy it. = some cases of novels with merit are not cases of the public buying. § . we have seen already that the disjunctive differs from the conjunctive proposition in this, that in the conjunctive the truth of the antecedent involves the truth of the consequent, whereas in the disjunctive the falsity of the antecedent involves the truth of the consequent. the disjunctive proposition therefore either a is b or c is d may be reduced to a conjunctive if a is not b, c is d, and so to a simple proposition with a negative term for subject. all cases of a not being b are cases of c being d. (every not-ab is a cd.) § . it is true that the disjunctive proposition, more than any other form, except u, seems to convey two statements in one breath. yet it ought not, any more than the e proposition, to be regarded as conveying both with equal directness. the proposition 'no a is b' is not considered to assert directly, but only implicitly, that 'no b is a.' in the same way the form 'either a is b or c is d' ought to be interpreted as meaning directly no more than this, 'if a is not b, c is d.' it asserts indeed by implication also that 'if c is not d, a is b.' but this is an immediate inference, being, as we shall presently see, the contrapositive of the original. when we say 'so and so is either a knave or a fool,' what we are directly asserting is that, if he be not found to be a knave, he will be found to be a fool. by implication we make the further statement that, if he be not cleared of folly, he will stand condemned of knavery. this inference is so immediate that it seems indistinguishable from the former proposition: but since the two members of a complex proposition play the part of subject and predicate, to say that the two statements are identical would amount to asserting that the same proposition can have two subjects and two predicates. from this point of view it becomes clear that there is no difference but one of expression between the disjunctive and the conjunctive proposition. the disjunctive is merely a peculiar way of stating a conjunctive proposition with a negative antecedent. § . conversion of complex propositions. a / if a is b, c is always d. \ .'. if c is d, a is sometimes b. e / if a is b, c is never d. \ .'. if c is d, a is never b. i / if a is s, c is sometimes d. \ .'. if c is d, a is sometimes b. § . exactly the same rules of conversion apply to conjunctive as to simple propositions. § . a can only be converted per accidens, as above. the original proposition 'if a is b, c is always d' is equivalent to the simple proposition 'all cases of a being b are cases of c being d.' this, when converted, becomes 'some cases of c being d are cases of a being b,' which, when thrown back into the conjunctive form, becomes 'if c is d, a is sometimes b.' § . this expression must not be misunderstood as though it contained any reference to actual existence. the meaning might be better conveyed by the form 'if c is d, a may be b.' but it is perhaps as well to retain the other, as it serves to emphasize the fact that formal logic is concerned only with the connection of ideas. § . a concrete instance will render the point under discussion clearer. the example we took before of an a proposition in the conjunctive form-- 'if kings are ambitious, their subjects always suffer' may be converted into 'if subjects suffer, it may be that their kings are ambitious,' i.e. among the possible causes of suffering on the part of subjects is to be found the ambition of their rulers, even if every actual case should be referred to some other cause. it is in this sense only that the inference is a necessary one. but then this is the only sense which formal logic is competent to recognise. to judge of conformity to fact is no part of its province. from 'every ab is a cd' it follows that ' some cd's are ab's' with exactly the same necessity as that with which 'some b is a' follows from 'all a is b.' in the latter case also neither proposition may at all conform to fact. from 'all centaurs are animals' it follows necessarily that 'some animals are centaurs': but as a matter of fact this is not true at all. § . the e and the i proposition may be converted simply, as above. § . o cannot be converted at all. from the proposition 'if a man runs a race, he sometimes does not win it,' it certainly does not follow that 'if a man wins a race, he sometimes does not run it.' § . there is a common but erroneous notion that all conditional propositions are to be regarded as affirmative. thus it has been asserted that, even when we say that 'if the night becomes cloudy, there will be no dew,' the proposition is not to be regarded as negative, on the ground that what we affirm is a relation between the cloudiness of night and the absence of dew. this is a possible, but wholly unnecessary, mode of regarding the proposition. it is precisely on a par with hobbes's theory of the copula in a simple proposition being always affirmative. it is true that it may always be so represented at the cost of employing a negative term; and the same is the case here. § . there is no way of converting a disjunctive proposition except by reducing it to the conjunctive form. § . _permutation of complex propositions_. (a) if a is b, c is always d. .'. if a is b, c is never not-d. (e) (e) if a is b, c is never d. .'. if a is b, c is always not-d. (a) (i) if a is b, c is sometimes d. .'. if a is b, c is sometimes not not-d. (o) (o) if a is b, c is sometimes not d. .'. if a is b, c is sometimes not-d. (i) § . (a) if a mother loves her children, she is always kind to them. .'. if a mother loves her children, she is never unkind to them. (e) (e) if a man tells lies, his friends never trust him. .'. if a man tells lies, his friends always distrust him. (a) (i) if strangers are confident, savage dogs are sometimes friendly. .'. if strangers are confident, savage dogs are sometimes not unfriendly. (o) (o) if a measure is good, its author is sometimes not popular. .'. if a measure is good, its author is sometimes unpopular. (i) § . the disjunctive proposition may be permuted as it stands without being reduced to the conjunctive form. either a is b or c is d. .'. either a is b or c is not not-d. either a sinner must repent or he will be damned. .'. either a sinner must repent or he will not be saved. § . _conversion by negation of complex propositions._ (a) if a is b, c is always d. .'. if c is not-d, a is never b. (e) (e) if a is b, c is never d. .'. if c is d, a is always not-b. (a) (i) if a is b, c is sometimes d. .'. if c is d, a is sometimes not not-b. (o) (o) if a is b, c is sometimes not d. .'. if c is not-d, a is sometimes b. (i) (e per acc.) if a is b, c is never d. .'. if c is not-d, a is sometimes b. (i) (a per ace.) if a is b, c is always d. .'. if c is d, a is sometimes not not-d. (o) § . (a) if a man is a smoker, he always drinks. .'. if a man is a total abstainer, he never smokes. (e) (e) if a man merely does his duty, no one ever thanks him. .'. if people thank a man, he has always done more than his duty. (a) (i) if a statesman is patriotic, he sometimes adheres to a party. .'. if a statesman adheres to a party, he is sometimes not unpatriotic. (o) (o) if a book has merit, it sometimes does not sell. .'. if a book fails to sell, it sometimes has merit. (i) (e per acc.) if the wind is high, rain never falls. .'. if rain falls, the wind is sometimes high. (i) (a per acc.) if a thing is common, it is always cheap. .'. if a thing is cheap, it is sometimes not uncommon. (o) § . when applied to disjunctive propositions, the distinctive features of conversion by negation are still discernible. in each of the following forms of inference the converse differs in quality from the convertend and has the contradictory of one of the original terms (§ ). § . (a) either a is b or c is always d. .'. either c is d or a is never not-b. (e) (e) either a is b or c is never d. .'. either c is not-d or a is always b. (a) (i) either a is b or c is sometimes d. .'. either c is not-d or a is sometimes not b. (o) (o) either a is b or c is sometimes not d. .'. either c is d or a is sometimes not-b. (i) § . (a) either miracles are possible or every ancient historian is untrustworthy. .'. either ancient historians are untrustworthy or miracles are not impossible. (e) (e) either the tide must turn or the vessel can not make the port. .'. either the vessel cannot make the port or the tide must turn. (a) ( ) either he aims too high or the cartridges are sometimes bad. .'. either the cartridges are not bad or he sometimes does not aim too high. ( ) (o) either care must be taken or telegrams will sometimes not be correct. .'. either telegrams are correct or carelessness is sometimes shown. ( ) § . in the above examples the converse of e looks as if it had undergone no change but the mere transposition of the alternative. this appearance arises from mentally reading the e as an a proposition: but, if it were so taken, the result would be its contrapositive, and not its converse by negation. § . the converse of i is a little difficult to grasp. it becomes easier if we reduce it to the equivalent conjunctive-- 'if the cartridges are bad, he sometimes does not aim too high.' here, as elsewhere, 'sometimes' must not be taken to mean more than 'it may be that.' § . _conversion by contraposition of complex propositions._ as applied to conjunctive propositions conversion by contraposition assumes the following forms-- (a) if a is b, c is always d. .'. if c is not-d, a is always not-b. (o) if a is b, c is sometimes not d. .'. if c is not-d, a is sometimes not not-b. (a) if a man is honest, he is always truthful. .'. if a man is untruthful, he is always dishonest. (o) if a man is hasty, he is sometimes not malevolent. .'. if a man is benevolent, he is sometimes not unhasty. § . as applied to disjunctive propositions conversion by contraposition consists simply in transposing the two alternatives. (a) either a is b or c is d. .'. either c is d or a is b. for, when reduced to the conjunctive shape, the reasoning would run thus-- if a is not b, c is d. .'. if c is not d, a is b. which is the same in form as all not-a is b. .'. all not-b is a. similarly in the case of the o proposition (o) either a is b or c is sometimes not d. .'. either c is d or a is sometimes not b. § . on comparing these results with the converse by negation of each of the same propositions, a and , the reader will see that they differ from them, as was to be expected, only in being permuted. the validity of the inference may be tested, both here and in the case of conversion by negation, by reducing the disjunctive proposition to the conjunctive, and so to the simple form, then performing the process as in simple propositions, and finally throwing the converse, when so obtained, back into the disjunctive form. we will show in this manner that the above is really the contrapositive of the proposition. (o) either a is b or c is sometimes not d. = if a is not b, c is sometimes not d. = some cases of a not being b are not cases of c being d. (some a is not b.) = some cases of c not being d are not cases of a being b. (some not-b is not not-a.) = if c is not d, a is sometimes not b. = either c is d or a is sometimes not b. chapter xx. _of complex syllogisms_. § . a complex syllogism is one which is composed, in whole or part, of complex propositions. § . though there are only two kinds of complex proposition, there are three varieties of complex syllogism. for we may have ( ) a syllogism in which the only kind of complex proposition employed is the conjunctive; ( ) a syllogism in which the only kind of complex proposition employed is the disjunctive; ( ) a syllogism which has one premiss conjunctive and the other disjunctive. the chief instance of the third kind is that known as the dilemma. syllogism ___________________|_______________ | | simple complex (categorical) (conditional) _____________________|_______________ | | | conjunctive disjunctive dilemma (hypothetical) _the conjunctive syllogism_. § . the conjunctive syllogism has one or both premisses conjunctive propositions: but if only one is conjunctive, the other must be a simple one. § . where both premisses are conjunctive, the conclusion will be of the same character; where only one is conjunctive, the conclusion will be a simple proposition. § . of these two kinds of conjunctive syllogisms we will first take that which consists throughout of conjunctive propositions. _the wholly conjunctive syllogism_. § . wholly conjunctive syllogisms do not differ essentially from simple ones, to which they are immediately reducible. they admit of being constructed in every mood and figure, and the moods of the imperfect figures may be brought into the first by following the ordinary rules of reduction. for instance-- cesare. celarent. if a is b, c is never d. \ / if c is d, a is never b. if e is f, c is always d. | = | if e is f, c is always d. .'. if e is f, a is never b. / \ .'. if e is f, a is never b. if it is day, the stars never shine.\ /if the stars shine, it is never day. if it is night, the stars always \=/ if it is night, the stars always shine. / \ shine. .'. if it is night, it is never day / \.'. if it is night, it is never day. disamis. darii. if c is d, a is sometimes b. \ / if c is d, e is always f. if c is d, e is always f. | = | if a is b, c is sometimes d. if e is f, a is sometimes b. / \ .'. if a is b, e is sometimes f. .'. if e is f, a is sometimes b. if she goes, i sometimes go. \ / if she goes, he always goes, if she goes, he always goes. | = | if i go, she sometimes goes. .'. if he goes, i sometimes go. / \ .'. if i go, he sometimes goes. .'. if he goes, i sometimes go. _the partly conjunctive syllogism._ § . it is this kind which is usually meant when the conjunctive or hypothetical syllogism is spoken of. § . of the two premisses, one conjunctive and one simple, the conjunctive is considered to be the major, and the simple premiss the minor. for the conjunctive premiss lays down a certain relation to hold between two propositions as a matter of theory, which is applied in the minor to a matter of fact. § . taking a conjunctive proposition as a major premiss, there are four simple minors possible. for we may either assert or deny the antecedent or the consequent of the conjunctive. constructive mood. destructive mood. ( ) if a is b, c is d. ( ) if a is b, c is d. a is b. c is not d. .'. c is d. .'. a is not b. ( ) if a is b, c is d. ( ) if a is b, c is d. a is not b. c is d. no conclusion. no conclusion. § . when we take as a minor 'a is not b ' ( ), it is clear that we can get no conclusion. for to say that c is d whenever a is b gives us no right to deny that c can be d in the absence of that condition. what we have predicated has been merely inclusion of the case ab in the case cd. [illustration] § . again, when we take as a minor, 'c is d' ( ), we can get no universal conclusion. for though a being b is declared to involve as a consequence c being d, yet it is possible for c to be d under other circumstances, or from other causes. granting the truth of the proposition 'if the sky falls, we shall catch larks,' it by no means follows that there are no other conditions under which this result can be attained. § . from a consideration of the above four cases we elicit the following _canon of the conjunctive syllogism._ to affirm the antecedent is to affirm the consequent, and to deny the consequent is to deny the antecedent: but from denying the antecedent or affirming the consequent no conclusion follows. § . there is a case, however, in which we can legitimately deny the antecedent and affirm the consequent of a conjunctive proposition, namely, when the relation predicated between the antecedent and the consequent is not that of inclusion but of coincidence--where in fact the conjunctive proposition conforms to the type u. for example-- _denial of the antecedent_. if you repent, then only are you forgiven. you do not repent. .'. you are not forgiven. _affirmation of the consequent_. if you repent, then only are you forgiven. you are forgiven. .'. you repent. chapter xxi. _of the reduction of the partly conjunctive syllogism._ § . such syllogisms as those just treated of, if syllogisms they are to be called, have a major and a middle term visible to the eye, but appear to be destitute of a minor. the missing minor term is however supposed to be latent in the transition from the conjunctive to the simple form of proposition. when we say 'a is b,' we are taken to mean, 'as a matter of fact, a is b' or 'the actual state of the case is that a is b.' the insertion therefore of some such expression as 'the case in hand,' or 'this case,' is, on this view, all that is wanted to complete the form of the syllogism. when reduced in this manner to the simple type of argument, it will be found that the constructive conjunctive conforms to the first figure and the destructive conjunctive to the second. _constructive mood_. _barbara_. if a is b, c is d. \ / all cases of a being b are cases of \ = / c being d. a is b. / \ this is a case of a being b. .'. c is d. / \ .'. this is a case of c being d. _destructive mood._ camestres. if a is b, c is d. \ / all cases of a being b are cases of \ = / c being d. c is not d. / \ this is not a case of c being d. .'. a is not b. / \ .'. this is not a case of a being b. § . it is apparent from the position of the middle term that the constructive conjunctive must fall into the first figure and the destructive conjunctive into the second. there is no reason, however, why they should be confined to the two moods, barbara and carnestres. if the inference is universal, whether as general or singular, the mood is barbara or carnestres; if it is particular, the mood is darii or baroko. barbara. camestres. if a is b, c is always d. \ if a is b, c is always d. \ a is always b. \ c is never d. \ .'. c is always d. \ .'. a is never b. \ | | if a is b, c is always d. / if a is b, c is always d. / a is in this case b. / c is not in this case d. / .'. c is in this case d. / .'. a is not in this case b. / darii. baroko. if a is b, c is always d. if a is b, c is never d. a is sometimes b. c is sometimes not d. .'. c is sometimes d. .'. a is sometimes not b. § . the remaining moods of the first and second figure are obtained by taking a negative proposition as the consequent in the major premiss. celarent. ferio. if a is b, c is never d. if a is b, c is never d. a is always b. a is sometimes b. .'. c is never d. .'. c is sometimes not d. _cesare_. festino. if a is b, c is never d. if a is b, c is never d. c is always d. c is sometimes d. .'. a is never b. .'. a is sometimes not b. § . as the partly conjunctive syllogism is thus reducible to the simple form, it follows that violations of its laws must correspond with violations of the laws of simple syllogism. by our throwing the illicit moods into the simple form it will become apparent what fallacies are involved in them. _denial of anteceded_. if a is b, c is d. \ / all cases of a being b are cases of c \ = / being d. a is not b. / \ this is not a case of a being b. .'. c is not d. / \ .'. this is not a case of c being d. here we see that the denial of the antecedent amounts to illicit process of the major term. § _affirmation of consequent_. if a is b, c is d. \ / all cases of a being b are cases of c | = | being d. c is d. / \ this is a case of c being d. here we see that the affirmation of the consequent amounts to undistributed middle. § . if we confine ourselves to the special rules of the four figures, we see that denial of the antecedent involves a negative minor in the first figure, and affirmation of the consequent two affirmative premisses in the second. or, if the consequent in the major premiss were itself negative, the affirmation of it would amount to the fallacy of two negative premisses. thus-- if a is b, c is not d. \ / no cases of a being b are cases of c | = | being d. c is not d. / \ this is not a case of c being d. § . the positive side of the canon of the conjunctive syllogism--'to affirm the antecedent is to affirm the consequent,' corresponds with the dictum de omni. for whereas something (viz. c being d) is affirmed in the major of all conceivable cases of a being b, the same is affirmed in the conclusion of something which is included therein, namely, 'this case,' or 'some cases,' or even 'all actual cases.' § . the negative side--'to deny the consequent is to deny the antecedent'--corresponds with the dictum de diverse (§ ). for whereas in the major all conceivable cases of a being b are included in c being d, in the minor 'this case,' or 'some cases,' or even 'all actual cases' of c being d, are excluded from the same notion. § . the special characteristic of the partly conjunctive syllogism lies in the transition from hypothesis to fact. we might lay down as the appropriate axiom of this form of argument, that 'what is true in the abstract is true--in the concrete,' or 'what is true in theory is also true in fact,' a proposition which is apt to be neglected or denied. but this does not vitally distinguish it from the ordinary syllogism. for though in the latter we think rather of the transition from a general truth to a particular application of it, yet at bottom a general truth is nothing but a hypothesis resting upon a slender basis of observed fact. the proposition 'a is b' may be expressed in the form 'if a is, b is.' to say that 'all men are mortal' may be interpreted to mean that 'if we find in any subject the attributes of humanity, the attributes of mortality are sure to accompany them.' chapter xxii. _of the partly conjunctive syllogism regarded as an immediate inference_. § . it is the assertion of fact in the minor premiss, where we have the application of an abstract principle to a concrete instance, which alone entitles the partly conjunctive syllogism to be regarded as a syllogism at all. apart from this the forms of semi-conjunctive reasoning run at once into the moulds of immediate inference. § . the constructive mood will then be read in this way-- if a is b, c is d, .'. a being b, c is d. reducing itself to an instance of immediate inference by subaltern opposition-- every case of a being b, is a case of c being d. .'. some particular case of a being b is a case of c being d. § . again, the destructive conjunctive will read as follows-- if a is b, c is d, .'. c not being d, a is not b. which is equivalent to all cases of a being b are cases of c being d. .'. whatever is not a case of c being d is not a case of a being b. .'. some particular case of c not being d is not a case of a being b. but what is this but an immediate inference by contraposition, coming under the formula all a is b, .'. all not-b is not-a, and followed by subalternation? § . the fallacy of affirming the consequent becomes by this mode of treatment an instance of the vice of immediate inference known as the simple conversion of an a proposition. 'if a is b, c is d' is not convertible with 'if c is d, a is b' any more than 'all a is b' is convertible with 'all b is a.' § . we may however argue in this way if a is b, c is d, c is d, .'. a may be b, which is equivalent to saying, when a is b, c is always d, .'. when c is d, a is sometimes b, and falls under the legitimate form of conversion of a per accidens-- all cases of a being b are cases of c being d. .'. some cases of c being d are cases of a being b. § . the fallacy of denying the antecedent assumes the following form-- if a is b, c is d, .'. if a is not b, c is not d, equivalent to-- all cases of a being b are cases of c being d. .'. whatever is not a case of a being b is not a case of c being d. this is the same as to argue-- all a is b, .'. all not-a is not-b, an erroneous form of immediate inference for which there is no special name, but which involves the vice of simple conversion of a, since 'all not-a is not-b' is the contrapositive, not of 'all a is b,' but of its simple converse 'all b is a.' § . the above-mentioned form of immediate inference, however (namely, the employment of contraposition without conversion), is valid in the case of the u proposition; and so also is simple conversion. accordingly we are able, as we have seen, in dealing with a proposition of that form, both to deny the antecedent and to assert the consequent with impunity-- if a is b, then only c is d, .'. a not being b, c is not d; and again, c being d, a must be b. chapter xxiii. _of the disjunctive syllogism_. § . roughly speaking, a disjunctive syllogism results from the combination of a disjunctive with a simple premiss. as in the preceding form, the complex proposition is regarded as the major premiss, since it lays down a hypothesis, which is applied to fact in the minor. § . the disjunctive syllogism may be exactly defined as follows-- a complex syllogism, which has for its major premiss a disjunctive proposition, either the antecedent or consequent of which is in the minor premiss simply affirmed or denied. § . thus there are four types of disjunctive syllogism possible. _constructive moods._ ( ) either a is b or c is d. ( ) either a is b or c is d. a is not b. c is not d. .'. c is d. .'. a is b. either death is annihilation or we are immortal. death is not annihilation. .'. we are immortal. either the water is shallow or the boys will be drowned. the boys are not drowned. .'. the water is shallow. _destructive moods_. ( ) either a is b or c is d. ( ) either a is b or c is d. a is b. c is d. .'. c is not d. .'. a is not b. § . of these four, however, it is only the constructive moods that are formally conclusive. the validity of the two destructive moods is contingent upon the kind of alternatives selected. if these are such as necessarily to exclude one another, the conclusion will hold, but not otherwise. they are of course mutually exclusive whenever they embody the result of a correct logical division, as 'triangles are either equilateral, isosceles or scalene.' here, if we affirm one of the members, we are justified in denying the rest. when the major thus contains the dividing members of a genus, it may more fitly be symbolized under the formula, 'a is either b or c.' but as this admits of being read in the shape, 'either a is b or a is c,' we retain the wider expression which includes it. any knowledge, however, which we may have of the fact that the alternatives selected in the major are incompatible must come to us from material sources; unless indeed we have confined ourselves to a pair of contradictory terms (a is either b or not-b). there can be nothing in the form of the expression to indicate the incompatibility of the alternatives, since the same form is employed when the alternatives are palpably compatible. when, for instance, we say, 'a successful student must be either talented or industrious,' we do not at all mean to assert the positive incompatibility of talent and industry in a successful student, but only the incompatibility of their negatives--in other words, that, if both are absent, no student can be successful. similarly, when it is said, 'either your play is bad or your luck is abominable,' there is nothing in the form of the expression to preclude our conceiving that both may be the case. § . there is no limit to the number of members in the disjunctive major. but if there are only two alternatives, the conclusion will be a simple proposition; if there are more than two, the conclusion will itself be a disjunctive. thus-- either a is b or c is d or e is f or g is h. e is not f. .'. either a is b or c is d or g is h. § . the canon of the disjunctive syllogism may be laid down as follows-- to deny one member is to affirm the rest, either simply or disjunctively; but from affirming any member nothing follows. chapter xxiv. _of the reduction of the disjunctive syllogism._ § . we have seen that in the disjunctive syllogism the two constructive moods alone are formally valid. the first of these, namely, the denial of the antecedent, will in all cases give a simple syllogism in the first figure; the second of them, namely, the denial of the consequent, will in all cases give a simple syllogism in the second figure. _denial of antecedent_ = barbara. either a is b or c is d. a is not b. .'.c is d is equal to if a is not b, c is d. a is not b. .'. c is d. is equal to all cases of a not being b are cases of c being d. this is a case of a not being b. .'. this is a case of c being d. _denial of consequent_ = camestres. either a is e or c is d. c is not d. .'. a is b. is equal to if a is not b, c is d. c is not d. .'. a is b. is equal to all cases of a not being b are cases of c being d. this is not a case of c being d. .'. this is not a case of a being b. § . the other moods of the first and second figures can be obtained by varying the quality of the antecedent and consequent in the major premiss and reducing the quantity of the minor. § . the invalid destructive moods correspond with the two invalid types of the partly conjunctive syllogism, and have the same fallacies of simple syllogism underlying them. affirmation of the antecedent of a disjunctive is equivalent to the semi-conjunctive fallacy of denying the antecedent, and therefore involves the ordinary syllogistic fallacy of illicit process of the major. affirmation of the consequent of a disjunctive is equivalent to the same fallacy in the semi-conjunctive form, and therefore involves the ordinary syllogistic fallacy of undistributed middle. _affirmation of antecedent_ = _illicit major_. either a is b or c is d. a is b. .'. c is not d. is equal to if a is not b, c is d. a is b. .'. c is not d. is equal to all cases of a not being b are cases of c being d. this is not a case of a not being b. .'. this is not a case of c not being d. _affirmation of consequent_ = _undistributed middle_. either a is b or c is d. c is d. is equal to if a is not b, c is d. c is d. is equal to all cases of a not being b are cases of c being d. this is a case of c being d. § . so far as regards the consequent, the two species of complex reasoning hitherto discussed are identical both in appearance and reality. the apparent difference of procedure in the case of the antecedent, namely, that it is affirmed in the partly conjunctive, but denied in the disjunctive syllogism, is due merely to the fact that in the disjunctive proposition the truth of the consequent is involved in the falsity of the antecedent, so that the antecedent being necessarily negative, to deny it in appearance is in reality to assert it. chapter xxv. _the disjunctive syllogism regarded as an immediate inference_. § . if no stress be laid on the transition from disjunctive hypothesis to fact, the disjunctive syllogism will run with the same facility as its predecessor into the moulds of immediate inference. § . _denial of antecedent_. subalternation. either a is b or c is d, every case of a not being b is a case of c being d. .'. a not being b, c is d. .'. some case of a not being b is a case of c being d. § . _denial of consequent_. conversion by contraposition + subalternation. either a is b or c is d. all cases of a not being b are cases of c being d. .'. c not being d, a is b .'. all cases of c not being d are cases of a being b. .'. some case of c not being d is a case of a being b. § . similarly the two invalid types of disjunctive syllogism will be found to coincide with fallacies of immediate inference. § . _affirmation of antecedent_. contraposition without conversion. either a is b or c is d. all cases of a not being b are cases of c being d. .'. a being b, c is not d .'. all cases of a being b are cases of c not being d. § . the affirmation of the antecedent thus comes under the formula-- all not-a is b, .'. all a is not-b, a form of inference which cannot hold except where a and b are known to be incompatible. who, for instance, would assent to this?-- all non-boating men play cricket. .'. all boating men are non-cricketers. § . _affirmation of consequent_. simple conversion of a. either a is b or c is d. all cases of a not being b are cases of c being d. .'.c being d, a is not b. .'. all cases of c being d are cases of a not being b. § . we may however argue in this way-- conversion of a per accidens. either a is b or c is d. all cases of a not being b are cases of c being d. .'. c being d, a is sometimes b. .'. some cases of c being d are cases of a not being b. the men who pass this examination must have either talent or industry. .'. granting that they are industrious, they may be without talent. chapter xxvi. _of the mixed form of complex syllogism_. § . under this head are included all syllogisms in which a conjunctive is combined with a disjunctive premiss. the best known form is _the dilemma_. § . the dilemma may be defined as-- a complex syllogism, having for its major premiss a conjunctive proposition with more than one antecedent, or more than one consequent, or both, which (antecedent or consequent) the minor premiss disjunctively affirms or denies. § . it will facilitate the comprehension of the dilemma, if the following three points are borne in mind-- ( ) that the dilemma conforms to the canon of the partly conjunctive syllogism, and therefore a valid conclusion can be obtained only by affirming the antecedent or denying the consequent; ( ) that the minor premiss must be disjunctive; ( ) that if only the antecedent be more than one, the conclusion will be a simple proposition; but if both antecedent and consequent be more than one, the conclusion will itself be disjunctive. § . the dilemma, it will be seen, differs from the partly conjunctive syllogism chiefly in the fact of having a disjunctive affirmation of the antecedent or denial of the consequent in the minor, instead of a simple one. it is this which constitutes the essence of the dilemma, and which determines its possible varieties. for if only the antecedent or only the consequent be more than one, we must, in order to obtain a disjunctive minor, affirm the antecedent or deny the consequent respectively; whereas, if there be more than one of both, it is open to us to take either course. this gives us four types of dilemma. § . ( ). _simple constructive._ if a is b or c is d, e is f. either a is b or c is d. .'. e is f. ( ). _simple destructive._ if a is b, c is d and e is f. either c is not d or e is not f. .'. a is not b. ( ). _complex constructive._ if a is b, c is d; and if e is f, g is h. either a is b or e is f. .'. either c is d or g is h. ( ). _complex destructive_. if a is b, c is d; and if e is f, g is h. either c is not d or g is not h. .'. either a is not b or e is not f. § . ( ). _simple constructive_. if she sinks or if she swims, there will be an end of her. she must either sink or swim. .'. there will be an end of her. ( ). _simple destructive_. if i go to town, i must pay for my ticket and pay my hotel bill. either i cannot pay for my ticket or i cannot pay my hotel bill. .'. i cannot go to town. ( ). _complex constructive_. if i stay in this room, i shall be burnt to death, and if i jump out of the window, i shall break my neck. i must either stay in the room or jump out of the window. .'. i must either be burnt to death or break my neck. ( ). _complex destructive_. if he were clever, he would see his mistake; and if he were candid, he would acknowledge it. either he does not see his mistake or he will not acknowledge it. .'. either he is not clever or he is not candid. § . it must be noticed that the simple destructive dilemma would not admit of a disjunctive consequent. if we said, if a is b, either c is d or e is f, either c is not d or e is not f, we should not be denying the consequent. for 'e is not f' would make it true that c is d, and 'c is not d' would make it true that e is f; so that in either case we should have one of the alternatives true, which is just what the disjunctive form 'either c is d or e is f' insists upon. § . in the case of the complex constructive dilemma the several members, instead of being distributively assigned to one another, may be connected together as a whole--thus-- if either a is b or e is f, either c is d or g is h. either a is b or e is f. .'. either c is d or g is h. in this shape the likeness of the dilemma to the partly conjunctive syllogism is more immediately recognisable. the major premiss in this shape is vaguer than in the former. for each antecedent has now a disjunctive choice of consequents, instead of being limited to one. this vagueness, however, does not affect the conclusion. for, so long as the conclusion is established, it does not matter from which members of the major its own members flow. § . it must be carefully noticed that we cannot treat the complex destructive dilemma in the same way. if either a is b or e is f, either c is d or g is h. either c is not d or g is not h. since the consequents are no longer connected individually with the antecedents, a disjunctive denial of them leaves it still possible for the antecedent as a whole to be true. for 'c is not d' makes it true that g is h, and 'g is not h' makes it true that c is d. in either case then one is true, which is all that was demanded by the consequent of the major. hence the consequent has not really been denied. § . for the sake of simplicity we have limited the examples to the case of two antecedents or consequents. but we may have as many of either as we please, so as to have a trilemma, a tetralemma, and so on. trilemma. if a is b, c is d; and if e is f, g is h; and if k is l, m is n. either a is b or e is f or k is l. .'. either c is d or g is h or k is l. § . having seen what the true dilemma is, we shall now examine some forms of reasoning which resemble dilemmas without being so. § . this, for instance, is not a dilemma-- if a is b or if e is f, c is d. but a is b and e is f. .'. c is d. if he observes the sabbath or if he refuses to eat pork, he is a jew. but he both observes the sabbath and refuses to eat pork. .'. he is a jew. what we have here is a combination of two partly conjunctive syllogisms with the same conclusion, which would have been established by either of them singly. the proof is redundant. § . neither is the following a dilemma-- if a is b, c is d and e is f. neither c is d nor e is f. .'. a is not b. if this triangle is equilateral, its sides and its angles will be equal. but neither its sides nor its angles are equal. .'. it is not equilateral. this is another combination of two conjunctive syllogisms, both pointing to the same conclusion. the proof is again redundant. in this case we have the consequent denied in both, whereas in the former we had the antecedent affirmed. it is only for convenience that such arguments as these are thrown into the form of a single syllogism. their real distinctness may be seen from the fact that we here deny each proposition separately, thus making two independent statements--c is not d and e is not f. but in the true instance of the simple destructive dilemma, what we deny is not the truth of the two propositions contained in the consequent, but their compatibility; in other words we make a disjunctive denial. § . nor yet is the following a dilemma-- if a is b, either c is d or e is f. neither c is d nor e is f. .'. a is not b. if the barometer falls there will be either wind or rain. there is neither wind nor rain. .'. the barometer has not fallen. what we have here is simply a conjunctive major with the consequent denied in the minor. in the consequent of the major it is asserted that the two propositions, 'c is d' and 'e is f' cannot both be false; and in the minor this is denied by the assertion that they are both false. § . a dilemma is said to be rebutted or retorted, when another dilemma is made out proving an opposite conclusion. if the dilemma be a sound one, and its premisses true, this is of course impossible, and any appearance of contradiction that may present itself on first sight must vanish on inspection. the most usual mode of rebutting a dilemma is by transposing and denying the consequents in the major-- if a is b, c is d; and if e is f, g is h. either a is b or e is f. .'. either c is d or g is h. the same rebutted-- if a is b, g is not h; and if e is f, c is not d. either a is b or e is f. .'. either g is not h or c is not d. = either c is not d or g is not h. § . under this form comes the dilemma addressed by the athenian mother to her son--'do not enter public life: for, if you say what is just, men will hate you; and, if you say what is unjust, the gods will hate you' to which the following retort was made--'i ought to enter public life: for, if say what is just, the gods will love me; and, if say what is unjust, men will love me.' but the two conclusions here are quite compatible. a man must, on the given premisses, be both hated and loved, whatever course he takes. so far indeed are two propositions of the form either c is d or g is h, and either c is not d or g is not h, from being incompatible, that they express precisely the same thing when contradictory alternatives have been selected, e.g.-- either a triangle is equilateral or non-equilateral. either a triangle is non-equilateral or equilateral. § . equally illusory is the famous instance of rebutting a dilemma contained in the story of protagoras and euathlus (aul. gell. noct. alt. v. ), euathlus was a pupil of protagoras in rhetoric. he paid half the fee demanded by his preceptor before receiving lessons, and agreed to pay the remainder when he won his first case. but as he never proceeded to practise at the bar, it became evident that he meant to bilk his tutor. accordingly protagoras himself instituted a law-suit against him, and in the preliminary proceedings before the jurors propounded to him the following dilemma--'most foolish young man, whatever be the issue of this suit, you must pay me what i claim: for, if the verdict be given in your favour, you are bound by our bargain; and if it be given against you, you are bound by the decision of the jurors.' the pupil, however, was equal to the occasion, and rebutted the dilemma as follows. 'most sapient master, whatever be the issue of this suit, i shall not pay you what you claim: for, if the verdict be given in my favour, i am absolved by the decision of the jurors; and, if it be given against me, i am absolved by our bargain.' the jurors are said to have been so puzzled by the conflicting plausibility of the arguments that they adjourned the case till the greek kalends. it is evident, however, that a grave injustice was thus done to protagoras. his dilemma was really invincible. in the counter-dilemma of euathlus we are meant to infer that protagoras would actually lose his fee, instead of merely getting it in one way rather than another. in either case he would both get and lose his fee, in the sense of getting it on one plea, and not getting it on another: but in neither case would he actually lose it. § . if a dilemma is correct in form, the conclusion of course rigorously follows: but a material fallacy often underlies this form of argument in the tacit assumption that the alternatives offered in the minor constitute an exhaustive division. thus the dilemma 'if pain is severe, it will be brief; and if it last long it will be slight,' &c., leaves out of sight the unfortunate fact that pain may both be severe and of long continuance. again the following dilemma-- if students are idle, examinations are unavailing; and, if they are industrious, examinations are superfluous, students are either idle or industrious, .'. examinations are either unavailing or superfluous, is valid enough, so far as the form is concerned. but the person who used it would doubtless mean to imply that students could be exhaustively divided into the idle and the industrious. no deductive conclusion can go further than its premisses; so that all that the above conclusion can in strictness be taken to mean is that examinations are unavailing, when students are idle, and superfluous, when they are industrious--which is simply a reassertion as a matter of fact of what was previously given as a pure hypothesis. chapter xxvii. _of the reduction of the dilemma._ § . as the dilemma is only a peculiar variety of the partly conjunctive syllogism, we should naturally expect to find it reducible in the same way to the form of a simple syllogism. and such is in fact the case. the constructive dilemma conforms to the first figure and the destructive to the second. ) _simple constructive dilemma_. barbara. if a is b or if e is f, c is d. all cases of either a being b or e being f are cases of c being d. either a is b or e is f. all actual cases are cases of either a being b op e being f. .'. c is d. .'. all actual cases are cases of c being d. ( ) _simple destructive_. camstres. if a is b, c is d and e is f. all cases of a being b are cases of c being d and e being f. either c is not d or e is not f. no actual cases are cases of c being d and e being f. .'. a is not b. .'. no actual cases are cases of a being b. ( ) _complex constructive_. barbara. if a is b, c is d; and if e is f, all cases of either a being b or g is h. being f are cases of either c being d or g being h. either a is b or e is f. all actual cases are cases of either a being b or e being f. .'. either c is d or g is h. .'. all actual cases are cases of either c being d or g being h. ( ) _complex destructive_. if a is b, c is d; and if e is f, all cases of a being b and e being f g is h. are cases of c being d and g being h. either c is not d or g is no actual cases are cases of c being not h d and g being h. either a is not b or e is no actual cases are cases of a being not f. b and e being f. § . there is nothing to prevent our having darii, instead of barbara, in the constructive form, and baroko, instead of camestres, in the destructive. as in the case of the partly conjunctive syllogism the remaining moods of the first and second figure are obtained by taking a negative proposition as the consequent of the major premiss, e.g.-- _simple constructive_. celarent or ferio. if a is b or if e is f, c is not d no cases of either a being b or e being f are cases of c being d. either a is b or e is f. all (or some) actual cases are cases of either a being b or e being f .'. c is not d. .'. all (or some) actual cases are not cases of c being d. chapter xxviii. _of the dilemma regarded as an immediate inference._ § . like the partly conjunctive syllogism, the dilemma can be expressed under the forms of immediate inference. as before, the conclusion in the constructive type resolves itself into the subalternate of the major itself, and in the destructive type into the subalternate of its contrapositive. the simple constructive dilemma, for instance, may be read as follows-- if either a is b or e is f, c is d, .'. either a being b or e being f, c is d, which is equivalent to every case of either a being b or e being f is a case of c being d. .'. some case of either a being b or e being f is a case of c being d. the descent here from 'every' to 'some' takes the place of the transition from hypothesis to fact. § . again the complex destructive may be read thus-- if a is b, c is d; and if e is f, g is h, .'. it not being true that c is d and g is h, it is not true that a is b and e is f, which may be resolved into two steps of immediate inference, namely, conversion by contraposition followed by subalternation-- all cases of a being b and e being f are cases of c being d and g being h. .'. whatever is not a case of c being d and g being h is not a case of a being b and e being f. .'. some case which is not one of c being d and g being h is not a case of a being b and e being f. chapter xxix. _of trains of reasoning._ § . the formal logician is only concerned to examine whether the conclusion duly follows from the premisses: he need not concern himself with the truth or falsity of his data. but the premisses of one syllogism may themselves be conclusions deduced from other syllogisms, the premisses of which may in their turn have been established by yet earlier syllogisms. when syllogisms are thus linked together we have what is called a train of reasoning. § . it is plain that all truths cannot be established by reasoning. for the attempt to do so would involve us in an infinite regress, wherein the number of syllogisms required would increase at each step in a geometrical ratio. to establish the premisses of a given syllogism we should require two preceding syllogisms; to establish their premisses, four; at the next step backwards, eight; at the next, sixteen; and so on ad infinitum. thus the very possibility of reasoning implies truths that are known to us prior to all reasoning; and, however long a train of reasoning may be, we must ultimately come to truths which are either self-evident or are taken for granted. § . any syllogism which establishes one of the premisses of another is called in reference to that other a pro-syllogism, while a syllogism which has for one of its premisses the conclusion of another syllogism is called in reference to that other an epi-syllogism. _the epicheirema_. § . the name epicheirema is given to a syllogism with one or both of its premisses supported by a reason. thus the following is a double epicheirema-- all b is a, for it is e. all c is b, for it is f. .'. all c is a. all virtue is praiseworthy, for it promotes the general welfare. generosity is a virtue, for it prompts men to postpone self to others. .'. generosity is praiseworthy. § . an epicheirema is said to be of the first or second order according as the major or minor premiss is thus supported. the double epicheirema is a combination of the two orders. § . an epicheirema, it will be seen, consists of one syllogism fully expressed together with one, or, it may be, two enthymemes (§ ). in the above instance, if the reasoning which supports the premisses were set forth at full length, we should have, in place of the enthymemes, the two following pro-syllogisms-- (i) all e is a. all b is e. .'. all b is a. whatever promotes the general welfare is praiseworthy. every virtue promotes the general welfare. .'. every virtue is praiseworthy. ( ) all f is b. all c is f. .'. all c is b. whatever prompts men to postpone self to others is a virtue. generosity prompts men to postpone self to others. .'. generosity is a virtue. § . the enthymemes in the instance above given are both of the first order, having the major premiss suppressed. but there is nothing to prevent one or both of them from being of the second order-- all b is a, because all f is. all c is b, because all f is. .'. all c is a. all mahometans are fanatics, because all monotheists are. these men are mahometans, because all persians are. .'. these men are fanatics. here it is the minor premiss in each syllogism that is suppressed, namely, ( ) all mahometans are monotheists. ( ) these men are persians. _the sorites_. § . the sorites is the neatest and most compendious form that can be assumed by a train of reasoning. § . it is sometimes more appropriately called the chain-argument, and map be defined as-- a train of reasoning, in which one premiss of each epi-syllogism is supported by a pro-syllogism, the other being taken for granted. this is its inner essence. § . in its outward form it may be described as--a series of propositions, each of which has one term in common with that which preceded it, while in the conclusion one of the terms in the last proposition becomes either subject or predicate to one of the terms in the first. § . a sorites may be either-- ( ) progressive, or ( ) regressive. _progressive sorites_. all a is b. all b is c. all c is d. all d is e. .'. all a is e. _regressive sorites_. all d is e. all c is d. all b is c. all a is b. .'. all a is e. § . the usual form is the progressive; so that the sorites is commonly described as a series of propositions in which the predicate of each becomes the subject of the next, while in the conclusion the last predicate is affirmed or denied of the first subject. the regressive form, however, exactly reverses these attributes; and would require to be described as a series of propositions, in which the subject of each becomes the predicate of the next, while in the conclusion the first predicate is affirmed or denied of the last subject. § . the regressive sorites, it will be observed, consists of the same propositions as the progressive one, only written in reverse order. why then, it may be asked, do we give a special name to it, though we do not consider a syllogism different, if the minor premiss happens to precede the major? it is because the sorites is not a mere series of propositions, but a compressed train of reasoning; and the two trains of reasoning may be resolved into their component syllogisms in such a manner as to exhibit a real difference between them. § . the progressive sorites is a train of reasoning in which the minor premiss of each epi-syllogism is supported by a pro-syllogism, while the major is taken for granted. § . the regressive sorites is a train of reasoning in which the major premiss of each epi-syllogism is supported by a pro-syllogism, while the minor is taken for granted. _progressive sorites_. (i) all b is c. all a is b. .'. all a is c. ( ) all c is d. all a is c. .'. all a is d. ( ) all d is e. all a is d. .'. all a is e. _regressive sorites_. ( ) all d is e. all c is d. .'. all c is e. ( ) all c is e. all b is c. .'. all b is e. ( ) all b is e. all a is b. .'. all a is e. § . here is a concrete example of the two kinds of sorites, resolved each into its component syllogisms-- _progressive sorites_. all bideford men are devonshire men. all devonshire men are englishmen. all englishmen are teutons. all teutons are aryans. .'. all bideford men are aryans. ( ) all devonshire men are englishmen. all bideford men are devonshire men. .'. all bideford men are englishmen. ( ) all englishmen are teutons. all bideford men are englishmen. .'. all bideford men are teutons. ( ) all teutons are aryans. all bideford men are teutons. .'. all bideford men are aryans. _regressive sorites._ all teutons are aryans. all englishmen are teutons. all devonshiremen are englishmen. all bideford men are devonshiremen. .'. all bideford men are aryans. ( ) all teutons are aryans. all englishmen are teutons. .'. all englishmen are aryans. ( ) all englishmen are aryans. all devonshiremen are englishmen. .'. all devonshiremen are aryans. ( ) all devonshiremen are aryans. all bideford men are devonshiremen. .'. all bideford men are aryans. § . when expanded, the sorites is found to contain as many syllogisms as there are propositions intermediate between the first and the last. this is evident also on inspection by counting the number of middle terms. § . in expanding the progressive form we have to commence with the second proposition of the sorites as the major premiss of the first syllogism. in the progressive form the subject of the conclusion is the same in all the syllogisms; in the regressive form the predicate is the same. in both the same series of means, or middle terms, is employed, the difference lying in the extremes that are compared with one another through them. [illustration] § . it is apparent from the figure that in the progressive form we work from within outwards, in the regressive form from without inwards. in the former we first employ the term 'devonshiremen' as a mean to connect 'bideford men' with 'englishmen'; next we employ 'englishmen' as a mean to connect the same subject 'bideford men' with the wider term 'teutons'; and, lastly, we employ 'teutons' as a mean to connect the original subject 'bideford men' with the ultimate predicate 'ayrans.' § . reversely, in the regressive form we first use 'teutons' as a mean whereby to bring 'englishmen' under 'aryans'; next we use 'englishmen' as a mean whereby to bring 'devonshiremen' under the dame predicate 'aryans'; and, lastly, we use 'devonshiremen' as a mean whereby to bring the ultimate subject 'bideford men' under the original predicate 'aryans.' § . a sorites may be either regular or irregular. § . in the regular form the terms which connect each proposition in the series with its predecessor, that is to say, the middle terms, maintain a fixed relative position; so that, if the middle term be subject in one, it will always be predicate in the other, and vice versâ. in the irregular form this symmetrical arrangement is violated. § . the syllogisms which compose a regular sorites, whether progressive or regressive, will always be in the first figure. in the irregular sorites the syllogisms may fall into different figures. § . for the regular sorites the following rules may be laid down. ( ) only one premiss can be particular, namely, the first, if the sorites be progressive, the last, if it be regressive. ( ) only one premiss can be negative, namely, the last, if the sorites be progressive, the first, if it be regressive. § . _proof of the rules for the regular sorites_. ( ) in the progressive sorites the proposition which stands first is the only one which appears as a minor premiss in the expanded form. each of the others is used in its turn as a major. if any proposition, therefore, but the first were particular, there would be a particular major, which involves undistributed middle, if the minor be affirmative, as it must be in the first figure. in the regressive sorites, if any proposition except the last were particular, we should have a particular conclusion in the syllogism in which it occurred as a premiss, and so a particular major in the next syllogism, which again is inadmissible, as involving undistributed middle. ( ) in the progressive sorites, if any premiss before the last were negative, we should have a negative conclusion in the syllogism in which it occurs. this would necessitate a negative minor in the next syllogism, which is inadmissible in the first figure, as involving illicit process of the major. in the regressive sorites the proposition which stands first is the only one which appears as a major premiss in the expanded form. each of the others is used in its turn as a minor. if any premiss, therefore, but the first were negative, we should have a negative minor in the first figure, which involves illicit process of the major. § . the rules above given do not apply to the irregular sorites, except so far as that only one premiss can be particular and only one negative, which follows from the general rules of syllogism. but there is nothing to prevent any one premiss from being particular or any one premiss from being negative, as the subjoined examples will show. both the instances chosen belong to the progressive order of sorites. ( ) barbara. all b is a. all c is b. all c is a. all b is a. all c is b. some c is d. all d is e .'. some a is e [illustration] ( ) disamis. some c is d. all c is a. some a is d. ( ) darii. all d is e some a is d. some a is e. ( ) barbara. all b is c. all a is b. all a is c. all a is b. all b is c. no d is c. all e is d. .'. no a is e. [illustration] ( ) cesare. no d is c. all a is c. .'. no a is d. ( ) camestres. all e is d. no a is d. .'. no a is e. § . a chain argument may be composed consisting of conjunctive instead of simple propositions. this is subject to the same laws as the simple sorites, to which it is immediately reducible. _progressive._ _regressive._ if a is b, c is d. if e is f, g is h. if c is d, e is f. if c is d, e is f. if e is f, g is h. if a is b, c is d. .'. if a is b, g is h. .'. if a is b, g is h. chapter xxx. _of fallacies_. § . after examining the conditions on which correct thoughts depend, it is expedient to classify some of the most familiar forms of error. it is by the treatment of the fallacies that logic chiefly vindicates its claim to be considered a practical rather than a speculative science. to explain and give a name to fallacies is like setting up so many sign-posts on the various turns which it is possible to take off the road of truth. § . by a fallacy is meant a piece of reasoning which appears to establish a conclusion without really doing so. the term applies both to the legitimate deduction of a conclusion from false premisses and to the illegitimate deduction of a conclusion from any premisses. there are errors incidental to conception and judgement, which might well be brought under the name; but the fallacies with which we shall concern ourselves are confined to errors connected with inference. § . when any inference leads to a false conclusion, the error may have arisen either in the thought itself or in the signs by which the thought is conveyed. the main sources of fallacy then are confined to two-- ( ) thought, ( ) language. § . this is the basis of aristotle's division of fallacies, which has not yet been superseded. fallacies, according to him, are either in the language or outside of it. outside of language there is no source of error but thought. for things themselves do not deceive us, but error arises owing to a misinterpretation of things by the mind. thought, however, may err either in its form or in its matter. the former is the case where there is some violation of the laws of thought; the latter whenever thought disagrees with its object. hence we arrive at the important distinction between formal and material fallacies, both of which, however, fall under the same negative head of fallacies other than those of language. | in the language | (in the signs of thought) | fallacy -| |--in the form. |--outside the language -| | (in the thought itself) | | |--in the matter. § . there are then three heads to which fallacies may be referred-namely, formal fallacies, fallacies of language, which are commonly known as fallacies of ambiguity, and, lastly, material fallacies. § . aristotle himself only goes so far as the first step in the division of fallacies, being content to class them according as they are in the language or outside of it. after that he proceeds at once to enumerate the infimæ species under each of the two main heads. we shall presently imitate this procedure for reasons of expediency. for the whole phraseology of the subject is derived from aristotle's treatise on sophistical refutations, and we must either keep to his method or break away from tradition altogether. sufficient confusion has already arisen from retaining aristotle's language while neglecting his meaning. § . modern writers on logic do not approach fallacies from the same point of view as aristotle. their object is to discover the most fertile sources of error in solitary reasoning; his was to enumerate the various tricks of refutation which could be employed by a sophist in controversy. aristotle's classification is an appendix to the art of dialectic. § . another cause of confusion in this part of logic is the identification of aristotle's two-fold division of fallacies, commonly known under the titles of in dictione and extra diotionem, with the division into logical and material, which is based on quite a different principle. § . aristotle's division perhaps allows an undue importance to language, in making that the principle of division, and so throwing formal and material fallacies under a common head. accordingly another classification has been adopted, which concentrates attention from the first upon the process of thought, which ought certainly to be of primary importance in the eyes of the logician. this classification is as follows. § . whenever in the course of our reasoning we are involved in error, either the conclusion follows from the premisses or it does not. if it does not, the fault must lie in the process of reasoning, and we have then what is called a logical fallacy. if, on the other hand, the conclusion does follow from the premisses, the fault must lie in the premisses themselves, and we then have what is called a material fallacy. sometimes, however, the conclusion will appear to follow from the premisses until the meaning of the terms is examined, when it will be found that the appearance is deceptive owing to some ambiguity in the language. such fallacies as these are, strictly speaking, non-logical, since the meaning of words is extraneous to the science which deals with thought. but they are called semi-logical. thus we arrive by a different road at the same three heads as before, namely, ( ) formal or purely logical fallacies, ( ) semi-logical fallacies or fallacies of ambiguity, ( ) material fallacies. § . for the sake of distinctness we will place the two divisions side by side, before we proceed to enumerate the infimae species. |--in the language | (fallacy of ambiguity) fallacy-| | |--in the form. |--outside the language -| | |--in the matter. |--formal or purely logical. |--logical -| fallacy-| |--semi-logical | (fallacy of ambiguity). |--material . of one of these three heads, namely, formal fallacies, it is not necessary to say much, as they have been amply treated of in the preceding pages. a formal fallacy arises from the breach of any of the general rules of syllogism. consequently it would be a formal fallacy to present as a syllogism anything which had more or less than two premisses. under the latter variety comes what is called 'a woman's reason,' which asserts upon its own evidence something which requires to be proved. schoolboys also have been known to resort to this form of argument--'you're a fool.' 'why?' 'because you are.' when the conclusion thus merely reasserts one of the premisses, the other must be either absent or irrelevant. if, on the other hand, there are more than two premisses, either there is more than one syllogism or the superfluous premiss is no premiss at all, but a proposition irrelevant to the conclusion. . the remaining rules of the syllogism are more able to be broken than the first; so that the following scheme presents the varieties of formal fallacy which are commonly enumerated-- |--four terms. formal fallacy-|--undistributed middle. |--illicit process. |--negative premisses and conclusion. § . the fallacy of four terms is a violation of the second of the general rules of syllogism (§ ). here is a palpable instance of it-- all men who write books are authors. all educated men could write books. .'. all educated men are authors. here the middle term is altered in the minor premiss to the destruction of the argument. the difference between the actual writing of books and the power to write them is precisely the difference between one who is an author and one who is not. § . since a syllogism consists of three terms, each of which is used twice over, it would be possible to have an apparent syllogism with as many as six terms in it. the true name for the fallacy therefore is the fallacy of more than three terms. but it is rare to find an attempted syllogism which has more than four terms in it, just as we are seldom tendered a line as an hexameter, which has more than seven feet. § . the fallacies of undistributed middle and illicit process have been treated of under §§ , . the heading 'negative premisses and conclusion' covers violations of the three general rules of syllogism relating to negative premisses (§§ - ). here is an instance of the particular form of the fallacy which consists in the attempt to extract an affirmative conclusion out of two negative premisses-- all salmon are fish, for neither salmon nor fish belong to the class mammalia. the accident of a conclusion being true often helps to conceal the fact that it is illegitimately arrived at. the formal fallacies which have just been enumerated find no place in aristotle's division. the reason is plain. his object was to enumerate the various modes in which a sophist might snatch an apparent victory, whereas by openly violating any of the laws of syllogism a disputant would be simply courting defeat. § . we now revert to aristotle's classification of fallacies, or rather of modes of refutation. we will take the species he enumerates in their order, and notice how modern usage has departed from the original meaning of the terms. let it be borne in mind that, when the deception was not in the language, aristotle did not trouble himself to determine whether it lay in the matter or in the form of thought. § . the following scheme presents the aristotelian classification to the eye at a glance:-- | |--equivocation. | |--amphiboly. |--in the language -|--composition. | |--division. | |--accent. | |--figure of speech. modes of -| refutation. | |--accident. | |--a dicto secundum quid. | |--ignoratio elenchi. |--outside the language -|--consequent. | |--petitio principii. | |--non causa pro causa. | |--many questions. [footnote: for "in the language": the greek is [greek: para ten lexin], the exact meaning of which is; 'due to the statement.'] § . the fallacy of equivocation [greek: òmonumía] consists in an ambiguous use of any of the three terms of a syllogism. if, for instance, anyone were to argue thus-- no human being is made of paper, all pages are human beings, .'. no pages are made of paper-- the conclusion would appear paradoxical, if the minor term were there taken in a different sense from that which it bore in its proper premiss. this therefore would be an instance of the fallacy of equivocal minor. § . for a glaring instance of the fallacy of equivocal major, we may take the following-- no courageous creature flies, the eagle is a courageous creature, .'. the eagle does not fly-- the conclusion here becomes unsound only by the major being taken ambiguously. § . it is, however, to the middle term that an ambiguity most frequently attaches. in this case the fallacy of equivocation assumes the special name of the fallacy of ambiguous middle. take as an instance the following-- faith is a moral virtue. to believe in the book of mormon is faith. .'. to believe in the book of mormon is a moral virtue. here the premisses singly might be granted; but the conclusion would probably be felt to be unsatisfactory. nor is the reason far to seek. it is evident that belief in a book cannot be faith in any sense in which that quality can rightly be pronounced to be a moral virtue. § . the fallacy of amphiboly ([greek: ámphibolía]) is an ambiguity attaching to the construction of a proposition rather than to the terms of which it is composed. one of aristotle's examples is this-- [greek: tò boúlesthai labeîn me toùs polemíous] which may be interpreted to mean either 'the fact of my wishing to take the enemy,' or 'the fact of the enemies' wishing to take me.' the classical languages are especially liable to this fallacy owing to the oblique construction in which the accusative becomes subject to the verb. thus in latin we have the oracle given to pyrrhus (though of course, if delivered at all, it must have been in greek)-- aio te, aeacida, romanos vincere posse. pyrrhus the romans shall, i say, subdue (whately), [footnote: cicero, de divinatione, ii. § ; quintilian, inst. orat. vii , § .] which pyrrhus, as the story runs, interpreted to mean that he could conquer the romans, whereas the oracle subsequently explained to him that the real meaning was that the romans could conquer him. similar to this, as shakspeare makes the duke of york point out, is the witch's prophecy in henry vi (second part, act i, sc. ), the duke yet lives that henry shall depose. an instance of amphiboly may be read on the walls of windsor castle--hoc fecit wykeham. the king mas incensed with the bishop for daring to record that he made the tower, but the latter adroitly replied that what he really meant to indicate was that the tower was the making of him. to the same head may be referred the famous sentence--'i will wear no clothes to distinguish me from my christian brethren.' § . the fallacy of composition [greek: diaíresis] is likewise a case of ambiguous construction. it consists, as expounded by aristotle, in taking words together which ought to be taken separately, e.g. 'is it possible for a man who is not writing to write?' 'of course it is.' 'then it is possible for a man to write without writing.' and again-- 'can you carry this, that, and the other?' 'yes.' 'then you can carry this, that, and the other,'-- a fallacy against which horses would protest, if they could. § . it is doubtless this last example which has led to a convenient misuse of the term 'fallacy of composition' among modern writers, by whom it is defined to consist in arguing from the distributive to the collective use of a term. § . the fallacy of division ([greek: diaíresis]), on the other hand, consists in taking words separately which ought to be taken together, e.g. [greek: ègó s' êteka doûlon ônt' èleúteron [footnote: evidently the original of the line in terence's _andria_, ,--feci ex servo ut esses libertus mihi.], where the separation of [greek: doûlon] from [greek: ôntra] would lead to an interpretation exactly contrary to what is intended. and again-- [greek: pentékont' àndrôn èkatòn lípe dîos Àchilleús], where the separation of [greek: àndrôn] from [greek: èkatòn] leads to a ludicrous error. any reader whose youth may have been nourished on 'the fairchild family' may possibly recollect a sentence which ran somewhat on this wise--'henry,' said mr. fairchild, 'is this true? are you a thief and a liar too?' but i am afraid he will miss the keen delight which can be extracted at a certain age from turning the tables upon mr. fairchild thus--henry said, 'mr. fairchild, is this true? are _you_ a thief and a liar too?' § . the fallacy of division has been accommodated by modern writers to the meaning which they have assigned to the fallacy of composition. so that by the 'fallacy of division' is now meant arguing from the collective to the distributive use of a term. further, it is laid down that when the middle term is used distributively in the major premiss and collectively in the minor, we have the fallacy of composition; whereas, when the middle term is used collectively in the major premiss and distributively in the minor, we have the fallacy of division. thus the first of the two examples appended would be composition and the second division. ( ) two and three are odd and even. five is two and three. .'. five is odd and even. ( ) the germans are an intellectual people. hans and fritz are germans. .'. they are intellectual people. § . as the possibility of this sort of ambiguity is not confined to the middle term, it seems desirable to add that when either the major or minor term is used distributively in the premiss and collectively in the conclusion, we have the fallacy of composition, and in the converse case the fallacy of division. here is an instance of the latter kind in which the minor term is at fault-- anything over a hundredweight is too heavy to lift. these sacks (collectively) are over a hundredweight. .'. these sacks (distributively) are too heavy to lift. § . the ambiguity of the word 'all,' which has been before commented upon (§ ), is a great assistance in the english language to the pair of fallacies just spoken of. § . the fallacy of accent ([greek: prosodía]) is neither more nor less than a mistake in greek accentuation. as an instance aristotle gives iliad xxiii. , where the ancient copies of homer made nonsense of the words [greek: tò mèn oú katapútetai ómbro] by writing [greek: oû] with the circumflex in place of [greek: oú] with the acute accent. [footnote: this goes to show that the ancient greeks did not distinguish in pronunciation between the rough and smooth breathing any more than their modern representatives.] aristotle remarks that the fallacy is one which cannot easily occur in verbal argument, but rather in writing and poetry. § . modern writers explain the fallacy of accent to be the mistake of laying the stress upon the wrong part of a sentence. thus when the country parson reads out, 'thou shall not bear false witness _against_ thy neighbour,' with a strong emphasis upon the word 'against,' his ignorant audience leap [sic] to the conclusion that it is not amiss to tell lies provided they be in favour of one's neighbour. § . the fallacy of figure of speech [greek: tò schêma tês léxeos] results from any confusion of grammatical forms, as between the different genders of nouns or the different voices of verbs, or their use as transitive or intransitive, e.g. [greek: úgiaínein] has the same grammatical form as [greek: témnein] or [greek: oìkodomeîn], but the former is intransitive, while the latter are transitive. a sophism of this kind is put into the mouth of socrates by aristophanes in the clouds ( - ). the philosopher is there represented as arguing that [greek: kápdopos] must be masculine because [greek: kleónumos] is. on the surface this is connected with language, but it is essentially a fallacy of false analogy. § . to this head may be referred what is known as the fallacy of paronymous terms. this is a species of equivocation which consists in slipping from the use of one part of speech to that of another, which is derived from the same source, but has a different meaning. thus this fallacy would be committed if, starting from the fact that there is a certain probability that a hand at whist will consist of thirteen trumps, one were to proceed to argue that it was probable, or that he had proved it. § . we turn now to the tricks of refutation which lie outside the language, whether the deception be due to the assumption of a false premiss or to some unsoundness in the reasoning. § . the first on the list is the fallacy of accident ([greek: tò sumbebekós]). this fallacy consists in confounding an essential with an accidental difference, which is not allowable, since many things are the same in essence, while they differ in accidents. here is the sort of example that aristotle gives-- 'is plato different from socrates ?' 'yes.' 'is socrates a man ?' 'yes.' 'then plato is different from man.' to this we answer--no: the difference of accidents between plato and socrates does not go so deep as to affect the underlying essence. to put the thing more plainly, the fallacy lies in assuming that whatever is different from a given subject must be different from it in all respects, so that it is impossible for them to have a common predicate. here socrates and plato, though different from one another, are not so different but that they have the common predicate 'man.' the attempt to prove that they have not involves an illicit process of the major. § . the next fallacy suffers from the want of a convenient name. it is called by aristotle [greek: tò áplos tóde ê pê légestai kaì mè kupíos] or, more briefly, [greek: tò áplôs ê mé], or [greek: tò pê kaí áplôs], and by the latin writers 'fallacia a dicto secundum quid ad dictum simpliciter.' it consists in taking what is said in a particular respect as though it held true without any restriction, e.g., that because the nonexistent ([greek: tò mè ôn]) is a matter of opinion, that therefore the non-existent is, or again that because the existent ([greek: tò ôn]) is not a man, that therefore the existent is not. or again, if an indian, who as a whole is black, has white teeth, we should be committing this species of fallacy in declaring him to be both white and not-white. for he is only white in a certain respect ([greek: pê]), but not absolutely ([greek: àplôs]). more difficulty, says aristotle, may arise when opposite qualities exist in a thing in about an equal degree. when, for instance, a thing is half white and half black, are we to say that it is white or black? this question the philosopher propounds, but does not answer. the force of it lies in the implied attack on the law of contradiction. it would seem in such a case that a thing may be both white and not-white at the same time. the fact is--so subtle are the ambiguities of language--that even such a question as 'is a thing white or not-white?' straightforward, as it seems, is not really a fair one. we are entitled sometimes to take the bull by the horns, and answer with the adventurous interlocutor in one of plato's dialogues--'both and neither.' it may be both in a certain respect, and yet neither absolutely. § . the same sort of difficulties attach to the law of excluded middle, and may be met in the same way. it might, for instance, be urged that it could not be said with truth of the statue seen by nebuchadnezzar in his dream either that it was made of gold or that it was not made of gold: but the apparent plausibility of the objection would be due merely to the ambiguity of language. it is not true, on the one hand, that it was made of gold (in the sense of being composed entirely of that metal); and it is not true, on the other, that it was not made of gold (in the sense of no gold at all entering into its composition). but let the ambiguous proposition be split up into its two meanings, and the stringency of the law of excluded middle will at once appear-- ( ) it must either have been composed entirely of gold or not. ( ) either gold must have entered into its composition or not. § . by some writers this fallacy is treated as the converse of the last, the fallacy of accident being assimilated to it under the title of the 'fallacia a dicto simpliciter ad dictum secundum quid.' in this sense the two fallacies may be defined thus. the fallacy of accident consists in assuming that what holds true as a general rule will hold true under some special circumstances which may entirely alter the case. the converse fallacy of accident consists in assuming that what holds true under some special circumstances must hold true as a general rule. the man who, acting on the assumption that alcohol is a poison, refuses to take it when he is ordered to do so by the doctor, is guilty of the fallacy of accident; the man who, having had it prescribed for him when he was ill, continues to take it morning, noon, and night, commits the converse fallacy. § . there ought to be added a third head to cover the fallacy of arguing from one special case to another. § . the next fallacy is ignoratio elenchi [greek: èlégchou âgnoia]. this fallacy arises when by reasoning valid in itself one establishes a conclusion other than what is required to upset the adversary's assertion. it is due to an inadequate conception of the true nature of refutation. aristotle therefore is at the pains to define refutation at full length, thus-- 'a refutation [greek: êlegchos] is the denial of one and the same--not name, but thing, and by means, not of a synonymous term, but of the same term, as a necessary consequence from the data, without assumption of the point originally at issue, in the same respect, and in the same relation, and in the same way, and at the same time.' the elenchus then is the exact contradictory of the opponent's assertion under the terms of the law of contradiction. to establish by a syllogism, or series of syllogisms, any other proposition, however slightly different, is to commit this fallacy. even if the substance of the contradiction be established, it is not enough unless the identical words of the opponent are employed in the contradictory. thus if his thesis asserts or denies something about [greek: lópion], it is not enough for you to prove the contradictory with regard to [greek: ìmátion]. there will be need of a further question and answer to identify the two, though they are admittedly synonymous. such was the rigour with which the rules of the game of dialectic were enforced among the greeks! § . under the head of ignoratio elenchi it has become usual to speak of various forme of argument which have been labelled by the latin writers under such names as 'argumentum ad hominem,' 'ad populum,' 'ad verecundiam,' 'ad ignorantiam,' 'ad baculum'--all of them opposed to the 'argumentum ad rem' or 'ad judicium.' § . by the 'argumentum ad hominem' was perhaps meant a piece of reasoning which availed to silence a particular person, without touching the truth of the question. thus a quotation from scripture is sufficient to stop the mouth of a believer in the inspiration of the bible. hume's essay on miracles is a noteworthy instance of the 'argumentum ad hominem' in this sense of the term. he insists strongly on the evidence for certain miracles which he knew that the prejudices of his hearers would prevent their ever accepting, and then asks triumphantly if these miracles, which are declared to have taken place in an enlightened age in the full glare of publicity, are palpably imposture, what credence can be attached to accounts of extraordinary occurrences of remote antiquity, and connected with an obscure corner of the globe? the 'argumentum ad judicium' would take miracles as a whole, and endeavour to sift the amount of truth which may lie in the accounts we have of them in every age. [footnote: on this subject see the author's _attempts at truth_ (trubner & co.), pp. - .] § . in ordinary discourse at the present day the term 'argumentum ad hominem' is used for the form of irrelevancy which consists in attacking the character of the opponent instead of combating his arguments, as illustrated in the well-known instructions to a barrister--'no case: abuse the plaintiff's attorney.' § . the 'argumentum ad populum' consists in an appeal to the passions of one's audience. an appeal to passion, or to give it a less question-begging name, to feeling, is not necessarily amiss. the heart of man is the instrument upon which the rhetorician plays, and he has to answer for the harmony or the discord that comes of his performance. § . the 'argumentum ad verecundiam' is an appeal to the feeling of reverence or shame. it is an argument much used by the old to the young and by conservatives to radicals. § . the 'argumentum ad ignorantiam' consists simply in trading on the ignorance of the person addressed, so that it covers any kind of fallacy that is likely to prove effective with the hearer. § . the 'argumentum ad baculum' is unquestionably a form of irrelevancy. to knock a man down when he differs from you in opinion may prove your strength, but hardly your logic. a sub-variety of this form of irrelevancy was exhibited lately at a socialist lecture in oxford, at which an undergraduate, unable or unwilling to meet the arguments of the speaker, uncorked a bottle, which had the effect of instantaneously dispersing the audience. this might be set down as the 'argumentum ad nasum.' § . we now come to the fallacy of the consequent, a term which has been more hopelessly abused than any. what aristotle meant by it was simply the assertion of the consequent in a conjunctive proposition, which amounts to the same thing as the simple conversion of a (§ ), and is a fallacy of distribution. aristotle's example is this-- if it has rained, the ground is wet. .'. if the ground is wet, it has rained. this fallacy, he tells us, is often employed in rhetoric in dealing with presumptive evidence. thus a speaker, wanting to prove that a man is an adulterer, will argue that he is a showy dresser, and has been seen about at nights. both these things however may be the case, and yet the charge not be true. § . the fallacy of petitio or assumptio principii [greek: tò èn àrchê aìteîstai or lambánein] to which we now come, consists in an unfair assumption of the point at issue. the word [greek: aìteîstai], in aristotle's name for it points to the greek method of dialectic by means of question and answer. this fact is rather disguised by the mysterious phrase 'begging the question.' the fallacy would be committed when you asked your opponent to grant, overtly or covertly, the very proposition originally propounded for discussion. § . as the question of the precise nature of this fallacy is of some importance we will take the words of aristotle himself (top. viii. . §§ , ). 'people seem to beg the question in five ways. first and most glaringly, when one takes for granted the very thing that has to be proved. this by itself does not readily escape detection, but in the case of "synonyms," that is, where the name and the definition have the same meaning, it does so more easily. [footnote: some light is thrown upon this obscure passage by a comparison with cat. i. § , where 'synonym' is defined. to take the word here in its later and modern sense affords an easy interpretation, which is countenanced by alexander aphrodisiensis, but it is flat against the usage of aristotle, who elsewhere gives the name 'synonym,' not to two names for the same thing, but to two things going under the same name. see trendelenberg on the passage.] secondly, when one assumes universally that which has to be proved in particular, as, if a man undertaking to prove that there is one science of contraries, were to assume that there is one science of opposites generally. for he seems to be taking for granted along with several other things what he ought to have proved by itself. thirdly, when one assumes the particulars where the universal has to be proved; for in so doing a man is taking for granted separately what he was bound to prove along with several other things. again, when one assumes the question at issue by splitting it up, for instance, if, when the point to be proved is that the art of medicine deals with health and disease, one were to take each by itself for granted. lastly, if one were to take for granted one of a pair of necessary consequences, as that the side is incommensurable with the diagonal, when it is required to prove that the diagonal is incommensurable with the side.' § . to sum up briefly, we may beg the question in five ways-- ( ) by simply asking the opponent to grant the point which requires to be proved; ( ) by asking him to grant some more general truth which involves it; ( ) by asking him to grant the particular truths which it involves; ( ) by asking him to grant the component parts of it in detail; ( ) by asking him to grant a necessary consequence of it. § . the first of these five ways, namely, that of begging the question straight off, lands us in the formal fallacy already spoken of (§ ), which violates the first of the general rules of syllogism, inasmuch as a conclusion is derived from a single premiss, to wit, itself. § . the second, strange to say, gives us a sound syllogism in barbara, a fact which countenances the blasphemers of the syllogism in the charge they bring against it of containing in itself a petitio principii. certainly aristotle's expression might have been more guarded. but it is clear that his quarrel is with the matter, not with the form in such an argument. the fallacy consists in assuming a proposition which the opponent would be entitled to deny. elsewhere aristotle tells us that the fallacy arises when a truth not evident by its own light is taken to be so. [footnote: [greek: Ôtan tò mè dí aùtoû gnostòn dí aùtoû tis èpicheiraê deiknúnai, tót' aìteîtai tò èx àrchês.]. anal. pr. ii. . § i ad fin.] § . the third gives us an inductio per enumerationem simplicem, a mode of argument which would of course be unfair as against an opponent who was denying the universal. § . the fourth is a more prolix form of the first. § . the fifth rests on immediate inference by relation (§ ). § . under the head of petitio principii comes the fallacy of arguing in a circle, which is incidental to a train of reasoning. in its most compressed form it may be represented thus-- ( ) b is a. c is b. .'. c is a. ( ) c is a. b is c. .'. b is a. § . the fallacy of non causa pro causa ([greek: tò mè aîtion] or [greek: aîtoin]) is another, the name of which has led to a complete misinterpretation. it consists in importing a contradiction into the discussion, and then fathering it on the position controverted. such arguments, says aristotle, often impose upon the users of them themselves. the instance he gives is too recondite to be of general interest. § . lastly, the fallacy of many questions ([greek: tò tà déo èrotémata ên poieîn]) is a deceptive form of interrogation, when a single answer is demanded to what is not really a single question. in dialectical discussions the respondent was limited to a simple 'yes' or 'no'; and in this fallacy the question is so framed as that either answer would seem to imply the acceptance of a proposition which would be repudiated. the old stock instance will do as well as another--'come now, sir, answer "yes" or "no." have you left off beating your mother yet?' either answer leads to an apparent admission of impiety. a late senior proctor once enraged a man at a fair with this form of fallacy. the man was exhibiting a blue horse; and the distinguished stranger asked him--'with what did you paint your horse?' exercises. these exercises should be supplemented by direct questions upon the text, which it is easy for the student or the teacher to supply for himself. part i. chapter i. classify the following words according as they are categorematic, syncategorematic or acategorematic;-- come peradventure why through inordinately pshaw therefore circumspect puss grand inasmuch stop touch sameness back cage disconsolate candle. chapter ii. classify the following things according as they are substances, qualities or relations;-- god likeness weight blueness grass imposition ocean introduction thinness man air spirit socrates raillery heat mortality plum fire. chapter iii. . give six instances each of-attribute, abstract, singular, privative, equivocal and relative terms. . select from the following list of words such as are terms, and state whether they are ( ) abstract or concrete, ( ) singular or common, ( ) univocal or equivocal:-- van table however enter decidedly tiresome very butt solomon infection bluff czar short although caesarism distance elderly nihilist. . which of the following words are abstract terms?-- quadruped event through hate desirability thorough fact expressly thoroughness faction wish light inconvenient will garden inconvenience volition grind. . refer the following terms to their proper place under each of the divisions in the scheme:-- horse husband london free lump empty liberty rational capital impotent reason capitol impetuosity irrationality grave impulsive double calf. . give six instances each of proper names and designations. . give six instances each of connotative and non-connotative terms. . give the extension and intension of-- sermon animal sky clock square gold sport fish element bird student fluid art river line gas servant language chapter iv. arrange the following terms in order of extension--carnivorous, thing, matter, mammal, organism, vertebrate, cat, substance, animal. * * * * * part ii. chapter i. give a name to each of the following sentences:-- ( ) oh, that i had wings like a dove! ( ) the more, the merrier. ( ) come rest in this bosom, my own stricken deer. ( ) is there balm in gilead? ( ) hearts may be trumps. chapter ii. analyse the following propositions into subject, copula and predicate:-- ( ) he being dead yet speaketh. ( ) there are foolish politicians. ( ) little does he care. ( ) there is a land of pure delight. ( ) all's well that ends well. ( ) sweet is the breath of morn. ( ) now it came to pass that the beggar died. ( ) who runs may read. ( ) great is diana of the ephesians. ( ) such things are. ( ) not more than others i deserve. ( ) the day will come when ilium's towers shall perish. chapter iii. . express in logical form, affixing the proper symbol:-- ( ) some swans are not white. ( ) all things are possible to them that believe. ( ) no politicians are unprincipled. ( ) some stones float on water. ( ) the snow has melted. ( ) eggs are edible. ( ) all kings are not wise. ( ) moths are not butterflies. ( ) some men are born great. ( ) not all who are called are chosen. ( ) it is not good for man to be alone. ( ) men of talents have been known to fail in life. ( ) 'tis none but a madman would throw about fire. ( ) every bullet does not kill. ( ) amongst unionists are whigs. ( ) not all truths are to be told. ( ) not all your efforts can save him. ( ) the whale is a mammal. ( ) cotton is grown in cyprus. ( ) an honest man's the noblest work of god. ( ) no news is good news. ( ) no friends are like old friends. ( ) only the ignorant affect to despise knowledge. ( ) all that trust in him shall not be ashamed. ( ) all is not gold that glitters. ( ) the sun shines upon the evil and upon the good. ( ) not to go on is to go back. ( ) the king, minister, and general are a pretty trio. ( ) amongst dogs are hounds. ( ) a fool is not always wrong. ( ) alexander was magnanimous. ( ) food is necessary to life. ( ) there are three things to be considered, ( ) by penitence the eternal's wrath's appeased. ( ) money is the miser's end. ( ) few men succeed in life. ( ) all is lost, save honour. ( ) it is mean to hit a man when he is down. ( ) nothing but coolness could have saved him. ( ) books are generally useful. ( ) he envies others' virtue who has none himself. ( ) thankless are all such offices. ( ) only doctors understand this subject. ( ) all her guesses but two were correct. ( ) all the men were twelve. ( ) gossip is seldom charitable. . give six examples of indefinite propositions, and then quantify them according to their matter. . compose three propositions of each of the following kinds:-- ( ) with common terms for subjects; ( ) with abstract terms for subjects; ( ) with singular terms for predicates; ( ) with collective terms for predicates; ( ) with attributives in their subjects; ( ) with abstract terms for predicates. chapter iv. . point out what terms are distributed or undistributed in the following propositions:-- ( ) the chinese are industrious. ( ) the angle in a semi-circle is a right angle. ( ) not one of the crew survived. ( ) the weather is sometimes not propitious. the same exercise may be performed upon any of the propositions in the preceding list. . prove that in a negative proposition the predicate must be distributed. chapter v. affix its proper symbol to each of the following propositions:-- ( ) no lover he who is not always fond. ( ) there are irishmen and irishmen. ( ) men only disagree, of creatures rational. ( ) some wise men are poor. ( ) no popes are some fallible beings. ( ) some step-mothers are not unjust. ( ) the most original of the roman poets was lucretius. ( ) some of the immediate inferences are all the forms of conversion. chapter vi. . give six examples of terms standing one to another as genus to species. . to which of the heads of predicables would you refer the following statements? and why? ( ) a circle is the largest space that can be contained by one line. ( ) all the angles of a square are right angles. ( ) man alone among animals possesses the faculty of laughter. ( ) some fungi are poisonous. ( ) most natives of africa are negroes. ( ) all democracies are governments. ( ) queen anne is dead. chapter vii. . define the following terms-- sun inn-keeper tea-pot hope anger virtue bread diplomacy milk carpet man death sincerity telescope mountain poverty senate novel. . define the following terms as used in political economy-- commodity barter value wealth land price money labour rent interest capital wages credit demand profits. . criticise the following as definitions-- ( ) noon is the time when the shadows of bodies are shortest. ( ) grammar is the science of language. ( ) grammar is a branch of philology. ( ) grammar is the art of speaking and writing a language with propriety. ( ) virtue is acting virtuously. ( ) virtue is that line of conduct which tends to produce happiness. ( ) a dog is an animal of the canine species. ( ) logic is the art of reasoning. ( ) logic is the science of the investigation of truth by means of evidence. ( ) music is an expensive noise. ( ) the sun is the centre of the solar system. ( ) the sun is the brightest of those heavenly bodies that move round the earth. ( ) rust is the red desquamation of old iron. ( ) caviare is a kind of food. ( ) life is the opposite of death. ( ) man is a featherless biped. ( ) man is a rational biped. ( ) a gentleman is a person who has no visible means of subsistence. ( ) fame is a fancied life in others' breath. ( ) a fault is a quality productive of evil or inconvenience. ( ) an oligarchy is the supremacy of the rich in a state. ( ) a citizen is one who is qualified to exercise deliberative and judicial functions. ( ) length is that dimension of a solid which would be measured by the longest line. ( ) an eccentricity is a peculiar idiosyncrasy. ( ) deliberation is that species of investigation which is concerned with matters of action. ( ) memory is that which helps us to forget. ( ) politeness is the oil that lubricates the wheels of society. ( ) an acute-angled triangle is one which has an acute angle. ( ) a cause is that without which something would not be. ( ) a cause is the invariable antecedent of a phenomenon. ( ) necessity is the mother of invention. ( ) peace is the absence of war. ( ) a net is a collection of holes strung together. ( ) prudence is the ballast of the moral vessel. ( ) a circle is a plane figure contained by one line. ( ) superstition is a tendency to look for constancy where constancy is not to be expected. ( ) bread is the staff of life. ( ) an attributive is a term which cannot stand as a subject. ( ) life is bottled sunshine. ( ) eloquence is the power of influencing the feelings by speech or writing. ( ) a tombstone is a monument erected over a grave in memory of the dead. ( ) whiteness is the property or power of exciting the sensation of white. ( ) figure is the limit of a solid. ( ) an archdeacon is one who exercises archidiaconal functions. ( ) humour is thinking in jest while feeling in earnest. chapter viii. . divide the following terms-- soldier end book church good oration apple cause school ship government letter vehicle science verse. . divide the following terms as used in political economy-- requisites of production, labour, consumption, stock, wealth, capital. . criticise the following as divisions-- ( ) great britain into england, scotland, wales, and ireland. ( ) pictures into sacred, historical, landscape, and mythological. ( ) vertebrate animals into quadrupeds, birds, fishes, and reptiles. ( ) plant into stem, root, and branches. ( ) ship into frigate, brig, schooner, and merchant-man. ( ) books into octavo, quarto, green, and blue. ( ) figure into curvilinear and rectilinear. ( ) ends into those which are ends only, means and ends, and means only. ( ) church into gothic, episcopal, high, and low. ( ) sciences into physical, moral, metaphysical, and medical. ( ) library into public and private. ( ) horses into race-horses, hunters, hacks, thoroughbreds, ponies, and mules. . define and divide-- meat, money, virtue, triangle; and give, as far as possible, a property and accident of each. part iii. chapters i-iii. . what kind of influence have we here? the author of the iliad was unacquainted with writing. homer was the author of the iliad. .'. homer was unacquainted with writing. . give the logical opposites of the following propositions-- ( ) knowledge is never useless. ( ) all europeans are civilised. ( ) some monks are not illiterate. ( ) happy is the man that findeth wisdom. ( ) no material substances are devoid of weight. ( ) every mistake is not culpable. ( ) some irishmen are phlegmatic. . granting the truth of the following propositions, what other propositions can be inferred by opposition to be true or false? ( ) men of science are often mistaken. ( ) he can't be wrong, whose life is in the right. ( ) sir walter scott was the author of waverley. ( ) the soul that sinneth it shall die. ( ) all women are not vain. . granting the falsity of the following propositions, what other propositions can be inferred by opposition to be true or false?-- ( ) some men are not mortal. ( ) air has no weight. ( ) all actors are improper characters. ( ) none but dead languages are worth studying. ( ) some elements are compound. chapter iv. . give, as far as possible, the logical converse of each of the following propositions-- ( ) energy commands success. ( ) mortals cannot be happy. ( ) there are mistakes which are criminal. ( ) all's well that ends well. ( ) envious men are disliked. ( ) a term is a kind of word or collection of words. ( ) some frenchmen are not vivacious. ( ) all things in heaven and earth were hateful to him. ( ) the square of three is nine. ( ) all cannot receive this saying. ( ) p struck q. ( ) amas. . 'more things may be contained in my philosophy than exist in heaven or earth: but the converse proposition is by no means true.' is the term converse here used in its logical meaning? chapter v. permute the following propositions-- ( ) all just acts are expedient. ( ) no display of passion is politic. ( ) some clever people are not prudent. ( ) some philosophers have been slaves. the same exercise may be performed upon any of the propositions in the preceding lists. chapter vi. . give the converse by negation of-- ( ) all women are lovely. ( ) some statesmen are not practical. ( ) all lawyers are honest. ( ) all doctors are skilful. ( ) some men are not rational. . give the contrapositive of-- ( ) all solid substances are material. ( ) all the men who do not row play cricket. ( ) all impeccable beings are other than human, ( ) some prejudiced persons are not dishonest. . prove indirectly the truth of the contrapositive of 'all a is b.' . criticise the following as immediate inferences-- ( ) all wise men are modest. .'. no immodest men are wise. ( ) some german students are not industrious. .'. some industrious students are not germans. ( ) absolute difference excludes all likeness. .'. any likeness is a proof of sameness. ( ) none but the brave deserve the fair. .'. all brave men deserve the fair. ( ) all discontented men are unhappy. .'. no contented men are unhappy. ( ) books being a source of instruction, our knowledge must come from our libraries. ( ) all jews are semitic. .'. some non-semitic people are not jews. . show by what kind of inference each of the subjoined propositions follows from all discontented men are unhappy. ( ) all happy men are contented. ( ) some discontented men are unhappy. ( ) some contented men are happy. ( ) some unhappy men are not contented. ( ) no discontented men are happy. ( ) some happy men are contented. ( ) some contented men are not unhappy. ( ) some unhappy men are discontented. ( ) no happy men are discontented. ( ) some discontented men are not happy. ( ) some happy men are not discontented. ( ) none but unhappy men are discontented. from how many of these propositions can the original one be derived? and why not from all? chapter vii. what kind of inference have we here?-- ( ) none but the ignorant despise knowledge. .'. no wise man despises knowledge. ( ) a is superior to b. .'. b is inferior to a. chapter viii. fill up the following enthymemes, mentioning to which order they belong, and state which of them are expressed in problematic form-- ( ) i am fond of music: for i always like a comic song. ( ) all men are born to suffering, and therefore you must expect your share. ( ) job must have committed some secret sins: for he fell into dreadful misfortunes. ( ) latin was the language of the vestals, and therefore no lady need be ashamed of speaking it. ( ) none but physicians came to the meeting. there were therefore no nurses there. ( ) the human soul extends through the whole body, for it is found in every member. ( ) no traitor can be trusted, and you are a traitor. ( ) whatever has no parts does not perish by the dissolution of its parts. therefore the soul of man is imperishable. is the suppressed premiss in any case disputable on material grounds? chapters ix-xviii. refer the following arguments to their proper mood and figure, or show what rules of syllogism they violate. ( ) no miser is a true friend, for he does not assist his friend with his purse. ( ) governments are good which promote prosperity. the government of burmah does not promote prosperity. .'. it is not a good government. ( ) land is not property. land produces barley. .'. beer is intoxicating. ( ) nothing is property but that which is the product of man's hand. the horse is not the product of man's hand. .'. the horse is not property. ( ) some europeans at least are not aryans, because the finns are not. ( ) saturn is visible from the earth, and the moon is visible from the earth. therefore the moon is visible from saturn. ( ) some men of self-command are poor, and therefore some noble characters are poor. ( ) sparing the rod spoils the child: so john will turn out very good, for his mother beats him every day. ( ) some effects of labour are not painful, since every virtue is an effect of labour. ( ) the courageous are confident and the experienced are confident. therefore the experienced are courageous. ( ) no tale-bearer is to be trusted, and therefore no great talker is to be trusted, for all tale-bearers are great talkers. ( ) socrates was wise, and wise men alone are happy: therefore socrates was happy. ii. . from the major 'no matter thinks' draw, by supplying the minor, the following conclusions-- ( ) some part of man does not think. ( ) the soul of man is not matter. ( ) some part of man is not matter. ( ) some substance does not think. name the figured mood into which each syllogism falls. . construct syllogisms in the following moods and figures, stating whether they are valid or invalid, and giving your reasons in each case-- aee in the first figure; eao in the second; iai in the third; aii in the fourth. . prove that 'brass is not a metal,' using as your middle term 'compound body.' . construct syllogisms to prove or disprove-- ( ) some taxes are necessary. ( ) no men are free. ( ) laws are salutary. . prove by a syllogism in bokardo that 'some socialists are not unselfish,' and reduce your syllogism directly and indirectly. . prove the following propositions in the second figure, and reduce the syllogisms you use to the first-- ( ) all negroes are not averse to education. ( ) only murderers should be hanged. . prove in baroko and also in ferio that 'some irishmen are not celts.' . construct in words the same syllogism in all the four figures. . invent instances to show that false premisses may give true conclusions. iii. . what moods are peculiar to the first, second, and third figures respectively? . what moods are common to all the figures? . why can there be no subaltern moods in the third figure? . what is the only kind of conclusion that can be drawn in all the figures? . show that ieo violates the special rules of all the figures. . in what figures is aee valid? . show that aeo is superfluous in any figure. . prove that o cannot be a premiss in the first figure, nor a minor premiss anywhere but in the second. . show that in the first figure the conclusion must have the quality of the major premiss and the quantity of the minor. . why do the premisses ea yield a universal conclusion in the first two figures and only a particular one in the last two? . show that aai is the only mood in the fourth figure in which it is possible for the major term to be distributed in the premiss and undistributed in the conclusion. . why are the premisses of fesapo and fresison not transposed in reduction like those of the other moods of the fourth figure? iv. . why is it sufficient to distribute the middle term once only? . prove that from two affirmative premisses you cannot get a negative conclusion. . prove that there must be at least one more term distributed in the premisses than in the conclusion. . prove that the number of distributed terms in the premisses cannot exceed those in the conclusion by more than two. . prove that the number of undistributed terms in the premisses cannot exceed those in the conclusion by more than one. . prove that wherever the minor premiss is negative, the major must be universal. . prove that wherever the minor term is distributed, the major premiss must be universal. . if the middle term be twice distributed, what mood and figure are possible? . if the major term of a syllogism be the predicate of the major premiss, what do we know about the minor premiss? . when the middle term is distributed in both premisses, what must be the quantity of the conclusion? . prove that if the conclusion be universal, the middle term can only be distributed once in the premisses. . show how it is sometimes possible to draw three different conclusions from the same premisses. chapter xix. . convert the following propositions-- ( ) if a man is wise, he is humble. ( ) where there is sincerity there is no affectation. ( ) when night-dogs run, all sorts of deer are chased. ( ) the nearer the church, the further from god. ( ) if there were no void, all would be solid. ( ) not to go on is sometimes to go back. . express in a single proposition-- if he was divine, he was not covetous; and if he was covetous, he was not divine. . exhibit the exact logical relation to one another of the following pairs of propositions-- ( ) if the conclusion be false, the premisses are false. if the conclusion be true, the premisses are not necessarily true. ( ) if one premiss be negative, the conclusion must be negative. if the conclusion be negative, one of the premisses must be negative. ( ) the truth of the universal involves the truth of the particular. the falsity of the particular involves the falsity of the universal. ( ) from the truth of the particular no conclusion follows as to the universal. from the falsity of the universal no conclusion follows as to the particular. ( ) if the conclusion in the fourth figure be negative, the major premiss must be universal. if the major premiss in the fourth figure be particular, the conclusion must be affirmative. ( ) if both premisses be affirmative, the conclusion must be affirmative. if the conclusion be negative, one of the premisses must be negative. . 'the method of agreement stands on the ground that whatever circumstance can be eliminated is not connected with the phenomenon by any law; the method of difference stands on the ground that whatever circumstance cannot be eliminated is connected with the phenomenon by a law.' do these two principles imply one another? chapters xx-xxviii. . fill up the following enthymemes, and state the exact nature of the resulting syllogism-- ( ) if livy is a faultless historian, we must believe all that he tells us; but that it is impossible to do. ( ) if they stay abroad, the wife will die; while the husband's lungs will not stand the english climate. it is to be feared therefore that one must fall a victim. ( ) he is either very good, very bad, or commonplace. but he is not very good. ( ) either a slave is capable of virtue or he is not. .'. either he ought not to be a slave or he is not a man. ( ) does not his feebleness of character indicate either a bad training or a natural imbecility? ( ) those who ask shan't have; those who don't ask don't want. ( ) if a man be mad, he deviates from the common standard of intellect. .'. if all men be alike mad, no one is mad. ( ) 'i cannot dig; to beg i am ashamed.' . 'the infinite divisibility of space implies that of time. if the latter therefore be impossible, the former must be equally so.' formulate this argument as an immediate inference. . examine the following arguments-- ( ) if we have a dusty spring, there is always a good wheat harvest. we shall therefore have a poor harvest this year, for the spring has not been dusty. ( ) virtues are either feelings, capacities, or states; and as they are neither feelings nor capacities, they must be states. ( ) everything must be either just or unjust. justice is a thing, and is not unjust. .'. justice is just. similarly justice is holy. but the virtues of knowledge, justice, courage, temperance, and holiness were declared to be different from one another. .'. justice is unholy and holiness unjust. chapter xxix. formulate the following trains of reasoning, resolve them into their component parts, and point out any violations of the rules of syllogism which they may contain-- ( ) no church institutions are useful; for they teach religious matters, not business matters, which latter are useful, being profitable. ( ) mr. darwin long ago taught us that the clover crop is dependent on the number of maiden ladies in the district. for the ladies keep cats, and the cats destroy the field-mice, which prey on the bees, which, in their turn, are all-important agents in the fertilisation of the clover flowers. ( ) athletic games are duties; for whatever is necessary to health is a duty, and exercise is necessary to health, and these games are exercise. ( ) the iron-trade leads to the improvement of a new country; for furnaces require to be fed with fuel, which causes land to be cleared. ( ) 'is stone a body?' 'yes.' 'well, is not an animal a body?' 'yes,' 'and are you an animal?' 'it seems so.' 'then you are a stone, being an animal.' ( ) if a is b, c is d. if e is f, g is h. but if a is b, e is f. .'. if c is d, g is sometimes h. ( ) the soul is not matter. my arm is not myself. ( ) honesty deserves reward and a negro is a fellow-creature. therefore an honest negro is a fellow-creature deserving of reward. chapter xxx. . point out any ambiguities which underlie the following propositions-- ( ) every one who has read the book in french will recommend those who have not to read it in english. ( ) i will not do this because he did it. ( ) these are all my books. ( ) by an old statute of the date of edward iii it was accorded 'that parliament should be holden every year once or more often if need be.' ( ) they found mary and joseph and the babe lying in a manger. ( ) the king and his minister are feeble and unscrupulous. ( ) heres meus uxori meae triginta pondo vasorum argenteorum dato, quae volet. . examine the following arguments, formulating them when sound, and referring them, when unsound, to the proper head of fallacy-- ( ) we know that thou art a teacher come from god; for no man can do these signs that thou doest, except god be with him. s. john iii. . ( ) 'sir walter scott's novels have ceased to be popular.' 'well, that's only because nobody reads them.' ( ) what we produce is property. the sheriff produces a prisoner. .'. a prisoner is property. ( ) as all metals are not necessarily solid, we may expect some metals to be liquid. ( ) moses was the son of pharaoh's daughter. .'. moses was the daughter of pharaoh's son. ( ) if aeschines took part in the public rejoicings over the success of my policy, he is inconsistent in condemning it now; if he did not, he was a traitor then. ( ) it is wrong to stick knives into people. .'. surgeons ought to be punished. ( ) if a thing admits of being taught, there must be both teachers and learners of it. .'. if there are neither teachers nor learners of a thing, that thing does not admit of being taught. ( ) it is unnecessary to lend books, if they are common, and wrong to lend them, if they are rare. therefore books should not be lent from public libraries. ( ) seeing is believing. .'. what is not seen cannot be believed. ( ) st. paul was not of jewish blood, for he was a roman citizen. ( ) to call you an animal is to speak the truth. to call you an ass is to call you an animal. .'. to call you an ass is to speak the truth. ( ) pain chastens folly. a life of ease must therefore be one of folly incurable. ( ) we cannot be happy in this world; for we must either indulge our passions or combat them. ( ) it must be clear to the most unlettered mind that, as all things were originally created by the deity, including the hair on our heads and the beards on our faces, there can be no such thing as property. ( ) the crime was committed by the criminal. the criminal was committed by the magistrate. .'. the crime was committed by the magistrate. ( ) general councils are as likely to err as the fallible men of whom they consist. ( ) dead dogs are heavier than living ones, because vitality is buoyant. ( ) deliberation is concerned with actions. actions are means. .'. deliberation is concerned with means. ( ) 'no beast so fierce but has a touch of pity; but i have none: therefore i am no beast.' ( ) practical pursuits are better than theoretical. .'. mathematics are better than logic. ( ) death must be a good. for either the soul, ceasing to be, ceases ta suffer, or, continuing to be, lives in a better state. ( ) what is right should be enforced by law. .'. charity should be so enforced. ( ) all animals were in the ark. .'. no animals perished in the flood. ( ) if he robs, he is not honourable. if he pays all his dues, he does not rob. .'. if he pays all his dues, he is honourable. ( ) a dove can fly a mile in a minute. a swallow can fly faster than a dove. .'. a swallow can fly more than a mile in a minute. ( ) 'i must soap myself, because it's sunday.' 'then do you only soap yourself on sunday.' ( ) if the charge is false, the author of it is either ignorant or malicious. but the charge is true. therefore he is neither. ( ) all the angles of a triangle are equal to two right angles. the angle at the vertex is an angle of a triangle. .'. it is equal to two right angles. ( ) si gravis sit dolor, brevis est; si longus, levis. ergo fortiter ferendus. ( ) you are not what i am. i am a man. .'. you are not a man. ( ) the extension of the franchise is necessary, for it is imperative that the right of voting should be granted to classes who have hitherto not possessed this privilege. ( ) if hannibal is really victorious, he does not need supplies; while, if he is deluding us, we ought certainly not to encourage him by sending them. livy, xxiii. . § . ( ) laws must punish, and punishment hurts. all laws therefore are hurtful. ( ) the sun is an insensible thing. the persians worship the sun. .'. the persians worship an insensible thing. ( ) some ores are not metals; for they are not fluids, and some metals are not fluids. ( ) all the grecian soldiers put the persians to flight. .'. every grecian soldier could rout the persians. ( ) the resurrection of jesus christ is either an isolated fact or else admits of parallel. but if it be an isolated fact, it cannot be rendered probable to one who denies the authority of christianity; and, if it admit of parallel, it no longer proves what is required. therefore it is either incapable of being substantiated or else makes nothing for the truth of christianity. ( ) the resurrection of christ in the flesh and his ascension into heaven were events either intrinsically incredible in their nature or not. if the former, the prevalent belief in them can only be accounted for by miracles; if the latter, they ought to be believed even without miracles. st. aug. de civ. dei, xxii. . ( ) only contented people are wise. therefore the tramp contented in his rags is necessarily a wise man. ( ) four-legged things are brutes. tables are four-legged things. .'. tables are brutes. ( ) the apparent volcanoes in the moon are not volcanoes; for eruptions are produced by gases only, and there are no gases in the moon. ( ) to read the scriptures is our duty. therefore the captain was wrong in punishing the helmsman for reading the bible at the time when the ship struck. ( ) the divine law orders that kings should be honoured. louis quatorze is a king. .'. the divine law orders that louis quatorze should be honoured. ( ) those who desire the same object are unanimous. caesar and pompey both desire the same object, namely, supreme power. .'. they are unanimous. ( ) either the ministers left at home will be ciphers or they will not be ciphers. if they are ciphers, cabinet government, which is equivalent to constitutional government, will receive a rude blow. if they are not ciphers, the cabinet will be considering matters of the utmost importance in the absence, and the gratuitous absence, of two of its most important members. 'the standard,' wed. june , . ( ) one patent stove saves half the ordinary amount of fuel. therefore two would save it all. ( ) one number must win in the lottery. my ticket is one number. .'. it must win. ( ) all good shepherds are prepared to lay down their lives for the sheep. few in this age are so prepared. .'. few in this age are good shepherds. ( ) you cannot define the sun; for a definition must be clearer than the thing defined, and nothing can be clearer than the source of all light. ( ) to give the monopoly of the home market to the produce of domestic industry ... must in almost all cases be either a useless or a hurtful regulation. if the produce of domestic can be brought there as cheap as that of foreign industry, the regulation is evidently useless; if it cannot, it is generally hurtful. adam smith, wealth of nations, bk. iv. ch. . ( ) verberare est actio. ergo et vapulare. ( ) the ages of all the members of this family are over . the baby is a member of this family. .'. its age is over . ( ) romulus must be an historical person; because it is not at all likely that the romans, whose memory was only burdened with seven kings, should have forgotten the most famous of them, namely, the first. ( ) all scientific treatises that are clear and true deserve attention. few scientific treatises are clear and true. .'. few scientific treatises deserve attention. ( ) the conservative government is an expensive one; for, on their going out of office, there was a deficit. ( ) a man is forbidden to marry his brother's wife, or, in other words, a woman is forbidden to marry her husband's brother, that is, a woman is directly forbidden to marry two brothers. therefore a man may not marry two sisters, so that a man may not marry his wife's sister. index. the references refer to the sections. abstraction, . acategorematic words, . accent, fallacy of, . accident, . accident, fallacy of, . a dicto secundum quid, fallacy of, . amphiboly, fallacy of, . antecedent of a complex proposition, . of an inference, . a posteriori truth, . a priori truth, . 'a' propositions, . conversion of, . arguing in a circle, . argumentum ad hominem, etc., . art, . attribute, sqq. essential and non-essential, . attributives, sqq. basis of division, . categorematic words, . circulus in definiendo, . common terms, . how formed, . nature of, . complex proposition, . conversion of, . conversion by contraposition of, . conversion by negation of, . divided into conjunctive and disjunctive, . permutation of, . complex syllogism, . mixed form of, . composition, fallacy of, . concept, , sqq. conception, . conceptualists, . conclusion, . predicate of, . subject of, . conjunctive syllogisms, . canon of, . reduction of partly, . partly conjunctive syllogisms as an immediate inference, . connotation of terms, . consequent of a complex proposition, . of an inference, . consequent, fallacy of, . contingent, . contradiction, law of, sqq. contradictory propositions, . terms, . contrary propositions, . terms, . converse, . conversion, . of complex propositions, . by contraposition, . illative, . by negation, . per accidens, . simple, . rules of, . convertend, . copula, , , sqq. modality of, . correlatives, . deduction and induction, difference of, sqq. deductive inference, . deductive logic, definition of, . definition of terms, sqq. of aristotle ([greek: òrismós]), . final, . nominal, . provisional, . real, . rules of, . denotation of terms, . description, . designations, . determination, . dictum de omni et nullo, . de diverso, . de exemplo et excepto, . difference, , . generic, . specific, . dilemma, , . rebutted, . reduction of, . regarded as an immediate inference, . disjunctive syllogism, . canon of, . reduction of, . regarded as an immediate inference, . distinction, . distribution of terms, . four rules for, . divided whole, . dividing members, . division, sqq. by dichotomy, . rules of, . division, fallacy of, . division of propositions, . of terms, . of things, . enthymeme, incorrectly so-called, . enumeration, , . epicheirema, . episyllogism, . 'e' propositions, . conversion of, . equivocation, fallacy of, . excluded middle, law of, sqq., . extension of terms, sqq., sqq. fallacy, sqq. of ambiguity, . definition of, . formal, . logical, . material, , . of undisturbed middle, . figure of speech, fallacy of, . figures, of a syllogism, . special canons of, . special rules of, . special uses of, . formal logic, . four terms, fallacy of, . fundamentum divisionis, . generalisation, . genus, . as used by aristotle, . cognate, . proximate, . subaltern, . summum, , . heads of predicables, . as given by aristotle, . 'ideas' of plato, . identity, law of, sqq. ignoratio elenchi, fallacy of, . ignotum per ignotius, . illicit process, fallacy of, . immediate inference, sqq. by added determinants, . by complex conception, . applied to complex propositions, . immediate inference, compound forms of, . partly conjunctive syllogisms regarded as, . by conversion, . disjunctive syllogisms regarded as, . by opposition, . by permutation, . induction, differing from deduction, sqq. inductive logic, , . inferences in general, . classification of, . deductive, . inductive, . intimae species, . intension of terms, , . intuition, . inverse variation, law of, . 'i' propositions, . conversion of, . 'judgement,' various meanings of, , . 'law,' ambiguities of the word, sqq. major premiss, . major term, . many questions, fallacy of, . mediate inferences or syllogisms, , sqq. axioms of, . membra dividentia, . middle term, . position of, in a syllogism, . minor premiss, . minor term, . modality, question of, . mode, the, . moods of a syllogism, . determination of the legitimate, . subaltern, . valid in the four figures, . mnemonics of, valid in four figures, . name, definition of, . negative premisses and conclusion, fallacy of, . nominalists, , . non causa pro causa, fallacy of, . nouns, . opposition, sqq. contradictory, . contrary, . laws of, . subaltern, . sub-contrary, . 'o' propositions, . conversion of, . partition, . permutation, sqq. of complex propositions, . petitio principii, fallacy of, . predicable, . predicate of a proposition, , . read in extension, . quantification of, sqq. quantity of, , . predication, . in quid or in quale, . premisses, . major, . minor, . primary existences, . problema, the, . proper names, . property, . generic, . specific, . proposition, sqq. accidental, . affirmative, . complex or conditional, . conjunctive or hypothetical, , . conversion of, . definition of, . disjunctive, . divisions of, . essential, . exceptive, . exclusive, . extensive, . general, . indefinite, . intensive, . modal, . negative, . particular, . pure, . quality of, . quantity of, . real or synthetical, . simple or categorical, . singular, . tautologous or identical, . universal, . verbal or analytical, . proprium, . pro-syllogism, . quaestio, the, . quality, a, . quality of the matter, . of propositions, . quantification of the predicate, sqq., . quantity of propositions, . of terms, . realists, . real kinds, . reasoning or inference, . the canon of, . trains of, . reduction of propositions, . of the dilemma, . of disjunctive syllogisms, . indirect, . mnemonics for, . ostensive or direct, . of partly conjunctive syllogisms, . relation, a, , . relation, immediate inference by, . compatible and incompatible, . science, . secondary existences, . simple apprehension, . sorites, the, sqq. specialisation, . species, . cognate, . infimae, . subaltern, . subalternant, . subalternate, . subalternation, . subalterns, . sub-contraries, . sub-division, . subject, , . how used, . quantity of, . substance, , . summum genus, , . suppositio materialis, . syllogism, sqq. complex, . in common discourse, . conjunctive, . definition of, . disjunctive, . general rules of, . figures of, , . with three figures, . legitimate moods of, sqq. mnemonics for, . moods of, , . syncntegorematic words, . synonym, . term, sqq. absolute, . abstract, . analogous, . attributive, . collective, . common, . concrete, . connotative, . contradictory, . contrary, . definition of, . terms, distribution of, . distributive and collective use of, . division of, . equivocal, . incompatible, . individual, . major, middle, and minor, . negative, . non-connotative, . positive, . privative, . quantity of, . terms, relative, . repugnant, . singular, , . subject, . undistributed, . univocal, . universals, nature of, , . 'u' propositions, . verb, . words, their relation to terms, sqq, the end. a logic of facts: or every-day reasoning by g. j. holyoake "call him wise whose thoughts and words are a clear because to a clear why."--lavater. [fourth thousand.] london: f. farrah, , strand, w.c. . introduction of . the logic of the schools, however indispensable in its place, fails to meet half the common want in daily life. the logic of the schools begins with the _management_ of the premises of an argument; there is, however, a more practical lesson to be learned in beginning with the _premises_ themselves. a thousand errors arise through the assumption of premises for one arising in the misplacement of terms. the logic of the schools is an elaborate attack upon the lesser evil. sir james mackintosh has remarked that 'popular reason can alone correct popular sophistry'--and it is in vain that we expect amendment in the reasoning of the multitude, unless we make reasoning intelligible to the multitude. as to my object, could i, like gridiron-cobbett, adopt a symbol of it, i would have engraved Æsop's 'old man and his ass,' who, in a vain attempt to please everybody, failed (like his disciples--for even _he_ has disciples) to please anybody. the folly of that superfluously philanthropic old gentleman should teach us _proportion_ of purpose. to be of real service; to _some_ is in the compass of individual capacity, and consequently, the true way of serving, if not of pleasing _all_. the republic of literature, like society, has its aristocratic, its middle, and its lower classes. no one has combined, in one performance, the refinement applauded in the universities, with the practical purpose, popular among those who toil to live, and live to toil. the populace are my choice--of them i am one, and, like a recent premier, earl grey, am disposed 'to stand by my order.' i write for this class both from affection and taste. if i can benefit any, i can them. i know their difficulties, for i have encountered them--their wants, for they have been mine. this will account for the liberties taken with the subjects upon which i treat. there is more than one kind of hunger that will break through barriers, and i have taken with an unlicensed hand, wherever it was to be found, what i wanted for myself, and what i know to be wanted by those who stand at the anvil and the loom, and who never had the benefits of scholastic education, and who never will. many of the arts and sciences, which formerly resided exclusively in the colleges, and ministered only to the sons of opulence and leisure, have escaped from their retreat, and have become the hand-maids of the populace. but as respects logic, there still remains between the learned and the illiterate an impassable gulf. the uninformed look on the recondite structure of logic, and they are repelled by the difficulty of comprehending it, and wrap themselves up in absolute and obstinate ignorance, which they believe to be their destiny. the populace, in our manufactories, have to choose between subsistence and intelligence. for study, after protracted toil, they have not the strength--and to abridge their labour is to abridge their subsistence, and this they cannot afford. but because they are precluded by the destiny of civilisation from knowing much, they need not remain utterly unskilled in reasoning. their natural good sense may be systematized, their natural logic may be reduced to some rule and order--though it may not be refined it may be practical, it may give power, and develop capacity now dormant. the hints, general rules, and elementary remarks dispersed throughout this work, will probably be of service to the uninitiated, perhaps put them on the road to higher acquirements, give them a confidence in their own powers, perhaps inspire them with a love of these essential studies, and impart a taste for the refinements which lie beyond. my hope is that many will be induced to consult scholastic treatises, and acquire that accurate knowledge which makes the society of educated people so interesting. impulse has been given to knowledge, and the populace have begun to think, and both to speak and write their thinkings--and why should they not be enabled to do it free from obvious mistakes, and with a broad propriety commensurate with the native capacity they possess? why should they, like a certain learned politician on a public occasion, propose, as a sentiment, 'the three r's, reading, 'riting, and 'rithmetic?'* why, in writing, should they not express themselves with strong grammatical coherence, and a certain bold perspicuity, if not able to reach refinement and elegance? why, in pronunciation, should they not speak with a certain manly openness of vowel sound and a distinct articulation, if not with all elocutionary modulation? why should not their discourse be expressed in brief, clear sentences? if their punctuation went no farther than placing capital letters at the commencement of sentences and of proper names, and periods at the conclusion of sentences, it would render their writings more intelligible than are half the communications they now send to the press. if they mastered only brevity and abrupt directness, and learned to omit tedious prolixity, they would command a hearing in many cases where now they are denied one. if in logic they made a shrewd mastery of plain facts--being as sure as they could, when once set on surety, eschewing conjecture and pernicious supposition--if they followed the methods of nature and good sense, where the elaborate methods of art are hidden from them, who will not admit that they would be more intelligible than now, exercise a power they never yet possessed, and extort the attention and esteem of the public where now they excite only its pity, or contempt, or outrage what just taste it has? the people would be enabled to do these things, but that so many who prepare treatises for their guidance alarm them by the display of abstruse dissertation above their powers, their means, their time, and their wants. that a little learning is a dangerous thing is not a maxim alone believed in by the race of country squires steeped in port and prejudice, but by schoolmen who cannot bring themselves to give a little proportion of sound knowledge, but must give all, the reconite as well. the statesman decries the ignorance and want of wisdom displayed by embryo politicians who will accept no instalment of liberty, but insist on the concession of _all_ their claims--but the scholar does the same thing when he will impart none but the completest information to the people. * this case is cited by s. g. goodrich, the original peter parley, in his preface to 'fireside education.' sir william curtis, to whom, probably, mr. goodrich refers, gave also 'the three k's--king, church, and constitution.' in quoting, i have been a borrower, but not a plagiarist. in no case am i conscious of having taken from others without at the same time making the fairest acknowledgment in my power. if the references to the highest authorities are sometimes through others, it is because the highest authorities have not always been accessible. those who have had ordinary experience estimate highly the value of minute integrity in this respect. fruitless hours are spent in tracing false and careless references, and to one whose time is his means, no little injury is done when it is thus wasted. unbounded gratitude is due to those authors, old and new, who, with learning and grace, with care and patience, have put the world in possession of thoughts which are real additions to its knowledge--and corresponding should be the contempt of those whose high-sounding and pretending books seduce readers to wade through them only to find in them the millioneth echo of some commonplace idea. the 'spectator' was pleased to say that i wrote 'practical grammar' in the spirit of an 'ultra-radical, setting the world to rights.' yet i have always declared, with butler-- reforming schemes are none of mine, to mend the world's a vast design; like those who toil in little boat to drag to them the ship afloat. utopianism is not my idiosyncracy. but i have confidence in endeavour. continuity of ameliorative effort is the sole enthusiasm that can serve the cause of improvement. it is useful to do what seems to be useful, whether little or much--a moderate rule, but one that will take those who carry it out, a long way. my illustrations, i need scarcely say, are neutral in politics and theology. in the grammar of j. a. d. d'orsey, published in 'chambers' educational course,' there are disputations, biblicisms, and bits of intense theology. professor john radford young, in his treatise on algebra, has introduced a reply to hume's controverted theory of miracles--and dr. whately makes his 'logic' an avowedly theological auxiliary, showing that much passes for good taste in this country which is only an irrelevant propitiation of powerful opinion. i have not, however, been seduced by this species of example. there are distinct provinces in intellect as well as in industry--and what political economy justifies in one case, good sense dictates in the other. no man has a right to intrude theology into every question, and agitate points of faith when he pretends to instruct the understanding. there is less occasion to speak of the utility of logic, than to show it to be easy of acquisition. mr. stuart mill, in confirmation of this view, observes: we need not seek far for a solution of the question so often agitated, respecting the utility of logic. if a science of logic exists, or is capable of existing, it must be useful. if there be rules to which every mind conforms, in every instance in which it judges rightly, there seems little necessity for discussing whether a person is more likely to observe those rules when he knows the rules, than when he is unacquainted with them.* certainly people are not so much prejudiced against logic on account of its supposed uselessness as on account of its supposed difficulties. deserved or not, logic has always had a good reputation. well or ill founded, the popular impression has uniformly been in its favour. it has been valued like the diamond--but considered, like that precious stone, of very uncertain access. *'system of logic,' p. . second edition. the high popularity of common sense--'the exercise of the judgment unaided by rule'--has been interpreted into a virtual rejection of logic by the multitude. but it ought not to be overlooked, that the credit in which mere common sense is held, is a matter of necessity as well as choice. it being the best sense the untutored have, they wisely use it, and no wonder that they are inclined to laud what they are constrained to employ. doubtless they always perceived that common sense would be the better for being made orderly, as a spirited horse is the fitter for use after being 'broken.' logical sense, among the masses, is secretly supposed to be disciplined sense, and to have all the advantage of the trained soldier over the raw recruit. it is quite true, as abram tucker puts it, that 'the science of abstruse learning, when completely attained, is like achilles' spear, that healed the wounds it had made before; so this knowledge serves to repair the damage itself had occasioned, it casts no additional light upon the paths of life.' but few persons sensible of the value of exact knowledge will complain of the _necessary_ elaboration to which it sometimes leads. nor will those who have felt the thrill of pleasure which complete analysis imparts, regret the patience which put them in possession of a secret of science, or made them master of a new field of knowledge. common sense is the substratum of all logic. common sense is the natural sense of mankind. it is founded on common observation and experience. it is modest and plain and unsophisticated. it sees with everybody's eyes and hears with everybody's ears. it has no capricious distinctions, no partialities, and no mysteries. it never equivocates and never trifles. its language is always the same, and is always intelligible. it is known by its perspicuity of speech and singleness of purpose. the most prudent of all the children of fact, it never forsakes nature or reason. some outline laws for its employment, if they can be indicated, must be better than its popular aimless and desultory use. preface of . one has no right to make a literary subject political--that is, to make it partisan; but to give a political motive which concerns all equally, for promoting a literary study, is allowable, and does not partake of the nature of party politics. one may, like cobbett, look on literature with political eyes, without, like him, making it a vehicle of party attacks. in this country, where the political genius of the people lies in self-government--where the public growth of the people and their internal liberty depend upon their capacity to manage their own affairs--the art of public speaking has political importance to every aide in politics. to be able to take a subject well in hand, like a stage-coach driver does his horses--to hold the reins of your arguments firmly--to direct and drive well home the burden of your meaning, is a power which every man ought to study to attain, who rises to address a council, or stands up on a platform to convince a meeting. a logic of facts. chapter i. the logic of the schools it is a humiliating reflection that mankind never reasoned so ill as when they most professed to cultivate the art of reasoning.--life of galileo, p. . society for the diffusion of useful knowledge. common sense--the foundation of logic--first received (to a limited extent) the regularity of an art and the certainty of a science, from the master hand of aristotle. impartial scholars, familiar with his writings on logic, allow them to have not only ingenuity but real merit; and his admirers contend that he has been misunderstood by some and abused by others. this is highly probable, as we are certain that when his works were interpreted by the schools, and his logic proclaimed the great text-book of knowledge and the only weapon of truth, 'men's minds, instead of studying nature, were in an endless ferment about occult qualities and imaginary essences; little was talked of but intention and remission, proportion and degree, infinity, formality, quiddity and individuality.'* logic then was jargon, controversy chicane, and truth a shuttlecock, with which the disputants respectively played, or the object which they mutually disguised. logic was a labyrinth in which the subtlest lost their way--a bourne from which the traveller after truth seldom returned. * account of lord bacon's novum organon scientiarum, lib. of useful knowledge, p. . a striking illustration of this has been furnished by a candid and distinguished writer--dr. reid. 'of the analytics and of the topics of aristotle, ingenuousness requires me to confess, that though i have often purposed to read the whole with care, and to understand _what is intelligible_, yet my courage and patience always failed me before i had done. why should i throw away so much time and painful attention upon a thing of so little real use? if i had lived in those ages when the knowledge of aristotle's organon entitled a man to the highest rank in philosophy, ambition might have induced me to employ upon it some years of painful study; and, less, i conceive, would not be sufficient. such reflections as these always got the better of my resolution.'* dr. whately, who has for many years occupied the throne of logic and whose work maybe taken, from its currency in our colleges and academies, as the representative of the logic of the schools, seems to obviate all objections to the abstruseness of this subject by a counter charge, to the effect that logic is now underrated only because it has been overrated. but it is not the complexity found in it, but the laudations bestowed upon it which have brought it into neglect. dr. whately contends that certain writers, 'by representing logic as furnishing the sole instrument for the discovery of truth in all subjects, and as teaching the use of the intellectual faculties in general, raised expectations which could not be realised, and which naturally led to a reaction--to logic being regarded as utterly futile and empty.'** deeply deploring this kind of injury, from which many important arts have suffered, i am neither disposed to defend such a course, nor to imitate it. but i demur to the truth of this representation with regard to logic. if logic be not the 'sole instrument for the discovery of truth in all subjects,' it is certainly the _principal_ one. instead of charging scholastic logicians with having unduly 'raised,' it would be nearer the truth, in my opinion, to say that they have _confused_ 'expectations' by intricate machinery and extreme elaborations. * lord kamet's sketches vol. , chap. s. aristotle's logic. ** dr. whately: elements of logic, preface, p. vii. second edition. intricacy and minuteness of detail might be a trifling disqualification did they lead to something immediately practical. but dr. whately contends that logic, in the most extensive sense which the name can, with propriety, be made to bear, is that of the science, and also the art of reasonings 'inasmuch as logic institutes an analysis of the process of the mind in reasoning, it is strictly a _science_, while considered in reference to the practical rules it furnishes it is an _art_.'* he confines the province of logic, as an art, to 'employing language properly for the purpose of reasoning,' and restricts the logician to the use of the syllogism as the sole test of argument. mr. augustus de morgan thus exhibits the spirit of whately's restriction:-- logic has nothing to do with the truth of the facts, opinions, or presumptions, from which an inference is derived; but simply takes care that the inference shall certainly be true if the premises be true.' it has been, and _is_ to be, objected, that logic, thus confined, 'leaves untouched the greatest difficulties, and those which are the sources of the greatest errors in reasoning.' to this powerful objection dr. whately thinks it sufficient to reply, that 'no art is to be censured for not teaching more than falls within its province, and, indeed, more than can be taught by any conceivable art. such a system of universal knowledge as should instruct us in the full meaning or meanings of every term, and the truth or falsity, certainty or uncertainty of every proposition, thus superseding all other studies, it is most unphilosophical to expect, or even to imagine. and to find fault with logic for not performing this, is as if one should object to optics for not giving sight to the blind--or complain of a reading glass for being of no service to a person who had never learnt to read.'*** this would be a most conclusive answer if confident assertion could be accepted in lieu of proof. the objection still remains to be removed. we may still demand, does it not fall within the legitimate province of logic to provide means of encountering the 'greatest difficulties' with which it is confessed logic is beset? true, there is no art can teach everything, but is that a reason why logic should teach nothing, or next to nothing, compared with what seems essentially necessary? * intro., p. . ** klein. of logic, synthetical compendium, chap. , part , sec. . *** elem. of logic, intro., pp. , . dr. whately contends that the 'difficulties' and 'errors' in the objection adduced, are in the _subject matter_ about which logic is employed, and _not_ in the process of reasoning--which alone is the appropriate province of logic. but it seems to me that dr. whately has found it impossible to keep within the bounds of the restriction he thus endeavours to establish. in treating upon 'apprehension,' he introduces, as indeed he was obliged to do, from the department of metaphysics, several speculations on 'generalisation' and 'abstractions,' and from ontology (the science which explains the most general conceptions respecting the phenomena of nature) he borrows the leading principles of definition. because he thus goes so far, it is not to be contended that _therefore_ he should have gone further; but when he found he must depart from his rule and borrow from other branches of knowledge (no matter for what end), why did he not depart from it to some purpose, and borrow from natural philosophy such rules as would have guarded the logician from the 'chief errors' into which he may fall? dr. whately informs us, indeed, that logic furnishes certain syllogistic forms to which all sound arguments may be reduced, and thus establishes universal tests for the detection of fallacy--but it is to be observed that it is only _such_ fallacy as may creep in _between_ the premises and the conclusion of an argument. it is to this narrow and aristotelian object that logic is restricted. 'the process of reasoning itself is alone the appropriate province of logic. this process will have been correctly conducted if it have conformed to the logical rules, which preclude the possibility of any error creeping in _between_ the principles from which we are arguing, and the conclusions we deduce from them.'* we learn from our authority, that as arithmetic does not profess to introduce any notice of the _things_, whether coins, persons, or dimensions, respecting which calculations are made; neither does logic undertake 'the ascertainment of facts, or the degree of evidence of doubtful propositions.' and just as an arithmetical result will be useless if the data of the calculation be incorrect, so a logical conclusion is liable to be false if the premises are so. neither does the logic, now under consideration, concern itself with the 'discovery of truth,' excepting so far as that may be said to be implied by the detection of error in a false inference.** logic thus, confined to the actual process of reasoning, however important its functions there, evidently leaves us in the dark as to the value of what we reason about. for the information thus missing, this logic refers us to knowledge in general--to grammar and composition for the art of expressing, with correctness and perspicuity, the terms of propositions--to natural, moral, political, or other philosophy, for the facts which alone can establish the truth of the premises reasoned from. * intro., p. . ** for the grounds of these representations, see dissertation on the province of reasoning, chap. , sec. dr. whately's logic. the exclusion from logic of all consideration of the facts on which propositions are founded, is thus endeavoured to be justified by the archbishop of dublin:--'no arithmetical skill will secure a correct result, unless the data are correct from which we calculate: nor does any one on that account undervalue arithmetic; and yet the objection against logic rests on no better foundation.' this is true, but is it true that arithmetic is on _this account_ to be imitated? if the arithmetician must take his data for granted, it is what the searcher after truth must never do--_he_ must use his eyes and examine for himself, in all cases, as far as possible, unless he intends to be deceived. and for want of such precaution as this, the arithmetician is at sea the moment he steps out of the narrow path of mechanical routine. who is not aware of the failures of calculation when applied to the general business of life--to statistics, moral and political? every day, facts have to be called in to correct the egregious blunders of figures.* the calculations are conducted in most approved form, but are of no use. does not this demonstrate that when arithmetic, like logic, is applied to the business of life, general rules for securing the accuracy of data would be of essential service? supposing, however, that arithmetic could do very well without them, does it follow that logic should, when it would be safer and more efficient with them? * 'in art, in practice, innumerable critics will demonstrate that most things are impossible. it was proved by fluxionary calculus, that steam-ships could never get across from the farthest point of ireland to the nearest of newfoundland; impelling force, resisting force, maximum here, minimum there; by law of nature, and geometric demonstration--what could be done? the great western could weigh anchor from bristol port; that could be done. the great western, bounding safe through the gullets of the hudson, threw her cable out on the capstan of new york, and left our still moist paper-demonstration to dry itself at leisure.'-- thomas carlyle, chartism, pp. - . since our author's canons are held absolute in the schools, it may be useful to consider this last cited argument in another light. a stronger objection may be urged, one which particularly addresses itself to those who mistake mere pertinence for general relevance, and suppose that a single analogy decides a case. his grace reasons, that, because arithmetic does not concern itself about its data, logic should follow the same example. but why overlooks he pure mathematics--a much higher science than arithmetic? surely geometry, which through all time has been the model of the sciences, was better worthy than arithmetic to be the model of logic! was it classical in the principal of st. alban's college to abandon euclid and cleave unto cocker or walkingame? arithmetic is mechanical--geometry is reasoning; surely it was more befitting to compare reason with reason, when endeavouring to discover the true way of perfecting reason. geometry is, of all sciences, reputed the most conclusive in its arguments--and we know it is distinguished above all sciences for carefulness in its data. it begins with axioms, the most indubitable of all data, and its subsequent conclusions are founded only on established facts--and to be sure that they are established facts, the geometer, before he employs them, establishes them himself. if an analogy is to decide the province of logic, here is an analogy whose pretensions over those of arithmetic are eminent. so conclusive did dr. whately deem the argument just examined, that he many times, in various forms, reproduced it. one of the last instances is under the head of 'fallacies.' 'it has been made a subject of bitter complaint against logic, that it presupposes the most difficult point to be already accomplished; viz., the sense of the terms to be ascertained. a similar objection might be urged against every other art in existence e.g., against agriculture, that all the precepts for the cultivation of land presuppose the possession of a farm.'* * logic, chap. . fallacies, sec. . already has been pointed out what may reasonably induce a suspicion of the soundness of these analogies; viz., that their author found it necessary to disregard them and introduce, from other branches of knowledge, certain disquisitions on the 'sense of terms.' with regard to this particular instance, it may be observed, that though treatises on agriculture do presuppose the possession of a farm, they do not presuppose the knowledge requisite for cultivating it, but inform _fully_ of soil, and seed, and crops. so logic may be allowed to presuppose the existence of the universe, whence truth is drawn, or the existence of language, 'whereby it is expressed; but it is surely not to _pre-suppose_ the knowledge of facts and terms, the great instruments for the cultivation of truth. agricultural treatises hardly warrant this inference. there are the representations that induced the confession that 'logic is not so much an instrument of acquirement as of defence. it is a good armour to buckle on when compelled to battle for our heritage, but a poor implement for its cultivation.'* all _practical_ arts include a knowledge of materials as well as implements. platers, ignorant of the nature of metals, cabinetmakers, of the different species of wood, make but sorry artizans; and in like manner, reasoners, unacquainted, at least in a general way, with the accuracy of what is reasoned about, make but sorry logicians.** it will readily be expected that in the modern progress of knowledge, the aristotelian province of logic would be enlarged. the far-seeing intellect of lord verulam heralded the innovation--'our glorious bacon led philosophy forth from the jargon of schools and the fopperies of sects. he made her to be--the handmaid of nature, friendly to her creatures, and faithful to her laws.'*** * w. j. fox, mon. rep., p. : . ** the reader will find that logician is need in the sense of skilfulness in eliciting and exhibiting reality. by that which i call logical is meant that which is truthful. i presume that is the sense to which this high word should be confined. it is the lax application of this term to mere dexterity in evading the truth according to rule, that has so increased the unsatisfactory race of professed sceptics. --see scepticism, chap. xii. *** langhornea' preface to the lives of plutarch. the general object of lord bacon's philosophy, writes bruce, an edinburgh professor of logic of the last century, is to connect the reasoning powers of man with experiments for the improvement of natural knowledge. to create a just taste for philosophical investigation, required-- . a display of the true, that they may be distinguished from the false subjects of inquiry. . scientific rules to direct the discovery of the laws of nature. but to 'display the true,' is to display the _facts_ on which the truth rests. the 'discovery of the laws of nature' implies _observation_ of the operations of nature. the philosophy of bacon, says macaulay, began in observation and ended in arts. it is most obvious, as the reader will gather from what has been advanced, that for guarding, to the greatest possible extent, against error in conclusions, it is necessary to take into consideration the character of the data from which we reason--and to do this, we must draw from the general sources of knowledge to which the logic of the schools refers us. if we happen not to possess an accurate acquaintance with these branches, we must draw upon the best notions we have of them, or apply such natural sagacity as we happen to possess. but whether the information we happen to possess be complete or partial, it is not well that we are left to apply it at random, without any definite mode of procedure; and if logic refuses to assist us, and gives only a vague reference elsewhere, we must endeavour to assist ourselves. the datum of all arguments is a proposition, an assertion, or denial; and to ascertain its truth (upon which the value of the whole reasoning depends) we have to do with the facts upon which it rests, and the terms in which it is expressed. for it may be here observed, that the truth or falsity of every proposition depends upon facts. to ascertain the general accuracy of facts, we have to appeal to received standards of certainty; and to fix the meaning of terms, we have recourse to a plain principle of definition. in the task of recognising truth, so necessary in examining the premises of an argument, one is wonderfully assisted by being familiarised with the sources of truth, and the mode of its discovery. in these operations the tutored and untutored may alike be assisted by simple general rules. if these rules prove not infallible in every case, they will prove successful in the majority of cases. since general rules are the only, rules that the vast field of facts admits of, they are not to be rejected on light grounds. they enable us to set forth intelligibly the reasons of our own conviction, and to detect and expose the fundamental fallacies of apparent arguments. since they direct us where the logic of the schools leaves us without a guide, their value is apparent. the logical management of the syllogism involves much abstruseness respecting 'genus' and 'species,' the 'quantity' and 'quality' of 'propositions', 'contraries,' 'sub-contraries,' 'contradictions,' and 'subalterns.' stepping by 'illative conversion,' 'six rules to be observed with respect to categorical syllogism' next demand attention, followed hard by eleven moods which can be used in a legitimate syllogism, viz.---- a, a, a, a, a, i, a., e, e, a, e, o, a, i, i, a, o, o, e, a, e, e, a, o, e, i, o, i, a, i, o, a, o.' in the middle of this abstract train march the 'undistributed middle' and the 'illicit process,' attended by four figures represented by the following mnemonic lines, which must be carefully committed to memory:'-- fig. . barbara, celarent, darii, ferioque prioris. fig. . cesare, damestres, festino, baroko,* secundæ. fig. . tertia, darapti, disamis, datisi, felapton, bokardo,** ferlso, habet; quarta insuper addit. fig. . bramantip, camenes, dimaris, fesapo, fresison. a motley group, too numerous to be particularised, bring up the complex rear of 'modals,' 'hypotheticals,' 'conditionals,' and 'disjunctives.' this is certainly not the portal through which the populace can at present pass to logic, even if such logic helped them to all truth, and saved them from all fallacy. but this species of logic is not without interest. symbolic letters and mnemonic lines are not without attractions to those who understand them. there is poetry in an algebraic sign, when it is the emblem of a difficulty solved, and a wonderful result simply arrived at. to try the whole power of words, and discover every form of language in which a legitimate deduction can be expressed, is no ignoble task. it is a high discipline, but it belongs rather to the age of leisure than this of 'copperasfames, cotton-fuz, gin-riot, wrath, and toil'--to the luxuries rather than the utilities of learning. there is the inefficiency of the syllogism, and also the vitiation produced by its employment. . it corrupts the taste for philosophical invention by placing philosophy in abstractions, and withdrawing it from the observation of nature. . it creates a reliance on principles, which originate in the _hypotheses_ of philosophers, not in the laws of nature. . it makes truth the result of the forms of argument, not of scientific evidence.*** * or, fakoro, as indeed all the particulars in this place recited. ** or, dokamo. but a brief summary of the subjects comprised in his logic in reference to the syllogism. ***bruce. these references to fakoro and dokamo are whately's. lord kames cites from the father of logic the following syllogism, which will bear repetition as an extraordinary instance of that assumption for which the logic of the schools provides no remedy:-- heavy bodies naturally tend to the centre of the universe. we know, by experience, that heavy bodies tend to the centre of the earth. therefore the centre of the earth is the centre of the universe. but by what experience did aristotle discover the centre of the universe, so as to become aware that heavy bodies _naturally_ tend there? on what facts rest the measurement of the radii from our earth to the boundless circumference of space? how did he ascertain the limits of that which has no limits? yet, strange to say, the logic of the schools prides itself in leaving us where the stagyrite left us. 'when mankind began to reason on the phenomena of nature, they were solicitous to _abstract_, and they formed general propositions from a _limited_ observation. though these propositions were assumed, they were admitted as true. they were not examined _by appeals to nature_, but by comparison with other propositions.'* in this syllogism from aristotle, there is the usual compliance with accredited rules, and the same defiance of common sense. such examples are deemed perfect reasoning and legitimate argument; but is it not a mockery to encourage the belief that we can have reason and argument, without the truth? only this shallow consolation remains to us. if the logician of the schoole does not enlighten the understanding, he is at least reputed not to offend the taste, and he wins the equivocal praise of butler:-- 'he'll run in debt by disputation, and pay with ratiocination; all this by syllogism, true in mood and figure, he will do.' syllogisms are to truth what rhyme is to poetry. 'it is a well known fact that verse, faultless in form, may be utterly destitute of poetic fire or feeling.'** * bruce. ** a. j. d. d'orsey, eng. gram., part , article prosody. according to the logic of the schools, 'the question respecting the validity of an argument is not whether the conclusion be _true_, but whether it _follows_ from the premises adduced.' it was the bitter experience of bordon of the delusiveness of such partial logic that induced him to exclaim, '_one_ fact is worth fifty _arguments_.' with such authorities, 'a valid argument is that which it so stated that its conclusiveness is evident from the mere _form_ of the expression.' but since it is admitted that if the data reasoned upon be incorrect, no logical skill can secure a correct result; it is evident that however _faultless the form_, the inquirer after truth is in no way nearer his object, unless he be instructed how to lay a foundation of _faultless facts_. he then, who is in love with truth rather than logomachy, will admit, in spite of the most ingenious analogies, that there is some room for a logic of facts, as well as a logic of words. chapter ii. locke-logic. logic is a general guide to the discovery of truth, and teaches us its systematic communication to others. this definition is intended to combine logic and rhetoric into one system. according to a quotation in pinnock's guide to knowledge, locke defined logic as 'that art by which we rightly use our mental faculties in the discovery and communication of truth,' a definition, called by the writer, the definition of nature echoed by genius. there exists a natural connection between logic and rhetoric. the discovery of truth could avail us little if we were without the means of communicating it; and it is easy to see that it would be in vain to possess the means of communicating truth, unless we had the truth to communicate. therefore, ingenuity is but ill employed in separating these mutual departments of learning which nature has connected together. besides, the skill of the logician is as serviceable in the statement of a case, as in arguing it. arrangement is as much a matter of logic as ratiocination; and to impress this neglected truth upon the young inquirer, is one reason for proposing a combined definition. the mutual connection of logic and rhetoric is illustrated by the fact, that the logic of the schools is purely a branch of rhetoric. it consists in putting an argument into 'the most perspicuous form in which it can be exhibited,'*--i. e., in _communicating_ it in the most efficient way to others. * dr. whatetly: anal. ont., chap. , aec. , p. . indeed, dr. whately (who makes logic to consist in reasoning) defines reasoning as _discourse_, and discourse is rhetoric. '_grammar_,' says doherty,' represents the mechanism of letters in forming words--_rhemar_, the mechanism of words in forming sentences. we have _grammar_ for letters, _rhemar_ for words, _logic for arguments_, and _rhetoric_ for discourse.' locke-logic, therefore--i. e., logic in the sense in which locke treated it--seems to come nearer the truth, as well as nearer the common requirement, than the restricted definition of it by others insisted on. chapter iii. logical truth all men know something of truth. happily it is the first impulse of childhood, and nature teaches us its pleasure before reason instructs us in its truth. in infancy we own its beauty, in manhood its power. there is nothing, says cicero, sweeter to man than the light of truth. truth, observes godwin, is the native element of an intellectual nature. it has been wisely remarked, said lord kames, that truth is to the understanding what beauty is to the eye, or music to the ear. philosophy sanctions what unsophisticated feelings suggested. he that has made but a little progress beyond ignorance and privilege, cannot be edified by anything but truth.** truth, like a mathematical point, has had various descriptions; and it may be useful to select those which graduate to its logical definition. bulwer tells us, that 'the agitation of thought is the beginning of truth.' locke, lord kames, mill, and others, agree that truth, or falsehood, is an affair of language. an assertion which represents things as they really are, is a truth--an assertion that represents things what in reality they are _not_, is a falsehood. ** mr. hobhouse: note . to th canto of childe harold. truth, in sculpture, means an exact similitude of some living form, chiselled in stone or marble. truth, in painting, is a natural representation on canvass of some person, or object. in the same manner, moral 'truth is an exact image of things set forth in speech, or writing.' the logical definition of truth is given in these words:--'truth is that which admits of proof,'* that is, an assertion or denial which can be substantiated by facts. * chambers' information. a fact is commonly called a truth, but this practice leads to great confusion in reasoning. a fact is only an element in truth, a logical truth is a proposition supported by facts. facts compose the premises of an argument--a truth is the inference from the facts. unless this distinction is observed, recourse must be had to the expedient of calling a fact a particular truth, and an induction from facts a general truth. or we must adopt this distinction, that a moral truth, that is, the truth of parlance, is the coincidence of language with reality; and a logical truth, a proposition which admits of demonstration. a lady, who has given intellectual laws to many whom i address, has said--'a truth i consider to be an ascertained fact, which truth would be changed into an error the moment the fact on which it rested was disproved.' but that which can be disproved cannot be an '_ascertained_ fact.' allowing, however, the relevancy of this definition of a truth, it would, in a treatise on logic, be considered as a definition only of a particular truth. many such truths are required to make a logical truth. chapter iv. discovery of truth the great treasure-house of nature is open to all, and the only fee demanded for inspection is attention.--detrosibr. observation** of nature is the only source of truth. discursive observation is the art of noticing circumstances evident to the senses. men who do this intentionally and carefully, with a view of acquiring a knowledge of phenomena and their causes, are distinguished for their varied knowledge and often for their great discoveries. shakspere must have owed the varied facts interwoven into his delineations of human character to this source. the clever personations of garrick were suggested by his curious observations of men and manners. sir walter scott is known to have been a careful observer. it is said, 'no expression escaped him if it bore on the illustration of character.' ** the term observation is used here in the sense in which it is commonly understood, signifying cognisance in general. it includes whatever information we acquire by the meant of consciousness, or experience, or through the agency of the senses. claude lorraine, with a passionate sympathy for the beautiful, sate in the fields from sun-rise to dewy eve, watching, catching, and saturating his very soul, as it were, with all the evanescent beauties of a summer's day, as they chased each other over the face of the fair scene; fixing on canvass, taking captive and imprisoning in our cabinets, the wanton daughters of nature, that before his time never were caught, but flitted before the fascinated eye only long enough to make the heart afterwards feel more achingly the void of their vanishing. and the artist who has done all this, do we not justly call him an _imaginative_ painter, to distinguish him from those meaner geniuses who were, in painting, very like crabbe in poetry, merely faithful delineators of the vulgarer objects of social life, bunches of carrots, drunken boors, chamber maids and chimney corners. 'has the reader ever seen mr. macready in the character of macbeth? if he have, he can never forget the stupefied murderer withdrawing from the chamber in which he has just done the dread act, with fascinated gaze retreatingly regarding his royal victim, and awaking with a guilty start as he runs unconsciously against his hard-souled partner in guilt, who in vain tries to infuse into the weaker spirit of her paralysed husband her own metaphysical superiority. in this scene we know that mr. macready's acting was perfect, for the pressure at our heart, the suspension of our breathing, and the creeping of our hair, made us _feel_ that it was so. we see him now, as stealthily he places his foot over the threshold of the chamber of death to re-appear on the stage; the intensely staring eye, that cannot remove from what 'tis horror to look upon; the awfully natural absorption of his soul by that "sorry sight," which one little minute has brought about; his starting and awaking from his entranced state, as he runs against his wife in his retreat, and his full passionate burst of blended remorse, terror, and superstition, as refusing counsel, regardless of remonstrance, heedless of probable detection, he pours forth his "brain-sickly" convictions, of having in one little moment cut the cable that had held him to the rest of the great human family. all this we can see in our mind's eye, for the actor gave us a picture of passion that time can never obliterate. but how would it have been with a cloddish unimaginative fellow, whom nature never intended should understand shakspere? would he not, conscious that he was among shoals and quicksands of feelings, too nice for his appreciation, seek to tear over all by a tempest of rant, which would be a more ruthless murder on shakspere than macbeth's on the king? and why should we be delighted with mr. macready's delineation, and disgusted with the ranter? simply because the former has _observed_, treasured up, and felt every genuine exhibition of human feeling that came in his way, and applied it appropriately to all the situations to which it was related in nature. a single instance will make this clear. mr. kean one night, in the concluding part of the combat scene of richard iii., when supposed to be wounded to the death, before falling, steadily regarded his foe, and painfully raising his right arm in act to strike, the relaxed and dying limb, unable to second the spirit, fell heavily and harmlessly to his side, indicating merely the fierce bravery of the usurper living in all its strength, when the body which it would move, was all but a senseless clod. pit, gallery, and boxes arose with an enthusiasm beyond description, and by their repeated plaudits bore testimony the intense naturalness of the struggle. the actor being afterwards complimented upon the _hit_, said, that he had taken the action from jack painter, the prize-fighter, when the latter was beaten in some one of his contests, and it immediately struck the tragedian that the very same thing would come in beautifully in the dying scene of richard iii. what was this, if not imagination? kean saw painter's action to be the natural effects of undying valour in vain endeavouring to contend against overwhelming power. remembering and associating it with his previous conception of the character of richard iii., the actor saw it could be most strikingly incorporated with that picture of passion the usurper's death should present to our view. seeing this, he combined it with his previous delineation, and thereby did precisely the same thing as the poet in using a fine simile, or the painter in introducing sun-light over a part of his picture. it was a portion of nature carried away by the actor to be reproduced on a future and fitting occasion.'* the beginning of all knowledge is observation. it has been shown by mr. mill that 'axioms,' which lie at the foundation of all reasoning and all science, 'are experimental truths--generalisations _from observation_. the proposition that two straight lines cannot inclose a space--or, in other words, two straight lines which have once met do not meet again, but continue to diverge--is an induction from the _evidence of our senses._'** 'axioms are but a class of inductions from _experience_: the simplest and easiest cases of generalisation,' from the facts furnished to, us by our senses or by our internal consciousness.'*** autobiography, or the metaphysical revelation of a man to himself, is a source of valuable psychological and moral truths. from this centre frequently radiate new lights upon human nature. but this is resolvable into a species of mental observation. it is self-inspection. we have lately been told that 'poetry is called upon to work in the _discovery_ of truth. the imagination has always been the great discovering power. discoveries are the poetry of science. the case is rare indeed in which, by merely advancing step by step in the exercise of the logical faculty, any new truth has been arrived at. logic comes afterwards, to verify that which imagination sees with its far-darting glance.'**** * phrenology tested, by a. m., of the middle temple, pp. - . ** logic, vol , p. . *** idem, pp. - . **** w. j. fox's lectures to the working classes: genius and poetry of campbell, p.; . this seems to call upon us to recognise the imagination as fresh source of truth. but the definition of imagination, as given by emerson, reveals to us its origin in observation;--'the imagination may be defined to be the use which reason makes of the material world. shakspere's imperial muse tosses the creation like a bauble from hand to hand, to embody any capricious shade of thought that is uppermost in his mind.' hence, though we agree with gilfillan that imagination is thought on fire, we must confess that the ignition is material. we will, however, hear a poet's defence of his fraternity:--'poets are vulgarly considered deficient in the reasoning faculty; whereas no man was ever a great poet without having it in excess, and after a century or two, men become convinced of it. they jump the middle terms of their syllogisms, it is true, and assume premises to which the world has not yet arrived; but time stamps their deductions as invincible.'* imagination is based on observation, and bears the same relation to the 'material world' that the magician bears to the appliances of his art. imagination is the dexterous and astonishing use of realities. it is a species of mental experiment, whereby, without permission of the line-and-rule men, we join strange things together, and to the surprise of every body, the junction is a happy one. 'angelo's greatness lay in searching for untried existence.'** but observation primarily suggests the combination. if, as in the case of angelo, imagination essays the highest flights of genius, and goes in search of untried existence, it is not existence out of nature, but founded upon nature--its success is a revelation of some hidden reality. * lowell's conversations on the old poets. ** j. t. seymour; oracle of reason. some of the most praised conceptions of shakspere have been traced by critics to the tritest observation. instance hamlet's remark:-- there's a divinity doth shape our ends, bough-hew them as we will. critics tell us, that shakspere here fell into the conventional cant of a mechanic making skewers. but it is no detraction to cull the best phrases from the most common sources. knight remarks:--'philosophy, as profound as it is beautiful! says the uninitiated reader of shakspere. but he that is endued with the wisdom of the commentators, will learn how easy it is to mistake for philosophy and poetry what really only proceeded from the very vulgar recollection of an ignorant mind. dr. farmer informs me, says steevens, that these words are merely technical. a woodman, butcher, and dealer in skewers, lately observed to him, that his nephew (an idle lad), could only assist in making them; he could rough-hew them, but i was obliged to shape their ends. to shape the ends of wood skewers, i. e., to point them, requires a degree of skill: any one can rough-hew them. whoever recollects the profession of shakspere's father, will admit that his son might be no stranger to such terms. i have frequently seen packages of wool pinned up with skewers.'* to admit the likelihood of all this, notwithstanding mr. knight's jeer at the 'wisdom of the commentators,' is rather to exalt than degrade the genius of shakspere, who could derive exalted figures from humble sources. the 'athenæum,' far more wisely than mr. knight, in this instance, observes:--'this is the test of a truly great man; that his thoughts should be _things_, and become things in instantaneous act, and not for a moment mere speculations and abstractions.' as the theories of the schoolmen subside, and men no longer ignore nature, it will become recognised as the source rather than the tool of intellect. we shall have less occasion to contend that all lofty and sublime ideas derive their value and beauty from their coherence with the instincts of sensation, 'poetry, we grant, creates a world of its own; but it creates it out of _existing_ materials.' 'imagination' may be but 'thought on fire,' but the spark, which ignites it, is material. is there any other distinction between the nights of the rhapsodist and those of genius, than that genius _illumines_ reality and rhapsody _obscures_ it? 'we know of no great generalisation that has ever been made by a man unacquainted with the details on which it rests.' experiment is invented observation. it is putting into operation certain supposed causes in order to observe their effects. an experiment may be defined as an observation, which we are at some trouble to make. experiment is usually set down as being a process of discovering truth different from observation. it is evidently included under observation, and there is no practical advantage in separating it. discursive, general, ordinary, or common observation is the observation of the phenomena we _find_. experiment is observation of the phenomena we _bring together_. experimental observation has been the great agent of modern discovery. newton ranked it as the most valuable knowledge. whatever is not founded on phenomena is hypothesis, and has no place in experimental philosophy. it is the principal source of accurate facts. when jenner first communicated to john hunter, what he thought respecting the prevention of small pox--'don't think, but try; be patient, be accurate,' was hunter's characteristic reply. locke remarks--'while the philosophy of aristotle prevailed in the schools, which dealt often in words without meaning, the knowledge of nature was at a stand; men argued concerning things of which they had no idea; in this enlightened age, we keep to trial and experiment, as the only certain foundation of philosophy.' * philosophy and religion of shakspere, pp. - ** no . p. . *** athenæum, no. , p. . hypothesis may be noticed here as being a species of _embryo_ experiment. hypothesis is guessing at the truth. it is a conjecture or supposition relating to the cause of an effect. it imagines that where certain conditions exist, the desired result will ensue. but all these conjectures must be founded on observation. for, in the wildest conjecture, unless made by a madman, there is some reason. hypothesis is incipient truth founded on a few facts which make it probable, but not on sufficient to make it certain. hypothesis does not directly discover truth, but it is a guide to experiment, which does. the hypotheses of columbus respecting an unknown continent, did not of itself discover america--but it directed the experiment of his voyage there, which did. to hypothesise alone is the error of the visionary and the dreamer. practical wisdom, as far as possible, tests hypothesis by experiment. sir c. bell conjectured that the nervous fluid of the human body was analogous to galvanic fluid, and then, by experiments on various animals, he endeavoured to test his hypothesis. however, great thinkers arise who are best employed in contriving plans for others to execute--in telling others what they are to do. great poets belong to this class. they are often incapable of the concentrated labour of furnishing proofs of their hypothesis. gladly should we recognise the mission of such men. they work for humanity by thinking for humanity. 'all who think,' says lytton, 'are co-operative with all who work.' labour supplies our wants, thought teaches us dominion over nature. labour is but the means of subsistence, it is thought that makes it the source of wealth by multiplying its powers. to the value of hypothesis mr. mill bears this testimony, that by suggesting observations and experiments, it puts us upon the road to, independent evidence, if it be really attainable, and till it be attained, the hypothesis ought not to count for more than a suspicion. the function of hypothesis is one which must be reckoned absolutely indispensable in science. without such assumption, science would not have attained its present state. nearly everything which is now theory was once hypothesis.* * logic, vol. ii, p. . induction is systematic observation of a given class of phenomena. it consists in bringing together a variety of facts and instances, carefully and patiently viewing them in all possible lights to discover from a comparison of the whole what, if any, new principle is elicitable. induction is an experiment with a number of facts, to see if any general result can be arrived at. thus observation is of three kinds--discursive, experimental, and inductive. for brevity of speech, we use respectively the terms observation, experiment, and induction, as the names of the three recognised modes of investigation. but it facilitates a clear view of this subject, to note that experiment and induction are but phases of observation--and that observation is the great source of the discovery of truth. discursive observation and experiment are the sources of facts or particular truths. nature, poetically says dr. reid, is put to the question by a thousand observations and experiments, and forced to confess her secrets. out of these secrets induction gathers its general truths, which become the premises of argument. facts, like stones, are of little service while scattered--it is in the edifice raised by them that their value is apparent. they have been compared to blocks, upon _one_ of which, if a person stand, he has but a partially increased view; but when many are piled up, a person from their summit commands the prospect round. particular truth seldom proves anything but itself. argument is proving something else, and we have seen that that which is proved must be _contained_ in something which proves it. in other words, an argument is an assertion or denial of something substantiated by other things--by facts. gall _observed_ the peculiar formation of a certain head, but the one fact proved nothing, except that the head had a certain form. it was a barren observation, except that it suggested to his imagination the hypothesis that the peculiar form of the head might be caused by peculiarity of mind. this set him upon the experiment of observing the habits and dispositions of the individual in order to test his hypothesis. but the one fact of finding a peculiarity proved nothing new of any value. the two facts, though incident, were hardly convincing. they proved only that a peculiar head was accompanied in one case by peculiar habits--but whether one was the cause of the other, or whether the phenomena were in any way connected, still remained unknown. when, however, gall, spurzheim, and others, had travelled through europe, making observations and experiments, and at last putting all the facts and instances together, and carefully and patiently viewing them in all possible lights, and finding that they shadowed forth that the brain was the organ, the map and measure of intelligence, they inducted a general truth, which enters the lists of argument and takes its place as an addition to our metaphysical and moral treasures. mr. macaulay, who, perhaps, might be accused of underrating both bacon and induction, with a view of exalting aristotle, remarks that 'the vulgar notion about bacon we take to be this, that he invented a new method of arriving at truth, which method is called induction, and that he detected some fallacy in the syllogistic reasoning which had been in vogue before his time. this notion is about as well founded as that of the people who, in the middle ages, imagined that virgil was a great conjurer. many who are far too well informed to talk such extravagant nonsense, entertain what we think incorrect notions as to what bacon really effected in this matter. the inductive method has been practised ever since the beginning of the world by every human being. it is constantly practised by the most ignorant clown, by the most thoughtless schoolboy, by the very child at the breast. that method leads the clown to the conclusion, that if he sows barley he shall not reap wheat. by that method, the schoolboy learns that a cloudy day is the best for catching trout. the very infant we imagine is led by induction to expect milk from his mother or nurse, and none from his father. not only is it not true that bacon invented the inductive method, but it is not true that he was the first person who correctly analysed that method and explained its uses. aristotle had long before pointed out the absurdity of supposing that syllogistic reasoning could ever conduct men to the discovery of any new principle, had shown that such discoveries must be made by induction and by induction alone, and had given the history of the inductive process concisely, indeed, but with great perspicuity and precision. we are not inclined to ascribe much practical value to that analysis of the inductive method which bacon has given in the second book of the novum organon. it is, indeed, an elaborate and correct analysis. but it is an analysis of that which we are all doing from morning to night, and which we continue to do even in our dream.'* * macaulay's hist essays, vol. , p. . it is not 'some fallacy in the syllogistic reasoning' which bacon is supposed to have detected, it is rather the partial protection against error afforded by syllogisms, which he exposed and provided against, for which he is estimated. certainly aristotle must have had a very different opinion of the value of inductive philosophy from that entertained by bacon, or he would have indoctrinated his disciples with it. few will doubt that had bacon's novum organon appeared in the place of aristotle's logic, and aristotle's work in the place of bacon's, that the advancement of learning in the world would now be in a very different state. could bacon have arrested the attention of the ancient sages with his methods of discovering new principles, ancient philosophy, instead of being a treadmill, would have been a path, and we should not have had a contempt for all learning which was useful. when posidonius said that we owed to philosophy the principles of the arch and the introduction of metals. we should not have had seneca repudiating such insulting compliments, nor archimedes considering that geometry was degraded by being employed in anything useful. but these observations of macaulay have the merit of showing us that induction has its foundation in nature, and afford a further confirmation of our views, that observation is the source of our knowledge, and that it is the province of logic to teach us to systematise our thoughts. observation, experiment, hypothesis and induction, are but different names for the operation--varying in degree, in method, in expedient, and elaboration--whereby we discover truth. nature is the treasure-house of truth, and the sole fee of appropriation is attention. much discussion has taken place upon the nature of necessary truths. mr. mill, however, after an elaborate analysis of dr. whewell's theory, pronounces that 'nothing is necessary except the connection between a conclusion and the premises.' a necessary truth is commonly defined as a proposition, the negation of which is not only false, but inconceivable. mr. mill contests this doctrine in words embodying suggestions of great value. 'now i cannot but wonder that so much stress should be laid upon the circumstance of inconceivableness, when there is such ample experience to show that our capacity or incapacity of conceiving a thing has very little to do with a possibility of the thing in itself; but is in truth very much an affair of accident, and depends upon the past history and habits of our own minds. there is no more generally acknowledged fact in human nature, than the extreme difficulty at first felt in conceiving anything as possible, which is in contradiction to long established and familiar experience; or even to old and familiar habits of thought. and this difficulty is a necessary result of the fundamental laws of the human mind. when we have often seen and thought of two things together, and have never in any one instance either seen or thought of them separately, there is by the primary law of association an increasing difficulty, which in the end becomes insuperable, of conceiving the two things apart. this is most of all conspicuous in uneducated persons, who are in general utterly unable to separate any two ideas which have once become firmly associated in their minds; and if persons of cultivated intellect have any advantage on the point, it is only because, having seen and heard and read more, and been more accustomed to exercise their imagination, they have experienced their sensations and thoughts in more varied combinations, and have been prevented from forming these inseparable associations. but this advantage has necessarily its limits. the man of the most practised intellect is not exempt from the universal laws of our conceptive faculty. if daily habit presents to him for a long period two facts in combination, and if he is not led during that period either by accident or intention to think of them apart, he will in time become incapable of doing so even by the strongest effort; and the supposition that the two facts can be separated in nature, will at last present itself to his mind with all the characters of an inconceivable phenomenon. there are remarkable instances of this in the history of science: instances, in which the wisest men rejected as impossible, because inconceivable, things which their posterity, by earlier practice and longer perseverance in the attempt, found it quite easy to conceive, and which everybody knows to be true. 'if, then, it be so natural to the human mind, even in its highest state of culture, to be incapable of conceiving, and on that ground to believe impossible, what is afterwards not only found to be conceivable but proved to be true; what wonder if in cases where the association is still older, more confirmed, and more familiar, and in which nothing ever occurs to shake our conviction, or even suggest to us any conception at variance with the association, the acquired incapacity should continue, and be mistaken for a natural incapacity? it is true our experience of the varieties in nature enables us, within certain limits, to conceive other varieties analogous to them. we can conceive the sun or moon falling; for although we never saw them fall, nor ever perhaps, imagined them falling, we have seen so many other things fall, that we have innumerable familiar analogies to assist the conception; which after all, we should probably have some difficulty in framing, were we not well accustomed to see the sun and moon move, (or appear to move,) so that we are only called upon to conceive a slight change in the direction of motion, a circumstance familiar to our experience. but when experience affords no model on which to shape the new conception, how is it possible for us to form it? how, for example, can we imagine an end to space or time? we never saw any object without something beyond it, nor experienced any feeling without something following it. when, therefore, we attempt to conceive the last point of space, we have the idea irresistibly raised of other points beyond it. when we try to imagine the last instant of time, we cannot help conceiving another instant after it nor is there any necessity to assume, as is done by a modern school of metaphysicians, a peculiar fundamental law of the mind to account for the feeling of infinity inherent in our conceptions of space and time; that apparent infinity is sufficiently accounted for by simpler and universally acknowledged laws.'* * mill's logic, vol. , pp. - . thus we stand on the verge of boundless possibility. what truths may yet be discovered in that great and untrodden field, which lies without our experience, no man can tell. all we have yet brought between assertion and proof, is all we have yet conquered, is all that we as yet know, is all that we can yet rely upon. the search after the untried is the highest and apparently the inherent aspiration of roan. the revelation of new worlds continually rewards his noble ambition. at once arrested and allured by the magnificence of nature--we wonder, we work, we wait. chapter v. facts we must never forget that accurate and multiplied quantitative facts form the only substantial basis of science.--parker. as clear fountains send forth pellucid streams, so do clear truths give accurate sciences. the more definite the facts, the more perfect the science; it is therefore of importance that all facts should be capable of being tested by the standard of physical certainty. dr. reid says, that 'the inquirer after truth must take only facts for his guide.' it is then of moment that he takes true and not false guides. a writer in the 'monthly repository' observes, that 'the basis of all knowledge is such an extensive induction from particular facts, as leads to general conclusions and fundamental axioms'--and if the facts are erroneous, evidently the conclusions will be also erroneous. he also remarks, that 'in reasoning, all sciences are the same, being founded on an examination of facts--comparison of ideas.' but if the examination is incomplete, or the facts admitted incorrect, the comparison will be alike defective and the reasoning vitiated. if suppositions or conjectures are mixed up with facts, the inductions from them will be suppositions, and the conclusions but conjectures. there are three words--consciousness, conscience, and conscientiousness--very much alike to the ear but very different in signification. consciousness, is feeling--conscience, the sense of right and wrong---conscientiousness, the practice of what is believed to be right. conscience and conscientiousness are often confounded. we say, lawyers have no conscience, we mean no conscientiousness. they know right from wrong as men, but not professionally. it is with consciousness that the logician has to deal. consciousness is the primary source of knowledge. consciousness and the 'evidences of the senses' are synonymous terms. facts referable to consciousness are said to be physically certain. the evidence of the senses is the highest standard of certainty. the intuitive principles of belief are-- st. a conviction of our own existence. nd. a confidence in the evidences of our senses. rd. in our mental operations. th. in our mental identity. th. in the conformity of the operations of nature. these truths of intuition or consciousness are the foundation of all knowledge. truths which we know, by way of inference, are occurrences which took place while we were absent--the events of history and the theorems of mathematics. but the truths known by intuition are the original premises from which all others axe inferred. our assent to the conclusion being grounded upon the truth of the premises, we could never arrive at any knowledge by reasoning, unless something could be known antecedently to all reasoning. 'whatever is known to us by consciousness, is known beyond possibility of question. what one sees, or feels, whether bodily or mentally, one cannot but be sure that one sees or feels. no science is required for the purpose of establishing such truths; no rules of art can render our knowledge of them more certain than it is in itself. there is no logic for this portion of our know ledge.'* all discussions pertaining to the nature and limits of intuition or consciousness are referred to the higher or transcendental metaphysics, but all the facts that compose evidence and become the grounds of inference are, according to the view taken here, necessarily subjects of examination. 'cogito ergo sum--i think, therefore i am, argued des cartes. we learn by this that consciousness of the operations of the mind is the strongest evidence of our existence. it cannot be proved so forcibly by any other means; and although des cartes' language may appear to involve a logical fallacy, yet the proof of our personal existence which we have from _thinking_, is the fullest and best we are acquainted with.'** * j. . mil: logic, vol. l, p. . ** rev. robert amalie. there is a numerous class of facts from which all men draw conclusions, which facts are not referable to the evidence of the senses. there are the facts of testimony. testimony is founded on laws almost as fixed and certain as those of nature. all our knowledge, scientific, literary, historical--all except what arises from our experience and consciousness--depends on it. in the administration of justice it is the sole guardian of property and life. if a man of known integrity and veracity state a fact, without any possible motive of self-interest, and evidently subject to no delusion; and if others of like character, who could have no understanding or collusion with him, state the same, men are nearly as certain of it as of any truth in mathematics. i believe in the existence of rome and the facts of astronomy on this evidence, although i never saw the city or examined the stars through a telescope. the conclusiveness of testimony is designated moral certainty. the value of testimony depends on three things. . on the nature of the subject. some subjects are capable of more accurate observation than others. . on the powers and character of the observer--his ability to understand or note that of which he testifies--and his honesty in common matters. . on the number of our informers. several persons are less likely to be imposed upon than one. testimony or moral certainty is inferior to physical certainty. a physical certainty bears uniformly the name of certainty, while a moral certainty is characterised as a probability. great, very great may be the probability, still it is less in reliableness than a physical certainty. the evidence of cato or aristides would be very conclusive--yet somewhat less certain than that which our own senses have proved. the conclusions from moral certainties are obtained like other conclusions, by induction. the induction from moral facts is like the induction from physical facts, with this difference--that the conclusions from moral facts are probabilities, like the facts on which they are founded. whatever has physical certainty in its favour is considered demonstrable, and when sufficient probable evidence is adduced in favour of a proposition, it is considered to be fairly proved. some persons, biased by the strictness of mathematical proof, insist upon the same accuracy in moral investigations. i have elsewhere pointed out the juvenility and infatuation of this error. insist upon demonstration where the nature of the questions admits it. less should not, in such case, suffice. accept probability where probability is the sole evidence attainable. never ask more than reason can grant. we must admit gradations of validity. what we are conscious of, we _know_. all we receive on testimony, we _believe_. physical certainty is _knowledge_: moral certainty, _belief_. hume remarks, in his 'essay on probabilities,' that 'mr. locke divides all arguments into demonstrative and probable. in this view, we must say, that it is only probable all men must die, or that the sun will rise to-morrow. but to conform our language more to common us, we ought to divide arguments into _demonstrations, proofs, and probabilities_. by proofs, meaning such arguments from experience as leave no room for doubt or opposition.'* * hume's essays, vol. , p. . conjecture is probable truth. some subjects only furnish a sufficient number of facts to make them probable in the lowest degree--not to decide them as positively true. the propositions expressing results pertaining to such subjects are called conjectures. a conjecture founded on no fact or upon too few to make it likely, is called a vagary. it will be seen that probability is a thing of degree. a probability may vary in weight from a moral certainty, where it ranks next to a physical certainty, down to a conjecture, and descend lower in likelihood till it is lost in conjecture. lord kames remarks, in his preface to his 'sketches'--'most of the subjects handled in the following sheets, admit but of probable reasoning: and, with respect to such reasoning, it is often difficult to say, what degree of conviction they ought to produce. it is easy to form plausible arguments; but to form such as can stand the test of time, is not always easy. i could amuse the reader with numerous examples of conjectural arguments, which, fair at a distant view, vanish like a cloud on a near approach'. did all authors so judiciously apprise their readers of the probable logical value of their speculations, fewer would be misled than now. to numerous questions of undoubted interest, which have been agitated in all ages, only a moderate degree of certainty attaches--these are termed speculative. such subjects may afford but few facts and instances, and the chances of conclusiveness may seem remote--yet ultimate results are not to be despaired of: the new comparison of conjectures and the arrangement of facts daily throws new light on age-contested points. systems of conduct should not be founded on conjectures in opposition to evident moral utility; but if speculation is kept 'within the sphere of speculation, it may be prosecuted with safety and prospect of success. there are problems in metaphysics as there are in mathematics, which may be demonstrated to be insolvable. to describe the limit of human power with respect to contested questions will yet result from speculative controversy. the capacities of our understanding will be one day well considered, the extent of our knowledge discovered, and the horizon found which sets bounds between the enlightened and the dark part of things--between what is and what is not comprehensible by us. but this will only be when the _untried_ has been _universally_ attempted in all directions. bailey, i think, has defined truth as being that which is universally accepted after having been universally examined. little of this truth is yet extant. when every man shall be a thinker, when the autobiography of intellect shall be more freely furnished than it ever yet has been, unanimity of opinion not yet dreamed of will prevail. harmony of opinion is the sign of intellectual conquest--the standard-bearer of truth no advocacy is victorious while dissent occupies the field. what we _know_ to be true, is _knowledge_; what we have only reason to believe true, is _opinion_. all human information is made up of knowledge and opinion. the primary importance of knowledge is evident from the fact that knowledge is the umpire of all opinion. we believe in the existence of the ruins of palmyra and thebes, and in certain discoveries of algebraists and astronomers. it is our _opinion_ that these things are true, although we may never have visited palmyra or thebes, nor made the calculations of the algebraist, nor the observations of the astronomer. in these cases our belief is founded on our _experience_ and knowledge of mankind. it is quite true that travellers exaggerate, and scientific men are sometimes mistaken; but we know that there is always _some_ truth at the bottom of what is communicated by well-meaning writers. more or less, every man's _experience_ assures him of this; and it is the cause of our reliance on the records of history, and the reports of science. therefore, since all information is made up of knowledge and opinion, plainly knowledge is the one thing which comprises all intelligence. 'questions of fact,' observes pascal, in his celebrated 'provincial letters,' 'are only to be determined by the senses. if what you assert be true, prove it to be so; if it be not, you labour in _vain_ to induce belief. all the authority in the world cannot enforce or alter belief as to facts; nothing can possibly have power to cause that not to be which actually _is_.'* a remarkable instance of the verification of what was assumed to be is related of pascal by goodrich. 'pascal was a philosopher even in childhood. at a very early age he was taught the ten commandments. for several days after, he was observed to be measuring the growth of a blade of grass. when asked the meaning of this, he replied, "the fourth commandment says, 'six days shalt thou labour, but the seventh is the sabbath in which thou shalt do no work.' now i wished to ascertain if nature obeyed this great law, and therefore measured the grass, to see if it grew as much on sunday as on other days." '** 'we are informed,' says beattie, 'by father malebranche, that the senses were at first as honest faculties as one could desire to be endued with, till after they were debauched by original sin; an adventure from which they contracted such an invincible propensity to cheating, that they are now continually lying in wait to deceive us. but there is in man, it seems, a certain clear-sighted, stout, old faculty, called _reason_, which, without being deceived by appearances, keeps an eye upon the rogues, and often proves too cunning for them.'*** * letter xviii. ** fireside education, p. . *** essay on truth, p. . though it is so abundantly obvious that the evidences of our senses, internal and external, are, in effect, the sources of all certainty, yet we are not warranted in rejecting, as mere hypothesis, every theory which we cannot at once corroborate. when euler remarked of his new law of arches, 'this will be found true, though contrary to all experience'--when gall exclaimed of his new philosophy of the sensorium, 'this is true, though opposed to the philosophy of ages'--they expressed demonstrable truths hidden from the multitude. they announced new generalisations to man. new truths are commonly found to be old unnoted experiences, for the first time subjected to classification, and presented in a scientific form. to me it seems almost in vain to urge men to notice facts who have never noticed themselves. the truest standards of certainty arise from individuality of retrospection. an intelligent man is, himself to himself, the measure of all things in the universe. in appealing to the young on the aspiration after improvement, one cannot say 'consult your aptitudes--follow your bias.' this is the sole appeal-injunctive to which all natures can respond. but in this half-natured, half-trained, doubtfully-conditioned state of society, though the generous would be incited to noble deeds, the sordid would lay their vulture claws on the world, and the unprincipled victimise their fellows. you have, therefore, to say, 'man, do what thou listest, provided it be compatible with the welfare of thy fellow men.' men are not well-natured, and we have thus to guard individuality, and qualify the appeal, and so we miss the soil of great enterprise. great is the disadvantage. for the fulcrum which is to raise men is without their natures--remote in the wide world. man should begin with himself. he loves truth--it is the first impulse of his nature. he loves justice--the bandit on the throne, as well as the bandit in the forest, respects justice in some form or other. man loves cheerfulness--it is the attribute of innocence and courage. he loves fraternity--it knits society together in brotherhood. these are standards. his codes of life and judgment arise from these aspirations. that which accords with these principles is _reasonable_. whatever develops these principles in conduct is _moral_. these sentiments are to be confirmed by his own observations. his experience in connection with these rules is the right with which he may examine religions, creeds, books, systems, opinions. the right understanding of physical and moral facts greatly depends upon intellectual character--and there enters largely into the recondite and ultimate inquiries of intelligent men another class of facts, called mental facts. there is no chance of identifying these without the power of self-analysis, which is one reason why metaphysic ability belongs to so few, and why questions involving metaphysical considerations are such profound enigmas to the majority of the people. the illiterate in these things are easily led or misled by words. they who will not bow before a throne fall prostrate before a sound. the first principles of things are few. the axioms from which men date their reasoning are chiefly personal. they are expressed in an infinite variety of ways, occasioned by the various conceptions of those who conceive them, and by the different capacities to which they are adapted when offered for the instruction and guidance of others. but this must not mislead us as to the number, and overwhelm us with a sense of complexity, where in fact simplicity reigns. those who have the power of self-analysis make for themselves rules of conduct, and the best are originated in this way--for when a man recasts his acquirements of sense and education, in order to see on what all rests, and what are essential standards of action and judgment, he resolves all into few, and those the clear and strong. rob roy's self-examination paper is presented to us in those lines which sir walter scott, with grace and justice, characterised as the 'high-toned poetry of his gifted friend wordsworth.' say, then, that he was wise as brave, as wise in thought as bold in deed; for in the principles of things he sought his morai creed. said generous rob, 'what need of books? burn all the statutes and their shelves! they stir us up against our kind, and worse, against ourselves. we have a passion, make a law, too false to guide us or control; and for the law itself we fight in bitterness of soul. and puzzled, blinded, then we lose distinctions that are plain and few; these find i graven on my heart, that tells me what to do. sir walter scott himself has enforced the same views:--'how much do i need such a monitor,' said waverley to flora. 'a better one by far mr. waverley will always find in his own bosom, when he will give its still small voice leisure to be heard. all that hath been majestical in life or death, since time began, is native in the simple heart of all,-- the angel heart of man.--lowell. to awaken the senses and instruct them and direct them aright in the art of observation, is a great and essential undertaking. all scattered aids need collecting together. de la beche in 'geology,' and miss martineau have written books, entitled 'how to observe.' this quality is the distinction between the natural and artificial man--the natural man observes what is in nature--the artificial notes what he finds in books--the one depends on himself--the other on an encyclopaedia. we want contrast, in order to know as well as to explain. foreigners observe us better than we observe ourselves. the common escapes our attention. to know a fact fully we seek its opposite to compare it with. were men reared with the powers of men without the genius of the child being impaired, the ability to observe would be more general and perfect among us. children stop at everything to question its nature, at every word to ask its import. it was the aim of pestalozzi to cultivate by his system of tuition this incessant questioning. but parents among the poor know not the value of the habit, or knowing it have not time to gratify it, and thus this happiest aptitude of childhood is repressed. with regard to the analysis of groups of facts, mr. j. s. mill remarks--'the observer is not he who merely sees the thing before his eyes, but he who sees what parts that thing is composed of. to do this well is a rare talent. one person from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers $ another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing things into one mass which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse, than if no analysis had been attempted at all.'* * logic, vol. , p. . in the case of the leigh peerage there was a number of witnesses examined in the house of lords, as to the existence of a certain monument in stonely church--'the first witness described the monument as being black; the second spoke of it as a kind of dove-colour; the third said it was black and white; the fourth said it was originally white, but dirty, when he saw it; the fifth differing from the others, said it was blue; the next witness described it as a light marble, but said it had a dark appearance as if it had been bronzed, and the last witness spoke of it as feeing of a light grey colour. then, as to the form of the monument, the first witness said it was oblong; the next said it was square at the top, and came down narrower to the bottom, and there rested on a single truss; the third witness described it as being square at the bottom, testing upon two trusses; and went up narrower and narrower to a point at the top; the fourth witness said it was angular at the top; the next said it was square at the bottom, was brought to a point in the middle, and was then curved into a sort of festoon; the sixth witness stated that it was square at the top and bottom, and had a curve; and the last said it was square at the top and bottom. as to the language of the inscriptions, the first witness stated that the names of _thomas_ and _christopher leigh_ were in english; the next said the inscription was not in english; the third said there was a great deal in english; the fourth witness said the whole, (with the exception of the name christopher lee), was in a language, which he did not understand; the next witness stated that the inscription was all in english, except the words _anno domini_; and the last witness said it was not in english.'* * times, may , . all these witnesses agree as to the fact in dispute, but their variances in testimony illustrate the common inattention of observation--and this case farther admonishes us that if such differences may exist as to a question of fact, where the senses are the same, little wonder that differences exist as to matters of opinion, where intellectual capacity and information are so various. we know from experience that the sportsman sees a point which is hidden from the unpractised aimer--the painter sees traits of character of light and shade in an object which the untaught limner never observes; the musician distinguishes harmonies and discords that fall unnoted on the uneducated ear. thus we learn that by cultivation we can increase natural susceptibility to observe. the extent is surprising to which the unanalytic are in ignorance of the real nature of phenomena. 'there is nothing which we appear to ourselves more directly conscious of, than the distance of an object from us. yet it has long been ascertained, that what is perceived by the eye, is at most nothing more than a variously coloured surface; that when we fancy we see distance, all we really see is certain variation of apparent size, and more or less faintness of colour.'* in preparing to support an argument on any question, we must first determine the sources whence the facts are to be collected. instance: the objects of municipal laws are rights and crimes. the evidence of rights are:-- . public consent. . testimony. . records. the evidence of crimes are:-- . confession. . previous malice. . testimony. this outline of the investigation prosecuted, the inquirer next consults the authors who treat of the rules which are applied for determining the facts of public consent, testimony, records, confessions: he is then able to support his own argument in a valid manner, or prepared to examine the facts offered by an opponent in support of an opposite view. the opinion may be hazarded that it is not so much from want of capacity to observe that error arises, as from the want of conviction that we should observe well before we attempt to infer. nature is inventive, and desire, once awakened, will, without formal rules, find out a thousand modes of gratification. the foundation for a soldier logic than now prevails will be laid when the people are impressed with the great importance of looking well to facts as the data of all inferential truth. there is a noted aphorism of cendillac, to the effect that the one sufficient rule for discovering the nature and properties of objects is to name them properly, as if, observes mr. j. s. mill, 'the reverse was not the truth, that it is impossible to name them properly except in proportion as we are already acquainted with their nature and properties.' need it be added that this knowledge is only to be had by patient observation? * mill logic vol. l, p. . to assist this habit, dr. watts recommends the thinker to ascertain if a given idea is clear and distinct, obscure and confused, learned or vulgar, perfect or imperfect, adequate or inadequate--true or false. 'view a subject, says he, as through a telescope, so as to command a clear view of it; examine its whole bearings as you look over a globe; consider it in its several properties--anatomise it as with a scalpel. take cognizance of its various aspects as though inspecting it through a prismatic glass. whenever we contemplate a single object in nature is obvious it must have duration, size, weight, form, colour, such qualities being essentially present in all adequate conceptions of physical phenomena.' it was objected to the 'cricket' of mr. dickens, that his delineation of bertha was wanting in truthfulness. the teachers of the blind who knew their nature could detect the departure from the reality of their habits in the sketch of bertha. the study of the blind was necessary to insure success. we may not be able in any one book to give rules for the study of all subjects, but we may indicate that we ought not to speak of what we do not know, and that if we mean to introduce certain facts into our speech or writing, we should consult the records and experienee of those persons who are known to have written upon the subject, and follow the best directions they give, and we shall generally attain accuracy. mr. combe observes, in his introduction to his notes on the united states of north america, p. xi.--'i was told that a _certain person_ boasts of having given miss martineau erroneous information for the purpose of leading her into mistakes; and another in philadelphia assures his friends that he "crammed" capt. marryatt with old "joe millers," which the capt. embodied into his books as facts illustrative of american manners. this seems to be a case in which some uncertainty must ever exist as to the value of the facts collected by travellers. they cannot observe all, or test half that they do observe. they must rely on testimony. but they might do this--they might tell us precisely the kind of authority they followed, and then the reader could form some opinion of the value of what was communicated. had miss martineau and captain marryatt given the name and addresses of their informants, the latter would now be punished by being infamously known throughout europe; and all future travellers warned from them--and all future informants warned by their example. where informants cannot be mentioned by name and address, the chances are, they cannot be trusted. when first connected with public proceedings, i found myself made the depository of innumerable bits of scandal, and ominous reports of public characters. to all who told me anything, if i attached importance to it, i made it a rule to ask--'may i mention it to the party with your name?' 'o, no, i would rather not,' was the common reply. to all written communications answer--'please add your name and address--and may i publish them if occasion requires?' 'o, no, don't,' would be the general injunction. thus i found that huge reports, inflated as balloons, shrunk like them when pricked by the pin of a question--'will you answer for it?' thus i saved myself from being imposed upon by, or being the retailer of, reports for which the originator or relator would not or could not vouch. 'upwards of twenty years ago,' says george combe, 'i accompanied a member of the bar of paris, a philosopher and a man of letters, on a visit to the highlands of scotland. at callendar a boy of twelve or thirteen years of age attended as a guide to some interesting spot, and in external appearance he seemed to be in every respect one of the common lads of the village. my parisian friend entered into conversation with him; asked him if he had been at school, and soon discovered that to a tolerable acquaintance with the greek and latin languages, he added a pretty extensive-knowledge of arithmetic and geography, and was then engaged in the study of mathematics. my friend conceived that the boy was an average specimen of the peasantry of the country; and greatly admired the educational attainments of the scotch people, which he had previously heard highly extolled. but,' adds mr. combe, 'the boy was the natural son of an english officer, who had resided in the neighbourhood, and who, while he ordered him to be reared in the hardy habits of the scottish highlanders, had provided ample funds for his mental education.'* * intro, to notes on united states of north america, p. ., vol. it is difficult to believe in this frenchman being a 'philosopher, making, as he did, a national induction from a single instance. had he previously inquired, as he ought to have done, the particulars of that lad's life and rearing, before coming to so large a conclusion, he would at once have discovered the error he was falling into. in the registrar general's report of , the mean of married persons unable to write is presented. the conclusion is based upon the statistics of nine counties. but when it was found that only three per cent, of the persons marriageable, did marry, the datum was found insufficient to afford sure results. this fact; is given by mr. combe in the same book. then how many boys ought our 'philosopher' to have questioned before making his vast inference? another instance of the value of a question i extract from the same work. mr. combe says:--'a few years ago, when travelling in somersetshire, i saw four horses, attended by two men, drawing a light plough in a light soil. "what a waste of labour is here," said i to an intelligent farmer; "in scotland, two horses and one man will accomplish this work." "we rear and train young horses for the london market," said he; "two of the four which you see are serving an apprenticeship to labour."' had mr. combe asked a few questions as to the correctness of his assumed inference, he would have been saved from his erroneous conclusion. we should be wary of unquestioned data. when murray's grammar was first placed in my hands, i found in it certain references to the canons of language in the larger edition. i questioned my teacher as to what it meant. 'it is a trick of the printer,' he answered, 'to induce you to buy the larger volume.' i do not believe this now. i believe that it was a necessary reference. an author who has written upon a given subject, naturally finds his own ideas coincident illustrations of his views, and honestly refers to them. in this book i have made a few references to previous works of mine, and it has struck me that nine ont of ten of the readers will set this down to artifice or egotism. yet it is neither. i have referred only to avoid the full quotation of some necessary illustration of the argument. yet few will penetrate to the fact, and most will be apt to infer a trick from appearances. chapter vi. science whatever we know must be in the number of the primitive data, or of the conclusions which can be drawn therefrom.-- j.s. mill to have reached, in the study of observed phenomena, the point of perception indicated in this motto, and to feel the full force of the remark, is to have imbibed the spirit of science---whose traits are dear distinctions, accurate classification, and strict reference to primitive data. the bases of all science are methodical facts. the first step to the perfection and enlargement of a science is the resolution of its propositions into axioms, and into propositions which are to be proved. dr. reid observes--'this has been done in mathematics from the beginning, and has tended greatly to the emolument of that science. it has lately been done in natural philosophy, and by this means that science has advanced more in years than it had done before in , . every science is in an unformed state until its first principles are ascertained; after this it advances regularly, and secures the ground it has gained.' classification is one of the first steps to science. the maxim in government, divide and conquer, retains, when applied to science, all its wisdom without its machiavelialism. the young grammarian reduces the mass of words, that so threaten to confound his powers, to a few natural classes, and he conquers them separately with ease. 'the single power by which we discover resemblance or relation in general, is a sufficient aid to us in the perplexity and confusion of our first attempts at arrangement. it begins by converting thousands, and more than thousands, into one; and, reducing in the same manner the numbers tiros formed, it arrives at last at the few distinctive characters of those great comprehensive tribes, on which it ceases to operate, 'because there is nothing left to oppress the memory or the understanding.'* * brown's moral philosophy, lect, xvi. merell has spoken more comprehensively on this subject--'that human knowledge dees not consist in the bare collection and enumeration of facts; this alone would be of little service were we net to attempt the classification of them, and to educe from such classification general laws and principles. the knowledge, which consists in individual truths, could never be either extensive ear definite--for the multiplicity of objects which then must crowd in upon the mind only tends to confound and perplex it, while the memory, overburdened with particulars, is not able to retain a hundredth part of the materials which are collected. to prevent this, the power el generalisation comes to our aid, by which the individual facts are so classified under their proper conceptions, that they may at the same time be more easily retained, and their several relations to all other branches of knowledge accurately defined. the colligation and classification of facts, then, we may regard as the two first steps, which are to be taken in the attainment of truth.'* aristotle, says morell, classified the _matter_, kant the _forms_. aristotle was the first man who undertook the gigantic task of reducing the multiplicity of all the objects of human knowledge to a few general heads--- . substance. . quality. . quantity. . relation. action. . passion. . place. . time. . posture. . habit. aristotle's philosophy was _objective_, kant's _subjective_. kant's categories were twelve. . unity. . plurality. . totality. . affirmation. negation. . limitation. . substance. . casualty. . reciprocity. . possibility. . actuality. . necessity. 'it is a fundamental principle in logic, that the power of framing classes is unlimited as long as there is any (even the smallest) difference to found a distinction upon.** what geoffroy saint hilaire has said of natural history is applicable to all science:--'the first problem to be solved by him who wishes to penetrate deeply into this; study, consists evidently in the formation of clear and precise distinctions between the various brings. this is the most elementary problem, in so-far as it precedes all the others; but it is in reality, in most cases, complicated and full of difficulties. its accurate solution requires--first, _observation_, which makes known the facts; next, _description_, which fixes them permanently; then _characterisation_, which selects and displays prominently the most important of them--and lastly, _classification_, which arranges them in systematic order.'*** of the value of classification, lamartine has given a fine illustration:----'montesquieu had sounded the institutions and analysed the laws of all people. by _classing_ governments he had compared them, by comparing them he passed judgment on them; and this judgment brought out, in its bold relief and contrast, on every page, right and force, privilege and equality, tyranny and liberty.'**** * morell's hist. of speculative phil., p. , vol. . ** mill, p. , vol. . *** t. w. thornton: reasoner no. , p. . **** lamartine's hist. girondists, pp. - , vol. . familiarity with the characteristics of science imparts considerable power for the detection of fallacy. a logician is imperfect without scientific tastes and habits. the man of science has all his knowledge systematised and arranged. what other people have in confusion, he has in order. the elements of knowledge are, more or less, as has been observed, known to all men--but in their perfect, communicable, and usable state, they are-known only to the educated and scientific man. what training is to the soldier, science is to the thinker. it enables him to control all his resources and employ his natural powers to the best advantage. it is this which constitutes the superiority of the educated over the ignorant. astronomy, navigation, architecture, geometry, political economy, morals, all rest, or should rest, and do rest, if they have-attained to the perfection of science, on primary facts and first principles. every step can be measured by an axiom--every result can be traced to a first principle.* to detect error, then, in any province of investigation, or any domain of argument, the logician first looks to the primary principles on which it is based, and thus tests the legitimacy of its conclusions. as respects those who deal in things professedly above reason, it was well said by an anonymous writer of the old school of sturdy thinkers,--'of such men as these i usually demand, whether their own assent to things they would have us believe, be grounded upon some _rational argument_. if they say 'tis not, they are fools to believe it themselves; and i should add to the number of fools, if, after this acknowledgment, i should believe them: but if they say it is, i desire them to produce their argument; for since 'tis framed by a human understanding, the force of it may also be comprehended and judged of by a human understanding: and tis to no purpose to say that the subject surpasses human reason: for if it do so indeed, it will surpass _theirs_ as well as _mine_, and so leave us both upon even terms. and let the thing assented to be what it will, the assent itself must be founded upon a _sufficient reason_, and consequently upon one that is _intelligible_ to the human intellect that is wrought on by it.'** * see beauties and uses of euclid, chap. vi., logic of euclid. ** a discourse on things above reason, . "what is it?--" "'tis impossible the same thing should be, and not be at the same time," are maxims of such universal usefulness, that without them we could neither _judge, discourse,_ nor _act_. these principles may not always make their appearance in formal propositions, but still they guide all our thoughts in the same manner as when a musician plays a careless voluntary upon a harpsichord--he is guided by rules of music he long since became familiar with, though now scarcely sensible of them. 'a butcher loses his knife, and looks all about for it, and remarks as the motive of his search, "i am sure it must be somewhere or other." by which rude saying it is evident he is guided by the axiom last mentioned. had he not the knowledge of this axiom beforehand, did he think it possible that his knife could be _no where_ or in _no place_ he would never take pains to look for it. we may observe many such axioms as this guiding the actions of the vulgar, and it is no unworthy speculation to observe their behaviour and words, which proceed from uncorrupted nature, and retrieve the axioms from which their conduct proceeds.'* * solid philosophy, asserted against the fancies of the idealists. (locke's understanding is the work controverted.) by j. s.. london, . the outlines of the science of morality are thus comprehensively sketched by sir james mackintosh: the origin, value, and application of first principles are indicated with his usual felicity. 'the usages and laws of nations, the events of history, the opinions of philosophers, the sentiments of orators and poets, as well as the observations of common life, are in truth, the materials out of which the science of morality to formed; and those who neglect them are justly chargeable with a vain attempt to philosophise without regard to fact and experienee--the sole foundation of all true philosophy. the natural order undoubtedly dictates that we should first search for the _original principles_ of the science in human nature; then apply them to the regulation of the conduct of individuals, and lastly employ them for the decision of those difficult and complicated questions that arise with respect to the intercourse of nations.' to search for ultimate principles is to discover at a glance the whole bearings of a great question. through what clouds of politics had the historian of rome penetrated when he announced that the principles of a free constitution are irrecoverably lost when the legislative power is nominated by the executive. this habit--it cannot be too often insisted on aids not only the acquisition of knowledge, but also its _retention_. around these first principles, as around a standard, the thoughts naturally associate. touch but a remote chord of any question, and it will vibrate to the central principle to which it has once been well attached. every relative impression owns a kindred connection, and the moment one is attacked, it, like a faithful sentinel, arouses a whole troop, which, marshalled and disciplined, bear down and challenge the enemy.'* * beauties and uses of euclid, pp. - . what rogers has so exquisitely sung of the associations of childhood, is true of the associations of science. childhood's loved group revisit! every scene,-- the tangled wood-walk and the tufted green. the school's lone porch, with reverend mosses grey, just tells the pensive pilgrim where it lay. mute is the bell which rang at peep of dawn, quick'ning my truant steps across the lawn: unheard the shout that rent the noontide air, when the slow dial gave a pause to care. up springs at every step, to claim a tear, some little friendship formed and cherished here? and not the lightest leaf but trembling teems with golden visions and romantic dreams. chapter vii. propositions all truth and all error lie in propositions.--j. s. mill. in accordance with that experience which directs to the profoundest books for the simplest statements, we turn to mill's logic for the philosophy of propositions. the answer to every question which it is possible to frame is contained in a proposition or assertion. whatever can be an object of belief or even of disbelief, must, when put into words, assume the form of a proposition * * what we call a truth is simply a true proposition; and errors are false propositions. to know the import of all possible propositions would be to know all questions which can be raised, all matters which are susceptible of being either believed or disbelieved. * * since then the objects of all belief and all inquiry express themselves in propositions, a sufficient scrutiny of propositions and of their varieties will apprise us what questions mankind have asked themselves, and what it the nature of the answers to those questions they have actually thought they had grounds to believe. 'now the first glance at a proposition shows that it is formed by putting together two names. a proposition, according to the common simple definition, which is sufficient for our purpose, is, _discourse in which something is affirmed or denied of something_. thus, in the proposition, gold is yellow, the quality _yellow_ is affirmed of the substance _gold_. in the proposition, franklin was not born in england, the fact expressed by the words _born in england_ is denied of the man franklin. 'every proposition consists of three parts: the subject, the predicate, and the copula. the predicate is the name denoting that which is affirmed or denied. the subject is the name denoting the person or thing which something is affirmed or denied of. the copula is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. thus, in the proposition, the earth is round, the predicate is the word _round_, which denotes the quality affirmed, or (as the phrase is) predicated: _the earth_ words denoting the object which that quality is affirmed of, compose the subject; the word it, which serves as the connecting mark between the subject and predicate, to show that one of them is affirmed of the other, is called the copula.' chapter viii. definitions no difficulty is unsurmountable, if words be allowed to pass without meaning.--lord kames. as every proposition consists of two names, and as every proposition affirms or denies one of these names of the other, the value of definition, which fixes the import of names, is apparent. 'a _name_ is a word taken at pleasure to serve for a mark, which may raise in our mind a thought like to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker had before in his mind [hobbes]. this simple definition of a name, as a word (or set of words) serving the double purpose of a mark to recall to ourselves the likeness of a former thought, and a sign to make it known to others, appears unexceptionable.'* definition originates in accurate and comprehensive observation. 'there cannot be,' says mill, 'agreement about the definition of a thing, until there is agreement about the thing itself. _to define a thing is to select from among the whole of its properties those which shall be understood to be designated and declared by its name_; and the properties must be very well known to us before we can be competent to determine which of them are fittest to be chosen for this purpose.'** 'the simplest and most correct notion of a definition is, a proposition declaratory of the meaning of a word; namely, either the meaning which it bears in common acceptation, or that which the speaker or writer, for the particular purposes of his discourse, intends to annex to it.'*** * j. stuart mill: system of logic, nd ed., chap. , sec. i. p. . ** introduction to logic, p. . *** mill's logic, p. , vol. . but with most persons the object of a definition is merely to guide them to the correct use of a term as a protection against applying it in a manner inconsistent with custom and convention. anything, therefore, is to them a sufficient definition of a term which will serve as a correct index to what the term denotes; although not embracing the whole, and sometimes perhaps not even any part of what it connotes. definitions are sometimes explained as being of two kinds--of things and words. the definition of _words_ is the explanation of the sense in which they are used. the definition of _things_ is an explanation of the specific properties by which they differ from all other things. to define a thing, says dr. watts, we must ascertain with what it agrees, then note the most remarkable attribute of difference, and join the two together. probity--the disposition to acknowledge the rights of mankind. justice--the disposition to maintain the rights of mankind. benevolence--the disposition to improve the rights of mankind. deceit--the concealed violation of the rights of mankind. injustice--the open violation of the rights of mankind. malevolence--hatred of the rights of mankind. in defining a word we seek some class to which to refer it, that we may identify it, and fix attention upon that peculiarity by which we can distinguish it from all other things. 'probity and 'justice' are referred to 'disposition,' with reference to the 'rights of mankind' as their sphere of existence: and _acknowledgment, and maintenance_, are mentioned as the distinguishing features. distinctions must not be made without differences. the definition should be plainer than the thing defined. aristotle's definition of motion is considered defective in this respect:--'motion--an act of a being in power, so far forth as it is in power.' tautological definitions cause more to be supposed than is true--the too terse explanation leaves some necessary thing unmentioned. a perfect definition requires the union of the concise, the clear, and the adequate. some persons are so unskilful in the analysis of terms as to occasion the advice _nil explicare_--never explain yourself if you wish to be understood. double meanings should be avoided. the writer may himself alternate in their use, and the reader may take the word in the unintended meaning. all men have not the strong sense of johnson. when caleb whiteford inquired seriously of the doctor, whether he really considered that a man ought to be transported, like barrington, the pickpocket, for being guilty of a double meaning. 'sir,' said johnson, 'if a man means well, the more he means the better'--which, whether real or fictitious, is one of the happiest answers that ever crushed a quibble.* * hood's own. i have frequently put the question--what is consciousness? to persons who have been conscious for twenty or thirty years, but who were yet unable to reply. had any one deprived these persons of consciousness, a judge would have hanged him for the offence; yet, could they themselves have been interrogated as to what harm they had suffered, they could not have told what they had lost. and upon the principle, that he not knowing what he has lost, is no loser, these persons, though murdered, had suffered no harm. the various definitions of the same subject which prevail, originate in the caprice, or partial, or profound knowledge the definer may have of his subject. it seems to be admitted by logicians, that an author has a right to give whatever provisional definition he pleases of his terms. but having once given them, perspicuity requires that he should adhere to them. any new sense in which a term is employed should be specially defined. in discoursing on an ordinary subject, as the right of public assembly,--such words as perception, conception, apprehension, might be used reciprocally, but in a dissertation on metaphysics each requires restriction in use and precision in purport. often genius strikes out new relations of words. in recent political debates, mr. cobden resorted with new force and point to a charge of rashness against ministers: he showed that rashness consisted more frequently in inaction than action. he is rash who stands surrounded by the elements of danger without taking; any precaution against the contingencies of peril; he is rash who does not take advantage of the calm, to repair his shattered rigging; he is rash who looks not out for a proper supply of water until the conflagration is raging around him; and more rash than all is he who exercises no provident care for supplying a nation with food, but waits for the pressure of famine and the perils of starvation. at the last soiree of the leeds mechanics' institution, mr. dickens referred to ignorance, commonly considered as a passive negation, and placed it in the light of a power. 'look where we will, do we not find ignorance powerful for every kind of wrong and evil? powerful to take its enemies to its heart and strike its best friends down--powerful to fill the prisons, the hospitals, and the graves--powerful for blind violence, prejudice, and error in all their destructive shapes.' the variations which not only common but technical terms undergo, is a considerable source of perplexity in reasoning. mr. mill cites the instance of the term felony. no lawyer will undertake to tell what a felony is otherwise than by enumerating the various kinds of offences which are so called. originally, felony denoted all offences, the penalty of which included forfeiture of goods; but, subsequent acts of parliament have declared various offences to be felonies without enjoining that penalty, and have taken away the penalty from others which continue still to be called felonies, insomuch that the acts so called have now no property whatever in common, save that of being unlawful and punishable. this inattention to precision in terms has arisen not among the vulgar, but among educated english lawyers. 'language,' says mr. mill, borrowing a political simile from sir james mackintosh, '"is not made, but grows." a name not unfrequently passes by successive links of resemblance from one object to another, until it becomes applied to things having nothing in common with the first things to which the name was given; which, however, do not, for that reason, drop the name; so that it at last denotes a confused huddle of objects, having nothing whatever in common; and connotes nothing, not even a vague and general resemblance. when a name has fallen into this state, in which by predicating it of any object we assert literally nothing about the object, it has become unfit for the purposes either of thought or of the communication of thought; and can only be made serviceable by stripping it of some part of its multifarious denotation, and confining it to objects possessed of some attributes in common, which it may be made to connote. such are the inconveniences of a language which "is not made, but grows." like a road which is not made, but has made itself, it requires continual mending in order to be passable.'* * logic, p. . it is well observed, that the spontaneous growth of language is of the utmost importance to the thinker. there seems to be so palpable a substratum of right sense, in the rude classifications of the multitude, that the logician has little else to do, in many cases, than to retouch them and give them precision. guizot observes, there is frequently more truth in common acceptations of general terms than in the more precise definitions of science. common sense gives to words their ordinary signification. the leading terms of philosophy are clothed in innumerable shades of meaning acquired in their transitional use, and immense is the knowledge of _thing:_ requisite to enable a man to affirm that any given argument turns wholly on _words_. the study of terms, for which logicians have provided multiplied means, is one of the most interesting and profitable upon which men can enter. if it be worth while to speak at all, it is worth while to know certainly what we speak about. philanthropic genius has pointed out a perversion of power, arising through definitional incapacity, which makes it a moral duty to study analysis of terms, and exactitude of expression. 'all battle,' says carlyle, 'is _misunderstanding_--did the parties know one another, the battle would cease. no man at bottom means injustice; he contends for some distorted image of right. _clear_, undeniable right--_clear_, undeniable might--either of these, once ascertained, puts an end to battle. battle is a confused experiment to ascertain these.' of the power of names to impose on the multitude, history furnishes too many examples. strength to forefend us against they delusion ability to see that the meaning governs the term, and not the term the meaning--are species of intellectual self-defence. 'augustus,' says gibbon, 'was sensible that mankind is governed by names; nor was he deceived in his expectation that the senate and people would submit to slavery provided that they were respectably assured that they still enjoyed their ancient freedom.' 'never,' adjures w. j. fox, 'be deceived by words. always try to penetrate to realities. have your wits sharpened, your senses exercised to discern good and evil. be not imposed upon by pompous manners. many a solemnly-uttered sentence is often a sheer inanity, which will not bear the scrutiny of an observant intellect. be not frightened by denunciations; by being told that you are not a good subject or a good christian, if you do not believe, or say that you believe this or that. be not led astray by iteration--mistake not the familiar for the intelligible. ascertain what words are meant to convey, and what they actually do convey. go to the substance and soul of whatever is propounded. be on your guard against bold assumptions, nor let them bear you away against the dictates of your own understanding. look at phrases as counters, or paper money, that may pass for much or little according to circumstances. endeavour to arrive at truth, and make that your treasure. be ever wide awake to see through any veil of sophistry and cant; nor by the agency of words be made the dupe of critic or lawyer, of priest of politician.'* * lectures to the working classes, p. , vol. . chapter ix. syllogisms propositions being assertions--as soon as sufficient reasons are adduced to make the proposition credible, it becomes a truth probable or certain, as the case may be. reasoning is a simple business. to reason is to state facts in support of a proposition. a conclusive fact so advanced is called a reason. all the reasons offered in proof of a proposition are called premises. the pythagorean, who lays down the proposition that fruits and grain are the proper food of man, and cites facts to prove his assertion--reasons. a proposition and its reasons are called an argument. reason is the faculty of perceiving coherences. effective reasoning is stating them so that others cannot but see them too. 'reasoning on the abstrusest questions is nothing more than arriving at a remote truth by discovering its coherence with the preceding facts in the same chain.'* * uses and beauties of euclid, p. . a syllogism is a peculiar _form_ of expression, in which every argument may be stated. it consists of three propositions. . whoever have their heads cut off ought to be allowed to ask the reason why. . women have their heads cut off. . therefore women ought to be allowed to ask (politically) the reason why. this is an argument of mad. de stael, in allusion to the beheading of women in france, without allowing them any voice in making the laws which determine the offences for which they suffered. a syllogism is constructed upon the principle (known as the dictum of aristotle) that whatever is affirmed or denied universally of a whole class of things, may be affirmed or denied of anything comprehended in that class. thus the first proposition introduces the class of persons who have their heads cut off. of this class it is affirmed that they ought to be allowed to ask the reason why. but women are included in the class of persons who have their heads cut off, and consequently that may be affirmed of them which is affirmed of the whole class--that they should be allowed to ask the reason why. 'to prove an affirmative,' says mr. mill, 'the argument must admit of being stated in this form:-- all animals are mortal; all men | some men } are animals; socrates | therefore all men | some men } are mortal. socrates | 'to prove a negative, the argument must be capable of being expressed in this form:-- 'no one who is capable of self-control is necessarily vicious; all negroes | some negroes } are capable of self-control; mr. a.'s negro | therefore no negroes are | some negroes are not } necessarily vicious. mr. a.'s negro is not | 'although all ratiocination admits of being thrown into one or the other of these forms, and sometimes gains considerably by the transformation, both in clearness and in the obviousness of its consequence; there are, no doubt, cases in which the argument falls more naturally into one of the other three figures, and in which its conclusiveness is more apparent at the first glance in those figures, than when reduced into the first. thus, if the proposition were that pagans may be virtuous, and the evidence to prove it were the example of aristides; a syllogism in the third figure, aristides was virtuous, aristides was a pagan, therefore some pagan was virtuous, would be a more natural mode of stating the argument, and would carry conviction more instantly home, than the same ratiocination strained into the first figure, thus-- aristides was virtuous, some pagan was aristides, therefore some pagan was virtuous.' the best thing that can be said in favour of the syllogism, as an instrument of reasoning, is that it is a regular form to which every valid argument can be reduced; and may be accompanied by a rule, showing the validity of every argument in that form, and consequently the unsoundness of any apparent argument which cannot be reduced to it. this would be high praise if every 'valid argument' was a trusty one. but unfortunately 'the question respecting the validity of an argument is not whether the conclusion be _true_, but whether it _follows_ from the premises adduced.'* even this small advantage is purchased at a greater expense of tedium and trouble than the bulk of mankind are willing to pay, or able to pay if they were willing. * logic, vol. , pp. - . there is some reason to believe that the syllogistic form, as a _test_ of valid arguments, may be entirely dispensed with, if we can secure accuracy of data, and intelligibility in terms. it is not contended now that we discover new truths by the syllogism. the syllogism is allowed to be only a form of _stating_ a truth. example:-- no predacious animals are ruminant, the lion is predacious, therefore the lion is not ruminant. * whately's logic, anal. out. chap. , sec. . of course, if we know that no animal that lives by prey chews the cud, and know, also, that the lion lives by prey, we know that the lion does not chew the cud. this conclusion, as lord kames contends, and dr. whately admits, is not a truth _inferred_ from the fundamental premises, but _included_ in it. smart, whom mr. j. s. mill calls acute and often profound, remarks--'every one, as to the _mere_ act of reasoning, _reasons rightly_: we may reason from wrong premises, or mistake right ones; we may be unable to infer from proper ones; but from such premises as we do reason from, we reason _correctly_: for all premises contain their conclusion; and in knowing the premises, we therefore know the conclusion. the art wanted is one that will enable us to use language perspicuously in expressing our premises:' and he might have added--_direct us in selecting proper materials of which to make premises_. the strength and weakness of the syllogism as an instrument of reasoning will now be understood. whately remarks, that 'since all reasoning may be resolved into syllogisms, and since in a syllogism the premises do virtually assert the conclusion, it follows at once that no new truth can be elicited by any process of reasoning.'* we therefore no longer look to the syllogism to discover truth, its value is in stating it. in this sense it is worthy of all attention. it is the form of nature. * logic, p. . of such a syllogism as the one quoted-- no predacious animals are ruminant, the lion is predacious, therefore the lion is not ruminant. it has been insisted by some logicians that the genius required for its construction was _invention_. having made a general proposition like the first, we then have to invent or find out a middle term as the second--but if we bear in mind that the general affirmation of the first proposition relates to a class of (predacious animals in this case) objects which include the middle term, the necessity of invention is consequently dispensed with. we need only look well to what we have there. simplicity will be promoted by returning to our previous remark, viz.--that reasoning is asserting a proposition, and then showing why it is true--in other words, adducing the fact or facts, on which the assertion rests. in the logic given in 'chambers' information,' it is said--' in choosing your middle terms, or arguments to prove any question, always take such topics as are purest and least fallible, and which carry the greatest evidence and strength with them,' but it rather appears that we have not to invent a middle term, but only to look to the major premises, and find it included there. by methodical questioning any argument may be tested. thus, on any assertion being made, ask--why is the assertion true? in this manner, if an argument has truth in it, it may be elicited. in this manner you dig through assertions down to premises, and discover whether any ore of truth lies there. the value of the argument depends upon the final answer which reveals the premises or data of facts, upon which the conclusion rests. forms of speech, classification of propositions, figures of syllogisms, are of minor importance when you have once elicited the rough truth. the best test of an argument is the soundness of its data, and the simplest formula for drawing out and exhibiting such data, is of the greatest service in enabling us to judge of the validity thereof. tyranny, says cobbett, has no enemy so formidable as the pen, why? 'because the pen pursues tyranny both in life and beyond the grave.' how is this proved to be the most formidable enemy of tyranny? 'from the fact that tyranny has no enemy so formidable as that which assails not only its existence, but its reputation, which pursues it in life and beyond the grave.' such interrogatories and replies generate the expository syllogism. . tyranny has no enemy so formidable as that which assails not only its existence, but its reputation, which pursues it in life and beyond the grave. . the pen pursues tyranny in life and beyond the grave. . therefore, tyranny has no enemy so formidable as the pen. a syllogism is made up of collective and single facts. it is the process of reasoning, whereby we show that a single truth is proved by a collective one which contains it, or a less quantity is proved by a greater, or that an assertion is proved by an induction from a class of facts. from the class of the enemies of tyranny the pen is selected, and is proved, by passing in inductive review the whole class, to be the most formidable. the usual manner in which an argument is presented is called the entihymeme. thus:-- he is an industrious man, therefore he will acquire wealth. the first or major proposition is in this form suppressed. the syllogistic form would be this:-- every industrious man acquires wealth, he is an industrious man, therefore he will acquire wealth. but if we ask for the proof that every industrious man acquires wealth, we find the facts wanting--for the idle are often rich, and the diligent poor. the industrious _may_ acquire wealth, the chances are in their favour. again. we must cherish self-respect, because self-respect is the stay of virtue. the suppressed proposition is--'we must cherish whatever is the stay of virtue.' the whole syllogism then stands thus:-- we must cherish whatever is the stay of virtue, self-respect is the stay of virtue, therefore we must cherish self-respect. dilemma is derived from a greek word, and signifies twice an argument. it is an argument divided into several members, and infers of each part what is to be inferred of the whole. thus: either we shall live or die. if we live, we can only live happily by being virtuous; and if we die, we can only die happy by being virtuous; therefore, we ought always to be virtuous. in the dilemma, question one argument at a time, as in preceding cases. the sorites uses several middle terms by which the predicate of the last proposition is connected with the first subject. of this argument the well-known speech of themistocles is a specimen. 'my son,' said that eminent person, 'governs his mother, his mother governs me, i govern the athenians, the athenians govern greece, greece governs europe, and europe governs the world; therefore, my son governs the world.' in these instances, question each assertion, as there are as many acts of reasoning as intermediate propositions. the onus probandi, or burden of proof, is said to rest with him who would dispute any point in favour of a presumptive, or generally allowed truth. but manly logic holds no quibbling about who shall prove. whatever he asserts, the honest reasoner should be prompt to prove. chalmers, it is said, made morell known--but morell has written a synopsis of metaphysical philosophy that only needed to be known to be appreciated. if chalmers gave morell distinction, morell had previously earned it. from his work i extract the following passage, which passes in review the steps taken, marks the analytic point reached, and outlines the ground before us:--'different as were the minds of those two great men [bacon and descartes] in themselves, different as were their respective labours, and opposite as were, in many respects, the results at which they arrived, yet the writings of both were marked by one and the same great characteristic, namely, by the _spirit of method_. the most important works of bacon, it will be remembered, were the "instanratio magna," and the "novum organum;" those of descartes were his "dissertatio de methodo," and his "meditationes de prima philosophia," the fruitlessness of the ancient logic, as an instrument of discovery, had been abundantly proved by past experience, and the watchword which these two great thinkers of their age both uttered, and which has been ever since the guiding principle of all philosophy, was--analysis. bacon, who gave his attention chiefly to the direction and improvement of physical science, taught to analyse nature, while descartes, who aimed rather at grounding all human knowledge upon its ultimate principles, instructed how to analyse _thought_. all modern philosophy, therefore, whether it arise from the baconian or the cartesian point of view, bears upon it the broad outline of the analytic method. it matters not whether it be the outer or the inner world to which its investigations apply, in each case it teaches us to observe and analyse _facts_ to induce instances, and upon such observation and induction to ground our knowledge of laws and principles. in this alone consists the unity of modern science, and from this arises its broad distinction from that of the ancient world. every natural philosopher since bacon has grounded his success upon an induction of the facts of the outward world, and every metaphysician, since descartes, has progressed onwards in his department of knowledge by analysing the facts of our inward consciousness.'* * morell: modern philosophy, pp. - . chapter x. induction induction is an inference from many facts. induction is verification. just as in a syllogism we show that a part is contained in the whole, so in induction we show that a part is illustrated by the whole. it seems that every single fact contains many truths, but induction establishes their _universality_. a single brain contains all the truths of phrenology, a single stone includes the phenomena of gravitation, the temperance of a single individual exhibits the whole law of moderation, but we learn the universality of these truths by induction. every legal statute, says dr. johnson, is founded on induction. 'law is the science in which the greatest powers of understanding are applied to the greatest number of facts.' the _basis of all_ science is such an extensive induction of particulars as leads to general definitions and fundamental axioms, and furnishes the premises from which inferences may be deduced. inductive observation is the great instrument of discovering important truths. 'what are called the principles of human nature are learned from individual instances. it is the only possible way of learning them. * * when we reason from a general law or principle, we are in truth reasoning from a number of instances represented by it.'* * rationale of political representation, p. . a general election is an induction of the intelligence of the country represented by the members of parliament. the difference between democracy and monarchy is in one sense an affair of logic. where electors are limited in franchise, and candidates restricted by property qualification, the induction is partial, but where all can vote and many can be chosen from, the premises are more capacious and the inference sounder. dr. whately says, that 'in natural philosophy a _single instance_ is often accounted a _sufficient_ induction; e.g., having once ascertained that an individual magnet will attract iron, we are authorised to conclude that this property is universal.' 'the edinburgh reviewer of whewell's "history of the inductive sciences," observes that, "by the _accidental_ placing of a rhomb of calcareous spar, upon a book or line, bartholinus discovered the property of the double refraction of light. by _accidentally_ combining two rhombs in different positions, huygens discovered the polarisation of light. by _accidentally_ looking through a prism of the same substance, and turning it round, mains discovered the polarisation of light by reflection; and by placing thin chrystalline films between two similar prisms or rhombs, m. arago discovered the phenomena of polarised tints." 'to this mr. whewell, in his "philosophy of the inductive sciences," makes the following reply:--"but bartholinus could have seen no such consequence in the accident, if he had not previously had a clear conception of single refraction. a lady, in describing an optical experiment which had been shown her, said of her teacher, 'he told me to increase and diminish the angle of refraction: and, at last, i found that he only meant me to move my head up and down.' at any rate, till the lady had acquired a knowledge of the meaning which the technical terms convey, she could not have made bartholinus's discovery by means of this accident. suppose that huygens made the experiment alluded to, without design, what he really observed was that the images appeared and disappeared alternately as he turned the rhomb round. his success depended on his clearness of thought, which enabled him to perform the intellectual analysis which would never have occurred to most men, however often they had combined two rhombs in different positions. malus saw that in some positions the light reflected from the windows of the louvre became dim. another person would have attributed this to accident; he, however, considered the position of the prism, and the window; repeated the experiment often; and by virtue of the eminently distinct conceptions of space which he possessed, resolved the phenomenon into its geometrical conditions."* "if it were true, that the fall of an apple was the occasion of newton's pursuing that train of thought which led to the doctrine of universal gravitation, the habits and constitution of newton's intellect were the real source of this great event in the progress of knowledge."** "in whatever manner facts may be presented to the notice of a discoverer, they can never become the materials of exact knowledge, except they find his mind already provided with precise and suitable conceptions, by which they may be analysed and connected."'*** * whewell: phil. induct. sciences, vol. . pp. - . ** ibid, vol. , p. . *** see j. n. bailey's essays pp. - - . these admissions seem to me to prove that whenever a casual fact proves to us a new truth, it does so by its coincidence with previously known facts, and that the novelty of the occasion attracts all credit to itself, and we lose sight of the generalisation below--the fruitful soil of experience on which the new fact, like a seed, falls. we only recognise difference by comparison, and the comparison is an induction, however slender. monsieur de montmorine was recaptured and brought to the scaffold, through the trifling circumstance of some chicken bones being found near the door of his landlady--a woman too poor to indulge in such dainties.* the discovery of de montmorine was not, as at first sight appears, an inference from a single fact, but from an adjacent induction. it was a general truth, (known to the party who observed the bones) a truth inducted from a number of facts that poor people could not afford to luxuriate on chickens. it was, therefore, from this induction, inferred that some one of superior fortune must be living in that particular place. * chambers' miscellany of useful and entertaining tracts, no. : the story of lavaiette, p. the judicious care which the great fathers of science have exhibited in making their inferences, incontestably establishes their conviction of the danger of any other reasoning than that from inductions. lord brougham informs us, that what newton's principia is to science, locke's essay to metaphysics, demosthenes in oratory, and homer in poetry, cuvier's researches to our fossil osteology. but cuvier never attempted to draw any inferences until he had examined the _whole_ osteology of the living species. lord brougham remarks, that 'from examining a _single_ fragment of bone we infer that, in the wilds where we found it, there lived and ranged, some thousands of years ago, an animal of a peculiar kind.' this is a case in which the inference spoken of is arrived at in a way different from that apparently stated. we recognise in the 'fragment of bone' a link in a chain of facts constituting the basis of a well-known induction, which comparative anatomy has many times verified. it is important to distinguish well the grounds from which accurate inferences, such as these in the cases before us, have really been adduced, in order to ascertain the grounds from which we should reason generally. it will be found that solid reasoning can only proceed from general rules--i.e., inductions from facts. it will be found that the prime source of fallacy lies in reasoning from isolated facts. it is not to be denied that such reasoning is sometimes right, but it is to be remembered that it is right by accident, not by design. there is no science or certainty in it. it is hazard, not logic. this habit however, is very common. mr. mill says, that 'not only _may_ we reason from particulars to particulars, without passing through generals, but we perpetually do so reason. all our earliest inferences are of this nature. from the first dawn of intelligence we draw inferences, but years elapse before we learn the use of general language. the child, who, having burnt his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has never thought of the general maxim--fire burns. he knows from memory that he has been burnt, and on this evidence believes, when he sees a candle, that if he puts his fingers into the flame of it, he will be burnt again. he believes this in every case which happens to arise; but without looking, in each instance, beyond the present case. he is not generalising; he is inferring a particular from particulars. in the same way, also, brutes reason. there is little or no ground, for attributing to any of the lower animals the use of conventional signs, without which general propositions are impossible. but those animals profit by experience, and avoid what they have found to cause them pain, in the same manner, though not always with the same skill, as a human creature. not only the burnt child, but the burnt dog, dreads the fire. 'i believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. we are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect our observations into general maxims of human or external nature. when we conclude that some person will, on some given occasion, feel or act so and so, we sometimes judge from an enlarged consideration of the manner in which men in general, or men of some particular character, are accustomed to feel and act; but much oftener from having known the feelings and conduct of the same man in some previous instance, or from considering how we should feel or act ourselves. it is not only the village matron who, when called to a consultation upon the case of a neighbour's child, pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her lucy. we all, where we have no definite maxims to steer by, guide ourselves in the same way; and if we have an extensive experience, and retain its impressions strongly, we may acquire, in this manner, a very considerable power of accurate judgment, which we may be utterly incapable of justifying or of communicating to others. among the higher order of practical intellects, there have been many of whom it was remarked how admirably they suited their means to their ends, without being able to give any sufficient reasons for what they did and applied, or seemed to apply, recondite principles which they were wholly unable to state. this is a natural consequence of having a mind stored with appropriate particulars, and having been long accustomed to reason at once from these to fresh particulars, without practising the habit of stating to oneself or to others the corresponding general propositions. an old warrior, on a rapid glance at the outlines of the ground, is able at once to give the necessary orders for a skilful arrangement of his troops; though if he has received little theoretical instruction, and has seldom been called upon to answer to other people for his conduct, he may never have had in his mind a single general theorem respecting the relation between ground and array. but his experience of encampments, under circumstances more or less similar, has left a number of vivid, unexpressed, ungeneralised analogies in his mind, the most appropriate of which, instantly suggesting itself, determines him to a judicious arrangement. 'the skill of an uneducated person in the use of weapons, or of tools, is of a precisely similar nature. the savage who executes unerringly the exact throw which brings down his game, or his enemy, in the manner most suited to his purpose, under the operation of all the conditions necessarily involved, the weight and form of the weapon, the direction and distance of the object, the action of the wind, &c., owes this power to a long series of previous experiments, the results of which he certainly never framed into any verbal theorems or rules. it is the same in all extraordinary manual dexterity. not long ago a scotch manufacturer procured from england, at a high rate of wages, a working dyer, famous for producing very fine colours, with a view of teaching to his other workmen the same skill. the workman came; but his mode of proportioning the ingredients, in which lay the secret of the effects he produced, was by taking them up in handfuls while the common method was to weigh them. the manufacturer sought to make him turn his handling system into an equivalent weighing system, that the general principle of his peculiar mode of proceeding might be ascertained. this, however, the man found himself quite unable to do, and therefore could impart his skill to nobody. he had, from the individual cases of his own experience, established a connection in his mind between fine effects of colour, and tactual perceptions in handling his dyeing materials; and from these perceptions he could, in any particular cases, infer the means to be employed, and the effect which would be produced, but could not put others in possession of the grounds on which he proceeded, from having never generalised them in his own mind, or expressed them in language. 'almost every one knows lord mansfield's advice to a man of practical good sense, who, being appointed governor of a colony, had to preside in its court of justice, without previous judicial practice or legal education. the advice was to give his decision boldly, for it would probably be right; but never to venture on assigning reasons, for they would almost infallibly be wrong. in cases like this, which are of no uncommon occurrence, it would be absurd to suppose that the bad reason was the source of the good decision. lord mansfield knew that if any reason were assigned it would be necessarily an afterthought, the judge being _in fact_ guided by impressions from past experience, without the circuitous process of framing general principles from them, and that if he attempted to frame any such he would assuredly fail. lord mansfield, however, would not have doubted that a man of equal experience, who had also a mind stored with general propositions derived by legitimate induction from that experience, would have been greatly preferable as a judge, to one, however sagacious, who could not be trusted with the explanation and justification of his own judgments. the cases of able men performing wonderful things they know not how, are examples of the less civilised and most spontaneous form of the operations of superior minds it is a _defect in them_, and _often a source of errors_, not to have generalised as they went on; but generalisation is a help, the most important indeed of all helps, yet not an essential.'* * mill's logic, pp. - . in illustration of generalising from single instances, miss martineau gives this example:--'a raw chinese traveller in england was landed by a thames waterman who had a wooden leg. the stranger saw that the wooden leg was used to stand in the water with, while the other was high and dry. the apparent economy of the fact struck the chinese; he saw in it strong evidence of design, and wrote home that in england one-legged men are kept for watermen, to the saving of all injury to health, shoe, and stocking, from standing in the river.'* reasoning on insufficient data-- falls like an inverted cone, wanting its proper base to stand upon. samuel bailey has furnished, in one passage, both a clear illustration of the process, and the validity of an induction:--'whoever had witnessed the acts of a landlord to his tenants, of a schoolmaster to his pupils, of artizans towards their apprentices, of husbands towards their wives, on points where the power of the superior could not be contested, and where his personal gratification was incompatible with just conduct to the subordinate, would necessarily have formed in his own mind a species of general rule; and from this rule he might safely draw an inference as to what would be the conduct of a despot, seated on a throne, in the possession of unchecked authority; assisted too, as the inquirer would be, by that _indispensable and inestimable guide to the knowledge of mankind, an appeal to his own feelings_, in a variety of _analogous_ instances. 'we conclude, that a ruler with uncontrolled power will act the tyrant, not merely from the fact that caligula, or nero, or bonaparte did, but from a thousand facts attesting that men, in, every situation, use uncontrolled power in this way--just as we infer that all bodies tend to the centre of the earth, _not merely from the circumstance of an apple dropping from a tree, but from seeing the tendency in stones, water, animals, and all things within our observation_. the use of uncontrolled power, for the gratification of the possessor, without an equitable respect to others, is no more peculiar to monarchs, than a tendency to the earth is peculiar to apples. it may be useful to know that _monarchs_ act in this way, as it may be useful to know that apples drop to the ground; but it is much more useful to know that _men_ act in this manner. _an inference is safer when gathered from the widest induction.'_ * how to observe, p. . ** rationale of political representation. introduction, pp. - . the last sentence of this extract is abridged--but, as the reader will find upon reference, the sense of the author is faithfully rendered. it may be useful to observe that, though a few instances are insufficient to establish a theory, one may be sufficient to overturn a theory, fancifully or hypothetically supported, gibbon overturns the entertaining theory of rudbeck, an antiquarian of upsal, of profound learning and easy faith, who, by the dim light of legends and traditions, of conjectures and etymologies, sought to establish the antiquity of sweden over half the earth. gibbon annihilated this well laboured system of german antiquities, by a single fact too well attested to admit of any doubt, and of too decisive a nature to leave room for any reply--the fact that the germans, of the age of tacitus, were unacquainted with the use of letters. a circumstance fatal to their literary claims, urged by olaus rudbeck. in the chapter on 'facts' i have cautioned the reader against unquestioned data. this seems the place to remark that the unsuspected sources of error and unfriendliness have their rise in the criminal implicitness with which we listen to reports, and infer from rumours as from facts. these are the very little handles which move men and women to strange performances.'* all the plots of dramas and romances are founded on misunderstandings, which a little sagacity of action (such as a wise resolution not to be imposed upon would lead to) would commonly suffice to arrest the error at its birth. with regard to character we constantly infer from data, partial, limited, and doubtful. if most quarrelers were called into a court of inquiry to confess the real grounds from which they have arrived at certain conclusions with regard to their neighbours, and often with regard to their friends, they would be at once overwhelmed with a conviction of the weakness of which they have been guilty. upon analysing the miserable sources of opinions of which scandal and calumny are born, i have found it impossible to restrain astonishment at the imbecility of logical power men will sometimes be content to exhibit, where meanness prevails, malice incites, and passion governs. well might bacon exclaim--'doth any man doubt, that if there were taken out of men's minds, vain opinions, flattering hopes, false valuations, imaginations, and the like, but it would leave the minds of a number of men poor shrunken things?'** the wise rule is, never judge from appearances when facts can be had--never receive a report without challenging its foundation, nor adopt it without permission to give the authority. * cricket on the hearth. ** essay on truth. in all cases, in which you must judge from appearances and reason from conjectures, adopt the _fairest_ interpretation possible. on this principle, credit will sometimes be given where none is due--but in nine cases out of ten, justice will be done, for i am satisfied that there is more worth among men than wisdom, and that we do well much oftener than we reason well. we seldom need judge charitably, did we always endeavour to judge justly. but we make a virtue of our own errors, and we often affect to _condescend_ to pronounce an opinion, which it would be criminal to withhold. if ever i go to the herald's, office, the motto i will have emblazoned shall be this--justice is sufficient. could we only get justice in the world, we could afford to excuse it all its 'charity' of judgment, and its benevolence even of act. where should a man's reputation be safe from suspicion if not in the hands of his friend? it ought to be a principle of action with all men, never to judge a friend except out of his own mouth. 'there was a generous friend of mine once, who never would have judged me or any other man unheard.'* with the sublime intensity of one who felt the infinite value of private justice, has schiller delineated this spirit in the interview between octavio and his son max piccolomini. after a violent and visible struggle with his feelings--wrought upon by his father's endeavours to sow suspicions in his mind, and detach him from the service of his friend, wallenstein--max exclaims:-- * edward to mr. peerybing. i will procure me light a shorter way. farewell. octavio. where now? max. (to the duke.) if thou hast believed that i shall act a part in this thy play---- thou hast miscalculated on me grievously. my way must be straight on. true with the tongue, false with the heart--i may not, cannot be: nor can i suffer that a man should trust me-- as his friend trust me--and then lull my conscience with such low pleas as these:--"i ask him not-- he did it all at his own hazard--and my mouth has never lied to him."--no, no what a friend takes me for, that i must be. --i'll to the duke; ere yet this day is ended will i demand of him that he do save his good name from the world, and with one stride break through and rend this fine-spun web of yours. he can, he will!--i still am his believer. yet i'll not pledge myself, but that those letters may furnish you, perchance, with proofs against him. how far may not this tertsky have proceeded-- what may not he himself too have permitted himself to do, to snare the enemy, the laws of war excusing? nothing, save his own mouth shall convict him--nothing less! and face to face will i go question him. ay--this state-policy? o how i curse it! you will some time, with your state-policy, compel him to the measure; it may happen because ye are _determined_ that he is guilty, guilty ye'll make him. all retreat cut off, you close up every outlet, hem him in narrower and narrower, till at length ye force him-- yes, ye,--ye force him in his desperation, to set fire to his prison. father! father! that never can end well--it cannot--will not! deem of it what thou wilt; but pardon me, that i must bear me on in my own way. all must remain pure betwixt him and me; and, ere the day-light dawns, it must be known which i must lose--my father, or my friend.* * shiller's piccolomini, act , scene . had othello been thus honourable to desdemona, he would never have murdered her. incalculable is the evil we bring on ourselves and society, by supposing and surmising facts we ought resolutely to question. the motto of the garter-- evil be to him who evil thinks, ought to be, evil is to him who evil thinks. every man will be his own lawyer and his own doctor, and such is the perversity of human nature, he will also be his own _iago_, and feed himself with suspicions. nearly all tragedies hinge on this error. to avoid being the cause of misunderstanding to others, it is a good rule never to speak critically of others, except in their presence, or in print. when i am obliged to do this in conversation, with persons of unknown or doubtful exactitude, i take care to keep much below the truth in matters of censure, as anything of that kind may gain ten or twenty per cent, in carriage. when with men of just habits of interpretation, i pay them the highest compliment of friendship, and speak to them of others, without reserve. notorious are the contumelies put upon the cases of grievance presented from the people in the house of commons. nor is it altogether causeless. so prone are the ignorant to mistake their prejudices for facts, and ascribe to others as crimes what exists only in their own surmises, that most popular cases may be stripped of half their pretensions without injuring their truth. exaggeration is the vice of ignorance. half the speeches addressed to 'king mob' are hyperbolic. the sentiments of public meetings minister too often to the prevalent inflation. the people will be powerful when they learn to be exact--and not till then. the only mode of correcting this evil is to instil into the people the wise rule of burlamiqui. to reason, (that is, inductively) says this writer, is to calculate, and as it were draw up an account, after balancing all arguments, in order to see on which side the advantage lies. burlamiqui had law chiefly in view in his remark, but the rule is of immense application. a logician is a secretary or banker's clerk, who keeps an account between truth and error. when a lady once consulted dr. johnson on the degree of turpitude to be attached to her son's robbing an orchard--'madam,' said johnson, 'it all depends upon the weight of the boy. i remember my schoolfellow, davy garrick, who was always a little fellow, robbing a dozen orchards with impunity, but the very first time i climbed up an apple tree, for i was always a heavy boy, the bough broke with me, and it was called a judgment. i suppose that is why justice is represented with a pair of scales.' this may not be the precise reason why justice has a pair of scales, but the point goes to the root of the matter. without weighing there can be neither justice nor fair induction. in illustration of these views mr. mill has some able remarks:--'in proportion to any person's deficiency of knowledge and mental cultivation, is generally his inability to discriminate between his inferences and the perceptions on which they were grounded. many a marvellous tale many a scandalous anecdote, owes its origin to this incapacity. the narrater relates, not what he saw or heard, but the impression which he derived from what he saw or heard, and of which perhaps the greater part consisted of inference, though the whole is related not as inference but as matter-of-fact. the difficulty of inducing witnesses to restrain, within any moderate limits, the intermixture of their inferences with the narrative of their perceptions, is well known to experienced cross-examiners; and still more is this the case when ignorant persons attempt to describe any natural phenomenon. "the simplest narrative," says dugald stewart, "of the most illiterate observer involves more or less of hypothesis nay, in general, it will be found that, in proportion to his ignorance, the greater is the number of conjectural principle involved in his statements. a village apothecary (and, if possible, in a still greater degree, an experienced nurse) is seldom able to describe; the plainest case, without employing a phraseology of which every word is a theory; whereas a simple and genuine specification of the phenomena which mark a particular disease--a specification unsophisticated by fancy, or by preconceived opinions, may be regarded as unequivocal evidence of a mind trained by long and successful study to the most difficult of all arts, that of the faithful _interpretation_ of nature."'* * logic, pp. - , vol. . it is in judgments formed, in reprehensible indifference to the actual facts of the case, that party rancour and the proverbial injustice of popular political opinion take their rise. a useful caution on this head is pronounced by lord brougham in his sketch of the life of lord wellesley:--'how often do we see,' observes his lordship, 'vehement: and unceasing; attacks made upon a minister or a statesman, perhaps not in the public service, for something which he does not choose to defend or explain, resting his claims to the confidence of his countrymen upon his past exertions and his known character. yet these assaults are unremittingly made upon him, and the people believe that so much noise could not be stirred up without something to authorise it. sometimes the objects of the calumny are silent from disdain; sometimes from knowing that the base propagators of it will only return to their slander the more eagerly alter their conviction of falsehood; but sometimes, also, the silencer may be owing to official reserve, of which we see a most remarkable instance in the ease of lord wellesly.' not only are enemies of the people afforded a justification for their opposition by wrongful judgment pronounced upon them, but the friends of the people often pass over to the other side through the same cause. when a leader of the people first comes in personal contact with the opposite party, and becomes acquainted with merits of feeling and judgment which he had as it were pledged himself to deny, and indeed achieved himself a position by disbelieving in, he becomes ashamed of the injustice exacted from him by his inexorable adherents, and forsakes his party when he should only forsake its errors. the case of barnave, in the first french revolution, is a memorable instance of this. on lesser theatres i have seen many instances of this kind of conversion; such changes have always been ascribed to venality, yet they are men of generous instincts who are thus overcome--but they want logical strength, and cannot correct themselves without falling. it is a wise rule in conversation, never to guess at meanings. when, an observation is made, capable of affording two inferences, at once put the question which shall elicit the meaning intended. conversation is held to no purpose unless explicitness comes out of it. innumerable are the errors that arise through letting remarks pass, of which we only _suppose_ we know the purport. this is a fruitful source of misunderstanding. when in scotland i was much instructed by the intellectual characteristics of the people. the scotch are essentially a reflective people. the english conceive doubts, but the scotch put them into queries. before i had been in the country many hours i was struck by the inductive habits of the people. a very old and illiterate woman, to whom i put an indefinite question, eyed me deliberately from head to foot before she gave me an answer. not in rudeness did she gaze, so much as in inquiry as to what could be my object. i spent more than a week in inquiring at places, where apartments were to be let, by which i acquired profitable acquaintance with the people. upon asking the terms of apartments, i was met, in all cases, by several preliminary questions, as for whom were they? what number of persons? what station, habits, and probable stay? then i received the precise answer required. it did not seem to me that they were answering one question by asking another, as is sometimes said of the scotch--but by a happy and wise presence of mind they asked, as all should do, at many questions as were required to complete the data of the specific answer they were called upon to give. a wise practice is followed in courts of law. no judge pronounces an opinion on a hypothetical case. what he would do? or what would be the judgment of the law, suppose a certain case should arise?--are questions he never condescends to answer. 'bring the plaintiff into court, let the evidence be taken, and then we will decide. we sit here to judge actual, not suppositious cases.' such would be the reply. people out of court might profit by the example. i remember one striking instance of the pernicious effects of surmise. some years ago i took part in a fraternal demonstration at highbury barn. the assembly was numerous, and composed of persons of all nations and all parties. the celebration was avowedly one of fraternity. the tone of the meeting reflected its object. pacific words were on every tongue, and harmony reigned up till eleven o'clock. at that hour monsieur chillman asked me if some steps could not be taken to annualize the meeting, and he requested me to prepare and propose a resolution to that effect. monsieur chillman, thinking the resolution ought to come from an englishman, strongly urged me to move it. i, thinking it too important to emanate from a young man, looked about for a person of experience and known discretion to introduce it. after several had declined, mr. hetherington undertook it. the english politicians were composed of two parties, the friends of mr. o'connor, and the members of the national hall. at that time they were pleased to be the antipodes of each other. no sooner had mr. hetherington spoken, he being the friend of mr. lovett, than his motion was supposed to come from mr. lovett's party, though they were utterly ignorant of its origination. clamour's hundred tongues were loosened. slumbering differences were awakened. suspicion spread like an infection. fraternity perished of the contagion. twenty amendments were proposed, and it was not till midnight, and then in a storm indescribably contradictory of the meeting's whole purport, that a common understanding was come to. had the least inquiry been made by the objecting party, previously to dissenting, they would have found that the suspicious proposition originated with one of themselves. but assuming premises, they inferred from conjecture instead of fact, and raised disastrous doubts as to the ability of that assembly for domestic or international fraternisation. the use and abuse of authority is a subject worthy of the young logician's serious attention. many great writers like bacon, through policy--burke through position, or shakspere through versatility of genius, have written on both sides of important questions. such men, taken piece-meal, may be quoted by the most opposite parties in favour of the most opposite opinions. unless there is time to make a broad induction from their writings, showing, by weighty, quantitive evidence, the side to which they leaned, better not quote them as _authorities_ at all, but give what expresses your own views on your own responsibility--indeed, in _all_ cases, the quoter ought to stand prepared, if possible, to justify all he cites from another in argument. 'there is perhaps something weak and servile in our wishing to rely on, or draw assistance from, ancient opinions. reason ought not, like vanity, to adorn herself with old parchments, and the display of a genealogical tree; more dignified in her proceedings, she ought to derive everything from herself; she should disregard past times, and be, if i may use the phrase, the contemporary of all ages.'* quote others as grotius did: not as judges from whose decision there is no appeal, but as witnesses whose conspiring testimony confirms the view taken. * necker. analogy has frequently been confounded with induction. analogy signifies reasoning from resemblances subsisting between phenomena--induction, reasoning from the sameness of phenomena. the phenomena affording an induction of a law of nature must be obvious, uniform, and universal. the rules to be observed in deducing general principles are, that the case be true and the facts universal. on this subject, as exhibiting the clearest results arrived at, i transcribe a passage from mill: 'there is no word which is used more loosely, or in a greater variety of senses, than analogy. it sometimes stands for arguments which may be examples of the most rigid induction. archbishop whately, for instance, following ferguson and other writers, defines analogy conformably to its primitive acceptation, that which was given to it by mathematicians, resemblance of relations. in this sense, when a country which has sent out colonies is termed the mother country, the expression is analogical, signifying that the colonies of a country stand in the same _relation_ to her in which children stand to their parents. and if any inference be drawn from this resemblance of relations, as, for instance, that the same obedience or affection is due from colonies to the mother country which is due from children to a parent, this is called reasoning by analogy. or if it be argued that a nation is most beneficially governed by an assembly elected by the people, from the admitted fact that other associations for a common purpose, such as joint stock companies, are best managed by a committee chosen by the parties interested; this, too, is an argument from analogy in the preceding sense, because its foundation is, not that a nation is like a joint stock company, or parliament like a board of directors, but that parliament stands in the same _relation_ to the nation in which a board of directors stands to a joint stock company. now, in an argument of this nature, there is no inherent inferiority of conclusiveness like other arguments from resemblance, it may amount to nothing, or it may be a perfect and conclusive induction. the circumstance in which the two cases resemble, may be capable of: being shown to be the _matereal_ circumstance; to be that on which all the consequences, necessary to be taken into account in the particular discussion, depend. in the case in question, the resemblance is one of relation; the _fundamentum relationis_ being the management, by a few persons, of affairs in which a much greater number are interested along with them. now, some may contend that this circumstance which is common to the two cases, and the various consequences which follow from it, have the chief share in determining all those effects which make up what we term good or bad administration. if they can establish this, their argument has the force of a rigid induction: if they cannot, they are said to have failed in proving the analogy between the two cases, a mode of speech which implies that when the analogy can be proved, the argument founded upon it cannot be resisted.'* * logic, pp. - , vol. . 'many of the most splendid and important discoveries in this science were the result of analogical reasonings. it was from this source that dr. priestley proved the compound nature of atmospheric air; and it is related that it was in consequence of hints which he had given, when on a visit to paris, to lavoisier, founded entirely upon analogical conjectures, that the latter philosopher was induced to commence experiments, with the view of proving the compound nature of water, and of reducing it to its constituent elements. indeed the whole history of this very important and useful department of human knowledge exhibits very striking and incontestable proofs how much of the art owed its existence to mere hints and conjectures, founded, in many cases, upon very slight resemblances or analogies.*. the chief province of analogy is confined to that of suggestion. analogies are the great hinters of experiments. they illustrate an argument, but do not establish it. they are probabilities, not proofs. hence lord brougham in one place exclaims:--'i have a dread, at least a suspicion, of all analogies, and never more than when on the slippery heights of an obscure subject; when we are, as it were, _inter apices_ of a metaphysical argument, and feeling, perhaps groping, our way in the dark, or among the clouds. i then regard analogy as a dangerous light, a treacherous _ignii fatuus_.'** a striking instance of the fallacy of analogy is afforded in the experiments of professor matteuoci, which seem to prove that though the analogies between electricity and nervous substance are nearly perfect, yet they are two distinct agencies.*** * blakey's logic, pp. - . ** pal. illus. vol. . *** see zoist no. , p. . chapter xi. detection of fallacies we hope to be able to save students from the fate of diodorus, (a great logician, who died in his school through shame at being, unable to resolve a quibble propounded by stilno)--not by hardening, but by enlightening them. though we bring neither mood nor figure wherewith to test the presence of error, we are not without the hope of qualifying the student for its discovery. it has been confessed from the throne of logic that, 'after all, in the practical detection of each individual fallacy, _much must depend on natural and acquired acuteness_: nor can any rules be given, the mere learning of which will enable us to _apply_ them with mechanical certainty and readiness.' bulwer, in remarking that error is a view of _some_ facts instead of a survey of _all_, indicated the key to logical fallacy. error lies principally in defective premises. sophistry in science is referable to incomplete analysis of nature, of systems--to artificial arrangements--to _supposing_ qualities, to _assuming_ principles, to false inductions from imperfect demonstration. dickens, in 'nicholas nickleby,' gives the case of a certain lady, who, because she knew _one_ young milliner, who retained red cheeks and did not die of consumption, was immovably of opinion that all representations of the injurious effect of such sedentary occupation were false. it is ever so with the vulgar. some one case has come under their notice, and it is in vain that you appeal to a chain of facts. they know nothing of induction--they know one case to the contrary, and that is enough. this error is the source of vulgar prejudice. once teach men that truth does not lie in a single instance, but in a calculation in a balance of probabilities, and you rationalise them. 'the chapter of accidents [or single instances] is the bible of the fool--it supplies him with a text against everything great, or good, or wise.'* * times. where others toil with philosophic force, their nimble nonsense takes a shorter course, flings at your head convictions in the lump, and gains' remote conclusions with a jump.--cowper, the first source of error is defective induction. we easily arrive at this point of examination by the questions we have proposed for use in the test of syllogism. formerly, one syllogism was required to be defeated by another--we now attack a fallacy by induction. no false syllogism, says biennan, can resist the inductive process of sifting particulars. i do not like thee. dr. fell, the reason why, i cannot tell-- but this i know, and know full well, i do not like thee, dr. fell. this kind of thing will not do. induction pursues the reasoner with an eternal _why_. a clear because to a clear why, is a demand that is never remitted in sound logic. lord melbourne, in giving his reason for his religion in the house of lords, said it was the religion of his forefathers and that of his country, _therefore_, he would support the church. (cheers from the opposition benches.) the brahmin and mussulman give the same reason for theirs. a logician in facts would have said, i hold and support my religion because it is _true_. what the standard of physical certainty is to facts, what axioms are to science, such is induction to syllogisms--it is the test of their correctness. dr. whately exhibits the following instance of a regularly expressed syllogism:-- every dispensation of providence is beneficial: afflictions are dispensations of providence, therefore, they are beneficial. every applicable rule of dr. whately's logic is, of course, applied here--it is true in mood and figure, and yet the argument is fallacious. a fallacy is defined as 'an ingenious mixture of truth and falsehood, so entangled as to be intimately blended--that the falsehood is, in chemical phrase, _held in solution_: one drop of sound logic is that test which immediately disunites them, makes the foreign substance visible, and precipitates it to the bottom.'* but whence is to come 'this drop of sound logic?' not from the doctor's _elements,_ they have sent forth the fallacy. but touch it with the talisman of facts and; the error will appear. * whately's logic, anal. out., chap. , stc. . what facts support the assertion that afflictions are dispensations of providence?' the simple question is fatal to the argument. can such a proposition have facts for its support? ignorance, congregating in narrow courts, and laziness, accumulating filth, generate sickness and affliction. are these the dispensations of providence, or the dispensations of folly and crime? to ascribe them to providence is virtually to allow ignorance and laziness to step into the throne of god, and call upon men to believe in _their_ beneficent dispensations. dr. watts, another writer on logic, set the christian congregations of england to sing the same species of fallacy:--- "diseases are the servants, lord, they come at thy command; i'll not attempt a murm'ring word, against thy chast'ning hand." according to this lyrical logician, whenever wise precautions arrest the progress of pestilence, or the physician's skill subdues disease, jehovah is robbed of a servant. by such an argument, humanity is made to be in rebellion against heaven, and our medical colleges are in antagonism with deity, and the recent appointment, by the russell government, of a sanatory commission, was high blasphemy. it is the degradation of language to employ it to such a purpose, and logic needs revising to save us from publishing such puerility in the name of learning and of reason. it must have been logic of this kind that induced a strong-thoughted woman to hazard the bold but tenable conjecture, that 'if an argument has truth in it, less than a philosopher will see it--and if it has not, less than a logician will refute it.'* * a few days in athens, by frances wright. r. g. latham, m.d., in his 'first outlines of logic applied to grammar and etymology,' has introduced the particular instance of the syllogism on providence here cited from whately. it would be no difficult task to present other instances of the same species of polemical fallacy from dr. whately and other writers on logic, did it comport with the rule i have chosen for observance. i give these cases chiefly to show how extensively and obtrusively they are introduced. 'we have,' says mr. mill, 'five distinguishable classes of fallacy, which may to expressed in the following synoptic table:-- [illustration: mill's fallacy table] it was the boast of archimedes, that if any one would find him a fulcrum, on which to rest a prop, he would raise the world, but this was mere assertion unsupported by facts, for if the fulcrum had been found him, archimedes could not have performed his promise. this has been proved by ferguson, who has demonstrated that if archimedes could have moved with the swiftness of a cannon ball-- miles every hour--it would have taken him just , , , , of years to have-raised the world one inch. bulwer remarks, 'critics have said, what a fine idea of archimedes! but how much finer is the fact that refutes it. _one of the sublimest things in the world is plain truth_.' all motion generates warmth, shaking (with cold) is motion, _ergo_, shaking with cold generates warmth. we look, in this case, to the facts on which the first proposition rests, and find the assertion too general. to one who said that none were happy who were not above opinion, a spartan replied, 'then none are happy but knaves and robbers.' mr. goodrich, the original peter farley gives, in his 'fireside education,' an instance to this effect of two boys arguing on the division of their beds. william exclaims, 'you take more than your share of the bed, james.' james answers, 'i only take half the bed.' william replies, 'true, but you take your half out of the middle, and i am obliged to lie on both sides to get my half.' innumerable sophisms are suffered to pass in consequence of some brilliancy of position which, dazzles us and prevents our seeing that they are wide of the' mark of reason. an instance occurs in bulwer--who says, 'helvetius erred upon education--but his dogma has been beneficial.' probably so--but not so beneficial as the truth would have been. many persons have argued from such an instance, that error is useful. dickens, in those incidental observations of striking good sense strewed up and down his writings, says, in the 'cricket on the hearth:'--'these remarks (of mrs. fielding) were quite unanswerable: which is the happy property of all remarks that are _sufficiently wide of the purpose_.' of the refutation of such remarks he has presented an able instance in 'martin chuzzlewit': 'bless my soul, westlock,' says pinch, is it nothing to see pecksniff moved to that extent and know one's self to be the cause? and did you not hear him say that he could have shed his blood for me? 'do you want any blood shed for you?' returned westlock with considerable irritation. 'does he shed anything for you that you _do_ want? does he shed employment for you, instruction for you pocket money for you? does he even shed legs of mutton for you in any decent proportion to potatoes and garden stuff?' chapter xii. scepticism man has been called the plaything of chance, but there is no logic more close and inflexible than that of human life: all is entwined together; and for him who is able to disentangle the premises and patiently await the conclusion it is the most correct of syllogisms.--jules sandau: people's journal, no. . 'to quote authors,' says harris, in his preface to his hermes,' 'who have lived in various ages, and in distant countries; some in the full maturity of grecian and roman literature; some in its declension; and others in periods still more barbarous and depraved; may afford, perhaps, no unpleasing speculation, to see how the same reason has at all times prevailed; how there is one truth like one sun, that has enlightened human intelligence through every age, and saved it from the darkness both of sophistry and error.' this is the assurance which right reason will ever impart. underneath all the change after which we pant, amid all the variety which surrounds us, and seem the very aliment of our nature, lies the instinct after the permanent. it is the province of sound logic to guarantee this in conclusion. the novelty, change, fluctuation, which scientific discovery has brought, and will yet bring, into the formerly settled worlds of opinion and social condition, will unsettle men's minds, and pave the way to an age of scepticism. sound logic is necessary to provide that this doubt is transitional and not ultimate. scepticism is of two kinds, that of pyrrho, and that of examination. the followers of pyrrho, it is said, made doubting a profession, until at last they doubted whether they did doubt. this is the scepticism of the scorner and trifler. he did not know that he did not know it, and if he did know it it was more than he knew. this is as far as the philosopher, of this school can go. dickens has drawn the portrait of these, logicians in mr. tigg:-- 'when a man like slyme,' said mr. tigg, 'is detained for such a thing as a bill' i reject the superstition of ages, and believe nothing. i don't even believe that i don't believe, curse me if i do.' hood is ironical on the professors of uncertainty. 'on a certain day of a certain year, certain officers went, on certain information, to a certain court, in a certain city, to take up a certain italian for a certain crime. what gross fools are they who say there is nothing certain in this world.' but scepticism is not capable of disturbing the well-grounded repose of the wise; for when the sceptic thinks he has involved everything in doubt, everything is still left in as much certainty as his scepticism. in the great maze of conflicting opinion, it matters little that we are cautioned that reason is not all-sufficient--it is the best sufficiency we have. if reason will not serve us well, will anything serve us better? bishop berkeley may demonstrate that we are not sure of matter's existence--but are we more sure of any thing else? we are not thus to be cajoled. but it is right to say that mr. j. s. mill contends that berkeley has been misunderstood--but if he did argue, as popularly believed, to such argument, the answer of byron is sufficient-- when berkeley said there was no matter, it was no matter what he said. if all is delusion, the delusion is very orderly--it observes regular laws, and we proceed in logical method to inform each other, how the delusion of things appears to our understandings or affects our fortunes. where nothing is, and all things seem, and we the shadows of a dream, we discuss the seemings with the same gravity as realities.' if a man seems to do wrong, and i seem to prevent him, and the wrong, therefore, seems not to be done, i am satisfied. the 'wise considerate scepticism' of inquiry has been well expressed by emerson, in his recent lecture on montaigne.--'who shall forbid a wise scepticism, seeing that there is no practical question on which anything more than a proximate solution is to be had? marriage itself is an open question: those "out" wish to be "in:" those "in" to be "out." the state. with all its obvious advantages, nobody loves it. is it; otherwise with the church? shall the young man enter trade or a profession without being vitiated? shall he stay on shore or put out to sea? there is much to be said on both sides. then there is competition and the attractions of the co-operative system. the labourer has a poor hut, is without knowledge, virtue, civilisation. if: we say, "let us have culture," the expression awakens a new indisposition; for culture destroys spontaneous and hearty unencumbered action. let us have a robust manly life; let us have to do with realities, not with shadowy ghosts. now this precisely is the right ground of the sceptic; not of unbelief, denying or doubting--least of all of scoffing and profligate jeering at what is stable and good. he is _the considerer_. he has, too many enemies around him to wish to be his own. the position of the sceptic is one taken up for defence; as we build a house not too high or too low; under the wind, but out of the dust. for him the spartan vigour is too-austere. st. john too thin and aerial. the wise sceptic avoids to be fooled by any extreme; he wishes to, see the game. he wishes to see all things, but mainly men. really our life in this world not of so easy interpretation as preachers and school-books are accustomed to describe it.' these have not so efficiently solved the problem, that the sceptic should yield himself contentedly to their interpretation. true, he does not wish to speak harshly of what is best in us,--to turn himself into a "devil's attorney." but he points out the room there is for doubt;--the power of moods;--the power of complexion, and so forth. shall we, then, because good-nature inclines us to virtue's side, smoothly cry: "there are no doubts!"--and lie for the right? we ask whether life is to be led in a brave or a cowardly way: whether the satisfaction of our doubts be not essential to all manliness: whether the name of virtue is to be a barrier to that which is virtue? the sceptic wants truth, wants to have things made plain to him, and has a right to be convinced in his own way. in such scepticism there is no malignity; it is honest, and does not hinder his being convinced; and this hard-headed man, once convinced will prove a giant in defence of his faith. the true and final answer in which all scepticism is lost is the moral sentiment: that never forfeits the supremacy. it is the drop that balances the universe.' science and logic have so far advanced as to abridge the field of doubtful questions. when syllogism answered syllogism, uncertainty reigned absolute--but now that the appeal is to facts, we can, wherever facts can be had, weigh or number them, and decide on one side or the other. when ali pacha was at janina, the case of a poor woman, who accused a man of the theft of all her property, was brought before him; but the plaintiff having no witnesses, the case was discharged, as the other asserted his innocence, and insisted as a proof, that he had not a farthing in the world. on their leaving his presence, ali ordered both to be weighed, and then released them without further notice. a fortnight afterwards, he commanded both into his presence, and again weighed them; the accuser had lost as much as the defendant had gained in weight. the thing spoke for itself, and ali decided that the accusation was just. ali pacha was the burlamiqui of justice. induction, too, has its scales, and seldom leaves us in doubt when it gets truth and falsehood in them. scepticism is now happily restricted to those questions resting on conjectures, and which do not pertain to the practical affairs of this life. on matter-of-fact questions, only the weak are perplexed. after men have been in deliberation till the time of action approach, if it be not then manifest what is best to be done, it is a sign the difference of motives the one way and the other is not great; therefore, not to resolve then is to lose the occasion by weighing of trifles, which is pusillanimity. quaint old bunyan tells us, that when he had completed his 'pilgrim's progress' he took the opinions of various friends on the propriety of publishing it. some said 'john, do;' others 'john, don't.' but solid old john was not to be thus confounded. 'then i will print it,' said he, 'and thus the case decide.' to this good sense the public owe that immortal dream. in the great field of physical investigation, science has conquered doubt. 'contingency and versimilitude are the offspring of human ignorance, and, with an intellect of the highest order, cannot be supposed to have any existence.'* *edinburgh review, september , article probabilities 'probability,' says laplace,' has reference partly to our ignorance, and partly to our knowledge.' 'chance,' observes mr. mill, 'is usually spoken of in direct antithesis to _law_; whatever (it is supposed) cannot be ascribed to law, if attributed to chance. it is, however, certain, that whatever happens is the result of some law; is an effect of causes, and could have been predicted from a knowledge of the existence of those causes, and from their laws. if i turn up a particular card, that is a consequence of its place in the pack. its place in the pack was a consequence of the manner in which the cards were shuffled, or of the order in which they were played in the last game; which, again, were the effects of prior causes. at every stage, if we had possessed an accurate knowledge of the causes in existence, it would have been abstractedly possible to foretell the effect.'* 'in the domain of morals, too, a certainty, not dreamed of in past times, now prevails. however much man, as an individual, may be an enigma, in the aggregate he is a mathematical problem.'** in the great world of opinion it is the duty of honest reasoners to endeavour to find out the truth, and take sides, undeterred by the philosophical frivolity now growing fashionable. if men are silent concerning objects and principles, it is said they have none, and it is impatiently asked 'where is their bond of union?' and no sooner is it explained than they are told 'it is very unphilosophical to think of setting up a creed.' where the alternatives are thus put against them they should take their own course. creeds are the necessary exponents of conviction. the creedless philosopher is out on the sea of opinion, without compass or chart. to bind yourself for the future to present opinions is doubtless unwise, but he who has inquired to any purpose has come to some conclusion, affirmative, negative, or neutral; and it is the province of a creed to avow the actual result, and the consequent; conduct intended to be followed. it is the vice of free thinking that it spreads universal uncertainty, and assumes right and wrong to be so protean that no man can tell one hour what opinion he shall hold the next. logic should correct this unsatisfactory extreme, and extirpate the tiresome race whom shelley described in peter bell:-- to peter's view, all seems one hue; he is no whig, he is no tory; no deist and no christian he-- but is so subtle, that to be nothing is all his glory** * logic, pp. - , vol. ** vestiges. chapter xiii. intellectual daring freedom has been hunted through the world, and is ever exposed to insult and injury. it is crushed by conquest; frowned from courts; expelled from colleges; scorned out of society; flogged in schools; and anathematised in churches. mind is her last asylum; and if freedom quail there, what becomes of the hope of the world, or the worth of human nature?--w. j. fox's lectures to the working classes, part , p. . we should be prepared to dare all things for truth. if the 'very hopes of man, the thoughts of his heart, the religion of nations, the manners and morals of mankind, are all at the mercy of a new generalisation,' we should be prepared to risk them. if we must choose between truth and repose, we ought not to hesitate. there is danger in having the truth--philosophers are obliged to conceal it. mankind vaunt their love of truth, but they are not to be trusted. from interest or ignorance they always persecute, and often kill, the discoverer. still the pursuit of truth is a _duty_, and we must find consolation in the heroic reflection of burke, that _in all exertions of duty there it something to be hazarded_. but intellectual daring will never be common while it is so generally believed to be criminal. we will, therefore, quote some considerations touching the rightfulness of inquiry. without inquiry it is impossible for us to know whether our opinions are true or false, and various are the pretences employed for declining investigation: frequently they are masked under vague and metaphorical phrases: "inquiry implies the weighing of evidence, and might lead to doubt and perplexity"--"to search into a subject might shake the settled convictions of the understanding"--to examine opposite arguments, and contradictory opinions, might contaminate the mind with false views. 'every one who alleges pretexts like these for declining inquiry, must obviously begin by assuming that his own opinions are unerringly in the right. nothing could justify a man for declining the investigation of a subject involving important opinions, but the possession of an understanding free from liability of error. not gifted with infallibility, in what way, except by diligent inquiry, can he obtain any assurance that he is not pursuing a course of injurious action? if he holds any opinion, he must have acquired it either by examination, by instillation, rote, or some other process. on the supposition that he has acquired it by proper examination, the duty on which i am now insisting has been discharged, and the matter is at an end--but if he has acquired it in any other manner, the mere plea, that his mind might become unsettled, can be no argument against the duty of investigation. for anything he can allege to the contrary, his present opinions are wrong--and, in that case, the disturbance of his blind convictions, instead of being an evil, is an essential step towards arriving at the truth. 'it may possibly be assigned, as a further reason for his declining inquiry, that he may come to some fallacy which he cannot surmount, although convinced of its character. if he is convinced of its character, he must either have grounds for that conviction or not. if he has grounds, let him examine them, draw them out, try if they are valid, and then the fallacy will stand exposed. if he has no grounds for suspecting a fallacy, what an irrational conclusion he confesses himself to have arrived at! but perhaps he will reply--he may be unable to solve the difficulty; his mind may become perplexed, and the issue may prove, after all, that it would have been much better had he remained in his former strong, though unenlightened, conviction. why better? if he is in perplexity let him read, think, consult the learned and the wise, and in the end he will probably reach a definite opinion on one side or the other. but if he should still remain in doubt, where is the harm? or rather, why is it not to be considered a good? the subject is evidently one which admits strong probabilities on opposite sides. doubt is therefore the proper sentiment for the occasion--it is the result of the best exercise of the faculties--and either positively to believe, or positively to disbelieve, would imply an erroneous appreciation of evidence. in the minds of some people a strong prejudice appears to exist against that state of the understanding which is termed doubt. a little reflection, however, will convince any one that on certain subjects "doubt" is as appropriate a state of the reasoning faculties as belief or disbelief on others. there are doctrines, propositions, facts, supported and opposed by every degree of evidence, and amongst them by that degree of evidence of which the proper effect is to leave the understanding in an equipoise between two conclusions. in these cages "doubt" is the appropriate result, which there can be no reason to shrink from or lament. but it may be further urged, that inquiry might contaminate the understanding with false views--and, therefore, it is wise and laudable to abstain from it. 'we can comprehend what is meant by contaminating a man's habits or disposition, or even imagination. but there is no analogy on these points in reference to the understanding. there is contamination, there is evil, in preposterous and obscene images crowding before the intellectual vision, notwithstanding a full and distinct perception of their character--but there is no contamination, no evil, in a thousand false arguments coming before the understanding, if their quality is clearly discerned. the only possible evil in this case is mistaking false for true--but the man who shrinks from investigation lest he should mistake false for true, can have no reason for supposing himself free from that delusion in his actual opinions. besides these objections to inquiry, there are other prejudices of a similar character, forming serious impediments to the attainment of truth. 'one of these is a _fear that we may search too far, and become chargeable with presumption in prying into things we ought not to know_. a few words will suffice to prove that nothing can be more irrational and absurd. we have already shown that true opinions are conducive to the welfare of mankind--and the prosecution of inquiry is therefore a process from which we have everything to hope and nothing to fear, and to which there are no limits but such as the nature of our own faculties pre scribes. 'a second prejudice--that _we may contract guilt, if, in the course of our researches, we miss the right conclusion, and had therefore better let inquiry alone_--is still more influential in preventing those investigations which it is our duty to make. as our opinions on any subject are not voluntary acts, but involuntary effects, in whatever conclusions our researches terminate they can involve us in no culpability. all that we have to take care of is, to bestow on every subject an adequate and impartial attention. having done this, we have discharged our duty; and it would be irrational and unmanly to entertain any apprehension for the result. 'in fact, there is the grossest inconsistency in the prejudice now under consideration. if we may contract guilt by searching after truth, wo may equally do so by remaining in our present state the reason alleged in the prejudice itself, and the only reason which can be assigned with any plausibility, why we may commit an offence by embarking in any inquiry, is that we may, by so doing, miss the right conclusion, or, in other words, fall into error--for no one would seriously contend that we incur any moral culpability by an investigation which conducts us to the truth. but it is obvious that we may equally miss the right conclusion by remaining in our actual opinions. it is, then, incumbent on us to ascertain whether we are committing an offence by remaining in them--in other words, it is necessary to examine whether those opinions are true. thus the reasons assigned for not inquiring, lead to the conclusion that it is necessary to inquire. 'the third prejudice is that acquiescence in received opinions, or forbearing to think for ourselves, shows a degree of humility highly proper and commendable--if closely examined will be found usually to evince nothing but a great degree of indolent presumption, or intellectual cowardice. there is often, in truth, as great a measure of presumption in this species of acquiescence as in the boldest hypothesis which human invention can start. that received and established opinions are true, is one of those sweeping conclusions which would require very strong reasons, and often elaborate research, to justify. on what grounds are they considered to be true by one who declines investigation? because (on the most favourable supposition) they have been handed down to us by our predecessors, and have been held with unhesitating faith by a multitude of illustrious men. but what comprehensive reasons are these? what investigation would it require to shew that they were valid? as the whole history of mankind teems with instances of the transmission of the grossest errors from one generation to another, and of their having been countenanced by the concurrence of the most eminent of our race--how, without examination, can we show that this particular instance is an exception from the general lot? 'from the necessity of using our own judgment, or, in other words, of arriving at a conclusion for ourselves, we cannot be absolved. far from being a virtue, blind acquiescence in the opinions of others is, in most cases, a positive vice, tending to stop all advancement in knowledge, and all improvement in practice. from the preceding it is evident that the inquirer may enter on his task with full confidence that he is embarking in no criminal, or forbidden, or presumptuous enterprise, but is, on the contrary, engaging in the discharge of a duty. let him be as circumspect as he pleases in collecting his facts and deducing his conclusions, cautious in the process, but fearless in the result. let him be fully aware of his liability to error, of the thousand sources of illusions, of the limited powers of the individual, of the paramount importance of truth--but let him dismiss all apprehensions of the issue of an investigation conducted with due application of mind and rectitude of purpose.'* * extracts of summary, by aliquis. of arguments on the duty of inquiry, from the 'pursuit of truth, and other essays, by s. bailey, in reasoner no. . marcus antoninus, indeed, said 'i seek after truth, by which no man yet was ever injured.' but there is a great practical mistake here. there is danger in truth---and the admission should be plainly made. men, where forewarned, make the choice more manfully. we have been wisely told by emerson, that the cherished thoughts and institutions of mankind are at the mercy of a new generalisation--rest, commodity, reputation. inconvenience, and suspense, are the consequences of the partizanship of truth. certain political truths annihilate the interests of whole classes. certain social truths war with life-cherished prejudices. certain sanitary truths reduce the value of all city property. certain scientific truths ruin the working classes by thousands. in a wiser state of society this could be prevented, but our present business is with what is. it is therefore idle to conceal the truth--that there is danger in truth. pope's dictum, that party is the madness of many for the gain of a few, is inversely true of truth. truth is the ultimate benefit of many, but the immediate ruin of the few. here, however, comes to our aid the wise and far-seeing aphorism of burke--'in all exertions of duty there is something to be hazarded'--and the brave man and wise friend of mankind will risk the fate which surely awaits him--the fate of galileo, newton, salomon de caus, volta, fulton, winser, arkwright, gall, and all who present themselves, with truth in their hands, at the door of this great bedlam called the world--the fate of being received with stones and hisses. chapter xiv. idols the term idol is employed by bacon to designate those prejudices which men prefer to truth. a prejudice is a bias without a reason for it, an opinion without a foundation, a judgment formed of persons and things without sufficient examination, an assent given to a proposition without sufficient evidence. the bias may be honourable, the opinion correct, the assent in the right direction, but still of the nature of prejudice, because, if right, it is right by accident rather than design. ignorance hides from us facts, and we decide partially rather than confess our deficiency. ill-directed education gives us pre-possessions, which are obstacles in the way of truth, and we continue to cherish what, having become a part of our nature, it pains us to discard. the senses will occasionally mislead us and although we are conscious that appearances are not to be wholly trusted, we reluctantly doubt our own infallibility. from early, and therefore unquestioned, associations, we have acquired certain habits, and from fashion certain sentiments, and we continue old customs, and fall into the current opinion unconsciously. of these sources of prejudice, logic warns us to beware. of so much importance did bacon regard these hindrances to truth, that he considered the pursuit of new truth hopeless while they were cherished. in a mixed vein of poetry and philosophy, he divided prejudices into four classes, which he called idols of the tribe, the den, the market and the theatre. idols of the tribe are prejudices men imbibe from early training, and love of hypothesis. they are so called because common to the whole race or tribe of mankind. idols of the den are those which relate to a man's particular character, idols of the market are those which are accommodated to common notions. idols of the theatre denote such as pertain to hypothetical systems of philosophy. remembering the declarations of euler and gall, and the daily discoveries of science, we should stand, as it were, on the verge of the old world of experience, and look out on the new world of troth. a young thinker should make for himself a chart of proposed reforms, systems, and changes, agitated in his day--place in relative positions in the scale of importance such as he deems of value, if true--and then analyse his experience to see what is soundly opposed thereto. such a practice would go far to rid men of idol-prejudices, which retard private improvement and public progress. chapter xv. illustrative exercises . all men possessed of an uncontrolled discretionary power, leading to the aggrandisement and profit of their own body, have always abused it.'--burke's thoughts on the present discontents. the student will find the proof of this proposition exhibited in the example of induction, quoted from mr. bailey, p. . . prosperity could never be reached and maintained in this country, without some provision for the regular employment of the poor.--mr. beckett's speech in the house of commons, feb. , . the demonstration, to universal conviction, of this proposition, would lead to an entire and beneficial change of the social condition of this country. . the pen is the tongue of the world.--paine. put this in the syllogistic form. . a good instance of a metaphorical argument drawn out is given by mr. mill:--'for instance, when mr. carlyle, rebuking the byronic vein, says that "strength does not manifest itself in spasms, but in stout bearing of burdens;" the metaphor proves nothing, it is no argument, only an allusion to an argument; in no other way however could so much of argument be so completely suggested in so few words. the expression suggests a whole train of reasoning, which it would take many sentences to write out at length. as thus: motions which are violent but brief, which lead to no end, and are not under the control of the will, are, in the physical body, more incident to a weak than to a strong constitution. if this be owing to a cause which equally operates in what relates to the mind, the same conclusion will told there likewise. but such is really the fact. for the body's liability to these sudden and uncontrollable motions arises from irritability, that is, unusual susceptibility of being moved out of its ordinary course by transient influences: which may equally be said of the mind. and this susceptibility, whether of mind or body, must arise from a weakness of the forces which maintain and carry on the ordinary action of the system. all this is conveyed in one short sentence. and since the causes are alike in the body and in the mind, the analogy is a just one, and the maxim holds of the one as much as of the other.'* * logic, pp. - , vol. . . a youth, named evathlus, engaged with protagoras to learn dialectics, and promised his tutor a large sum of money, _in case he gained the first cause he pleaded_, evathlus, when fully instructed, refused to pay his instructor. protagoras brought his action thus--'you must pay the money however the cause go, for if i gain you must pay in consequence of the sentence, as being cast in the cause; and if you gain it, you must pay in pursuance of our covenant.' 'nay,' evathlus retorts, 'which way soever the cause be decided, you will have nothing, for if i prevail, the sentence gives it that nothing is due: and if i lose, then there is nothing due by the covenant.' what should be the decision in this case? . the first case, says cervantes, requiring sancho's attention was a question put by a stranger, in presence of the stewards and rest of the attendants. 'my lord,' said he, 'a certain manor is divided by a large river. i beg your honour will be attentive, for the case is of great consequence and of some difficulty. i say then, upon this river is a bridge, and at one end of it the gibbet, together with a sort of court hall, in which four judges usually sit to execute the law enacted by the lord of the river, bridge, and manor, which runs to this effect: whoever shall pass this bridge, must first swear whence he comes and whither he goes; if he swear the truth he shall be allowed to pass, but if he forswear himself he shall die upon the gallows without mercy or respite. this law, together with the rigorous penalty, being known, numbers passed, and as it appeared they swore nothing but the truth, the judges permitted them to pass freely and without control. it happened, however, that one man's oath being taken, he affirmed and swore by his deposition that he was going to be hanged on that gibbet, and had no other errand or intention. the judges, having considered this oath, observed: if we allow this man to pass freely, he swore to a lie, and, therefore, ought to be hanged according to law; and if we ordered him to be hanged after he hath sworn he was going to be suspended on that gibbet, he will have sworn the truth, and by the same law he ought to be acquitted, i beg, therefore, to know, my lord governor [and student], what the judges must do with this man?' chapter xvi. technical terms. abstract names--the names of attributes.--j. s. mill. abstraction--fixing thought on the point of resemblance in one body.--drawing off and contemplating separately any part of an an object. action--a volition followed by an effect.--j. s. mill. analogy--resemblance of relation.--whately. analysis--the resolution of a complex whole into its component elements. --j. s. mill. argument--an expression in which, from something laid down as granted, something else is deduced--whately. argumentum ad hominem--appealing to an opponent's professed views. a priori--reasoning from cause to effect. a posteriori--arguing from effects to cause. body--the unknown cause of our sensations--j. s. mill. cause--the invariable antecedent, or thing going before.--the stimulus of an effect. conclusion--a proposition proved by argument. connotative terms--denote a subject, and imply an attribute.---. j.s. mill. consciousness--sensation of existences. definition--the separation of a thing, as by a boundary, from everything else. discovery--finding out something already existing. effect--the immediate, invariable consequent, or the change produced by power. enthymeme-an argument with one premiss suppressed being understood. experience--events which have taken place within a person's own knowledge.--whately. fallacy--an apparent argument. general terms--express the notion of partial similarity. generalisation--tracing certain points of resemblance.--naming one respect in which many things agree. induction--universalisation of truth by inference from uniform facts. intuition--imaginary looking.--whewell, logic--a scientific use of facts. logical truth--that which admits of proof.--chambers. mind--the unknown percipient of sensation.--j. s. mill. necessary truths--are those in which we not only learn that the proposition is true, but see that it must be true; in which the negative of the truth is not only false, but impossible; in which we cannot, even by an effort of the imagination, or in a supposition, conceive the reverse of that which is asserted.--dr. whewell: phil. inductive sciences, pp. - , vol. .* * as 'necessary truths' are much talked of i have introduced here, from whewell, the completest definition with which i am acquainted. for myself, i coincide on this question with j. s. mill, as quoted pp. - . non-connotative terms--denote a subject only and an attribute only.--j. s. mill. philosophy--the science of realities in opposition to that of mere appearances--the attempt to comprehend things as they are, rather than as they seem.--morell. point at issue--the real question to be decided. power in logic, is the relation of circumstances to each other in time. premises the propositions which precede a "conclusion."--the name of the propositions from which a conclusion is deduced. principle--an invariable rule. proof--sufficient evidence; the balance of probability in favour of a proposition. proposition--a sentence which affirms or denies something.--whately.--an expression in words of a judgment.--j. s. mill, reason--the recognition of facts.--the classification of facts.--following in the pathway of facts.--the power of discerning coherences.--a premiss placed after its conclusion.--the minor premiss--in the sense of reason for asserting something. reasoning--argumentation.--process, the same always. subject--first term of a proposition. syllogism-- . a general rule. . a fact contained under that rule. . a conclusion that the fact is so contained.--an argument stated regularly and at full length.--a valid argument so stated that its conclusiveness is evident from the mere form of the expression. technical terms--the tools of art.--whately. technical language--regularly formed, defined, and agreed on set of expressions. testimony--second-hand experience. direct evidence is that which is professedly given. incidental, is corroboration casually introduced on one subject in the course of an evidence delivered on another. theory--is a system of rules intended to explain a class of facts. the rules should be precise, and rest on a rigorous induction of facts or probabilities. tradition--the relation of a circumstance, not committed to writing by any person who observed it, but communicated orally from one to another for a long period of time. [transcriber's note: on p. , there are four instances of " " in brackets. { } indicates a subscript . ^{ } indicates a superscript . [+] in footnote indicates a larger than normal plus sign. remaining transcriber's notes are at the end of the text.] essays in experimental logic _by_ john dewey the university of chicago press chicago, illinois copyright by the university of chicago all rights reserved published june second impression may third impression october composed and printed by the university of chicago press chicago, illinois, u.s.a. prefatory note in a volume was published by the university of chicago press, entitled _studies in logical theory_, as a part of the "decennial publications" of the university. the volume contained contributions by drs. thompson (now mrs. woolley), mclennan, ashley, gore, heidel, stuart, and moore, in addition to four essays by the present writer who was also general editor of the volume. the edition of the _studies_ being recently exhausted, the director of the press suggested that my own essays be reprinted, together with other studies of mine in the same field. the various contributors to the original volume cordially gave assent, and the present volume is the outcome. chaps. ii-v, inclusive, represent (with editorial revisions, mostly omissions) the essays taken from the old volume. the first and introductory chapter has been especially written for the volume. the other essays are in part reprinted and in part rewritten, with additions, from various contributions to philosophical periodicals. i should like to point out that the essay on "some stages of logical thought" antedates the essays taken from the volume of _studies_, having been published in ; the other essays have been written since then. i should also like to point out that the essays in their psychological phases are written from the standpoint of what is now termed a behavioristic psychology, though some of them antedate the use of that term as a descriptive epithet. j. d. columbia university april , table of contents page i. introduction ii. the relationship of thought and its subject-matter iii. the antecedents and stimuli of thinking iv. data and meanings v. the objects of thought vi. some stages of logical thought vii. the logical character of ideas viii. the control of ideas by facts ix. naÏve realism vs. presentative realism x. epistemological realism: the alleged ubiquity of the knowledge relation xi. the existence of the world as a logical problem xii. what pragmatism means by practical xiii. an added note as to the "practical" xiv. the logic of judgments of practice index i introduction the key to understanding the doctrine of the essays which are herewith reprinted lies in the passages regarding the temporal development of experience. setting out from a conviction (more current at the time when the essays were written than it now is) that knowledge implies judgment (and hence, thinking) the essays try to show ( ) that such terms as "thinking," "reflection," "judgment" denote inquiries or the results of inquiry, and ( ) that inquiry occupies an intermediate and mediating place in the development of an experience. if this be granted, it follows at once that a philosophical discussion of the distinctions and relations which figure most largely in logical theories depends upon a proper placing of them in their temporal context; and that in default of such placing we are prone to transfer the traits of the subject-matter of one phase to that of another--with a confusing outcome. i . an intermediary stage for knowledge (that is, for knowledge comprising reflection and having a distinctively intellectual quality) implies a prior stage of a different kind, a kind variously characterized in the essays as social, affectional, technological, aesthetic, etc. it may most easily be described from a negative point of view: it is a type of experience which cannot be called a knowledge experience without doing violence to the term "knowledge" and to experience. it may contain knowledge resulting from prior inquiries; it may include thinking within itself; but not so that they dominate the situation and give it its peculiar flavor. positively, anyone recognizes the difference between an experience of quenching thirst where the perception of water is a mere incident, and an experience of water where knowledge of what water is, is the controlling interest; or between the enjoyment of social converse among friends and a study deliberately made of the character of one of the participants; between aesthetic appreciation of a picture and an examination of it by a connoisseur to establish the artist, or by a dealer who has a commercial interest in determining its probable selling value. the distinction between the two types of experience is evident to anyone who will take the trouble to recall what he does most of the time when not engaged in meditation or inquiry. but since one does not think about knowledge except when he is _thinking_, except, that is, when the intellectual or cognitional interest is dominant, the professional philosopher is only too prone to think of all experiences as if they were of the type he is specially engaged in, and hence unconsciously or intentionally to project _its_ traits into experiences to which they are alien. unless he takes the simple precaution of holding before his mind contrasting experiences like those just mentioned, he generally forms a habit of supposing that no qualities or things at all are present in experience except as objects of some kind of apprehension or awareness. overlooking, and afterward denying, that things and qualities are present to most men most of the time as things and qualities in situations of prizing and aversion, of seeking and finding, of converse, enjoyment and suffering, of production and employment, of manipulation and destruction, he thinks of things as either totally absent from experience or else there as objects of "consciousness" or knowing. this habit is a tribute to the _importance_ of reflection and of the knowledge which accrues from it. but a discussion of knowledge perverted at the outset by such a misconception is not likely to proceed prosperously. all this is not to deny that some element of reflection or inference may be required in any situation to which the term "experience" is applicable in any way which contrasts with, say, the "experience" of an oyster or a growing bean vine. men experience illness. what they experience is certainly something very different from an object of apprehension, yet it is quite possible that what makes an illness into a _conscious_ experience is precisely the intellectual elements which intervene--a certain taking of some things as representative of other things. my thesis about the primary character of non-reflectional experience is not intended to preclude this hypothesis--which appears to me a highly plausible one. but it is indispensable to note that, even in such cases, the intellectual element is set in a context which is non-cognitive and which holds within it in suspense a vast complex of other qualities and things that in the experience itself are objects of esteem or aversion, of decision, of use, of suffering, of endeavor and revolt, not of knowledge. when, in a subsequent reflective experience, we look back and find these things and qualities (quales would be a better word, or values, if the latter word were not so open to misconstruction), we are only too prone to suppose that they were then what they are now--objects of a cognitive regard, themes of an intellectual gesture. hence, the erroneous conclusion that things are either just out of experience, or else are (more or less badly) known objects. in any case the best way to study the character of those cognitional factors which are merely incidental in so many of our experiences is to study them in the type of experience where they are most prominent, where they dominate; where knowing, in short, is the prime concern. such study will also, by a reflex reference, throw into greater relief the contrasted characteristic traits of the non-reflectional types of experience. in such contrast the significant traits of the latter are seen to be internal organization: ( ) the factors and qualities hang together; there is a great variety of them but they are saturated with a pervasive quality. being ill with the grippe is an experience which includes an immense diversity of factors, but none the less is the one qualitatively unique experience which it is. philosophers in their exclusively intellectual preoccupation with analytic knowing are only too much given to overlooking the primary import of the term "thing": namely, _res_, an affair, an occupation, a "cause"; something which is similar to having the grippe, or conducting a political campaign, or getting rid of an overstock of canned tomatoes, or going to school, or paying attention to a young woman:--in short, just what is meant in non-philosophic discourse by "an experience." noting things only as if they were objects--that is, objects of knowledge--continuity is rendered a mystery; qualitative, pervasive unity is too often regarded as a subjective state injected into an object which does not possess it, as a mental "construct," or else as a trait of being to be attained to only by recourse to some curious organ of knowledge termed intuition. in like fashion, organization is thought of as the achieved outcome of a highly scientific knowledge, or as the result of transcendental rational synthesis, or as a fiction superinduced by association, upon elements each of which in its own right "is a separate existence." one advantage of an excursion by one who philosophizes upon knowledge into primary non-reflectional experience is that the excursion serves to remind him that every empirical situation has its own organization of a direct, non-logical character. ( ) another trait of every _res_ is that it has focus and context: brilliancy and obscurity, conspicuousness or apparency, and concealment or reserve, with a constant movement of redistribution. movement about an axis persists, but what is in focus constantly changes. "consciousness," in other words, is only a very small and shifting portion of experience. the scope and content of the focused apparency have immediate dynamic connections with portions of experience not at the time obvious. the word which i have just written is momentarily focal; around it there shade off into vagueness my typewriter, the desk, the room, the building, the campus, the town, and so on. _in_ the experience, and in it in such a way as to _qualify_ even what is shiningly apparent, are all the physical features of the environment extending out into space no one can say how far, and all the habits and interests extending backward and forward in time, of the organism which uses the typewriter and which notes the written form of the word only as temporary focus in a vast and changing scene. i shall not dwell upon the import of this fact in its critical bearings upon theories of experience which have been current. i shall only point out that when the word "experience" is employed in the text it means just such an immense and operative world of diverse and interacting elements. it might seem wiser, in view of the fact that the term "experience" is so frequently used by philosophers to denote something very different from such a world, to use an acknowledgedly objective term: to talk about the typewriter, for example. but experience in ordinary usage (as distinct from its technical use in psychology and philosophy) expressly denotes something which a specific term like "typewriter" does _not_ designate: namely, the indefinite range of context in which the typewriter is _actually_ set, its spatial and temporal environment, including the habitudes, plans, and activities of its operator. and if we are asked why not then use a general objective term like "world," or "environment," the answer is that the word "experience" suggests something indispensable which these terms omit: namely, an actual focusing of the world at one point in a focus of immediate shining apparency. in other words, in its ordinary human usage, the term "experience" was invented and employed previously because of the necessity of having some way to refer peremptorily to what is indicated in only a roundabout and divided way by such terms as "organism" and "environment," "subject" and "object," "persons" and "things," "mind" and "nature," and so on.[ ] ii had this background of the essays been more explicitly depicted, i do not know whether they would have met with more acceptance, but it is likely that they would not have met with so many misunderstandings. but the essays, save for slight incidental references, took this background for granted in the allusions to the universe of non-reflectional experience of our doings, sufferings, enjoyments of the world and of one another. it was their purpose to point out that reflection (and, hence, knowledge having logical properties) arises because of the appearance of incompatible factors within the empirical situation just pointed at: incompatible not in a mere structural or static sense, but in an active and progressive sense. then opposed responses are provoked which cannot be taken simultaneously in overt action, and which accordingly can be dealt with, whether simultaneously or successively, only after they have been brought into a plan of organized action by means of analytic resolution and synthetic imaginative conspectus; in short, by means of being taken cognizance of. in other words, reflection appears as the dominant trait of a situation when there is something seriously the matter, some trouble, due to active discordance, dissentiency, conflict among the factors of a prior non-intellectual experience; when, in the phraseology of the essays, a situation becomes tensional.[ ] given such a situation, it is obvious that the meaning of the situation as a whole is uncertain. through calling out two opposed modes of behavior, it presents itself as meaning two incompatible things. the only way out is through careful inspection of the situation, involving resolution into elements, and a going out beyond what is found upon such inspection to be given, to something else to get a leverage for understanding it. that is, we have (_a_) to locate the difficulty, and (_b_) to devise a method of coping with it. any such way of looking at thinking demands moreover that the difficulty be located _in_ the situation in question (very literally in question). knowing always has a _particular_ purpose, and its solution must be a function of its conditions in connection with _additional_ ones which are brought to bear. every reflective knowledge, in other words, has a specific task which is set by a concrete and empirical situation, so that it can perform that task only by detecting and remaining faithful to the conditions in the situation in which the difficulty arises, while its purpose is a reorganization of its factors in order to get unity. so far, however, there is no accomplished knowledge, but only knowledge coming to be--learning, in the classic greek conception. thinking gets no farther, as _thinking_, than a statement of elements constituting the difficulty at hand and a statement--a propounding, a proposition--of a method for resolving them. in fixing the framework of every reflective situation, this state of affairs also determines the further step which is needed if there is to be knowledge--knowledge in the eulogistic sense, as distinct from opinion, dogma, and guesswork, or from what casually passes current as knowledge. overt action is demanded if the worth or validity of the reflective considerations is to be determined. otherwise, we have, at most, only a hypothesis that the conditions of the difficulty are such and such, and that the way to go at them so as to get over or through them is thus and so. this way must be tried in action; it must be applied, physically, in the situation. by finding out what then happens, we test our intellectual findings--our logical terms or projected metes and bounds. if the required reorganization is effected, they are confirmed, and reflection (on that topic) ceases; if not, there is frustration, and inquiry continues. that all knowledge, as issuing from reflection, is experimental (in the literal physical sense of experimental) is then a constituent proposition of this doctrine. upon this view, thinking, or knowledge-getting, is far from being the armchair thing it is often supposed to be. the reason it is not an armchair thing is that it is not an event going on exclusively within the cortex or the cortex and vocal organs. it involves the explorations by which relevant data are procured and the physical analyses by which they are refined and made precise; it comprises the readings by which information is got hold of, the words which are experimented with, and the calculations by which the significance of entertained conceptions or hypotheses is elaborated. hands and feet, apparatus and appliances of all kinds are as much a part of it as changes in the brain. since these physical operations (including the cerebral events) and equipments are a part of thinking, thinking is mental, not because of a peculiar stuff which enters into it or of peculiar non-natural activities which constitute it, but because of what physical acts and appliances _do_: the distinctive purpose for which they are employed and the distinctive results which they accomplish. that reflection terminates, through a definitive overt act,[ ] in another non-reflectional situation, within which incompatible responses may again in time be aroused, and so another problem in reflection be set, goes without saying. certain things about this situation, however, do not at the present time speak for themselves and need to be set forth. let me in the first place call attention to an ambiguity in the term "knowledge." the statement that all knowledge involves reflection--or, more concretely, that it denotes an inference from evidence--gives offense to many; it seems a departure from fact as well as a wilful limitation of the word "knowledge." i have in this introduction endeavored to mitigate the obnoxiousness of the doctrine by referring to "knowledge which is intellectual or logical in character." lest this expression be regarded as a futile evasion of a real issue, i shall now be more explicit. ( ) it may well be admitted that there is a real sense in which knowledge (as distinct from thinking or inquiring with a guess attached) does not come into existence till thinking has terminated in the experimental act which fulfils the specifications set forth in thinking. but what is also true is that the object thus determined is an object of _knowledge_ only because of the thinking which has preceded it and to which it sets a happy term. to run against a hard and painful stone is not of itself, i should say, an act of knowing; but if running into a hard and painful thing is an outcome predicted after inspection of data and elaboration of a hypothesis, then the hardness and the painful bruise which define the thing as a stone also constitute it emphatically an object of knowledge. in short, the object of knowledge in the strict sense is its objective; and this objective is not constituted till it is reached. now this conclusion--as the word denotes--is thinking brought to a close, done with. if the reader does not find this statement satisfactory, he may, pending further discussion, at least recognize that the doctrine set forth has no difficulty in connecting knowledge with inference, and at the same time admitting that knowledge in the emphatic sense does not exist till inference has ceased. seen from this point of view, so-called immediate knowledge or simple apprehension or acquaintance-knowledge represents a critical skill, a certainty of response which has accrued in consequence of reflection. a like sureness of footing apart from prior investigations and testings is found in instinct and habit. i do not deny that these may be better than knowing, but i see no reason for complicating an already too confused situation by giving them the name "knowledge" with its usual intellectual implications. from this point of view, the subject-matter of knowledge is precisely that which we do _not_ think of, or mentally refer to in any way, being that which is taken as matter of course, but it is nevertheless knowledge in virtue of the inquiry which has led up to it. ( ) definiteness, depth, and variety of meaning attach to the objects of an experience just in the degree in which they have been previously thought about, even when present in an experience in which they do not evoke inferential procedures at all. such terms as "meaning," "significance," "value," have a double sense. sometimes they mean a function: the office of one thing representing another, or pointing to it as implied; the operation, in short, of serving as sign. in the word "symbol" this meaning is practically exhaustive. but the terms also sometimes mean an inherent quality, a quality intrinsically characterizing the thing experienced and making it worth while. the word "sense," as in the phrase "sense of a thing" (and non-sense) is devoted to this use as definitely as are the words "sign" and "symbol" to the other. in such a pair as "import" and "importance," the first tends to select the reference to another thing while the second names an intrinsic content. in reflection, the extrinsic reference is always primary. the height of the mercury means rain; the color of the flame means sodium; the form of the curve means factors distributed accidentally. in the situation which follows upon reflection, meanings are intrinsic; they have no instrumental or subservient office, because they have no office at all. they are as much qualities of the objects in the situation as are red and black, hard and soft, square and round. and every reflective experience adds new shades of such intrinsic qualifications. in other words, while reflective knowing is instrumental to gaining control in a troubled situation (and thus has a practical or utilitarian force), it is also instrumental to the enrichment of the immediate significance of subsequent experiences. and it may well be that this by-product, this gift of the gods, is incomparably more valuable for living a life than is the primary and intended result of control, essential as is that control to having a life to live. words are treacherous in this field; there are no accepted criteria for assigning or measuring their meanings; but if one use the term "consciousness" to denote immediate values of objects, then it is certainly true that "consciousness is a lyric cry even in the midst of business." but it is equally true that if someone else understands by consciousness the function of effective reflection, then consciousness is a business--even in the midst of writing or singing lyrics. but the statement remains inadequate until we add that knowing as a business, inquiry and invention as enterprises, as practical acts, become themselves charged with the meaning of what they accomplish as _their_ own immediate quality. there exists no disjunction between aesthetic qualities which are final yet idle, and acts which are practical or instrumental. the latter have their own delights and sorrows. iii speaking, then, from the standpoint of temporal order, we find reflection, or thought, occupying an intermediate and reconstructive position. it comes between a temporally prior situation (an organized interaction of factors) of active and appreciative experience, wherein some of the factors have become discordant and incompatible, and a later situation, which has been constituted out of the first situation by means of acting on the findings of reflective inquiry. this final situation therefore has a richness of meaning, as well as a controlled character lacking to its original. by it is fixed the logical validity or intellectual force of the terms and relations distinguished by reflection. owing to the continuity of experience (the overlapping and recurrence of like problems), these logical fixations become of the greatest assistance to subsequent inquiries; they are its working means. in such further uses, they get further tested, defined, and elaborated, until the vast and refined systems of the technical objects and formulae of the sciences come into existence--a point to which we shall return later. owing to circumstances upon which it is unnecessary to dwell, the position thus sketched was not developed primarily upon its own independent account, but rather in the course of a criticism of another type of logic, the idealistic logic found in lotze. it is obvious that the theory in question has critical bearings. according to it, reflection in its distinctions and processes can be understood only when placed in its intermediate pivotal temporal position--as a process of control, through reorganization, of material alogical in character. it intimates that thinking would not exist, and hence knowledge would not be found, in a world which presented no troubles or where there are no "problems of evil"; and on the other hand that a reflective method is the only sure way of dealing with these troubles. it intimates that while the results of reflection, because of the continuity of experience, may be of wider scope than the situation which calls out a particular inquiry and invention, reflection itself is always specific in origin and aim; it always has something special to cope with. for troubles are concretely specific. it intimates also that thinking and reflective knowledge are never an end-all, never their own purpose nor justification, but that they pass naturally into a more direct and vital type of experience, whether technological or appreciative or social. this doctrine implies, moreover, that logical theory in its usual sense is essentially a descriptive study; that it is an account of the processes and tools which have actually been found effective in inquiry, comprising in the term "inquiry" both deliberate discovery and deliberate invention. since the doctrine was propounded in an intellectual environment where such statements were not commonplaces, where in fact a logic was reigning which challenged these convictions at every point, it is not surprising that it was put forth with a controversial coloring, being directed particularly at the dominant idealistic logic. the point of contact and hence the point of conflict between the logic set forth and the idealistic logic are not far to seek. the logic based on idealism had, as a matter of fact, treated knowledge from the standpoint of an account of thought--of thought in the sense of conception, judgment, and inferential reasoning. but while it had inherited this view from the older rationalism, it had also learned from hume, via kant, that direct sense or perceptual material must be taken into account. hence it had, in effect, formulated the problem of logic as the problem of the connection of logical thought with sense-material, and had attempted to set forth a metaphysics of reality based upon various ascending stages of the completeness of the rationalization or idealization of given, brute, fragmentary sense material by synthetic activity of thought. while considerations of a much less formal kind were chiefly influential in bringing idealism to its modern vogue, such as the conciliation of a scientific with a religious and moral point of view and the need of rationalizing social and historic institutions so as to explain their cultural effect, yet this logic constituted the _technique_ of idealism--its strictly intellectual claim for acceptance. the point of contact, and hence of conflict, between it and such a doctrine of logic and reflective thought as is set forth above is, i repeat, fairly obvious. both fix upon thinking as the key to the situation. i still believe (what i believed when i wrote the essays) that under the influence of idealism valuable analyses and formulations of the work of reflective thought, in its relation to securing knowledge of objects, were executed. but--and the but is one of exceptional gravity--the idealistic logic started from the distinction between immediate plural data and unifying, rationalizing meanings as a distinction ready-made in experience, and it set up as the goal of knowledge (and hence as the definition of true reality) a complete, exhaustive, comprehensive, and eternal system in which plural and immediate data are forever woven into a fabric and pattern of self-luminous meaning. in short, it ignored the temporally intermediate and instrumental place of reflection; and because it ignored and denied this place, it overlooked its essential feature: control of the environment in behalf of human progress and well-being, the effort at control being stimulated by the needs, the defects, the troubles, which accrue when the environment coerces and suppresses man or when man endeavors in ignorance to override the environment. hence it misconstrued the criterion of the work of intelligence; it set up as its criterion an absolute and non-temporal reality at large, instead of using the criterion of specific temporal achievement of consequences through a control supplied by reflection. and with this outcome, it proved faithless to the cause which had generated it and given it its reason for being: the magnification of the work of intelligence in our actual physical and social world. for a theory which ends by declaring that everything is, really and eternally, thoroughly ideal and rational, cuts the nerve of the specific demand and work of intelligence. from this general statement, let me descend to the technical point upon which turns the criticism of idealistic logic by the essays. grant, for a moment, as a hypothesis, that thinking starts neither from an implicit force of rationality desiring to realize itself completely in and through and against the limitations which are imposed upon it by the conditions of our human experience (as all idealisms have taught), nor from the fact that in each human being is a "mind" whose business it is just to "know"--to theorize in the aristotelian sense; but, rather, that it starts from an effort to get out of some trouble, actual or menacing. it is quite clear that the human race has tried many another way out besides reflective inquiry. its favorite resort has been a combination of magic and poetry, the former to get the needed relief and control; the latter to import into imagination, and hence into emotional consummation, the realizations denied in fact. but as far as reflection does emerge and gets a working foothold, the nature of its job is set for it. on the one hand, it must discover, it must find out, it must detect; it must inventory what is there. all this, or else it will never know what the matter is; the human being will not find out what "struck him," and hence will have no idea of where to seek for a remedy--for the needed control. on the other hand, it must invent, it must project, it must bring to bear upon the given situation what is not, as it exists, given as a part of it. this seems to be quite empirical and quite evident. the essays submitted the thesis that this simple dichotomization of the practical situation of power and enjoyment, when menaced, into what is there (whether as obstacle or as resource), and into suggested inventions--projections of something else to be brought to bear upon it, ways of dealing with it--is the explanation of the time-honored logical determinations of brute fact, datum and meaning or ideal quality; of (in more psychological terminology) sense-perception and conception; of particulars (parts, fragments) and universals-generics; and also of whatever there is of intrinsic significance in the traditional subject-predicate scheme of logic. it held, less formally, that this view explained the eulogistic connotations always attaching to "reason" and to the work of reason in effecting unity, harmony, comprehension, or synthesis, and to the traditional combination of a depreciatory attitude toward brute facts with a grudging concession of the necessity which thought is under of accepting them and taking them for its own subject-matter and checks. more specifically, it is held that this view supplied (and i should venture to say for the first time) an explanation of the traditional theory of truth as a correspondence or agreement of existence and mind or thought. it showed that the correspondence or agreement was like that between an invention and the conditions which the invention is intended to meet. thereby a lot of epistemological hangers-on to logic were eliminated; for the distinctions which epistemology had misunderstood were located where they belong:--in the art of inquiry, considered as a joint process of ascertainment and invention, projection, or "hypothesizing"--of which more below. iv the essays were published in . at that time (as has been noted) idealism was in practical command of the philosophic field in both england and this country; the logics in vogue were profoundly influenced by kantian and post-kantian thought. empirical logics, those conceived under the influence of mill, still existed, but their light was dimmed by the radiance of the regnant idealism. moreover, from the standpoint of the doctrine expounded in the essays, the empirical logic committed the same logical fault as did the idealistic, in taking sense-data to be primitive (instead of being resolutions of the _things_ of prior experiences into elements for the aim of securing evidence); while it had no recognition of the specific service rendered by intelligence in the development of new meanings and plans of new actions. this state of things may explain the controversial nature of the essays, and their selection in particular of an idealistic logic for animadversion. since the essays were written, there has been an impressive revival of realism, and also a development of a type of logical theory--the so-called analytic logic--corresponding to the philosophical aspirations of the new realism. this marked alteration of intellectual environment subjects the doctrine of the essays to a test not contemplated when they were written. it is one thing to develop a hypothesis in view of a particular situation; it is another to test its worth in view of procedures and results having a radically different motivation and direction. it is, of course, impossible to discuss the analytic logic in this place. a consideration of how some of its main tenets compare with the conclusions outlined above will, however, throw some light upon the meaning and the worth of the latter. although this was formulated with the idealistic and sensationalistic logics in mind, the hypothesis that knowledge can be rightly understood only in connection with considerations of time and temporal position is a general one. if it is valid, it should be readily applicable to a critical placing of any theory which ignores and denies such temporal considerations. and while i have learned much from the realistic movement about the full force of the position sketched in the essays when adequately developed; and while later discussions have made it clear that the language employed in the essays was sometimes unnecessarily (though naturally) infected by the subjectivism of the positions against which it was directed, i find that the analytic logic is also guilty of the fault of temporal dislocation. in one respect, idealistic logic takes cognizance of a temporal contrast; indeed, it may fairly be said to be based upon it. it seizes upon the contrast in intellectual force, consistency, and comprehensiveness between the crude or raw data with which science sets out and the defined, ordered, and systematic totality at which it aims--and which in part it achieves. this difference is a genuine empirical difference. idealism noted that the difference may properly be ascribed to the intervention of thinking--that thought is what makes the difference. now since the outcome of science is of higher intellectual rank than its data, and since the intellectualistic tradition in philosophy has always identified degrees of logical adequacy with degrees of reality, the conclusion was naturally drawn that _the_ real world--absolute reality--was an ideal or thought-world, and that the sense-world, the commonsense-world, the world of actual and historic experience, is simply a phenomenal world presenting a fragmentary manifestation of that thought which the process of human thinking makes progressively explicit and articulate. this perception of the intellectual superiority of objects which are constituted at the conclusion of thinking over those which formed its data may fairly be termed the empirical factor in the idealistic logic. the essence of the realistic reaction, on its logical side, is exceedingly simple. it starts from those objects with which science, approved science, ends. since they are the objects which are _known_, which are true, they are the real objects. that they are also objects for intervening thinking is an interesting enough historical and psychological fact, but one quite irrelevant to their natures, which are precisely what knowledge finds them to be. in the biography of human beings it may hold good that apprehension of objects is arrived at only through certain wanderings, endeavors, exercises, experiments; possibly acts called sensation, memory, reflection may be needed by men in reaching a grasp of the objects. but such things denote facts about the history of the knower, not about the nature of the known object. analysis will show, moreover, that any intelligible account of this history, any verified statement of the psychology of knowing assumes objects which are unaffected by the knowing--otherwise the pretended history is merely pretense and not to be trusted. the history of the process of knowing, moreover, implies also the terms and propositions--truths--of logic. that logic must therefore be assumed as a science of objects real and true, quite apart from any process of thinking them. in short, the requirement is that we shall think things as they are themselves, not make them into objects constructed by thinking. this revival of realism coincided also with an important movement in mathematics and logic: the attempt to treat logical distinctions by mathematical methods; while at the same time mathematical subject-matter had become so generalized that it was a theory of types and orders of terms and propositions--in short, a logic. certain minds have always found mathematics the type of knowledge, because of its definiteness, order, and comprehensiveness. the wonderful accomplishments of modern mathematics, including its development into a type of highly generalized logic, was not calculated to lessen the tendency. and while prior philosophers have generally played their admiration of mathematics into the hands of idealism (regarding mathematical subject-matter as the embodiment or manifestation of pure thought), the new philosophy insisted that the terms and types of order constituting mathematical and logical subject-matter were real in their own right, and (at most) merely led up to and discovered by thinking--an operation, moreover, itself subjected (as has been pointed out) to the entities and relationships set forth by logic. the inadequacy of this summary account may be pardoned in view of the fact that no adequate exposition is intended; all that is wanted is such a statement of the general relationship of idealism to realism as may serve as the point of departure for a comparison with the instrumentalism of the essays. in bare outline, it is obvious that the two latter agree in regarding thinking as instrumental, not as constitutive. but this agreement turns out to be a formal matter in contrast with a disagreement concerning that _to which_ thinking is instrumental. the new realism finds that it is instrumental simply to knowledge of objects. from this it infers (with perfect correctness and inevitableness) that thinking (including all the operations of discovery and testing as they might be set forth in an inductive logic) is a mere psychological preliminary, utterly irrelevant to any conclusions regarding the nature of objects known. the thesis of the essays is that thinking is instrumental to a control of the environment, a control effected through acts which would not be undertaken without the prior resolution of a complex situation into assured elements and an accompanying projection of possibilities--without, that is to say, thinking. such an instrumentalism seems to analytic realism but a variant of idealism. for it asserts that processes of reflective inquiry play a part in shaping the objects--namely, terms and propositions--which constitute the bodies of scientific knowledge. now it must not only be admitted but proclaimed that the doctrine of the essays holds that intelligence is not an otiose affair, nor yet a mere preliminary to a spectator-like apprehension of terms and propositions. in so far as it is idealistic to hold that objects of knowledge _in their capacity of distinctive objects of knowledge_ are determined by intelligence, it is idealistic. it believes that faith in the constructive, the creative, competency of intelligence was the redeeming element in historic idealisms. lest, however, we be misled by general terms, the scope and limits of this "idealism" must be formulated. ( ) its distinguishing trait is that it defines thought or intelligence by function, by work done, by consequences effected. it does not start with a power, an entity or substance or activity which is ready-made thought or reason and which as such constitutes the world. thought, intelligence, is to it just a name for the events and acts which make up the processes of analytic inspection and projected invention and testing which have been described. these events, these acts, are wholly natural; they are "realistic"; they comprise the sticks and stones, the bread and butter, the trees and horses, the eyes and ears, the lovers and haters, the sighs and delights of ordinary experience. thinking is what some of the actual existences _do_. _they_ are in no sense constituted by thinking; on the contrary, the problems of thought are set by _their_ difficulties and its resources are furnished by _their_ efficacies; its acts are _their_ doings adapted to a distinctive end. ( ) the reorganization, the modification, effected by thinking is, by this hypothesis, a physical one. thinking ends in experiment and experiment is an _actual_ alteration of a physically antecedent situation in those details or respects which called for thought in order to do away with some evil. to suffer a disease and to try to do something for it is a primal experience; to look into the disease, to try and find out just what makes it a disease, to invent--or hypothecate--remedies is a reflective experience; to try the suggested remedy and see whether the disease is helped is the act which transforms the data and the intended remedy into _knowledge objects_. and this transformation into knowledge objects is also effected by changing physical things by physical means. speaking from this point of view, the decisive consideration as between instrumentalism and analytic realism is whether the operation of experimentation is or is not necessary to knowledge. the instrumental theory holds that it is; analytic realism holds that even though it were essential in _getting_ knowledge (or in learning), it has nothing to do with knowledge itself, and hence nothing to do with the known object: that it makes a change only in the knower, not in what is to be known. and for precisely the same reason, instrumentalism holds that an object as a knowledge-object is never a whole; that it is surrounded with and inclosed by things which are quite other than objects of knowledge, so that knowledge cannot be understood in isolation or when taken as mere beholding or grasping of objects. that is to say, while it is making the sick man better or worse (or leaving him just the same) which determines the knowledge-value of certain findings of fact and certain conceptions as to mode of treatment (so that by the treatment they become definitely knowledge-objects), yet improvement or deterioration of the patient is other than an object of cognitive apprehension. its knowledge-object phase is a selection in reference to prior reflections. so the laboratory experiment of a chemist which brings to a head a long reflective inquiry and settles the intellectual status of its findings and theorizings (thereby making them into cognitive concerns or terms and propositions) is itself much more than a knowledge of terms and propositions, and only by virtue of this surplusage is it even contemplative knowledge. he knows, say, tin, when he has made tin into an outcome of his investigating procedures, but tin is much more than a term of knowledge. putting the matter in a slightly different way, logical (as distinct from naïve) realism confuses means of knowledge with objects of knowledge. the means are twofold: they are (_a_) the data of a particular inquiry so far as they are significant because of prior experimental inquiries; and (_b_) they are the meanings which have been settled in consequence of prior intellectual undertakings: on the one hand, particular things or qualities as signs; on the other, general meanings as possibilities of what is signified by given data. our physician has in advance a technique for telling that certain particular traits, if he finds them, are symptoms, signs; and he has a store of diseases and remedies in mind which may possibly be meant in any given case. from prior reflective experiments he has learned to look for temperature, for rate of heartbeats, for sore spots in certain places; to take specimens of blood, sputum, of membrane, and subject them to cultures, microscopic examination, etc. he has acquired certain habits, in other words, in virtue of which certain physical qualities and events are more than physical, in virtue of which they are signs or indications of something else. on the other hand, this something else is a somewhat not physically present at the time: it is a series of events still to happen. it is suggested by what is given, but is no part of the given. now, in the degree in which the physician comes to the examination of what is there with a large and comprehensive stock of such possibilities or meanings in mind, he will be intellectually resourceful in dealing with a particular case. they (the concepts or universals of the situation) are (together with the sign-capacity of the data) the _means_ of knowing the case in hand; they are the agencies of transforming it, through the actions which they call for, into an object--an object of knowledge, a truth to be stated in propositions. but since the professional (as distinct from the human) knower is particularly concerned with the elaboration of these tools, the professional knower--of which the class philosopher presents of course one case--ungenerously drops from sight the situation in its integrity and treats these instrumentalities of knowledge as objects of knowledge. each of these aspects--signs and things signified--is sufficiently important to deserve a section on its own account. v the position taken in the essays is frankly realistic in acknowledging that certain brute existences, detected or laid bare by thinking but in no way constituted out of thought or any mental process, set every problem for reflection and hence serve to test its otherwise merely speculative results. it is simply insisted that as a matter of fact these brute existences are equivalent neither to the objective content of the situations, technological or artistic or social, in which thinking originates, nor to the things to be known--to the objects of knowledge. let us take the sequence of mineral rock in place, pig iron and the manufactured article, comparing the raw material in its undisturbed place in nature to the original _res_ of experience, compare the manufactured article to the objective and object of knowledge, and the brute datum to the metal undergoing extraction from raw ore for the sake of being wrought into a useful thing. and we should add that just as the manufacturer always has a lot of already extracted ore on hand for use in machine processes as it is wanted, so every person of any maturity, especially if he lives in an environment affected by previous scientific work, has a lot of extracted data--or, what comes to the same thing, of ready-made tools of extraction--for use in inference as they are required. we go about with a disposition to identify certain shapes as tables, certain sounds as words of the french language, certain cries as evidences of distress, certain massed colors as woods in the distance, certain empty spaces as buttonholes, and so on indefinitely. the examples are trivial enough. but if more complicated matters were taken, it would be seen that a large part of the technique of science (all of science which is specifically "inductive" in character) consists of methods of finding out just what qualities are unambiguous, economical, and dependable signs of those other things which cannot be got at as directly as can the sign-bearing elements. and if we started from the more obscure and complex difficulties of identification and diagnosis with which the sciences of physiology, botany, astronomy, chemistry, etc., deal, we should be forced to recognize that the identifications of everyday life--our "perceptions" of chairs, tables, trees, friends--differ only in presenting questions much easier of solution. in every case, it is a matter of fixing some given physical existence as a sign of some other existences not given in the same way as is that which serves as a sign. these words of mill might well be made the motto of every logic: "to draw inferences has been said to be the great business of life. everyone has daily, hourly, and momentary need of ascertaining facts which he has not directly observed.... it is the only occupation in which the mind never ceases to be engaged." such being the case, the indispensable condition of doing the business well is the careful determination of the sign-force of specific things in experience. and this condition can never be fulfilled as long as a thing is presented to us, so to say, in bulk. the complex organizations which are the subject-matter of our direct activities and enjoyments are grossly unfit to serve as intellectual indications or evidence. their testimony is almost worthless, they speak so many languages. in their complexity, they point equally in all directions; in their unity, they run in a groove and point to whatever is most customary. to break up the complexity, to resolve it into a number of independent variables each as irreducible as it is possible to make it, is the only way of getting secure pointers as to what is indicated by the occurrence of the situation in question. the "objects" of ordinary life, stones, plants, cats, rocks, moon, etc., are neither the data of science nor the objects at which science arrives. we are here face to face with a crucial point in analytic realism. realism argues that we have no alternative except either to regard analysis as falsifying (à la bergson), and thus commit ourselves to distrust of science as an organ of knowledge, or else to admit that something eulogistically termed reality (especially as _existence_, being as subject to space and time determinations) is but a complex made up of fixed, mutually independent simples: viz., that reality is truly conceived only under the caption of whole and parts, where the parts are independent of each other and consequently of the whole. for instrumentalism, however, the alleged dilemma simply does not exist. the results of abstraction and analysis are perfectly real; but they are real, like everything else, _where_ they are real: that is to say, in some _particular_ _co_existence in the situation where they originate and operate. the remark is perhaps more cryptic than enlightening. its intent is that reflection is an actual occurrence as much so as a thunderstorm or a growing plant, and as an actual existence it is characterized by specific existential traits uniquely belonging to it: the entities of simple data as such. it is in control of the evidential function that irreducible and independent simples or elements exist. they certainly are found there; as we have seen they _are_ "common-sense" objects broken up into expeditious and unambiguous signs of conclusions to be drawn, conclusions about other things with which they--the elements--are continuous in some respects, although discrete[ ] with respect to their sensory conditions. but there is no more reason for supposing that they exist _elsewhere_ in the same manner than there is for supposing that centaurs coexist along with domestic horses and cows because they coexist with the material of folk-tales or rites, or for supposing that pigs of iron pre-existed as pigs in the mine. there is no falsifying in analysis _because_ the analysis is carried on within a situation which controls it. the fallacy and falsifying is on the part of the philosopher who ignores the contextual situation and who transfers the properties which things have as dependable evidential signs over to things in other modes of behavior. it is no reply to this position to say that the "elements" or simples were there prior to inquiry and to analysis and abstraction. of course their subject-matter was in some sense "there"; and, being there, was found, discovered, or detected--hit upon. i am not questioning this statement; rather, i have been asserting it. but i am asking for patience and industry to consider the matter somewhat further. i would ask the man who takes the terms of logical analysis (physical resolution for the sake of getting assured evidential indications of objects as yet unknown) to be things which coexist with the things of a non-inferential situation, to inquire _in what way_ his independent given ultimates were there prior to analysis. i would point out that in any case they did _not_ pre-exist _as_ signs. (_a_) consequently, whatever traits or properties they possess as signs must at least be referred exclusively to the reflective situation. and they must possess some distinguishing traits _as_ signs; otherwise they would be indistinguishable from anything else which happens to be thought of, and could not be employed as evidence: could not be, in short, what they are. if the reader will seriously ask just what traits data do possess as signs, or evidence, i shall be quite content to leave the issue to the results of his own inquiries. (_b_) any inquiry as to _how_ the data antecedently exist will, i am confident, show that they do not exist in the same purity, the same external exclusiveness and internal homogeneity, which they present within the situation of inference, any more than the iron which pre-existed in the rocks in the mountains was just the same as the fluxed and extracted ore. hence they did not exist in the same isolated simplicity. i have not the slightest interest in exaggerating the scope of this difference. the important matter is not its extent or range, but what such a change--however small--indicates: namely, that the material is entering into a new environment, and has been subjected to the changes which will make it useful and effective in that environment. it is trivial to suppose that the sole or even the primary difficulty which an analytic realism has to face is the occurrence of error and illusions, of "secondary" qualities, etc. the difficulty resides in the contrast of the world of a naïve, say aristotelian, realism with that of a highly intellectualized and analytic disintegration of the everyday world of things. if realism is generous enough to have a place _within_ its world (as a _res_ having social and temporal qualities as well as spatial ones) for data in process of construction of _new_ objects, the outlook is radically different from the case where, in the interests of a theory, a realism insists that analytic determinations are the sole real things.[ ] if it be not only conceded but asserted that the subject-matter generating the data of scientific procedure antedates the procedure, it may be asked: what is the point of insisting so much upon the fact that data exist only within the procedure? is not the statement either a trivial tautology or else an attempt to inject, _sub rosa_, a certain idealistic dependence upon thought into even brute facts? the question is a fair one. and the clew to the reply may be found in the consideration that it was not historically an easy matter to reduce the iron of the rocks to the iron which could freely and effectively be used in the manufacture of articles. it involved hitting upon a highly complicated art, but an art, nevertheless, which anyone with the necessary capital and education can command today as a matter of course, giving no thought to the fact that one is using an art constructed originally with vast pains. similarly it is by art, by a carefully determined technique, that the things of our primary experience are resolved into unquestioned and irreducible data, lacking in inner complexity and hence unambiguous. there is no call for the scientific man in the pursuit of his calling to take account of this fact, any more than the manufacturer need reckon with the arts which are required to deliver him his material. but a logician, a philosopher, is supposed to take a somewhat broader survey; and for his purposes the fact which the scientific inquirer can leave out of account, because it is no part of his business, may be the important fact. for the logician, it would seem, is concerned not with the significance of these or those data, but with the significance of there being such things as data, with their traits of irreducibleness, bruteness, simplicity, etc. now, as the special scientific inquirer answers the question as to the significance of his special brute facts by discovering other facts with which they are connected, so it would seem that the logician can find out the significance of the existence of data (the fact which concerns him) only by finding out the other facts with which _they_ coexist--their significance being their factual continuities. and the first step in the search for these other facts which supply significance is the recognition that they have been extracted for a purpose--for the purpose of guiding inference. it is this purposeful situation of inquiry which supplies the _other_ facts which give the existence of brute data their significance. and unless there is such a discovery (or some better one), the logician will inevitably fail in conceiving the import of the existence of brute data. and this misconception is, i repeat, just the defect from which an analytic presentative realism suffers. to perceive that the brute data laid bare in scientific proceedings are always traits of an extensive situation, and of that situation as one which needs control and which is to undergo modification in some respects, is to be protected from any temptation to turn logical specification into metaphysical atomism. the need for the protection is sufficiently great to justify spending some energy in pointing out that the brute objective facts of scientific discovery are discovered facts, discovered by physical manipulations which detach them from their ordinary setting. we have stated that, strictly speaking, data (as the immediate considerations from which controlled inference proceeds) are not objects but means, instrumentalities, of knowledge: things by which we know rather than things known. it is by the color stain that we know a cellular structure; it is by marks on a page that we know what some man believes; it is by the height of the barometer that we know the probability of rain; it is by the scratches on the rock that we know that ice was once there; it is by qualities detected in chemical and microscopic examination that we know that a thing is human blood and not paint. just what the realist asserts about so-called mental states of sensations, images, and ideas, namely, that they are not the subject-matter of knowledge but its agencies, holds of the chairs and tables to which he appeals in support of his doctrine of an immediate cognitive presentation, apart from any problem and any reflection. and there is very solid ground for instituting the comparison: the sensations, images, etc., of the idealist are nothing but the chairs, tables, etc., of the realist in their ultimate irreducible qualities.[ ] the problem in which the realist appeals to the immediate apprehension of the table is the epistemological problem, and he appeals to the table not as an object of knowledge (as he thinks he does), but as evidence, as a means of knowing his conclusion--his real _object_ of knowledge. he has only to examine his own evidence to see that it is evidence, and hence a term in a reflective inquiry, while the nature of knowledge is the _object_ of his knowledge. again, the question may be asked: since instrumentalism admits that the table is really "there," why make such a fuss about whether it is there as a means or as an object of knowledge? is not the distinction mere hair-splitting unless it is a way of smuggling in a quasi-idealistic dependence upon thought? the reply will, i hope, clinch the significance of the distinction, whether or no it makes it acceptable. respect for knowledge and its object is the ground for insisting upon the distinction. the object of knowledge is, so to speak, a more dignified, a more complete, sufficient, and self-sufficing thing than any datum can be. to transfer the traits of the object as known to the datum of reaching it, is a material, not a merely verbal, affair. it is precisely this shift which leads the presentative realist to substitute for irreducibility and unambiguity of logical function (use in inference) physical and metaphysical isolation and elementariness. it is this shift which generates the need of reconciling the deliverances of science with the structure and qualities of the world in which we directly live, since it sets up a rivalry between the claims of the data, of common-sense objects, and of scientific objects (the results of adequate inquiry). above all it commits us to a view that change is in some sense unreal, since ultimate and primary entities, being simple, do not permit of change. no; whatever is to be said about the validity of the distinction contended for, it cannot be said to be insignificant. a theory which commits us to the conception of a world of eleatic fixities as primary and which regards alteration and organization as secondary has such profound consequences for thought and conduct that a detection of its motivating fallacy makes a substantial difference. no more fundamental question can be raised than the range and force of the applicability to nature, life, and society of the whole-and-part conception. and if we confuse our premises by taking the existential instrumentalities of knowledge for its real objects, all distinctions and relations in nature, life, and society are thereby requisitioned to be really only cases of the whole-and-part nature of things. vi the instrumental theory acknowledges the objectivity of _meanings_ as well as of data. they are referred to and employed in reflective inquiry with the confidence attached to the hard facts of sense. pragmatic, as distinct from sensational, empiricism may claim to have antedated neo-realism in criticism of resolution of meanings into states or acts of consciousness. as previously noted, meanings are indispensable instrumentalities of reflection, strictly coincident with and correlative to what is analytically detected to be given, or irremovably there. data in their fragmentary character pose a problem; they also define it. they suggest possible meanings. whether they _indicate_ them as well as suggest them is a question to be resolved. but the meanings suggested are genuinely and existentially suggested, and the problem described by the data cannot be solved without their acknowledgment and use. that this instrumental necessity has led to a metaphysical hypostatizing of meanings into essences or subsistences having some sort of mysterious being apart from qualitative things and changes is a source of regret; it is hardly an occasion for surprise. to be sure of our footing, let us return to empirical ground. it is as certain an empirical fact that one thing suggests another as that fire alters the thing burned. the suggesting thing has to be there or given; something has to be there to do the suggesting. the suggested thing is obviously not "there" in the same way as that which suggests; if it were, it would not have to be suggested. a suggestion tends, in the natural man, to excite action, to operate as a stimulus. i may respond more readily and energetically to a suggested fire than to the thing from which the suggestion sprang: that is, the thing by itself may leave me cold, the thing as suggesting something else may move me vigorously. the response if effected has all the force of a belief or conviction. it is _as if_ we believed, on intellectual grounds, that the thing _is_ a fire. but it is discovered that not all suggestions are indications, or signifiers. the whale suggested by the cloud form does not stand on the same level as the fire suggested by smoke, and the suggested fire does not always turn out fire in fact. we are led to examine the original point of departure and we find out that it was not really smoke. in a world where skim-milk and cream suggestions, acted upon, have respectively different consequences, and where a thing suggests one as readily as the other (or skim-milk masquerades as cream), the importance of examination of the thing exercising the suggestive force prior to acting upon what it suggests is obvious. hence the act of response naturally stimulated is turned into channels of inspection and experimental (physical) analysis. we move our body to get a better hold on it, and we pick it to pieces to see what it is. this is the operation which we have been discussing in the last section. but experience also testifies that the thing suggested is worth attention on its own account. perhaps we cannot get very readily at the thing which, suggesting flame, suggests fire. it may be that reflection upon the meaning (or conception), "fire," will help us. fire--here, there, or anywhere, the "essence" fire--means thus and so; _if_ this thing really means fire, it will have certain traits, certain attributes. are they there? there are "flames" on the stage as part of the scenery. do they really indicate fire? fire would mean danger; but it is not possible that such a risk would be taken with an audience (other meanings, risk, audience, danger, being brought in). it must be something else. well, it is probably colored tissue-paper in strips rapidly blown about. this meaning leads us to closer inspection; it directs our observations to hunt for corroborations or negations. if conditions permitted, it would lead us to walk up and get at the thing in close quarters. in short, devotion to a suggestion, prior to accepting it as stimulus, leads first to other suggestions which may be more applicable; and, secondly, it affords the standpoint and the procedure of a physical experimentation to detect those elements which are the more reliable signs, indicators (evidence). _suggestions thus treated are precisely what constitute meanings, subsistences, essences_, etc. without such development and handling of what is suggested, the process of analyzing the situation to get at its hard facts, and especially to get at just those which have a right to determine inference, is haphazard--ineffectively done. in the actual stress of any such needed determination it is of the greatest importance to have a large stock of possible meanings to draw on, and to have them ordered in such a way that we can develop each promptly and accurately, and move quickly from one to another. it is not to be wondered at then that we not only conserve such suggestions as have been previously converted successfully into meanings, but also that we (or some men at least) turn professional inquirers and thinkers; that meanings are elaborated and ordered in related systems quite apart from any immediately urgent situation; or that a realm of "essences" is built up apart from that of existences. that suggestion occurs is doubtless a mystery, but so is it a mystery that hydrogen and oxygen make water. it is one of the hard, brute facts that we have to take account of. we can investigate the conditions under which the happening takes place, we can trace the consequences which flow from the happening. by these means we can so control the happening that it will take place in a more secure and fruitful manner. but all this depends upon the hearty acceptance of the happening as fact. suggestion does not of itself yield meanings; it yields only suggested things. but the moment we take a suggested thing and develop it in connection with other meanings and employ it as a guide of investigation (a method of inquiry), that moment we have a full-fledged meaning on our hands, possessing all the verifiable features which have been imported at any time to ideas, forms, species, essences, subsistences. this empirical identification of meaning by means of the specific fact of suggestion cuts deep--if occam's razor still cuts. a suggestion lies between adequate stimulation and logical indication. a cry of fire may start us running without reflection; we may have learned, as children are taught in school, to react without questioning. there is overt stimulation, but no suggesting. but if the response is held off or postponed, it may persist as suggestion: the cry suggests fire and suggests the advisability of flight. we may, in a sense we must, call suggestion "mental." but it is important to note what is meant by this term. fire, running, getting burned, are not mental; they are physical. but in their status of being suggested they may be called mental when we recognize this distinctive status. this means no more than that they are implicated in a specific way in a reflective situation, in virtue of which they are susceptible of certain modes of treatment. their status as suggested by certain features of the actual situation (and possibly meant or indicated as well as suggested) may be definitely fixed; then we get meanings, logical terms--determinations.[ ] words are of course the agencies of fixation chiefly employed, though any kind of physical existence--a gesture, a muscular contraction in the finger or leg or chest--under ready command may be used. what is essential is that there be a specific physical existence at hand which may be used to concrete and hold on to the suggestion, so that the latter may be handled on its own account. until thus detached and refixed there are things suggested, but hardly _a_ suggestion; things meant, but hardly a meaning; things ideated, but hardly an idea. and the suggested thing until detached is still too literal, too tied up with other things, to be further developed or to be successfully used as a method of experimentation in new directions so as to bring to light new traits. as data are signs which _indicate_ other existences, so meanings are signs which _imply_ other meanings.[ ] i am doubtful, for example, whether _this_ is a man or not; that is, i am doubtful as to some given traits when they are taken as signs or evidences, but i am inclined to the hypothesis of a man. having such a tentative or conceptual object in mind, i am enabled to explore economically and effectively, instead of at random, what is present, _provided_ i can elaborate the implications of the term "man." to develop its implications is all one with telling its meaning in connection with other meanings. being a man means, for example, speaking when spoken to--another meaning which need have been no part of "man" as originally suggested. this meaning of "answering questions" will then suggest a procedure which the term "man" in its first meaning did not possess; it is an implication or implied meaning which puts me in a new and possibly more fruitful relation to the thing. (the process of developing implications is usually termed "discourse" or ratiocination.) now, be it noted, replying to questions is no part of the _definition_ of man; it would not be now an implication of plato or of the russian czar for me. in other words, there is something in the actual situation which suggests _inquiring_ as well as _man_; and it is the interaction between these two suggestions which is fruitful. there is consequently no mystery about the fruitfulness of deduction--though this fruitfulness has been urged as though it offered an insuperable objection to instrumentalism. on the contrary, instrumentalism is the only theory to which deduction is not a mystery. if a variety of wheels and cams and rods which have been invented with reference to doing a given task are put together, one expects from the assembled parts a result which could not have been got from any one of them separately or from all of them together in a heap. because they are independent and unlike structures, working on one another, something new happens. the same is true of terms in relation to one another. when these are brought to bear upon one another, something new, something quite unexpected happens, quite as when one tries an acid with which he is not familiar upon a rock with which he is unfamiliar--that is, unfamiliar in such a conjunction, in spite of intimate acquaintance elsewhere. a definition may fix a certain modicum of meaning in the abstract, as we say; it is a specification of a minimum which gives the point of departure in every interaction of a term with other terms. but nothing follows from the definition by itself or in isolation. it is explicit (boringly so) and has no implications. but bring it in connection with another term with which it has not previously interacted and it may behave in the most delightful or in the most disgustingly disappointing way. the necessity for independent terms is made obvious in the modern theory of axioms. it escapes attention in much of the contemporary logic of transitive and non-transitive, symmetrical and non-symmetrical relations, because the terms are so loaded that there are no propositions at all, but only discriminations of orders of terms. the terms which figure in the discussions, in other words, are correlatives--"brother," "parent," "up," "to the right of," "like," "greater," "after." such terms are not logical terms; they are _halves_ of such terms as "brother-other-offspring-of-the-same-parents"; "parent-child"; "up-down"; "right-left"; "thing-similar-to-another-thing"; "greater-less"; "after-before." they express positions in a _determined_ situation; they are _relatives_, not relations. they lack implications, being explicit. but a man who is a brother and also a rival in love, and a poorer man than his rival brother, expresses an interaction of different terms from which something might happen: terms with implications, terms constituting a proposition, which a correlative term never does--till brought into conjunction with a term of which it is not a relative. to have called a thing "up" or "brother" is to have already solved its import in some situation. it is dead till set to work in some _other_ situation. experience shows, moreover, that certain qualities of things are much more fruitful and much more controllable than others when taken as meanings to be used in drawing conclusions. the term must be of a nature to develop a method of behavior by which to test whether it is the meaning of the situation. since it is desirable to have a stock of meanings on hand which are so connected that we can move readily from one to another in any direction, the stock is effective in just the degree in which it has been worked into a system--a comprehensive and orderly arrangement. hence, while all meanings are derived from things which antedate suggestion--or thinking or "consciousness"--not all qualities are equally fitted to be meanings of a wide efficiency, and it is a work of art to select the proper qualities for doing the work. this corresponds to the working over of raw material into an effective tool. a spade or a watchspring is made out of antecedent material, but does not pre-exist as a ready-made tool; and, the more delicate and complicated the work which it has to do, the more art intervenes. these summary remarks will have to pass muster as indicating what a more extensive treatment of a mathematical system of terms would show. man began by working such qualities as hate and love and fear and beauty into the meanings by which to interpret and control the perplexities of life. when they demonstrated their inefficacy, he had recourse to such qualities as heavy and light, wet and dry, making them into natural essences or explanatory and regulatory meanings. that greek mediaeval science did not get very far on these lines is a commonplace. scientific progress and practical control as systematic and deliberate matters date from the century of galileo, when qualities which lend themselves to mathematical treatment were seized upon. "the most promising of these ideal systems at first were of course the richer ones, the sentimental ones. the baldest and least promising ones were the mathematical ones; but the history of the latter's application is a history of steadily advancing successes, while that of the sentimentally richer ones is one of relative sterility and failure."[ ] there is no problem of why and how the plow fits, or applies to, the garden, or the watchspring to time-keeping. they were made for those respective purposes; the question is how well they do their work, and how they can be reshaped to do it better. yet they were made out of physical material; men used ready limbs or roots of trees with which to plow before they used metal. we do not measure the worth or reality of the tool by its closeness to its natural prototype, but by its efficiency in doing its work--which connotes a great deal of intervening art. the theory proposed for mathematical distinctions and relations is precisely analogous. they are not the creations of mind except in the sense in which a telephone is a creation of mind. they fit nature because they are derived from natural conditions. things naturally bulge, so to speak, and naturally alter. to seize upon these qualities, to develop them into keys for discovering the meanings of brute, isolated events, and to accomplish this effectively, to develop and order them till they become economical tools (and tools upon tools) for making an unknown and uncertain situation into a known and certain one, is the recorded triumph of human intelligence. the terms and propositions of mathematics are not fictions; they are not called into being by that particular act of mind in which they are used. no more is a self-binding reaper a figment, nor is it called momentarily into being by the man who wants to harvest his grain. but both alike are works of art, constructed for a purpose in doing the things which have to be done. we may say of terms what santayana so happily said of expression: "expression is a misleading term which suggests that something previously known is imitated or rendered; whereas the expression is itself an original fact, the values of which are then referred to the thing expressed, much as the honors of a chinese mandarin are attributed retroactively to his parents." the natural history of imputation of virtue should prove to the philosopher a profitable theme. even in its most superstitious forms (perhaps more _obviously_ in them than elsewhere) it testifies to the sense of a service to be performed and to a demand for application. the superstition lies in making the application to antecedents and to ancestors, where it is but a shroud, instead of to descendants, where it is a generating factor. every reflection leaves behind it a double effect. its immediate outcome is (as i tried to show earlier) the direct reorganization of a situation, a reorganization which confers upon its contents new increments of intrinsic meaning. its indirect and intellectual product is the defining of a meaning which (when fixed by a suitable existence) is a resource in subsequent investigations. i would not despise the assistance lent by the words "term" and "proposition." as slang has it, a pitched baseball is to the batter a "proposition"; it states, or makes explicit, what he has to deal with next amid all the surrounding and momentarily irrelevant circumstance. every statement extracts and sets forth the net result of reflection up to date as a condition of subsequent reflection. this extraction of the kernel of past reflections makes possible a throwing to one side of all the consequences of prior false and futile steps; it enables one to dispense with the experiences themselves and to deal only with their _net_ profit. in a favorite phrase of realism, it gives an object "as if there were no experience." it is unnecessary to descant upon the economy of this procedure. it eliminates everything which in spite of its immediate urgency, or vividness, or weight of past authority, is rubbish for the purpose in hand. it enables one to get down to business with just that which (presumably) is of importance in subsequent procedure. it is no wonder that these logical kernels have been elevated into metaphysical essences. the word "term" suggests the limiting condition of every process of reflection. it sets a fence beyond which it is, presumably, a waste to wander--an error. it sets forth that which _must_ be taken into account--a limit which is inescapable, something which is to ratiocination what the brute datum is to observation. in classic phrase, it is a notion, that is, a _noting_, of the distinctions which have been fixed for the purposes of the kind of inquiry now engaged in. one has only to compare the terms of present scientific discourse with those of, say, aristotle, to see that the importance of terms as instruments of a proper survey of and attack upon existential situations is such that the terms resulting naturally and spontaneously from reflection have been dropped and more effective ones substituted. in one sense, they are all equally objective; aquosity is as genuine, as well as more obvious, a notion as the present chemical conception. but the latter is able to enter a much wider scope of inquiries and to figure in them more prosperously. as a special class of scientific inquirers develops, terms that were originally _by-products_ of reflection become primary objects for the intellectual class. the "troubles" which occasion reflection are then _intellectual_ troubles, discrepancies within some current scheme of propositions and terms. the situation which undergoes reorganization and increase of comprised significance is that of the subject-matter of specialized investigation. nevertheless the same general method recurs within it, and the resulting objects--the terms and propositions--are for all, except those who produce them, instruments, not terminal objects. the objection to analytic realism as a metaphysics of existence is not so much an undue formalism as its affront to the commonsense-world of action, appreciation, and affection. the affront, due to hypostatizing terms into objects, is as great as that of idealism. a naïve realism withstands both affronts. my interest, however, is not to animadvert upon analytic realism. it is to show how the main tenets of instrumental logic stand in relation to considerations which, although ignored by the idealism which was current when the theory received its first formulation, demand attention: the objective status of data and terms with respect to states of mind or acts of awareness. i have tried to show that the theory, without mutilation or torturing, makes provision for these considerations. they are not objections to it; they are considerations which are involved in it. there are questions at issue, but they concern not matters of logic but matters of fact. they are questions of the _existential_ setting of certain logical distinctions and relations. as to the comparative merits of the two schemes, i have nothing to say beyond what has been said, save that the tendency of the analytic realism is inevitably to treat a difference between the logic of inquiry and of dialectic as if it were itself a matter to be settled by the logic of dialectic. i confess to some fear that a philosophy which fails to identify science with terms and propositions about things which are not terms and propositions, will first exaggerate and then misconstrue the function of dialectics, and land philosophy in a formalism like unto the scholasticism from which the older empiricism with all its defects emancipated those who took it to heart. vii return with me, if you please, to fundamentals. the word "experience" is used freely in the essays and without much explanation. in view of the currency of subjectivistic interpretations of that term, the chief wonder is probably that the doctrine of the essays was not more misunderstood than was actually the case. i have already said something designed to clarify the sense in which the term was used. i now come back to the matter. what is the reason for using the term at all in philosophy? the history of philosophy supplies, i think, the answer. no matter how subjective a turn was given to the word by hume and kant, we have only to go to an earlier period to see that the appeal to experience in philosophy was coincident with the emancipation of science from occult essences and causes, and with the substitution of methods of observation, controlled by experimentation and employing mathematical considerations, for methods of mere dialectic definition and classification. the appeal to experience was the cry of the man from missouri--the demand to be shown. it sprang from the desire to command nature by observing her, instead of anticipating her in order to deck her with aesthetic garlands and hold her with theological chains. the significance of experience was not that sun and moon, stick and stone, are creatures of the senses, but that men would not put their trust any longer in things which are said, however authoritatively, to exist, unless these things are capable of entering into specifiable connections with the organism and the organism with them. it was an emphatic assertion that until men could see _how_ things got into belief, and what they did when they got there, intellectual acceptance would be withheld. has not the lesson, however, been so well learned that we can drop reference to experience? would that such were the case. but the time does not seem to have come. some things enter by way of the imagination, stimulated by emotional preferences and biases. for _certain_ purposes, they are not the worse for having entered by that gate, instead of through sensory-motor adjustments. or they may have entered because of the love of man for logical form and symmetry and system, and because of the emotional satisfaction which harmony awakens in a sensitive soul. they too need not be any worse for all that. but surely it is among the businesses of philosophy to discriminate between the kinds of goodness possessed by different kinds of things. and how can it discriminate unless by telling by what road they got into our experience and what they do after they get there? assuredly the difference is not in _intrinsic_ content. it is not because of self-obvious and self-contained traits of the immediate terms that dante's world belongs to poetry and newton's to scientific astronomy. no amount of pure inspection and excogitation could decide which belongs to which world. the difference in status and claim is made by what we call experience: by the place of the two systems in experience with respect to their generation and consequences. and assuredly any philosophy which takes science to be not an _account_ of the world (which it is), but a literal and exhaustive apprehension of it in its full reality, a philosophy which therefore has no place for poetry or possibilities, still needs a theory of experience. if a scientific man be asked what is truth, he will reply--if he frame his reply in terms of his practice and not of some convention--that which is accepted upon adequate evidence. and if he is asked for a description of adequacy of evidence, he certainly will refer to matters of observation and experiment. it is not the self-inclosed character of the terms and propositions nor their systematic ordering which settles the case for him; it is the way they were obtained and what he can do with them in getting other things. and when a mathematician or logician asks philosophy to abandon this method, then is just the time to be most vigorous in insisting upon the necessity of reference to "experience" in order to fix the import of mathematical and logical pretensions. when students influenced by the symmetry and system of mathematics cease building up their philosophies in terms of traits of mathematical subject-matter in isolation, then empirical philosophers will have less call to mention experience. meantime, i know of no way of fixing the scope and claims of mathematics in philosophy save to try to point out just at what juncture it enters experience and what work it does after it has got entrance. i have made such an attempt in my account of the fixation and handling of suggestions as meanings. it is defective enough, but the defects are to be remedied by a better empirical account and not by setting up against experience the claims of a logic aloof from experience. the objection then to a logic which rules out knowledge getting, and which bases logic exclusively upon the traits of known objects, is that it is self-contradictory. there is no way to know what are the traits of known objects, as distinct from imaginary objects, or objects of opinion, or objects of unanalytic common-sense, save by referring to the operations of getting, using, and testing evidence--the processes of knowledge getting. i am making no appeal for skepticism at large; i am not questioning the right of the physicist, the mathematician, or the symbolic logicist to go ahead with accepted objects and do what he can with them. i am pointing out that anyone who professes to be concerned with finding out what knowledge _is_, has for his primary work the job of finding out why it is so much safer to proceed with just these objects, than with those, say, of aristotelian science. aristotle was not lacking in acuteness nor in learning. to him it was clear that objects of knowledge are the things of ordinary perception, so far as they are referred to a form which comparison of perceived things, in the light of a final cause, makes evident. if this view of the objects of knowledge has gone into the discard, if quite other objects of knowledge are now received and employed, it is because the methods of _getting_ knowledge have been transformed, till, for the working scientist, "objects of knowledge" mean precisely the objects which have been obtained by approved processes of inquiry. to exclude consideration of these processes is thus to throw away the key to understanding knowledge and its objects. there is a certain ironical humor in taking advantage of all the improved methods of experimental inquiry with respect to all objects of knowledge--save one, knowledge itself; in denying their relevancy to knowing knowledge, and falling back upon the method everywhere else disavowed--the method of relying upon isolated, self-contained properties of subject-matter. one of the points which gave much offense in the essays was the reference to genetic method--to a natural history of knowledge. i hope what has now been said makes clearer the nature of that reference. i was to blame for not making the point more explicit; but i cannot altogether blame myself for my naïveté in supposing that others understood by a natural history of knowledge what i understood by it. it had not occurred to me that anyone would think that the history by which human ignorance, error, dogma, and superstition had been transformed, even in its present degree of transformation, into knowledge was something which had gone on exclusively inside of men's heads, or in an inner consciousness. i thought of it as something going on in the world, in the observatory and the laboratory, and in the application of laboratory results to the control of human health, well-being, and progress. when a biologist says that the way to understand an organ, or the sociologist that the way to know an institution, resides in its genesis and history, he is understood to mean _its_ history. i took the same liberty for knowledge, that is, for science. the accusation of "subjectivisim" taken in this light appears as a depressing revelation of what the current opinion about the processes of knowledge is. to stumble on a stone need not be a process of knowledge; to hit it with a hammer, to pour acid upon it, to put pieces in the crucible, to subject things to heat and pressure to see if one can make a similar stone, _are_ processes of knowledge. so is fixing suggestions by attaching names, and so is devising ways of putting these terms together so that new suggestions will arise, or so that suggestions may be transferred from one situation to another. but not one of these processes is "subjective" in any sense which puts subjectivity in opposition to the public out-of-doors world of nature and human companionship. to set genesis in opposition to analysis is merely to overlook the fact that the sciences of existence have found that considerations of genesis afford their most effective methods of analysis.[ ] the same kind of consideration applies to the favorable view taken of psychology. if reference to modes and ways of experience--to experiencing--is important for understanding the things with which philosophy deals, then psychology is useful as a matter of course. for what is meant by psychology is precisely a discrimination of the acts and attitudes of the organism which have a bearing upon respective subject-matters and which have accordingly to be taken account of before the subject-matters can be properly discriminated. the matter was especially striking in the case of lotze. he protested constantly against the use of psychology, and yet his own data and procedures were infected at every turn by psychology, and, if i am at all correct, by a false psychology. the particular separation which he made between psychology and logic rested indeed upon a particular psychological assumption. the question is worth asking: is not the marked aversion on the part of some philosophers to any reference to psychology a freudian symptom? a word more upon the place assigned by the essays to _need_ and _purpose_ and the humanistic factor generally. to save time i may quote a sentence from an early review which attributes to the essays the following doctrine: "if the plan turns out to be useful for our need, it is correct--the judgment is true. the real-ideal distinction is that between stimulus of environment and plan of action or tentative response. both real and ideal are equally experiences of the individual man." these words can be interpreted either so as to convey the position fairly, or so as radically to misconceive it; the latter course is a little easier, as the words stand. that "real and ideal" are experiences of the individual man in the sense that they actually present themselves as specifications which can be studied by any man who desires to study them is true enough. that such a study is as much required for determining their characters as it is for determining those of carbon dioxide or of the constitution of great britain is also the contention of the paper. but if the words quoted suggest to anyone that the real or even the ideal are somehow possessions of an individual man, things secreted somewhere about him and then ejected, i can only say that i cannot understand the doctrine. i know of no ready-made and antecedent conception of "the individual man." instead of telling about the nature of experience by means of a prior conception of individual man, i find it necessary to go to experience to find out what is meant by "individual" and by "man"; and also by "the." consequently even in such an expression as "my experience," i should wish not to contradict this idea of method by using the term "my" to swallow up the term "experience," any more than if i said "my house," or "my country." on the contrary, i should expect that any intelligible and definite use of such phrases would throw much more light upon "me" than upon "house" or "country"--or "experience." the possible misunderstanding is, i think, actual in the reference to "our needs" as a criterion of the correctness of truth of an idea or plan. according to the essays, it is the needs of a _situation_ which are determinative. they evoke thought and the need of knowing, and it is only within the situation that the identification of the needs with a self occurs; and it is only by reflection upon the place of the agent in the encompassing situation that the nature of _his_ needs can be determined. in fact, the actual occurrence of a disturbed, incomplete, and needy _situation_ indicates that _my_ present need is precisely to investigate, to explore, to hunt, to pull apart things now tied together, to project, to plan, to invent, and then to test the outcome by seeing how it works as a method of dealing with hard facts. one source of the demand, in short, for reference to experience as the encompassing universe of discourse is to keep us from taking such terms as "self," "my," "need," "satisfaction," etc., as terms whose meanings can be accepted and proved either by themselves or by even the most extensive dialectic reference to other terms. terms like "real" and "ideal," "individual," "man," "my," certainly allow of profitable dialectic (or purely prepositional) clarification and elaboration. but nothing is settled until these discursive findings have been applied, through action, to things, and an experience has been effected, which either meets or evades the specification conceptually laid down. to suppose, for example, that the import of the term "ideal" can be settled apart from exhibiting in experience some specific affair, is to maintain in philosophy that belief in the occult essence and hidden cause which science had to get rid of before it got on the right track. the idealistic misconception of experience is no reason for throwing away its significant point of contact with modern science and for having recourse then to objects distinguished from old-fashioned _dinge an sich_ only because they involve just that reference to those experiences by which they were established and to which they are applied that propositional or analytic realism professedly and elaborately ignores. in revenge, this ignoring leaves on our hands the "me," or knowing self, as a separate thing within which experience falls (instead of its falling in a specifiable place within experience), and generates the insoluble problem of how a subjective experience can beget objective knowledge. in concluding, let me say that reference to experience seems at present to be the easiest way of realizing the continuities among subject-matters that are always getting split up into dualisms. a creation of a world of subsistences or essences which are quite other than the world of natural existences (which are other than natural existences adapted to the successful performance of inference) is in itself a technical matter, though a discouraging one to a philosopher expertly acquainted with all the difficulties which that view has generated from the time of plato down. but the assistance which such a philosophy lends to the practical and current divorce of the "ideal" from the natural world makes it a thing to be dreaded for other than professional reasons. god only knows how many of the sufferings of life are due to a belief that the natural scene and operations of our life are lacking in ideal import, and to the consequent tendency to flee for the lacking ideal factors to some other world inhabited exclusively by ideals. that such a cut-off, ideal world is impotent for direction and control and change of the natural world follows as a matter of course. it is a luxury; it belongs to the "genteel tradition" of life, the persistence of an "upper" class given to a detached and parasitic life. moreover, it places the scientific inquirer within that irresponsible class. if philosophers could aid in making it clear to a troubled humanity that ideals are continuous with natural events, that they but represent their possibilities, and that recognized possibilities form methods for a conduct which may realize them in fact, philosophers would enforce the sense of a social calling and responsibility. i do not say that pointing out the continuity and interaction of various attitudes and interests in experience is the only way of effecting this consummation. but for a large number of persons today it is the readiest way. much may be said about that other great rupture of continuity which analytic realism would maintain: that between the world and the knower as something outside of it, engaged in an otiose contemplative survey of it. i can understand the social conditions which generated this conception of an aloof knower. i can see how it protected the growth of responsible inquiry which takes effect in change of the environment, by cultivating a sense of the innocuousness of knowing, and thus lulling to sleep the animosity of those who, being in control, had no desire to permit reflection which had practical import. i can see how specialists at any time, professional knowers, so to speak, find in this doctrine a salve for conscience--a solace which all thinkers need as long as an effective share in the conduct of affairs is not permitted them. above all, i can see how seclusion and the absence of the pressure of immediate action developed a more varied curiosity, greater impartiality, and a more generous outlook. but all this is no reason for continuing the idealization of a remote and separate mind or knower now that the method of intelligence is perfected, and changed social conditions not only permit but demand that intelligence be placed within the procession of events. an intellectual integrity, an impartiality and detachment, which is maintained only in seclusion is unpleasantly reminiscent of other identifications of virtue with the innocence of ignorance. to place knowledge where it arises and operates in experience is to know that, as it arose because of the troubles of man, it is confirmed in reconstructing the conditions which occasioned those troubles. genuine intellectual integrity is found in experimental knowing. until this lesson is fully learned, it is not safe to dissociate knowledge from experiment nor experiment from experience. footnotes: [ ] i am indebted to an unpublished manuscript of mr. s. klyce of winchester, massachusetts, for the significance of the fact that our words divide into _terms_ (of which more in the sequel) and into names which are not (strictly speaking) terms at all, but which serve to remind us of the vast and vague continuum, select portions of which only are designated by words as _terms_. he calls such words "infinity and zero" words. the word "experience" is a typical instance of an "infinity word." mr. klyce has brought out very clearly that a direct situation of experience ("situation" as i employ it is another such word) has no need of any word for itself, the thing to which the word would point being so egregiously there on its own behalf. but when communication about it takes place (as it does, not only in converse with others, but when a man attempts a mutual reference of different periods of his own life) a word is needed to remind both parties of this taken-for-granted whole (another infinity term), while confusion arises if explicit attention is not called to the fact that it is a very different sort of word from the definite terms of discourse which denote distinctions and their relations to one another. in the text, attention is called to the fact that the business man wrestling with a difficulty or a scientific man engaged in an inquiry finds his checks and control specifically in the situation in which he is employed, while the theorizer at large leaves out these checks and limits, and so loses his clews. well, the words "experience," "situation," etc., are used to _remind_ the thinker of the need of reversion to precisely something which never can be one of the terms of his reflection but which nevertheless furnishes the existential meaning and status of them all. "intuition," mysticism, philosophized or sophisticated monism, are all of them aberrant ways of protesting against the consequences which result from failing to note what is conveyed by words which are not terms. were i rewriting these essays _in toto_ i should try to take advantage of these and other indispensable considerations advanced by mr. klyce; but as the essays must stand substantially as they were originally written, and as an introduction to them must, in order to be intelligible, be stated in not incongruous phraseology, i wish simply to ask the reader to bear in mind this radical difference between such words as "experience," "reality," "universe," "situation," and such terms as "typewriter," "me," "consciousness," "existence," when used (as they must be used if they are to be terms) in a differential sense. the term "reality" is particularly treacherous, for the careless tradition of philosophy (a carelessness fostered, i am sure, by failure to make verbally explicit the distinction to which mr. klyce has called attention) uses "reality" both as a term of indifferent reference, equivalent to everything taken together or referred to _en masse_ as over against some discrimination, and also as a discriminative term with a highly eulogistic flavor: as _real_ money in distinction from counterfeit money. then, although every inquiry in daily life, whether technological or scientific, asks _whether_ a thing is real only in the sense of asking _what_ thing is real, philosophy concludes to a wholesale distinction between the real and the unreal, the real and the apparent, and so creates a wholly artificial problem. if the philosopher, whether idealistic or realistic, who holds that it is self-contradictory to criticize purely intellectualistic conceptions of the world, because the criticism itself goes on intellectualistic terms, so that its validity depends upon intellectual (or cognitive) conditions, will but think of the very brute doings in which a chemist engages to fix the meanings of his terms and to test his theories and conceptions, he will perceive that all intellectual knowing is but a method for conducting an experiment, and that arguments and objections are but stimuli to induce somebody to try a certain experiment--to have recourse, that is, to a non-logical non-intellectual affair. or again, the argument is an invitation to him to note that at the very time in which he is thinking, his thinking is set in a continuum which is not an object of thought. the importance attached to the word "experience," then, both in the essays and in this introduction, is to be understood as an invitation to employ thought and discriminative knowledge as a means of plunging into something which no argument and no term can express; or rather as an invitation to note the fact that no plunge is needed, since one's own thinking and explicit knowledge are already constituted by and within something which does not need to be expressed or made explicit. and finally, there is nothing mystical about this, though mysticism doubtless roots in this fact. its import is only to call notice to the meaning of, say, formulae communicated by a chemist to others as the result of his experiment. all that can be communicated or expressed is that one believes such and such a thing. the communication has scientific instead of merely social significance because the communicated formula is a direction to other chemists to try certain procedures and see what they get. the _direction_ is capable of expression; the result of the experiment, the experience, to which the propositions refer and by which they are tested, is not expressible. (poetry, of course, is a more competent organ of suggesting it than scientific prose.) the word "experience" is, i repeat, a notation of an inexpressible as that which decides the ultimate status of all which is expressed; inexpressible not because it is so remote and transcendent, but because it is so immediately engrossing and matter of course. [ ] there are certain points of similarity between this doctrine and that of holt regarding contradictions and that of montague regarding "consciousness" as a case of potential energy. but the latter doctrine seems to me to suffer, first, from an isolation of the brain from the organism, which leads to ignoring the active doing, and, secondly, from an isolation of the "moment" of reduction of actual to potential energy. it appears as a curiously isolated and self-sufficient event, instead of as the focus of readjustment in an organized activity at the pivotal point of maximum "tension"--that is, of greatest inhibition in connection with greatest tendency to discharge. and while i think holt is wholly right in connecting the possibility of error with objectively plural and conflicting forces, i should hardly regard it as linguistically expedient to call counterbalancing forces "contradictory." the counterbalancing forces of the vaulting do not seem to me contradictory in the arch. but if their presence led me to attempt to say "up" and "down" at the same time there would be contradiction. but even admitting that contradictory propositions are merely about forces which are contradictory--heating and cooling--it is still a long way to error. for propositions about such "contradictions" are obviously true propositions. it is only when we make that reaction to one factor which is appropriate to dealing with the other that there is error; and this can happen where there are no contradictory forces at all beyond the fact that the _agent_ is pulled two incompatible and opposed ways at the same time. [ ] for emphasis i am here exaggerating by condensing into a single decisive act an operation which is continuously going on. [ ] i would remark in passing that a recognition that a thing may be continuous in one respect and discrete in another would obviate a good many difficulties. [ ] in effect, the fallacy is the same as that of an idealistic theory which holds that all objects are "really" associations of sensations. [ ] this statement is meant literally. the "sensations" of color, sound, etc., to which appeal is made in a scientific inquiry are nothing mental in structure or stuff; they are actual, extra-organic things analyzed down to what is so indubitably there that it may safely be taken as a basis of inference. [ ] a term is not of course a mere word; a mere word is non-sense, for a sound by itself is not a word at all. nor is it a mere meaning, which is not even natural non-sense, being (if it be at all) supernatural or transcendental nonsense. "terms" signify that certain absent existences are indicated by certain given existences, in the respect that they are abstracted and fixed for intellectual use by some physically convenient means, such as a sound or a muscular contraction of the vocal organs. [ ] this distinction of indication as existential and implication as conceptual or essential, i owe to mr. alfred sidgwick. see his _fallacies_, p. . [ ] james, _psychology_, ii, . [ ] i have even seen, in a criticism of the essays, the method of genesis opposed to the method of experimentation--as if experimentation were anything but the generation of some special object! ii the relationship of thought and its subject-matter no one doubts that thought, at least reflective as distinct from what is sometimes called constitutive thought, is derivative and secondary. it comes after something and out of something, and for the sake of something. no one doubts that the thinking of everyday practical life and of science is of this reflective type. we think about; we reflect over. if we ask what it is which is primary and radical to thought; if we ask what is the final objective for the sake of which thought intervenes; if we ask in what sense we are to understand thought as a derived procedure, we are plunging ourselves into the very heart of the logical problem: the relation of thought to its empirical antecedents and to its consequent, truth, and the relation of truth to reality. yet from the naïve point of view no difficulty attaches to these questions. the antecedents of thought are our universe of life and love; of appreciation and struggle. we think about anything and everything: snow on the ground; the alternating clanks and thuds that rise from below; the relation of the monroe doctrine to the embroglio in venezuela; the relation of art to industry; the poetic quality of a painting by botticelli; the battle of marathon; the economic interpretation of history; the proper definition of cause; the best method of reducing expenses; whether and how to renew the ties of a broken friendship; the interpretation of an equation in hydrodynamics, etc. through the madness of this miscellaneous citation there appears so much of method: anything--event, act, value, ideal, person, or place--may be an object of thought. reflection busies itself alike with physical nature, the record of social achievement, and the endeavors of social aspiration. it is with reference to _such_ affairs that thought is derivative; it is with reference to them that it intervenes or mediates. taking some part of the universe of action, of affection, of social construction, under its special charge, and having busied itself therewith sufficiently to meet the special difficulty presented, thought releases that topic and enters into further more direct experience. sticking for a moment to this naïve standpoint, we recognize a certain rhythm of direct practice and derived theory; of primary construction and of secondary criticism; of living appreciation and of abstract description; of active endeavor and of pale reflection. we find that every more direct primary attitude passes upon occasion into its secondary deliberative and discursive counterpart. we find that when the latter has done its work it passes away and passes on. from the naïve standpoint such rhythm is taken as a matter of course. there is no attempt either to state the nature of the occasion which demands the thinking attitude, or to formulate a theory of the standard by which is judged its success. no general theory is propounded as to the exact relationship between thinking and what antecedes and succeeds it. much less do we ask how empirical circumstances can generate rationality of thought; nor how it is possible for reflection to lay claim to power of determining truth and thereby of constructing further reality. if we were to ask the thinking of naïve life to present, with a minimum of theoretical elaboration, its conception of its own practice, we should get an answer running not unlike this: thinking is a kind of activity which we perform at specific need, just as at other need we engage in other sorts of activity: as converse with a friend; draw a plan for a house; take a walk; eat a dinner; purchase a suit of clothes, etc. in general, its material is anything in the wide universe which seems to be relevant to this need--anything which may serve as a resource in defining the difficulty or in suggesting modes of dealing effectively with it. the measure of its success, the standard of its validity, is precisely the degree in which the thinking actually disposes of the difficulty and allows us to proceed with more direct modes of experiencing, that are forthwith possessed of more assured and deepened value. if we inquire why the naïve attitude does not go on to elaborate these implications of its own practice into a systematic theory, the answer, on its own basis, is obvious. thought arises in response to its own occasion. and this occasion is so exacting that there is time, as there is need, only to do the thinking which is needed in that occasion--not to reflect upon the thinking itself. reflection follows so naturally upon its appropriate cue, its issue is so obvious, so practical, the entire relationship is so organic, that once grant the position that thought arises in reaction to specific demand, and there is not the particular type of thinking called logical theory because there is not the practical demand for reflection of that sort. our attention is taken up with particular questions and specific answers. what we have to reckon with is not the problem of, how can i think _überhaupt_? but, how shall i think right _here and now_? not what is the test of thought at large, but what validates and confirms _this_ thought? in conformity with this view, it follows that a generic account of our thinking behavior, the generic account termed logical theory, arises at historic periods in which the situation has lost the organic character above described. the general theory of reflection, as over against its concrete exercise, appears when occasions for reflection are so overwhelming and so mutually conflicting that specific adequate response in thought is blocked. again, it shows itself when practical affairs are so multifarious, complicated, and remote from control that thinking is held off from successful passage into them. anyhow (sticking to the naïve standpoint), it is true that the stimulus to that particular form of reflective thinking termed logical theory is found when circumstances require the act of thinking and nevertheless impede clear and coherent thinking in detail; or when they occasion thought and then prevent the results of thinking from exercising directive influence upon the immediate concerns of life. under these conditions we get such questions as the following: what is the relation of rational thought to crude or unreflective experience? what is the relation of thought to reality? what is the barrier which prevents reason from complete penetration into the world of truth? what is it that makes us live alternately in a concrete world of experience in which thought as such finds not satisfaction, and in a world of ordered thought which is yet only abstract and ideal? it is not my intention here to pursue the line of historical inquiry thus suggested. indeed, the point would not be mentioned did it not serve to fix attention upon the nature of the logical problem. it is in dealing with this latter type of question that logical theory has taken a turn which separates it widely from the theoretical implications of practical deliberation and of scientific research. the two latter, however much they differ from each other in detail, agree in a fundamental principle. they both assume that every reflective problem and operation arises with reference to some _specific_ situation, and has to subserve a _specific_ purpose dependent upon its own occasion. they assume and observe distinct limits--limits from which and to which. there is the limit of origin in the needs of the particular situation which evokes reflection. there is the limit of terminus in successful dealing with the particular problem presented--or in retiring, baffled, to take up some other question. the query that at once faces us regarding the nature of logical theory is whether reflection upon reflection shall recognize these limits, endeavoring to formulate them more exactly and to define their relationships to each other more adequately; or shall it abolish limits, do away with the matter of specific conditions and specific aims of thought, and discuss thought and its relation to empirical antecedents and rational consequents (truth) at large? at first blush, it might seem as if the very nature of logical theory as generalization of the reflective process must of necessity disregard the matter of particular conditions and particular results as irrelevant. how, the implication runs, could reflection become generalized save by elimination of details as irrelevant? such a conception in fixing the central problem of logic fixes once for all its future career and material. the essential business of logic is henceforth to discuss the relation of thought as such to reality as such. it may, indeed, involve much psychological material, particularly in the discussion of the processes which antecede thinking and which call it out. it may involve much discussion of the concrete methods of investigation and verification employed in the various sciences. it may busily concern itself with the differentiation of various types and forms of thought--different modes of conceiving, various conformations of judgment, various types of inferential reasoning. but it concerns itself with any and all of these three fields, not on their own account or as ultimate, but as subsidiary to the main problem: the relation of thought as such, or at large, to reality as such, or at large. some of the detailed considerations referred to may throw light upon the terms under which thought transacts its business with reality; upon, say, certain peculiar limitations it has to submit to as best it may. other considerations throw light upon the ways in which thought gets at reality. still other considerations throw light upon the forms which thought assumes in attacking and apprehending reality. but in the end all this is incidental. in the end the one problem holds: how do the specifications of thought as such hold good of reality as such? in fine, logic is supposed to grow out of the epistemological inquiry and to lead up to its solution. from this point of view various aspects of logical theory are well stated by an author whom later on we shall consider in some detail. lotze[ ] refers to "universal forms and principles of thought which hold good everywhere both in judging of reality and in weighing possibility, _irrespective of any difference in the objects_." this defines the business of _pure_ logic. this is clearly the question of thought as such--of thought at large or in general. then we have the question "of how far the most complete structure of thought ... can claim to be an adequate account of that which we seem compelled to assume as the object and occasion of our ideas." this is clearly the question of the relation of thought at large to reality at large. it is epistemology. then comes "applied logic," having to do with the actual employment of concrete forms of thought with reference to investigation of specific topics and subjects. this "applied" logic would, if the standpoint of practical deliberation and of scientific research were adopted, be the sole genuine logic. but the existence of thought _in itself_ having been agreed upon, we have in this "applied" logic only an incidental inquiry of how the particular resistances and oppositions which "pure" thought meets from particular matters may best be discounted. it is concerned with methods of investigation which obviate defects in the relationship of thought at large to reality at large, as these present themselves under the limitations of human experience. it deals merely with hindrances, and with devices for overcoming them; it is directed by considerations of utility. when we reflect that this field includes the entire procedure of practical deliberation and of concrete scientific research, we begin to realize something of the significance of the theory of logic which regards the limitations of specific origination and specific outcome as irrelevant to its main problem, which assumes an activity of thought "pure" or "in itself," that is, "irrespective of any difference in its objects." this suggests, by contrast, the opposite mode of stating the problem of logical theory. generalization of the nature of the reflective process certainly involves elimination of much of the specific material and contents of the thought-situations of daily life and of critical science. quite compatible with this, however, is the notion that it seizes upon _certain_ specific conditions and factors, and aims to bring them to clear consciousness--not to abolish them. while eliminating the particular material of particular practical and scientific pursuits, ( ) it may strive to hit upon the common denominator in the various situations which are antecedent or primary to thought and which evoke it; ( ) it may attempt to show how typical features in the specific antecedents of thought call out diverse typical modes of thought-reaction; ( ) it may attempt to state the nature of the specific consequences in which thought fulfils its career. ( ) it does not eliminate dependence upon specific occasions as provocative of thought, but endeavors to define _what_ in the various occasions renders them thought-provoking. the specific occasion is not eliminated, but insisted upon and brought into the foreground. consequently, empirical considerations are not subsidiary incidents, but are of essential importance so far as they enable us to trace the generation of the thought-situation. ( ) from this point of view the various types and modes of conceiving, judging, and inference are treated, not as qualifications of thought _per se_ or at large, but of reflection engaged in its specific, most economic, effective response to its own particular occasion; they are adaptations for control of stimuli. the distinctions and classifications that have been accumulated in "formal" logic are relevant data; but they demand interpretation from the standpoint of use as organs of adjustment to material antecedents and stimuli. ( ) finally the question of validity, or ultimate objective of thought, is relevant; but relevant as a matter of the specific issue of the specific career of a thought-function. all the typical investigatory and verificatory procedures of the various sciences indicate the ways in which thought actually brings to successful fulfilment its dealing with various types of problems. while the epistemological type of logic may, as we have seen, leave (under the name of applied logic) a subsidiary place open for the instrumental type, the type which deals with thinking as a specific procedure relative to a specific antecedent occasion and to a subsequent specific fulfilment is not able to reciprocate the favor. from its point of view, an attempt to discuss the antecedents, data, forms, and objectives of thought, apart from reference to particular position occupied and particular part played in the growth of experience, is to reach results which are not so much either true or false as they are radically meaningless--because they are considered apart from limits. its results are not only abstractions (for all theorizing ends in abstractions), but abstractions without possible reference or bearing. from this point of view, the taking of something (whether that something be a thinking activity, its empirical stimulus, or its objective goal), apart from the limits of a historic or developing situation, is the essence of _metaphysical_ procedure--in that sense of metaphysics which makes a gulf between it and science. as the reader has doubtless anticipated, it is the object of this chapter to present the problem and industry of reflective thought from the standpoint of naïve experience, using the term in a sense wide enough to cover both practical procedure and concrete scientific research. i resume by saying that this point of view knows no fixed distinction between the empirical things and values of unreflective life and the most abstract process of rational thought. it knows no fixed gulf between the highest flight of theory and a control of the details of practical construction and behavior. it passes, according to the occasion and opportunity of the moment, from the attitude of loving and struggling and doing to that of thinking and the reverse. its contents or material shift their values back and forth from technological or utilitarian to aesthetic, ethical, or affectional. it utilizes data of perception, of meaning or of discursive ideation as need calls, just as an inventor now utilizes heat, now mechanical strain, now electricity, according to the demands set by his aim. anything from past experience may be taken which appears to be an element in either the statement or the solution of the present problem. thus we understand the coexistence, without contradiction, of an indeterminate possible field and a limited actual field. the undefined range of possible materials becomes specific through reference to an end. in all this, there is no difference of kind between the methods of science and those of the plain man. the difference is the greater control by science of the statement of the problem, and of the selection and use of relevant material, both sensible and conceptual. the two are related to each other just as the hit-or-miss, trial-and-error inventions of uncivilized man stand to the deliberate and consecutively persistent efforts of a modern inventor to produce a certain complicated device for doing a comprehensive piece of work. neither the plain man nor the scientific inquirer is aware, as he engages in his reflective activity, of any transition from one sphere of existence to another. he knows no two fixed worlds--reality on one side and mere subjective ideas on the other; he is aware of no gulf to cross. he assumes uninterrupted, free, and fluid passage from ordinary experience to abstract thinking, from thought to fact, from things to theories and back again. observation passes into development of hypothesis; deductive methods pass into use in description of the particular; inference passes into action, all with no sense of difficulty save those found in the particular task in question. the fundamental assumption is _continuity_. this does not mean that fact is confused with idea, or observed datum with voluntary hypothesis, theory with doing, any more than a traveler confuses land and water when he journeys from one to the other. it simply means that each is placed and used with reference to service rendered the other, and with reference to the future use of the other. only the epistemological spectator of traditional controversies is aware of the fact that the everyday man and the scientific man in this free and easy intercourse are rashly assuming the right to glide over a cleft in the very structure of reality. this fact raises a query not favorable to the epistemologist. why is it that the scientific man, who is constantly plying his venturous traffic of exchange of facts for ideas, of theories for laws, of real things for hypotheses, should be so wholly unaware of the radical and generic (as distinct from specific) difficulty of the undertakings in which he is engaged? we thus come afresh to our inquiry: does not the epistemological logician unwittingly transfer the specific difficulty which always faces the scientific man--the difficulty in detail of correct and adequate translation back and forth of _this_ set of facts and _this_ group of reflective consideration--into a totally different problem of the wholesale relation of thought at large to reality in general? if such be the case, it is clear that the very way in which the epistemological type of logic states the problem of thinking, in relation both to empirical antecedents and to objective truth, makes that problem insoluble. working terms, terms which as working are flexible and historic, relative and methodological, are transformed into absolute, fixed, and predetermined properties of being. we come a little closer to the problem when we recognize that every scientific inquiry passes historically through at least four stages. (_a_) the first of these stages is, if i may be allowed the bull, that in which scientific inquiry does not take place at all, because no problem or difficulty in the quality of the experience presents itself to provoke reflection. we have only to cast our eye back from the existing status of any science, or back from the status of any particular topic in any science, to discover a time when no reflective or critical thinking busied itself with the matter--when the facts and relations were taken for granted and thus were lost and absorbed in the net meaning which accrued from the experience. (_b_) after the dawning of the problem there comes a period of occupation with relatively crude and unorganized facts--hunting for, locating, and collecting raw material. this is the empiric stage, which no existing science, however proud in its attained rationality, can disavow as its own progenitor. (_c_) then there is also a speculative stage: a period of guessing, of making hypotheses, of framing ideas which later on are labeled and condemned as only ideas. there is a period of distinction-making and classification-making which later on is regarded as only mentally gymnastic in character. and no science, however proud in its present security of experimental assurance, can disavow a scholastic ancestor. (_d_) finally, there comes a period of fruitful interaction between the mere ideas and the mere facts: a period when observation is determined by experimental conditions depending upon the use of certain guiding conceptions; when reflection is directed and checked at every point by the use of experimental data, and by the necessity of finding such a form for itself as will enable it to serve in a deduction leading to evolution of new meanings, and ultimately to experimental inquiry which brings to light new facts. in the emerging of a more orderly and significant region of fact, and of a more coherent and self-luminous system of meaning, we have the natural limit of evolution of the logic of a given science. but consider what has happened in this historic record. unanalyzed experience has broken up into distinctions of facts and ideas; the factual side has been developed by indefinite and almost miscellaneous descriptions and cumulative listings; the conceptual side has been developed by unchecked and speculative elaboration of definitions, classifications, etc. then there has been a relegation of accepted meanings to the limbo of mere ideas; there has been a passage of some of the accepted facts into the region of mere hypothesis and opinion. conversely, there has been a continued issuing of ideas from the region of hypotheses and theories into that of facts, of accepted objective and meaningful objects. out of a world of only _seeming_ facts, and of only _doubtful_ ideas, there emerges a world continually growing in definiteness, order, and luminosity. this progress, verified in every record of science, is an absolute monstrosity from the standpoint of the epistemology which assumes a thought in general, on one side, and a reality in general, on the other. the reason that it does not present itself as such a monster and miracle to those actually concerned with it is because _continuity_ of reference and of use controls all diversities in the modes of existence specified and the types of significance assigned. the distinction of meaning and fact is treated in the growth of a science, or of any particular scientific problem, as an _induced_ and _intentional_ practical division of labor; as assignments of relative position with reference to performance of a task; as deliberate distribution of forces at command for their more economic use. the absorption of bald fact and hypothetical idea into the formation of a single world of scientific apprehension and comprehension is but the successful achieving of the aim on account of which the distinctions in question were instituted. thus we come back to the problem of logical theory. to take the distinctions of thought and fact, etc., as ontological, as inherently fixed in the makeup of the structure of being, results in treating the actual technique of scientific inquiry and scientific control as a mere subsidiary topic--ultimately of only utilitarian worth. it also states the terms upon which thought and being transact business in a way so totally alien to concrete experience that it creates a problem which can be discussed only in terms of itself--not in terms of the conduct of life. as against this, the logic which aligns itself with the origin and employ of reflective thought in everyday life and critical science follows the natural history of thinking as a life-process having its own generating antecedents and stimuli, its own states and career, and its own specific objective or limit. this point of view makes it possible for logical theory to come to terms with psychology. when logic is considered as having to do with the wholesale activity of thought _per se_, the question of the historic process by which this or that particular thought came to be, of how its object happens to present itself as sensory, or perceptual, or conceptual, is quite irrelevant. these things are mere temporal accidents. the psychologist (not lifting his gaze from the realm of the changeable) may find in them matters of interest. his whole industry is just with natural history--to trace events as they mutually excite and inhibit one another. but the logician, we are told, has a deeper problem and an outlook of more unbounded horizon. he deals with the question of the eternal nature of thought and its eternal validity in relation to an eternal reality. he is concerned, not with genesis, but with value, not with a historic cycle, but with absolute entities and relations. still the query haunts us: is this so in truth? or has the logician of a certain type arbitrarily made it so by taking his terms apart from reference to the specific occasions in which they arise and situations in which they function? if the latter, then the very denial of historic relationship, the denial of the significance of historic method, is indicative of the unreal character of his own abstraction. it means in effect that the affairs under consideration have been isolated from the conditions in which alone they have determinable meaning and assignable worth. it is astonishing that, in the face of the advance of the evolutionary method in natural science, any logician can persist in the assertion of a rigid difference between the problem of origin and of nature; between genesis and analysis; between history and validity. such assertion simply reiterates as final a distinction which grew up and had meaning in pre-evolutionary science. it asserts, against the most marked advance which scientific method has yet made, a survival of a crude period of logical scientific procedure. we have no choice save either to conceive of thinking as a response to a specific stimulus, or else to regard it as something "in itself," having just in and of itself certain traits, elements, and laws. if we give up the last view, we must take the former. in this case it will still possess distinctive traits, but they will be traits of a specific response to a specific stimulus. the significance of the evolutionary method in biology and social history is that every distinct organ, structure, or formation, every grouping of cells or elements, is to be treated as an instrument of adjustment or adaptation to a particular environing situation. its meaning, its character, its force, is known when, and only when, it is considered as an arrangement for meeting the conditions involved in some specific situation. this analysis is carried out by tracing successive stages of development--by endeavoring to locate the particular situation in which each structure has its origin, and by tracing the successive modifications through which, in response to changing media, it has reached its present conformation.[ ] to persist in condemning natural history from the standpoint of what natural history meant before it identified itself with an evolutionary process is not so much to exclude the natural-history standpoint from philosophic consideration as it is to evince ignorance of what it signifies. psychology as the natural history of the various attitudes and structures through which experiencing passes, as an account of the conditions under which this or that attitude emerges, and of the way in which it influences, by stimulation or inhibition, production of other states or conformations of reflection, is indispensable to logical evaluation the moment we treat logical theory as an account of thinking as a response to its own generating conditions, and consequently judge its validity by reference to its efficiency in meeting its problems. the historical point of view describes the sequence; the normative follows the history to its conclusion, and then turns back and judges each historical step by viewing it in reference to its own outcome. in the course of changing experience we keep our balance in moving from situations of an affectional quality to those which are practical or appreciative or reflective, because we bear constantly in mind the context in which any particular distinction presents itself. as we submit each characteristic function and situation of experience to our gaze, we find it has a dual aspect. wherever there is striving there are obstacles; wherever there is affection there are persons who are attached; wherever there is doing there is accomplishment; wherever there is appreciation there is value; wherever there is thinking there is material-in-question. we keep our footing as we move from one attitude to another, from one characteristic quality to another, because of the position occupied in the whole movement by the particular function in which we are engaged. the distinction _between_ each attitude and function and its predecessor and successor is serial, dynamic, operative. the distinctions _within_ any given operation or function are structural, contemporaneous, and distributive. thinking follows, we will say, striving, and doing follows thinking. each in the fulfilment of its own function inevitably calls out its successor. but coincident, simultaneous, and correspondent _within_ doing is the distinction of doer and of deed; _within_ the function of thought, of thinking and material thought upon; within the function of striving, of obstacle and aim, of means and end. we keep our paths straight because we do not confuse the sequential and functional relationship of types of experience with the contemporaneous and structural distinctions of elements within a given function. in the seeming maze of endless confusion and unlimited shiftings, we find our way by the means of the stimulations and checks occurring within the process in which we are actually engaged. operating within empirical situations we do not contrast or confuse a condition which is an element in the formation of one operation with the status which is one of the distributive terms of another function. when we ignore these specific empirical clues and limitations, we have at once an insoluble, because meaningless, problem upon our hands. now the epistemological logician deliberately shuts himself off from those cues and checks upon which the plain man instinctively relies, and which the scientific man deliberately searches for and adopts as constituting his technique. consequently he is likely to set the attitude which has place and significance only in one of the serial functional situations of experience over against the active attitude which describes part of the structural constitution of another situation; or with equal lack of justification to assimilate materials characteristic of different stages to one another. he sets the agent, as he is found in the intimacy of love or appreciation, over against the externality of the fact, as that is defined within the reflective process. he takes the material which thought selects as its problematic data as identical with the significant content which results from successful pursuit of inquiry; and this in turn he regards as the material which was presented before thinking began, whose peculiarities were the means of awakening thought. he identifies the final deposit of the thought-function with its own generating antecedent, and then disposes of the resulting surd by reference to some metaphysical consideration, which remains when logical inquiry, when science (as interpreted by him), has done its work. he does this, not because he prefers confusion to order, or error to truth, but simply because, when the chain of historic sequence is cut, the vessel of thought is afloat to veer upon a sea without soundings or moorings. there are but two alternatives: either there is an object "in itself" of mind "in itself," or else there are a series of situations where elements vary with the varying functions to which they belong. if the latter, the only way in which the characteristic terms of situations can be defined is by discriminating the functions to which they belong. and the epistemological logician, in choosing to take his question as one of thought which has its own form just as "thought," apart from the limits of the special work it has to do, has deprived himself of these supports and stays. the problem of logic has a more general and a more specific phase. in its generic form, it deals with this question: how does one type of functional situation and attitude in experience pass out of and into another; for example, the technological or utilitarian into the aesthetic, the aesthetic into the religious, the religious into the scientific, and this into the socio-ethical and so on? the more specific question is: how does the particular functional situation termed the reflective behave? how shall we describe it? what in detail are its diverse contemporaneous distinctions, or divisions of labor, its correspondent _statuses_; in what specific ways do these operate with reference to each other so as to effect the specific aim which is proposed by the needs of the affair? this chapter may be brought to conclusion by reference to the more ultimate value of the logic of experience, of logic taken in its wider sense; that is, as an account of the sequence of the various typical functions or situations of experience in their determining relations to one another. philosophy, defined as such a logic, makes no pretense to be an account of a closed and finished universe. its business is not to secure or guarantee any particular reality or value. _per contra_, it gets the significance of a method. the right relationship and adjustment of the various typical phases of experience to one another is a problem felt in every department of life. intellectual rectification and control of these adjustments cannot fail to reflect itself in an added clearness and security on the practical side. it may be that general logic cannot become an instrument in the immediate direction of the activities of science or art or industry; but it is of value in criticizing and organizing tools of immediate research. it also has direct significance in the valuation for social or life-purposes of results achieved in particular branches. much of the immediate business of life is badly done because we do not know the genesis and outcome of the work that occupies us. the manner and degree of appropriation of the goods achieved in various departments of social interest and vocation are partial and faulty because we are not clear as to the due rights and responsibilities of one function of experience in reference to others. the value of research for social progress; the bearing of psychology upon educational procedure; the mutual relations of fine and industrial art; the question of the extent and nature of specialization in science in comparison with the claims of applied science; the adjustment of religious aspirations to scientific statements; the justification of a refined culture for a few in face of economic insufficiency for the mass; the relation of organization to individuality--such are a few of the many social questions whose answer depends upon the possession and use of a general logic of experience as a method of inquiry and interpretation. i do not say that headway cannot be made in such questions apart from the method indicated: a logic of experience. but unless we have a critical and assured view of the juncture in which and with reference to which a given attitude or interest arises, unless we know the service it is thereby called upon to perform, and hence the organs or methods by which it best functions in that service, our progress is impeded and irregular. we take a part for a whole, a means for an end; or we attack wholesale some interest because it interferes with the deified sway of the one we have selected as ultimate. a clear and comprehensive consensus of social conviction and a consequent concentrated and economical direction of effort are assured only as there is some way of locating the position and rôle of each typical interest and occupation. the domain of opinion is one of conflict; its rule is arbitrary and costly. only intellectual method affords a substitute for opinion. a general logic of experience alone can do for social qualities and aims what the natural sciences after centuries of struggle are doing for activity in the physical realm. this does not mean that systems of philosophy which have attempted to state the nature of thought and of reality at large, apart from limits of particular situations in the movement of experience, have been worthless--though it does mean that their industry has been somewhat misapplied. the unfolding of metaphysical theory has made large contributions to positive evaluations of the typical situations and relationships of experience--even when its conscious intention has been quite otherwise. every system of philosophy is itself a mode of reflection; consequently (if our main contention be true), it too has been evoked out of specific social antecedents, and has had its use as a response to them. it has effected something in modifying the situation within which it found its origin. it may not have solved the problem which it consciously put itself; in many cases we may freely admit that the question put has been found afterward to be so wrongly put as to be insoluble. yet exactly the same thing is true, in precisely the same sense, in the history of science. for this reason, if for no other, it is impossible for the scientific man to cast the first stone at the philosopher. the progress of science in any branch continually brings with it a realization that problems in their previous form of statement are insoluble because put in terms of unreal conditions; because the real conditions have been mixed up with mental artifacts or misconstructions. every science is continually learning that its supposed solutions are only apparent because the "solution" solves, not the actual problem, but one which has been made up. but the very putting of the question, the very giving of the wrong answer, induces modification of existing intellectual habits, standpoints, and aims. wrestling with the problem, there is evolution of new technique to control inquiry, there is search for new facts, institution of new types of experimentation; there is gain in the methodic control of experience. and all this is progress. it is only the worn-out cynic, the de-vitalized sensualist, and the fanatical dogmatist who interpret the continuous change of science as proving that, since each successive statement is wrong, the whole record is error and folly; and that the present truth is only the error not yet found out. such draw the moral of caring naught for all these things, or of flying to some external authority which will deliver once for all the fixed and unchangeable truth. but historic philosophy even in its aberrant forms has proved a factor in the valuation of experience; it has brought problems to light, it has provoked intellectual conflicts without which values are only nominal; even through its would-be absolutistic isolations it has secured recognition of mutual dependencies and reciprocal reinforcements. yet if it can define its work more clearly, it can concentrate its energy upon its own characteristic problem: the genesis and functioning in experience of various typical interests and occupations with reference to one another. footnotes: [ ] _logic_ (translation, oxford, ), i, , . italics mine. [ ] see _philosophical review_, xi, - . iii the antecedents and stimuli of thinking we have discriminated logic in its wider sense--concerned with the sequence of characteristic functions and attitudes in experience--from logic in its stricter meaning, concerned with the function of reflective thought. we must avoid yielding to the temptation of identifying logic with either of these to the exclusion of the other; or of supposing that it is possible to isolate one finally from the other. the more detailed treatment of the organs and methods of reflection cannot be carried on with security save as we have a correct idea of the position of reflection amid the typical functions of experience. yet it is impossible to determine this larger placing, save as we have a defined and analytic, as distinct from a merely vague and gross, view of what we mean by reflection--what is its actual constitution. it is necessary to work back and forth between the larger and the narrower fields, transforming every increment upon one side into a method of work upon the other, and thereby testing it. the evident confusion of existing logical theory, its uncertainty as to its own bounds and limits, its tendency to oscillate from larger questions of the meaning of judgment and the validity of inference over to details of scientific technique, and to translate distinctions of formal logic into acts in an investigatory or verificatory process, are indications of the need of this double movement. in the next three chapters it is proposed to take up some of the considerations that lie on the borderland between the larger and the narrower conceptions of logical theory. i shall discuss the _locus_ of the function of thought in experience so far as such _locus_ enables us to characterize some of the most fundamental distinctions, or divisions of labor, within the reflective process. in taking up the problem of the subject-matter of thought, i shall try to make clear that it assumes three quite distinct forms according to the epochal moment reached in control of experience. i shall attempt to show that we must consider subject-matter from the standpoint, first, of the _antecedents_ or conditions that evoke thought; secondly, of the _datum_ or _immediate material_ presented to thought; and, thirdly, of the _proper objective_ of thought. of these three distinctions the first, that of antecedent and stimulus, clearly refers to the situation that is immediately prior to the thought-function as such. the second, that of datum or immediately given matter, refers to a distinction which is made within the thought-process as a part of and for the sake of its own _modus operandi_. it is a status in the scheme of thinking. the third, that of content or object, refers to the progress actually made in any thought-function; material which is organized by inquiry so far as inquiry has fulfilled its purpose. this chapter will get at the matter of preliminary conditions of thought indirectly rather than directly, by indicating the contradictory positions into which one of the most vigorous and acute of modern logicians, lotze, has been forced through failing to define logical distinctions in terms of the history of readjustment and control of things in experience, and being thereby compelled to interpret certain notions as absolute instead of as historic and methodological. before passing directly to the exposition and criticism of lotze, it will be well, however, to take the matter in a somewhat freer way. we cannot approach logical inquiry in a wholly direct and uncompromised manner. of necessity we bring to it certain distinctions--distinctions partly the outcome of concrete experience; partly due to the logical theory which has got embodied in ordinary language and in current intellectual habits; partly results of deliberate scientific and philosophic inquiry. these more or less ready-made results are resources; they are the only weapons with which we can attack the new problem. yet they are full of unexamined assumptions; they commit us to all sorts of logically predetermined conclusions. in one sense our study of the new subject-matter, let us say logical theory, is in truth only a review, a retesting and criticizing of the intellectual standpoints and methods which we bring with us to the study. nowadays everyone comes with certain distinctions already made between the subjective and the objective, between the physical and the mental, between the intellectual and the factual. ( ) we have learned to regard the region of emotional disturbance, of uncertainty and aspiration, as belonging peculiarly to ourselves; we have learned to set over against this the world of observation and of valid thought as something unaffected by our moods, hopes, fears, and opinions. ( ) we have also come to distinguish between what is immediately present in our experience and the past and the future; we contrast the realms of memory and anticipation with that of sense perception; more generally we contrast the given with the inferential. ( ) we are confirmed in a habit of distinguishing between what we call actual fact and our mental attitude toward that fact--the attitude of surmise or wonder or reflective investigation. while one of the aims of logical theory is precisely to make us critically conscious of the significance and bearing of these various distinctions, to change them from ready-made assumptions into controlled conceptions, our mental habits are so set that they tend to have their own way with us; we read into logical theory conceptions that were formed before we had even dreamed of the logical undertaking which after all has for its business to assign to the terms in question their proper meaning. our conclusions are thus controlled by the very notions which need criticism and revision. we find in lotze an unusually explicit inventory of these various preliminary distinctions, and an unusually serious effort to deal with the problems which arise from introducing them into the structure of logical theory. ( ) he expressly separates the matter of logical worth from that of psychological genesis. he consequently abstracts the subject-matter of logic as such wholly from the question of historic _locus_ and _situs_. ( ) he agrees with common-sense in holding that logical thought is reflective and thus presupposes a given material. he occupies himself with the nature of the antecedent conditions. ( ) he wrestles with the problem of how a material formed prior to thought and irrespective of it can yet afford stuff upon which thought may exercise itself. ( ) he expressly raises the question of how thought working independently and from without upon a foreign material can shape the latter into results which are valid--that is, objective. if this discussion is successful; if lotze can provide the intermediaries which span the gulf between the exercise of logical functions by thought upon a material wholly external to it; if he can show that the question of the origin of subject-matter of thought and of thought-activity is irrelevant to the question of its meaning and validity, we shall have to surrender the position already taken. but if we find that lotze's elaborations only elaborate the fundamental difficulty, presenting it now in this light and now in that, but always presenting the problem as if it were its own solution, we shall be confirmed in our idea of the need of considering logical questions from a different point of view. if we find that, whatever his formal treatment, he always, as a matter of fact, falls back upon some organized situation or function as the source of both the material and the process of inquiry, we shall have in so far an elucidation and even a corroboration of our theory. we begin with the question of the material antecedents of thought--antecedents which condition reflection, and which call it out as reaction or response, by giving its cue. lotze differs from many logicians of the same type in furnishing an explicit account of these antecedents. . the ultimate material antecedents of thought are found in impressions which are due to external objects as stimuli. taken in themselves, these impressions are mere psychical states or events. they exist in us side by side, or one after the other, according as the objects which excite them operate simultaneously or successively. the occurrence of these various psychical states is not, however, entirely dependent upon the presence of the exciting thing. after a state has once been excited, it gets the power of reawakening other states which have accompanied it or followed it. the associative mechanism of revival plays a part. if we had a complete knowledge of both the stimulating object and its effects, and of the details of the associative mechanism, we should be able from given data to predict the whole course of any given train or current of ideas (for the impressions as conjoined simultaneously or successively become ideas and a current of ideas). taken in itself, a sensation or impression is nothing but a "state of our consciousness, a mood of ourselves." any given current of ideas is a necessary sequence of existences (just as necessary as any succession of material events), happening in some particular sensitive soul or organism. "just because, under their respective conditions, every such series of ideas hangs together by the same necessity and law as every other, there would be no ground for making any such distinction of value as that between truth and untruth, thus placing one group in opposition to all the others."[ ] . thus far, as the last quotation clearly indicates, there is no question of reflective thought, and hence no question of logical theory. but further examination reveals a peculiar property of the current of ideas. some ideas are merely coincident, while others may be termed coherent. that is to say, the exciting causes of some of our simultaneous and successive ideas really belong together; while in other cases they simply happen to act at the same time, without there being a real connection between them. by the associative mechanism, however, both the coherent and the merely coincident combinations recur. the first type of recurrence supplies positive material for knowledge; the second gives occasion for error. . it is a peculiar mixture of the coincident and the coherent which sets the peculiar problem of reflective thought. the business of thought is to recover and confirm the coherent, the really connected, adding to its reinstatement an accessory justifying notion of the real ground of coherence, while it eliminates the coincident as such. while the mere current of ideas is something which just happens within us, the process of elimination and of confirmation by means of statement of real ground and basis of connection is an activity which mind, as such, exercises. this distinction marks off thought as activity from any psychical event and from the associative mechanism as mere happenings. one is concerned with mere _de facto_ coexistences and sequences; the other with the cognitive _worth_ of these combinations.[ ] consideration of the peculiar work of thought in going over, sorting out, and determining various ideas according to a standard of value will occupy us in our next chapter. here we are concerned with the material antecedents of thought as they are described by lotze. at first glance, he seems to propound a satisfactory theory. he avoids the extravagancies of transcendental logic, which assumes that all the matter of experience is determined from the very start by rational thought; and he also avoids the pitfall of purely empirical logic, which makes no distinction between the mere occurrence and association of ideas and the real worth and validity of the various conjunctions thus produced. he allows unreflective experience, defined in terms of sensations and their combinations, to provide material conditions for thinking, while he reserves for thought a distinctive work and dignity of its own. sense experience furnishes the antecedents; thought has to introduce and develop systematic connection--rationality. a further analysis of lotze's treatment may, however, lead us to believe that his statement is riddled through and through with inconsistencies and self-contradictions; that, indeed, any one part of it can be maintained only by the denial of some other portion. . the impression is the ultimate antecedent in its purest or crudest form (according to the angle from which one views it). it is that which has never felt, for good or for bad, the influence of thought. combined into ideas, these impressions stimulate or arouse the activities of thought, which are forthwith directed upon them. as the recipient of the activity which they have excited and brought to bear upon themselves, they furnish also the material content of thought--its actual stuff. as lotze says over and over again: "it is the relations themselves already subsisting between impressions, when we become conscious of them, by which the action of thought which is never anything but reaction, is attracted; and this action consists merely in interpreting relations which we find existing between our passive impressions into aspects of the matter of impressions."[ ] and again: "thought can make no difference where it finds none already in the matter of the impressions."[ ] and again: "the possibility and the success of thought's procedure depends upon this original constitution and organization of the whole world of ideas, a constitution which, though not necessary in thought, is all the more necessary to make thinking possible."[ ] the impressions and ideas thus play a versatile rôle; they now assume the part of ultimate antecedents and provocative conditions; of crude material; and somehow, when arranged, of content for thought. this very versatility awakens suspicion. while the impression is merely subjective and a bare state of our own consciousness, yet it is determined, both as to its existence and as to its relation to other similar existences, by external objects as stimuli, if not as causes. it is also determined by a psychical mechanism so thoroughly objective or regular in its workings as to give the same necessary character to the current of ideas that is possessed by any physical sequence. thus that which is "nothing but a state of our consciousness" turns out straightway to be a specifically determined objective fact in a system of facts. that this absolute transformation is a contradiction is no clearer than that just such a contradiction is indispensable to lotze. if impressions were nothing but states of consciousness, moods of ourselves, bare psychical existences, it is sure enough that we should never even know them to be such, to say nothing of conserving them as adequate conditions and material for thought. it is only by treating them as real facts in a real world, and only by carrying over into them, in some assumed and unexplained way, the capacity of representing the cosmic facts which cause them, that impressions or ideas come in any sense within the scope of thought. but if the antecedents are really impressions-in-their-objective-setting, then lotze's whole way of distinguishing thought-worth from _mere_ existence or event without objective significance must be radically modified. the implication that impressions have actually a quality or meaning of their own becomes explicit when we refer to lotze's theory that the immediate antecedent of thought is found in the _matter_ of ideas. when thought is said to "take cognizance of _relations_ which its own activity does not originate, but which have been prepared for it by the unconscious mechanism of the psychic states,"[ ] the attribution of objective content, of reference and meaning to ideas, is unambiguous. the idea forms a most convenient halfway house for lotze. on one hand, as absolutely prior to thought, as material antecedent condition, it is merely psychical, bald subjective event. but as subject-matter for thought, as antecedent which affords stuff for thought's exercise, it characteristically qualifies content. although we have been told that the impression is a mere receptive irritation without participation of mental activity, we are not surprised, in view of this capacity of ideas, to learn that the mind actually has a determining share in both the reception of stimuli and in their further associative combinations. the subject always enters into the presentation of any mental object, even the sensational, to say nothing of the perceptional and the imaged. the perception of a given state of things is possible only on the assumption that "the perceiving subject is at once enabled and compelled by its own nature to combine the excitations which reach it from objects into those forms which it is to perceive in the objects, and which it supposes itself simply to _receive_ from them."[ ] it is only by continual transition from impression and ideas as mental states and events to ideas as logical _objects or contents_, that lotze bridges the gulf from bare exciting antecedent to concrete material conditions of thought. this contradiction, again, is necessary to lotze's standpoint. to set out frankly with objects as antecedents would demand reconsideration of the whole viewpoint, which supposes that the difference between the logical and its antecedent is a matter of the difference between _worth_ and mere _existence_ or _occurrence_. it would indicate that since meaning or value is already there, the task of thought must be that of the transformation or _reconstruction of meaning_ through an intermediary process. on the other hand, to stick by the standpoint of _mere_ existence is not to get anything which can be called even antecedent of thought. . why is there a task of transformation? consideration of the material in its function of evoking thought, giving it its cue, will serve to complete the picture of the contradiction and of the real facts. it is the conflict between ideas as merely coincident and ideas as coherent which constitutes the need that provokes the response of thought. here lotze vibrates (_a_) between considering both coincidence and coherence as psychical events; (_b_) considering coincidence as purely psychical and coherence as at least quasi-logical, and (_c_) making them both determinations within the sphere of reflective thought. in strict accordance with his own premises, coincidence and coherence ought both to be mere peculiarities of the current of ideas as events within ourselves. but so taken the distinction becomes absolutely meaningless. events do not cohere; at the most certain sets of them happen more or less frequently than other sets; the only intelligible difference is one of frequency of coincidence. and even this attributes to an event the supernatural trait of reappearing after it has disappeared. even coincidence has to be defined in terms of relation of the _objects_ which are supposed to excite the psychical events that happen together. as recent psychological discussion has made clear enough, it is the matter, meaning, or content of ideas that is associated, not the ideas as states or existences. take such an idea as sun-revolving-about-earth. we may _say_ it means the conjunction of various sense impressions, but it is connection, or mutual reference, of _attributes_ that we have in mind in the assertion. it is absolutely certain that our psychical image of the sun is not psychically engaged in revolving about our psychical image of the earth. it would be amusing if such were the case; theaters and all dramatic representations would be at a discount. but in truth, sun-revolving-about-earth is a single meaning or intellectual object; it is a unified subject-matter within which certain distinctions of reference appear. it is concerned with what we intend when we think earth and sun, and think them in their relation to each other. it is a rule, specification, or direction of how to think when we have occasion to think a certain subject-matter. to treat this mutual reference as if it were simply a case of conjunction of mental events produced by psycho-physical irritation and association is a profound case of the psychological fallacy. we may, indeed, analyze an experience involving belief in an object of a certain kind and find that it had its origin in certain conditions of the sensitive organism, in certain peculiarities of perception and of association, and hence conclude that the belief involved in it was not justified by the facts themselves. but the significance of the belief in sun-revolving-about-earth by those who held it, consisted precisely in the fact that it was taken not as a mere association of feelings, but as a definite portion of the whole structure of objective experience, guaranteed by other parts of the fabric, and lending its support and giving its tone to them. it was to them part of the experienced frame of things--of the real world. put the other way, if such an instance meant a mere conjunction of psychical states, there would be in it absolutely nothing to evoke thought. each idea as event, as lotze himself points out (i, ), may be regarded as adequately and necessarily determined to the place it occupies. there is absolutely no question on the side of events of mere coincidence _versus_ genuine connection. as event, it is there and it belongs there. we cannot treat something as at once a bare fact of existence and a problematic subject-matter of logical inquiry. to take the reflective point of view is to consider the matter in a totally new light; as lotze says, it is to raise the question of rightful claims to a position or relation. the point becomes clearer when we contrast coincidence with connection. to consider coincidence as simply psychical, and coherence as at least quasi-logical, is to put the two on such different bases that no question of contrasting them can arise. the coincidence which precedes a valid or grounded coherence (the conjunction which as coexistence of objects and sequence of acts is perfectly adequate) never is, as antecedent, the coincidence which is set over against coherence. the side-by-sideness of books on my bookshelf, the succession of noises that rise through my window, do not trouble me logically. they do not appear as errors or even as problems. one coexistence is just as good as any other until some new point of view, or new end, presents itself. if it is a question of the convenience of arrangement of books, then the value of their present collocation becomes a problem. then i contrast their present state as bare conjunction over against another scheme as one which is coherent. if i regard the sequence of noises as a case of articulate speech, their order becomes important--it is a problem to be determined. the inquiry whether a given combination presents apparent or real connection shows that reflective inquiry is already going on. does this phase of the moon really mean rain, or does it just happen that the rain-storm comes when the moon has reached this phase? to ask such questions shows that a certain portion of the universe of objective experience is subjected to critical analysis for purposes of definitive restatement. the tendency to regard some combination as mere coincidence is absolutely a _part_ of the movement of mind in its search for the real connection. if coexistence as such is to be set against coherence as such, as the non-logical against the logical, then, since our whole spatial universe is one of collocation, and since thought in this universe can never get farther than substituting one collocation for another, the whole realm of space-experience is condemned offhand and in perpetuity to anti-rationality. but, in truth, coincidence as over against coherence, conjunction as over against connection, is just _suspected_ coherence, one which is under the fire of active inquiry. the distinction is one which arises only within the logical or reflective function. . this brings us explicitly to the fact that there is neither coincidence nor coherence in terms of the elements or meanings contained in any couple or pair of ideas taken by itself. it is only when they are co-factors in a situation or function which includes more than either the "coincident" or the "coherent" and more than the arithmetical sum of the two, that thought's activity can be evoked. lotze is continually in this dilemma: thought either shapes its own material or else just accepts it. in the first case (since lotze cannot rid himself of the presumption that thought must have a fixed ready-made antecedent) its activity can only alter this stuff and thus lead the mind farther away from reality. but if thought just accepts its material, how can there be any distinctive aim or activity of thought at all? as we have seen, lotze endeavors to escape this dilemma by supposing that, while thought receives its material yet checks it up, it eliminates certain portions of it and reinstates others, plus the stamp and seal of its own validity. lotze objects most strenuously to the kantian notion that thought awaits its subject-matter with certain ready-made modes of apprehension. this notion would raise the insoluble question of how thought contrives to bring the matter of each impression under that particular form which is appropriate to it (i, ). but he has not avoided the difficulty. how does thought know which of the combinations are merely coincident and which are merely coherent? how does it know which to eliminate as irrelevant and which to confirm as grounded? either this evaluation is an imposition of its own, or else gets its cue and clue from the subject-matter. now, if the coincident and the coherent taken in and of themselves are competent to give this direction, they are already labeled. the further work of thought is one of supererogation. it has at most barely to note and seal the material combinations that are already there. such a view clearly renders thought's work as unnecessary in form as it is futile in force. but there is no alternative except to recognize that an entire situation or environment, within which exist both that which is afterward found to be mere coincidence and that found to be real connection, actually provokes thought. it is only as an experience previously accepted comes up in its wholeness against another one equally integral; and only as some larger experience dawns which requires each as a part of itself and yet within which the required factors show themselves mutually incompatible, that thought arises. it is not bare coincidence, or bare connection, or bare addition of one to the other, that excites thought. the stimulus is a situation which is organized or constituted as a whole, and yet which is falling to pieces in its parts--a situation which is in conflict within itself--that arouses the search to find what really goes together, and a correspondent effort to shut out what only seemingly goes together. and real coherence means precisely capacity to exist within the comprehending whole. to read back into the preliminary situation those distinctions of mere conjunction of material and of valid coherence which get existence, to say nothing of fixation, only within the process of inquiry is a fallacy. we must not leave this phase of the discussion, however, until it is quite clear that our objection is not to lotze's position that reflective thought arises from an antecedent which is not reflectional in character; nor yet to his idea that this antecedent has a certain structure and content of its own setting the peculiar problem of thought, giving the cue to its specific activities and determining its object. on the contrary, it is this latter point upon which we would insist; so as (by insisting) to point out, negatively, that this view is absolutely inconsistent with lotze's theory that psychical impressions and ideas are the true antecedents of thought; and, positively, to show that it is the _situation as a whole_, and not any one isolated part of it, or distinction within it, that calls forth and directs thinking. we must beware the fallacy of assuming that some one element in the prior situation in isolation or detachment induces the reflection which in reality comes forth only from the whole disturbed situation. on the negative side, characterizations of impression and idea are distinctions which arise only within reflection upon that situation which is the genuine antecedent of thought. positively, it is the whole dynamic experience with its qualitative and pervasive continuity, and its inner active distraction, its elements at odds with each other, in tension against each other, each contending for its proper placing and relationship, which generates the thought-situation. from this point of view, at this period of development, the distinctions of objective and subjective have a characteristic meaning. the antecedent, to repeat, is a situation in which the various factors are actively incompatible with each other, and yet in and through the striving tend to a re-formation of the whole and to a restatement of the parts. this situation as such is clearly 'objective.' it is there; it is there as a whole; the various parts are there; and their active incompatibility with one another is there. nothing is conveyed at this point by asserting that any particular part of the situation is illusory or subjective, or mere appearance; or that any other is truly real. the experience exists as one of vital and active confusion and conflict among its elements. the conflict is not only objective in a _de facto_ sense (that is, really existent), but is objective in a logical sense as well; it is just this conflict which effects a transition into the thought-situation--this, in turn, being only a constant movement toward a defined equilibrium. the conflict has objective worth because it is the antecedent condition and cue of thought. deny an organization of things within which competing incompatible tendencies appear and thinking becomes merely "mental." every reflective attitude and function, whether of naïve life, deliberate invention, or controlled scientific research, has risen through the medium of some such total objective situation. the abstract logician may tell us that sensations or impressions, or associated ideas, or bare physical things, or conventional symbols, are antecedent conditions. but such statements cannot be verified by reference to a single instance of thought in connection with actual practice or actual scientific research. of course, by extreme mediation symbols may become conditions of evoking thought. they get to be objects in an active experience. but they are stimuli to thinking only in case their manipulation to form a new whole occasions resistance, and thus reciprocal tension. symbols and their definitions develop to a point where dealing with them becomes itself an experience, having its own identity; just as the handling of commercial commodities, or arrangement of parts of an invention, is a specific experience. there is always as antecedent to thought an experience of subject-matter of the physical or social world, or the previously organized intellectual world, whose parts are actively at war with each other--so much so that they threaten to disrupt the situation, which accordingly for its own maintenance requires deliberate redefinition and re-relation of its tensional parts. this redefining and re-relating is the constructive process termed thinking: the reconstructive situation, with its parts in tension and in such movement toward each other as tends to a unified arrangement of things, is the thought-situation. this at once suggests the subjective phase. the situation, the experience as such, is objective. there is an experience of the confused and conflicting tendencies. but just _what in particular_ is objective, just _what_ form the situation shall take as an organized harmonious whole, is unknown; that is the problem. it is the uncertainty as to the _what_ of the experience together with the certainty _that_ there is such an experience, that evokes the thought-function. viewed from this standpoint of uncertainty, the situation as a whole is subjective. no particular content or reference can be asserted offhand. definite assertion is expressly reserved--it is to be the outcome of the procedure of reflective inquiry now undertaken. this holding off of contents from definitely asserted position, this viewing them as candidates for reform, is what we mean, at this stage of the natural history of thought, by the subjective. we have followed lotze through his tortuous course of inconsistencies. it is better, perhaps, to run the risk of vain repetition than that of leaving the impression that these are _mere_ dialectical contradictions. it is an idle task to expose contradictions unless we realize them in relation to the fundamental assumption which breeds them. lotze is bound to differentiate thought from its antecedents. he is intent upon doing this, however, through a preconception that marks off the thought-situation radically from its predecessor, through a difference that is complete, fixed and absolute, or at large. it is a total contrast of thought as such to something else as such that he requires, not a contrast within experience of one temporal phase of a process, one period of a rhythm, from others. this complete and rigid difference lotze finds in the difference between an experience which is _mere existence_ or occurrence, and one which has to do with worth, truth, right relationship. now things have connection, organization, value or force, practical and aesthetic meaning, on their own account. the same is true of deeds, affections, etc. only states of feelings, bare impressions, etc., seem to fulfil the prerequisite of being given as existence, and yet without qualification as to worth, etc. then the current of ideas offers itself, a ready-made stream of events, of existences, which can be characterized as wholly innocent of reflective determination, and as the natural predecessor of thought. but this stream of existences is no sooner regarded than its total incapacity to officiate as material condition and cue of thought appears. it is about as relevant to thinking as are changes that may be happening on the other side of the moon. so, one by one, the whole series of determinations of force and worth already traced are introduced _into_ the very make-up, the inner structure, of what was to be _mere_ existence: viz., ( ) things of whose spatial and temporal relations the mere impressions are somehow _representative_; ( ) _meaning_--the idea as significant, possessed of quality, and not a mere event; ( ) distinguished traits of coincidence and coherence within the stream. all these features are explicitly asserted, as we have seen; underlying and running through them all is the recognition of the supreme value of a situation which has been organized as a whole, yet is now conflicting in its inner constitution. these contradictions all arise in the attempt to put thought's work, as concerned with objective validity, over against experience as a mere antecedent happening, or occurrence. this contrast arises because of the attempt to consider thought as an independent somewhat in general which nevertheless, in _our_ experience, is dependent upon a raw material of mere impressions given to it. hence the sole radical avoidance of the contradictions can be secured only when thinking is seen to be a specific event in the movement of experienced things, having its own specific occasion or demand, and its own specific place. the nature of the organization and force that the antecedent conditions of the thought-function possess is too large a question here to enter upon in detail. lotze himself suggests the answer. he speaks of the current of ideas, just as a current, supplying us with the "mass of well-grounded information which _regulates daily life_" (i, ). it gives rise to "useful combinations," "correct expectations," "seasonable reactions" (i, ). he speaks of it, indeed, as if it were just the ordinary world of naïve experience, the so-called empirical world, as distinct from the world as critically revised and rationalized in scientific and philosophic inquiry. the contradiction between this interpretation and that of a mere stream of psychical impressions is only another instance of the difficulty already discussed. but the phraseology suggests the real state of things. the unreflective world is a world of practical things; of ends and means, of their effective adaptations; of control and regulation of conduct in view of results. the world of uncritical experience also is a world of social aims and means, involving at every turn the goods and objects of affection and attachment, of competition and co-operation. it has incorporate also in its own being the surprise of aesthetic values--the sudden joy of light, the gracious wonder of tone and form. i do not mean that this holds in gross of the unreflective world of experience over against the critical thought-situation--such a contrast implies the very wholesale, at large, consideration of thought which i am striving to avoid. doubtless many and many an act of thought has intervened in effecting the organization of our commonest practical-affectional-aesthetic environment. i only mean to indicate that thought does take place _in_ such a world; not _after_ a world of bare existences; and that while the more systematic reflection we call organized science may, in some fair sense, be said to come _after_, it comes after affectional, artistic, and technological interests which have found realization. having entered so far upon a suggestion which cannot be followed out, i venture one other digression. the notion that value or significance as distinct from mere existentiality is the product of thought or reason, and that the source of lotze's contradictions lies in the effort to find _any_ situation prior or antecedent to thought, is a familiar one--it is even possible that my criticisms of lotze have been interpreted by some readers in this sense.[ ] this is the position frequently called neo-hegelian (though, i think, with questionable accuracy), and has been developed by many writers in criticizing kant. this position and that taken in this chapter do indeed agree in certain general regards. they are at one in denial of the factuality and the possibility of developing fruitful reflection out of antecedent bare existence or mere events. they unite in denying that there is or can be any such thing as _mere_ existence--phenomenon unqualified as respects organization and force, whether such phenomenon be psychic or cosmic. they agree that reflective thought grows organically out of an experience which is already organized, and that it functions within such an organism. but they part company when a fundamental question is raised: is all organized meaning the work of thought? does it therefore follow that the organization out of which reflective thought grows is the work of thought of some other type--of pure thought, creative or constitutive thought, intuitive reason, etc.? i shall indicate briefly the reasons for divergence at this point. to cover all the practical-social-aesthetic objects involved, the term "thought" has to be so stretched that the situation might as well be called by any other name that describes a typical form of experience. more specifically, when the difference is minimized between the organized and arranged scheme out of which reflective inquiry proceeds, and reflective inquiry itself (and there can be no other reason for insisting that the antecedent of reflective thought is itself somehow thought), exactly the same type of problem recurs which presents itself when the distinction is exaggerated into one between bare existences and rational coherent meanings. for the more one insists that the antecedent situation is constituted by thought, the more one has to wonder why another type of thought is required; what need arouses it, and how it is possible for it to improve upon the work of previous constitutive thought. this difficulty at once forces idealists from a logic of experience as it is concretely experienced into a metaphysic of a purely hypothetical experience. constitutive thought precedes _our_ conscious thought-operations; hence it must be the working of some absolute universal thought which, unconsciously to our reflection, builds up an organized world. but this recourse only deepens the difficulty. how does it happen that the absolute constitutive and intuitive thought does such a poor and bungling job that it requires a finite discursive activity to patch up its products? here more metaphysic is called for: the absolute reason is now supposed to work under limiting conditions of finitude, of a sensitive and temporal organism. the antecedents of reflective thought are not, therefore, determinations of thought pure and undefiled, but of what thought can do when it stoops to assume the yoke of change and of feeling. i pass by the metaphysical problem left unsolved by this flight: why and how should a perfect, absolute, complete, finished thought find it necessary to submit to alien, disturbing, and corrupting conditions in order, in the end, to recover through reflective thought in a partial, piecemeal, wholly inadequate way what it possessed at the outset in a much more satisfactory way? i confine myself to the logical difficulty. how can thought relate itself to the fragmentary sensations, impressions, feelings, which, in their contrast with and disparity from the workings of constitutive thought, mark it off from the latter; and which in their connection with its products give the cue to reflective thinking? _here we have again exactly the problem with which lotze has been wrestling_: we have the same insoluble question of the reference of thought-activity to a wholly indeterminate unrationalized, independent, prior existence. the absolute idealist who takes up the problem at this point will find himself forced into the same continuous seesaw, the same scheme of alternate rude robbery and gratuitous gift, that lotze engaged in. the simple fact is that here _is_ just where lotze began; he saw that previous transcendental logicians had left untouched the specific question of relation of _our_ supposedly finite, reflective thought to its own antecedents, and he set out to make good the defect. if reflective thought is required because constitutive thought works under externally limiting conditions of sense, then we have some elements which are, after all, mere existences, events, etc. or, if they have organization from some other source than thought, and induce reflective thought not as bare impressions, etc., but through their place in some whole, then we have admitted the possibility of organization in experience, apart from reason, and the ground for assuming pure constitutive thought is abandoned. the contradiction appears equally when viewed from the side of thought-activity and its characteristic forms. all our knowledge, after all, of thought as constitutive is gained by consideration of the operations of reflective thought. the perfect system of thought is so perfect that it is a luminous, harmonious whole, without definite parts or distinctions--or, if there are such, it is only reflection that brings them out. the categories and methods of constitutive thought itself must therefore be characterized in terms of the _modus operandi_ of reflective thought. yet the latter takes place just because of the peculiar problem of the peculiar conditions under which it arises. its work is progressive, reformatory, reconstructive, synthetic, in the terminology made familiar by kant. we are not only _not_ justified, accordingly, in transferring its determinations over to "constitutive" thought, but are prohibited from attempting any such transfer. to identify logical processes, states, devices, results which are conditioned upon the primary fact of resistance to thought as constitutive with the structure of constitutive thought is as complete an instance of the fallacy of recourse from one genus to another as could well be found. constitutive and reflective thought are, first, defined in terms of their dissimilarity and even opposition, and then without more ado the forms of the description of the latter are carried over bodily to the former! this is not a merely controversial criticism. it points positively toward the fundamental thesis of these chapters: all the distinctions discovered within thinking, of conception as over against sense perception, of various modes and forms of judgment, of inference in its vast diversity of operation--all these distinctions come within the thought-situation as growing out of a characteristic antecedent typical formation of experience; and have for their purpose the solution of the peculiar problem with respect to which the thought-function is generated or evolved: the restoration of a deliberately integrated experience from the inherent conflict into which it has fallen. the failure of transcendental logic has the same origin as the failure of the empiristic (whether taken pure or in the mixed form in which lotze presents it). it makes into absolute and fixed distinctions of existence and meaning, and of one kind of meaning and another kind, things which are historic or temporal in their origin and their significance. it views thought as attempting to represent or state reality once for all, instead of trying to determine some phases or contents of it with reference to their more effective and significant employ--instead of as reconstructive. the rock against which every such logic splits is that either existence already has the statement which thought is endeavoring to give it, or else it has not. in the former case, thought is futilely reiterative; in the latter, it is falsificatory. the significance of lotze for critical purposes is that his peculiar effort to combine a transcendental view of thought (i.e., of thought as active in forms of its own, pure in and of themselves) with certain obvious facts of the dependence of our thought upon specific empirical antecedents, brings to light fundamental defects in both the empiristic and the transcendental logics. we discover a common failure in both: the failure to view logical terms and distinctions with respect to their necessary function in the redintegration of experience. footnotes: [ ] lotze, _logic_ (translation, oxford, ), i, . for the preceding exposition see i, , , , , , ; also _microkosmus_, book v, chap. iv. [ ] lotze, _logic_, i, , . [ ] lotze, _logic_ (translation, oxford, ), i, . [ ] _ibid._, . [ ] _ibid._ [ ] _microkosmus_, book v, chap. iv. [ ] _logic_, ii, ; see the whole discussion, §§ - . [ ] we have a most acute and valuable criticism of lotze from this point of view in professor henry jones, _philosophy of lotze_, . my specific criticisms agree in the main with his, and i am glad to acknowledge my indebtedness. but i cannot agree in the belief that the business of thought is to qualify reality as such; its occupation appears to me to be determining the reconstruction of some aspect or portion of reality, and to fall within the course of reality itself; being, indeed, the characteristic medium of its activity. and i cannot agree that reality as such, with increasing fulness of knowledge, presents itself as a thought-system, though, as just indicated, i have no doubt that practical existence presents itself in its temporal course as thought-specifications, just as it does as affectional and aesthetic and the rest of them. iv data and meanings we have reached the point of conflict in the matters of an experience. it is _in_ this conflict and because of it that the matters, or significant quales, stand out _as_ matters. as long as the sun revolves about earth without question, this "content" is not in any way abstracted. its distinction from the form or mode of experience as its matter is the work of reflection. the same conflict makes other experiences assume discriminated objectification; they, too, cease to be ways of living, and become distinct objects of observation and consideration. the movements of planets, eclipses, etc., are cases in point.[ ] the maintenance of a unified experience has become a problem, an end, for it is no longer secure. but this involves such restatement of the conflicting elements as will enable them to take a place somewhere in the world of the new experience; they must be disposed of somehow, and they can be disposed of finally only as they are provided for. that is, they cannot be simply denied or excluded or eliminated; they must be taken into the fold. but such introduction clearly demands more or less modification or transformation on their part. the thought-situation is the deliberate maintenance of an organization in experience, with a critical consideration of the claims of the various conflicting contents to a place, and a final assignment of position. the conflicting situation inevitably polarizes or dichotomizes itself. there is somewhat which is untouched in the contention of incompatibles. there is something which remains secure, unquestioned. on the other hand, there are elements which are doubtful and precarious. this gives the framework of the general distribution of the field into "facts," the given, the presented, the datum; and ideas, the _quaesitum_, the conceived, the inferential. _a_) there is always something unquestioned in any problematic situation at any stage of its process,[ ] even if it be only the fact of conflict or tension. for this is never _mere_ tension at large. it is thoroughly qualified, or characteristically toned and colored, by the particular elements which are in strife. hence it is _this_ conflict, unique and irreplaceable. that it comes now means precisely that it has never come before; that it is now passed in review and some sort of a settlement reached, means that just _this_ conflict will never recur. in a word, the conflict is immediately of just this and no other sort, and this immediately given quality is an irreducible datum. _it_ is fact, even if all else be _doubtful_. as it is subjected to examination, it loses vagueness and assumes more definite form. only in very extreme cases, however, does the assured, unquestioned element reduce to terms as low as we have here imagined. certain things come to stand forth as facts, no matter what else may be doubted. there are certain _apparent_ diurnal changes of the sun; there is a certain annual course or track. there are certain nocturnal changes in the planets, and certain seasonal rhythmic paths. the significance of these may be doubted: do they _mean_ real change in the sun or in the earth? but change, and change of a certain definite and numerically determinate character, is there. it is clear that such out-standing facts (ex-istences) constitute the data, the given or presented, in the thought-function. _b_) it is obvious that this is only one correspondent, or status, in the total situation. with the consciousness of _this_ as certain, as given to be reckoned with, goes the consciousness of uncertainty as to _what it means_--of how it is to be understood or interpreted, that is, of its reference and connection. the facts qua presentations or existences are sure; _qua_ meanings (position and relationship in an experience yet to be secured) they are doubtful. yet doubt does not preclude memory or anticipation. indeed, it is possible only through them. the memory of past experience makes sun-revolving-about-earth an object of attentive regard. the recollection of certain other experiences suggests the idea of earth-rotating-daily-on-axis and revolving-annually-about-sun. these contents are as much present as is the observation of change, but as respects connection they are only possibilities. accordingly, they are categorized or disposed of as ideas, meanings, thoughts, ways of conceiving, comprehending, interpreting facts. correspondence of reference here is as obvious as correlation of existence. in the logical process, the datum is not just external existence, and the idea mere psychical existence. both are modes of existence--one of _given_ existence, the other of _possible_, of inferred existence. and if the latter is regarded, from the standpoint of the unified experience aimed at, as having only _possible_ existence, the datum also is regarded as incomplete and unassured. or, as we commonly put it, while the ideas are impressions, suggestions, guesses, theories, estimates, etc., facts are crude, raw, unorganized, brute. they lack relationship, that is, assured place; they are deficient as to continuity. mere change of relative position of sun, which is absolutely unquestioned as datum, is a sheer abstraction from the standpoint either of the organized experience left behind, or of the reorganized experience which is the end--the objective. it is impossible as a persistent object. in other words, datum and ideatum are divisions of labor, co-operative instrumentalities, for economical dealing with the problem of the maintenance of the integrity of experience. once more, and briefly, both datum and ideatum may (and positively, veritably, do) break up, each for itself, into physical and mental. in so far as the conviction gains ground that the earth revolves about the sun, the old fact is broken up into a new cosmic existence, and a new psychological condition--the recognition of a process in virtue of which movements of smaller bodies in relation to very remote larger bodies are interpreted in a reverse sense. we do not just eliminate the source of error in the old content. we reinterpret it as valid in its own place, viz., a case of the psychology of perception, although invalid as a matter of cosmic structure. until we have detected the source of error as itself a perfectly genuine existence, we are not, scientifically, satisfied. if we decide that the snake is but a hallucination, our reflection is not, in purport, complete until we have found some fact just as existential as the snake would have been had it been there, which accounts for the hallucination. we never stop, except temporarily, with a reference to the mind or knower as source of an error. we hunt for a specific existence. in other words, with increasing accuracy of determination of the given, there comes a distinction, for methodological purposes, between the _quality_ or matter of the sense experience and its _form_--the sense perceiving, as itself a psychological fact, having its own place and laws or relations. moreover, the old experience, that of sun-revolving, abides. but it is regarded as belonging to "me"--to this experiencing individual rather than to the cosmic world. here, then, _within_ the growth of the thought-situation and as a part of the process of determining _specific_ truth under _specific_ conditions, we get for the first time the clue to that distinction with which, as ready-made and prior to all thinking, lotze started out, namely, the separation of the matter of impression from impression as a personal event. the separation which, taken at large, engenders an insoluble problem, appears within a particular reflective inquiry, as an inevitable differentiation of a scheme of existence. the same sort of thing occurs on the side of thought, or meaning. the meaning or idea which is growing in acceptance, which is gaining ground as meaning-of-datum, gets logical or intellectual or objective force; that which is losing standing, which is increasingly doubtful, gets qualified as just a notion, a fancy, a prejudice, misconception--or finally just an error, a mental slip. evaluated as fanciful in _validity_ it becomes a mere fancy in its existence.[ ] it is not eliminated, but receives a new reference or meaning. thus the distinction between subjectivity and objectivity is not one between meaning as such and datum as such. it is a specification that emerges, correspondently, in _both_ datum and ideatum. that which is left behind in the evolution of accepted meaning is still characterized as real, but real now in relation only to a way of experiencing--to a peculiarity of the organism. that which is moved toward is regarded as real in a cosmic or extra-organic sense. . _the data of thought._--when we turn to lotze, we find that he makes a clear distinction between the presented material of thought, its datum, and the typical characteristic modes of thinking in virtue of which the datum gets organization or system. it is interesting to note also that he states the datum in terms different from those in which the antecedents of thought are defined. from the point of view of the data or material upon which ideas exercise themselves, it is not coincidence, collocation, or succession that counts, but gradation of degrees in a scale. it is not things in spatial or temporal arrangement that are emphasized, but qualities as mutually distinguished, yet resembling and classed. there is no inherent inconceivability in the idea that every impression should be as incomparably different from every other as sweet is from warm. but by a remarkable circumstance such is not the case. we have series, and networks of series. we have diversity of a common--diverse colors, sounds, smells, tastes, etc. in other words, the data are sense qualities which, fortunately for thought, are given arranged as shades, degrees, variations, or qualities of somewhat that is identical.[ ] all this is given, presented, to our ideational activities. even the universal, the common color which runs through the various qualities of blue, green, white, etc., is not a product of thought, but something which thought finds already in existence. it conditions comparison and reciprocal distinction. particularly all mathematical determinations, whether of counting (number), degree (more or less), and quantity (greatness and smallness), come back to this peculiarity of the datum. here lotze dwells at considerable length upon the fact that the very possibility, as well as the success, of thought is due to this peculiar universalization or _prima facie_ ordering with which its material is given to it. such pre-established fitness in the meeting of two things that have nothing to do with each other is certainly cause enough for wonder and congratulation. it should not be difficult to see why lotze uses different categories in describing the material of thought from those employed in describing its antecedent conditions, even though, according to him, the two are absolutely the same.[ ] he has different _functions_ in mind. in one case, the material must be characterized as evoking, as incentive, as stimulus--from this point of view the peculiar feature of spatial and temporal arrangement in contrast with coherence or connection is emphasized. but in the other case the material must be characterized as affording stuff, actual subject-matter. data are not only what is given _to_ thought, but they are also the food, the raw material, _of_ thought. they must be described as, on the one hand, wholly outside of thought. this clearly puts them into the region of sense perception. they are matters of _sensation_ given free from all inferring, judging, relating influence. sensation is just what is _not_ called up in memory or in anticipated projection--it is the immediate, the irreducible. on the other hand, sensory-_matter_ is qualitative, and quales are made up on a common basis. they are degrees or grades of a common quality. thus they have a certain ready-made setting of mutual distinction and reference which is already almost, if not quite, the effect of comparing, of relating, effects which are the express traits of thinking. it is easy to interpret this miraculous gift of grace in the light of what has been said. the data are in truth precisely that which is selected and set aside as present, as immediate. thus they are _given_ to _further_ thought. but the selection has occurred in view of the need for thought; it is a listing of the capital in the way of the undisturbed, the undiscussed, which thought can count upon in this particular problem. hence it is not strange that it has a peculiar fitness of adaptation for thought's further work. having been selected with precisely that end in view, the wonder would be if it were not so fitted. a man may coin counterfeit money for use upon others, but hardly with the intent of passing it off upon himself. our only difficulty here is that the mind flies away from the logical interpretation of sense datum to a ready-made notion of it brought over from abstract psychological inquiry. the belief in isolated sensory quales which are somehow forced upon us, and forced upon us at large, and thus conditioning thought wholly _ab extra_, instead of determining it as instrumentalities or elements selected from experienced things for that very purpose, is too fixed. sensory qualities _are_ forced upon us, but _not_ at large. the sensory data of experience always come _in a context_; they always appear as variations in a continuum. even the thunder which breaks in upon me (to take the extreme of apparent discontinuity and irrelevancy) disturbs me because it is taken as thunder: as a part of the same space-world as that in which my chair and room and house are located; and it is taken as an influence which interrupts and disturbs, _because_ it is part of a common world of causes and effects. the solution of continuity is itself practical or teleological, and thus presupposes and affects continuity of purpose, occupations, and means in a life-process. it is not metaphysics, it is biology which enforces the idea that actual sensation is not only determined as an event in a world of events,[ ] but is an occurrence occurring at a certain period in the control and use of stimuli.[ ] . _forms of thinking data._--as sensory datum is material set for work of thought, so the ideational forms with which thought does its work are apt and prompt to meet the needs of the material. the "accessory"[ ] notion of ground of coherence turns out, in truth, not to be a formal, or external, addition to the data, but a requalification of them. thought is accessory as accomplice, not as addendum. "thought" is to eliminate mere coincidence, and to assert grounded coherence. lotze makes it clear that he does not at bottom conceive of "thought" as an activity "in itself" imposing a form of coherence; but that the organizing work of "thought" is only the progressive realization of an inherent unity, or system, in the material experienced. the specific modes in which thought brings its "accessory" power to bear--names, conception, judgment, and inference--are successive stages in the adequate organization of the matter which comes to us first as data; they are successive stages of the effort to overcome the original defects of the data. conception starts from the universal (the common element) of sense. yet (and this is the significant point) it does not simply abstract this common element, and consciously generalize it over against its own differences. such a "universal" is _not_ coherence just because it does not _include_ and dominate the temporal and local heterogeneity. the _true_ concept (see i, ) is a system of attributes, held together on the basis of some ground, or determining, dominating principle--a ground which so controls all its own instances as to make them into an inwardly connected whole, and which so specifies its own limits as to be exclusive of all else. if we abstract color as the common element of various colors, the result is not a scientific idea or concept. discovery of a process of light-waves whose various rates constitute the various colors of the spectrum gives the concept. and when we get such a concept, the former mere temporal abruptness of color experiences gives way to ordered parts of a color system. the logical product--the concept, in other words--is not a formal seal or stamp; it is a thoroughgoing connection of data in a dynamic continuity of existence. the form or mode of thought which marks the continued transformation of the data and the idea in reference to each other is judgment. judgment makes explicit the assumption of a principle which determines connection within an individualized whole. it definitely states red as _this_ case or instance of the law or process of color, and thus further overcomes the defect in _subject-matter_ or data still left by conception.[ ] now judgment logically terminates in disjunction. it gives a universal which may determine any one of a number of alternative defined particulars, but which is arbitrary as to _what_ one is selected. systematic _inference_ brings to light the material conditions under which the law, or dominating universal, applies to this, rather than that alternative particular, and so completes the ideal organization of the subject-matter. if this act were complete, we should finally have present to us a whole on which we should know the determining and effective or authorizing elements, and the order of development or hierarchy of dependence, in which others follow from them.[ ] in this account by lotze of the operations of the forms of thought, there is clearly put before us the picture of a continuous correlative determination of datum on one side and of idea or meaning on the other, till experience is again integral, data being thoroughly defined and connected, and ideas being the relevant meanings of subject-matter. that we have here in outline a description of what actually occurs there can be no doubt. but there is as little doubt that the description is thoroughly inconsistent with lotze's supposition that the material or data of thought is precisely the same as the antecedent of thought; or that ideas, conceptions, are purely mental somewhats extraneously brought to bear, as the sole essential characteristics of thought, upon a material provided ready-made. it means but one thing: the maintenance of unity and wholeness in experience through conflicting contents occurs by means of a strictly correspondent setting apart of facts to be accurately described and properly related, and meanings to be adequately construed and properly referred. the datum is given _in_ the thought-situation, and _to_ further qualification of ideas or meanings. but even in this aspect it presents a problem. to find out _what is_ given is an inquiry which taxes reflection to the uttermost. every important advance in scientific method means better agencies, more skilled technique for simply detaching and describing what is barely there, or given. to be able to find out what can safely be taken as _there_, as given in any particular inquiry, and hence be taken as material for orderly and verifiable inference, for fruitful hypothesis-making, for entertaining of explanatory and interpretative ideas, is one phase of the effort of systematic scientific inquiry. it marks its inductive phase. to take what is discovered to be reliable evidence within a more complex _situation_ as if it were given absolutely and in isolation, or apart from a particular historic situs and context, is the fallacy of empiricism as a logical theory. to regard the thought-forms of conception, judgment, and inference as qualifications of "pure thought, apart from any difference in objects," instead of as successive dispositions in the progressive organization of the material (or objects), is the fallacy of rationalism. lotze, like kant, attempts to combine the two, thinking thereby to correct each by the other. lotze recognizes the futility of thought if the sense data as data are final, if they alone are real, the truly existent, self-justificatory and valid. he sees that, if the empiricist were right in his assumption as to the real worth of the given data, thinking would be a ridiculous pretender, either toilfully and poorly doing over again what needs no doing, or making a wilful departure from truth. he realizes that thought is evoked because it is needed; and that it has a work to do which is not merely formal, but which effects a modification of the subject-matter of experience. consequently he assumes a thought-in-itself, with certain forms and modes of action of its own, a realm of meaning possessed of a directive and normative worth of its own--the root-fallacy of rationalism. his attempted compromise between the two turns out to be based on the assumption of the indefensible ideas of both--the notion of an independent matter given to thought, on one side, and of an independent worth or force of thought-forms, on the other. this pointing out of inconsistencies becomes stale and unprofitable save as we bring them back into connection with their root-origin--the erection of distinctions that are genetic and historic, and working or instrumental divisions of labor, into rigid and ready-made structural differences of reality. lotze clearly recognizes that thought's nature is dependent upon its aim, its aim upon its problem, and this upon the situation in which it finds its incentive and excuse. its work is cut out for it. it does not what it would, but what it must. as lotze puts it, "logic has to do with thought, not as it would be under hypothetical conditions, but as it is" (i, ), and this statement is made in explicit combination with statements to the effect that the peculiarity of the material of thought conditions its activity. similarly he says, in a passage already referred to: "the possibility and the success of thought's production in general depends upon this original constitution and organization of the whole world of ideas, a constitution which, though not necessary in thought, is all the more necessary to make thought possible."[ ] as we have seen, the essential nature of conception, judgment, and inference is dependent upon peculiarities of the propounded material, they being forms dependent for their significance upon the stage of organization in which they begin. from this only one conclusion is possible. if thought's nature is dependent upon its actual conditions and circumstances, the primary logical problem is to study thought-in-its-conditioning; it is to detect the crisis within which thought and its subject-matter present themselves in their mutual distinction and cross-reference. but lotze is so thoroughly committed to a ready-made antecedent of some sort, that this genetic consideration is of no account to him. the historic method is a mere matter of psychology, and has no logical worth (i, ). we must presuppose a psychological mechanism and psychological material, but logic is concerned not with origin or history, but with authority, worth, value (i, ). again: "logic is not concerned with the manner in which the elements utilized by thought come into existence, but their value _after_ they have somehow come into existence, for the carrying out of intellectual operations" (i, ). and finally: "i have maintained throughout my work that logic cannot derive any serious advantage from a discussion of _the conditions under which thought as a psychological process comes about_. the significance of logical forms ... is to be found in the utterances of thought, the laws which it imposes, after or during the act of thinking, not in the conditions which lie back of any which produce thought."[ ] lotze, in truth, represents a halting-stage in the evolution of logical theory. he is too far along to be contented with the reiteration of the purely formal distinctions of a merely formal thought-by-itself. he recognizes that thought as formal is the form of some matter, and has its worth only as organizing that matter to meet the ideal demands of reason; and that "reason" is in truth only an adequate systematization of the matter or content. consequently he has to open the door to admit "psychical processes" which furnish this material. having let in the material, he is bound to shut the door again in the face of the processes from which the material proceeded--to dismiss them as impertinent intruders. if thought gets its data in such a surreptitious manner, there is no occasion for wonder that the legitimacy of its dealings with the material remains an open question. logical theory, like every branch of the philosophic disciplines, waits upon a surrender of the obstinate conviction that, while the work and aim of thought is conditioned by the material supplied to it, yet the _worth_ of its performances is something to be passed upon in complete abstraction from conditions of origin and development. footnotes: [ ] this is but to say that the presentation of objects as specifically different things in experience is the work of reflection, and that the discrimination of something experienc_ed_ from modes of experienc_ing_ is also the work of reflection. the latter statement is, of course, but a particular case of the first; for an act of experiencing is one object, among others, which may be discriminated out of the original experience. when so discriminated, it has exactly the same existential status as any other discriminated object; seeing and thing seen stand on the same level of existentiality. but primary experience is innocent of the discrimination of the _what_ experienced and the _how_, or mode, of experiencing. we are not in it aware of the seeing, nor yet of objects _as_ something seen. any experience in all of its non-reflective phases is innocent of any discrimination of subject and object. it involves within itself what may be reflectively discriminated into objects located outside the organism and objects referred to the organism. [note added in revision.] [ ] of course, this very element may be the precarious, the ideal, and possibly fanciful of some other situation. but it is to change the historic into the absolute to conclude that therefore everything is uncertain, all at once, or as such. this gives metaphysical skepticism as distinct from the working skepticism which is an inherent factor in all reflection and scientific inquiry. [ ] but this is a slow progress within reflection. plato, who was influential in bringing this general distinction to consciousness, still thought and wrote as if "image" were itself a queer sort of objective existence; it was only gradually that it was disposed of as a phase of personal experiencing. [ ] i, - . [ ] it is interesting to see how explicitly lotze is compelled finally to differentiate two aspects in the antecedents of thoughts, one of which is necessary in order that there may be anything to call out thought (a lack, or problem); the other in order that when thought is evoked it may find data at hand--that is, material in shape to receive and respond to its exercise. "the manifold matter of ideas is brought before us, not only in the _systematic order of its qualitative relationships_, but in the rich _variety of local and temporal combinations_.... the _combinations of heterogeneous ideas_ ... form the _problems_, in connection with which the efforts of thought to reduce coexistence to coherence will _subsequently_ be made. the _homogeneous or similar_ ideas, on the other hand, give occasion to separate, to connect, and to count their repetitions" (i, , ; italics mine). without the heterogeneous variety of the local and temporal juxtapositions there would be nothing to excite thought. without the systematic arrangement of quality there would be nothing to meet thought and reward it for its efforts. the homogeneity of qualitative relationships, _in the pre-thought material_, gives the tools or instruments by which thought is enabled successfully to tackle the heterogeneity of collocations and conjunctions also found in the same material! one would suppose that when lotze reached this point he might have been led to suspect that in his remarkable adjustment of thought-stimuli, thought-material, and thought-tools to one another, he must after all be dealing, not with something prior to the thought-function, but with the necessary structures and tools of the thought-situation. [ ] _supra_, p. . [ ] for the identity of sensory experience with the point of greatest strain and stress in conflicting or tensional experience, see "the reflex arc concept in psychology," _psychological review_, iii, . [ ] for the "accessory" character of thought, see lotze, i, , - , , etc. [ ] bosanquet (_logic_, i, - ) and jones (_philosophy of lotze_, , chap. iv) have called attention to a curious inconsistency in lotze's treatment of judgment. on one hand, the statement is as given above. judgment grows out of conception in making explicit the determining relation of universal to its own particular, implied in conception. but, on the other hand, judgment grows not out of conception at all, but out of the question of determining connection in change. lotze's nominal reason for this latter view is that the conceptual world is purely static; since the actual world is one of change, we need to pass upon what really goes together (is causal) in the change as distinct from such as are merely coincident. but, as jones clearly shows, it is also connected with the fact that, while lotze nominally asserts that judgment grows out of conception, he treats conception as the result of judgment since the first view makes judgment a mere explication of the content of an idea, and hence merely expository or analytic (in the kantian sense) and so of more than doubtful applicability to reality. the affair is too large to discuss here, and i will content myself with referring to the oscillation between conflicting contents and gradation of sensory qualities already discussed (p. , note). it is judgment which grows out of the former, because judgment is the whole situation as such; conception is referable to the latter because it _is_ one abstraction within the whole (the solution of possible meanings of the data) just as the datum is another. in truth, since the sensory datum is not absolute, but comes in a historical context, the qualities apprehended as constituting the datum simply define the locus of conflict in the entire situation. they are attributives of the contents-in-tension of the colliding things, not calm untroubled ultimates. on pp. and of vol. i, lotze recognizes (as we have just seen) that, as matter of fact, it is both sensory qualities in their systematic grading, or quantitative determinations (see i, , for the recognition of the necessary place of the quantitative in the true concept), and the "rich variety of local and temporal combinations," that provoke thought and supply it with material. but, as usual, he treats this simply as a historical accident, not as furnishing the key to the whole matter. in fine, while the heterogeneous collocations and successions constitute the problematic element that stimulates thought, quantitative determination of the sensory quality furnishes one of the two chief means through which thought deals with the problem. it is a reduction of the original colliding contents to a form in which the effort at redintegration gets maximum efficiency. the concept, as ideal meaning, is of course the other partner to the transaction. it is getting the various possible meanings-of-the-data into such shape as to make them most useful in construing the data. the bearing of this upon the subject and predicate of judgment cannot be discussed here. [ ] see i, , , , , , , for lotze's treatment of these distinctions. [ ] i, ; see also ii, , . [ ] ii, ; the same is reiterated in ii, , where the question of origin is referred to as a corruption in logic. certain psychical acts are necessary as "conditions and occasions" of logical operations, but the "deep gulf between psychical mechanism and thought remains unfilled." v the objects of thought in the foregoing discussion, particularly in the last chapter, we were repeatedly led to recognize that thought has its own distinctive objects. at times lotze gives way to the tendency to define thought entirely in terms of modes and forms of activity which are exercised by it upon a strictly foreign material. but two motives continually push him in the other direction. ( ) thought has a distinctive work to do, one which involves a qualitative transformation of (at least) the _relationships_ of the presented matter; as fast as it accomplishes this work, the subject-matter becomes somehow thought's subject-matter. as we have just seen, the data are progressively organized to meet thought's ideal of a complete whole, with its members interconnected according to a determining principle. such progressive organization throws backward doubt upon the assumption of the original total irrelevancy of the data and thought-forms to each other. ( ) a like motive operates from the side of the subject-matter. as merely foreign and external, it is too heterogeneous to lend itself to thought's exercise and influence. the idea, as we saw in the first chapter, is the convenient medium through which lotze passes from the purely heterogeneous psychical impression or event, which is totally irrelevant to thought's purpose and working, over to a state of affairs which can reward thought. idea as meaning forms the bridge over from the brute factuality of the psychical impression to the coherent value of thought's own content. we have, in this chapter, to consider the question of the idea or content of thought from two points of view: first the _possibility_ of such a content--its consistency with lotze's fundamental premises; secondly, its _objective_ character--its validity and test. i. the question of the possibility of a specific content of thought is the question of the nature of the idea as meaning. _meaning_ is the characteristic object of thought. we have thus far left unquestioned lotze's continual assumption of meaning as a sort of thought-unit; the building-stone of thought's construction. in his treatment of meaning, lotze's contradictions regarding the antecedents, data, and content of thought reach their full conclusion. he expressly makes meaning to be the product of thought's activity and also the unreflective material out of which thought's operations grow. this contradiction has been worked out in accurate and complete detail by professor jones.[ ] he summarizes it as follows (p. ): "no other way was left to him [lotze] excepting this of first attributing all to sense and afterwards attributing all to thought, and, finally, of attributing it to thought only because it was already in its material. this _seesaw_ is essential to his theory; the elements of knowledge as he describes them can subsist only by the alternate robbery of each other." we have already seen how strenuously lotze insists upon the fact that the given subject-matter of thought is to be regarded wholly as the work of a physical mechanism, "without any action of thought."[ ] but lotze also states that if the products of the psychical mechanism "are to admit of combination in the definite form of a _thought_, they each require some previous shaping to make them into logical building-stones and to convert them from _impressions_ into _ideas_. nothing is really more familiar to us than this first operation of thought; the only reason why we usually overlook it is that in the language which we inherit, it is already carried out, and it seems, therefore, to belong to the self-evident presuppositions of thought, _not to its own specific work_."[ ] and again (i, ), judgments "can consist of nothing but combinations of ideas which are no longer mere impressions: every such idea must have undergone at least the simple formation mentioned above." such ideas are, lotze goes on to urge, already rudimentary concepts--that is to say, logical determinations. the obviousness of the logical contradiction of attributing to a preliminary specific work of thought exactly the condition of affairs which is elsewhere explicitly attributed to a psychical mechanism prior to any thought-activity, should not blind us to its import and relative necessity. the impression, it will be recalled, is a mere state of our own consciousness--a mood of ourselves. as such it has simply _de facto_ relations as an event to other similar events. but reflective thought is concerned with the relationship of a content or matter to other contents. hence the impression must have a matter before it can come at all within the sphere of thought's exercise. how shall it secure this? why, by a preliminary activity of thought which objectifies the impression. blue as a mere sensuous irritation or feeling is given a quality, the meaning "blue"--blueness; the sense impression is objectified; it is presented "no longer as a condition which we undergo, but as a something which has its being and its meaning in itself, and which continues to be what it is, and to mean what it means whether we are conscious of it or not. it is easy to see here the _necessary beginning of that activity which we above appropriated to thought as such_: it has not yet got so far as converting coexistence into coherence. it has first to perform the previous task of investing each single impression with an independent validity, without which the later opposition of their real coherence to mere coexistence could not be made in any intelligible sense."[ ] this objectification, which converts a sensitive state into a sensible matter to which the sensitive state is referred, also gives this matter "position," a certain typical character. it is not objectified in a merely general way, but is given a specific sort of objectivity. of these sorts of objectivity there are three mentioned: that of a substantive content; that of an attached dependent content; that of an active relationship connecting the various contents with each other. in short, we have the types of meaning embodied in language in the form of nouns, adjectives, and verbs. it is through this preliminary formative activity of thought that reflective or _logical_ thought has presented to it a world of meanings ranged in an order of relative independence and dependence, and arranged as elements in a complex of meanings whose various constituent parts mutually influence one another's meanings.[ ] as usual, lotze mediates the contradiction between material constituted _by_ thought and the same material just presented _to_ thought, by a further position so disparate to each that, taken in connection with each by turns, it seems to bridge the gulf. after describing the prior constitutive work of thought as above, he goes on to discuss a _second_ phase of thought which is intermediary between this and the third phase, viz., reflective thought proper. this second activity is that of arranging experienced quales in series and groups, thus ascribing a sort of universal or common somewhat to various instances (as already described; see p. ). on one hand, it is clearly stated that this second phase of thought's activity is in reality the _same_ as the first phase: since all objectification involves positing, since positing involves distinction of one matter from others, and since this involves placing it in a series or group in which each is measurably marked off, as to the degree and nature of its diversity, from every other. we are told that we are only considering "a really inseparable operation" of thought from two different sides: first, as to the effect which objectifying thought has upon the matter as set over against the feeling _subject_; secondly, the effect which this objectification has upon the matter in relation to _other matters_.[ ] afterward, however, these two operations are declared to be radically different in type and nature. the first is determinant and formative; it gives ideas "the shape without which the logical spirit could not accept them." in a way it dictates "its own laws to its object-matter."[ ] the second activity of thought is rather passive and receptive. it simply recognizes what is already there. "thought can make no difference where it finds none already in the matter of impressions."[ ] "the first universal, as we saw, can only be experienced in immediate sensation. it is no product of thought, but something that thought finds already in existence."[ ] the obviousness of this further contradiction is paralleled only by its inevitableness. thought is in the air, is arbitrary and wild in dealing with meanings, unless it gets its start and cue from actual experience. hence the necessity of insisting upon thought's activity as just recognizing the contents already given. but, on the other hand, prior to the work of thought there is to lotze no content or meaning. it requires a work of thought to detach anything from the flux of sense irritations and invest it with a meaning of its own. this dilemma is inevitable to any writer who declines to consider as correlative the nature of thought-activity and thought-content from the standpoint of their generating conditions in the movement of experience. viewed from such a standpoint the principle of solution is clear enough. as we have already seen (p. ), the internal dissension of an experience leads to detaching certain factors previously integrated in the concrete experience as aspects of its own qualitative coloring, and to relegating them, for the time being (pending integration into further immediate qualities of a reconstituted experience), into a world of bare meanings, a sphere qualified as ideal throughout. these meanings then become the tools of thought in interpreting the data, just as the sense qualities which define the presented situation are the immediate matter for thought. the two _as mutually referred_ are content. that is, the datum and the meaning as reciprocally qualified by each other constitute the objective of thought. to reach this unification is thought's objective or goal. every successive cross-section of reflective inquiry presents what may be taken for granted as the outcome of previous thinking, and as the determinant of further reflective procedure. taken as defining the point reached in the thought-function and serving as constituent unit in further thought, it is content or logical object. lotze's instinct is sure in identifying and setting over against each other the material given to thought and the content which is thought's own "building-stone." his contradictions arise simply from the fact that his absolute, non-historic method does not permit him to interpret this joint identity and distinction in a working, and hence relative, sense. ii. the question of how the existence of meanings, or thought-contents, is to be understood merges imperceptibly into the question of the real objectivity or validity of such contents. the difficulty for lotze is the now familiar one: so far as his logic compels him to insist that these meanings are the possession and product of thought (since thought is an independent activity), the ideas are merely ideas; there is no test of objectivity beyond the thoroughly unsatisfactory and formal one of their own mutual consistency. in reaction from this lotze is thrown back upon the idea of these contents as the original matter given in the impressions themselves. here there seems to be an objective or external test by which the reality of thought's operations may be tried; a given idea is verified or found false according to its measure of correspondence with the matter of experience as such. but now we are no better off. the original independence and heterogeneity of impressions and of thought is so great that there is no way to compare the results of the latter with the former. we cannot compare or contrast distinctions of worth with bare differences of factual existence (i, ). the standard or test of objectivity is so thoroughly external that by original definition it is wholly outside the realm of thought. how can thought compare meanings with existences? or again, the given material of experience apart from thought is precisely the relatively chaotic and unorganized; it even reduces itself to a mere sequence of psychical events. what sense is there in directing us to compare the highest results of scientific inquiry with the bare sequence of our own states of feeling; or even with the original data whose fragmentary and uncertain character was the exact motive for entering upon scientific inquiry? how can the former in any sense give a check or test of the value of the latter? this is professedly to test the validity of a system of meanings by comparison with that whose defects call forth the construction of the system of meanings. our subsequent inquiry simply consists in tracing some of the phases of the characteristic seesaw from one to the other of the two horns of the now familiar dilemma: either thought is separate from the matter of experience, and then its validity is wholly its own private business, or else the objective results of thought are already in the antecedent material, and then thought is either unnecessary or else has no way of checking its own performances. . lotze assumes, as we have seen, a certain independent validity in each meaning or qualified content, taken in and of itself. "blue" has a certain meaning, in and of itself; it is an _object_ for consciousness as such, not merely its state or mood. after the original sense irritation through which it was mediated has entirely disappeared, it persists as a valid meaning. moreover, it is an object or content of thought for others as well. thus it has a double mark of validity: in the comparison of one part of my own experience with another, and in the comparison of my experience as a whole with that of others. here we have a sort of validity which does not raise at all the question of _metaphysical_ reality (i, , ). lotze thus seems to have escaped from the necessity of employing as check or test for the validity of ideas any reference to a real outside the sphere of thought itself. such terms as "conjunction," "franchise," "constitution," "algebraic zero," etc., claim to possess objective validity. yet none of these professes to refer to a reality beyond thought. generalizing this point of view, validity or objectivity of meaning means simply that which is "identical for all consciousness" (i, ); "it is quite indifferent whether certain parts of the world of thought indicate something which has beside an independent reality outside of thinking minds, or whether all that it contains exists only in the thoughts of those who think it, but with equal validity for them all" (i, ). so far it seems clear sailing. difficulties, however, show themselves the moment we inquire what is meant by a self-identical content for all thought. is this to be taken in a static or in a dynamic way? that is to say: does it express the fact that a given content or meaning is _de facto_ presented to the consciousness of all alike? does this coequal presence guarantee an objectivity? or does validity attach to a given meaning or content in the sense that it directs and controls the further exercise of thinking, and thus the formation of further _new_ objects of knowledge? the former interpretation is alone consistent with lotze's notion that the independent idea as such is invested with a certain validity or objectivity. it alone is consistent with his assertion that concepts precede judgments. it alone, that is to say, is consistent with the notion that reflective thinking has a sphere of ideas or meanings supplied to it at the outset. but it is impossible to entertain this belief. the stimulus which, according to lotze, goads thought on from ideas or concepts to judgments and inferences is in truth simply the lack of validity, of objectivity in its original independent meanings or contents. a meaning as independent is precisely that which is not invested with validity, but which is a mere idea, a "notion," a fancy, at best a surmise which may turn out to be valid (and of course this indicates possible reference); a standpoint to have its value determined by its further active use. "blue" as a mere detached floating meaning, an idea at large, would not gain in validity simply by being entertained continuously in a given consciousness, or by being made at one and the same time the persistent object of attentive regard by all human consciousnesses. if this were all that were required, the chimera, the centaur, or any other subjective construction could easily gain validity. "christian science" has made just this notion the basis of its philosophy. the simple fact is that in such illustrations as "blue," "franchise," "conjunction," lotze instinctively takes cases which are not mere independent and detached meanings, but which involve reference to a _region_ of experience, to a region of mutually determining social activities. the conception that reference to a _social_ activity does not involve the same sort of reference of a meaning beyond itself that is found in physical matters, and hence may be taken quite innocent and free of the problem of reference to existence beyond meaning, is one of the strangest that has ever found lodgment in human thinking. either both physical and social reference or neither is logical; if neither, then it is because the meaning functions, as it originates, in a specific situation which carries with it its own tests (see p. ). lotze's conception is made possible only by unconsciously substituting the idea of an object as a content of thought for a large number of persons (or a _de facto_ somewhat for every consciousness), for the genuine definition of object as a _determinant_ in a scheme of activity. the former is consistent with lotze's conception of thought, but wholly indeterminate as to validity or intent. the latter is the test used experimentally in all concrete thinking, but involves a radical transformation of all lotze's assumptions. a given idea of the conjunction of the franchise, or of blue, is valid, not because everybody happens to entertain it, but because it expresses the factor of control or direction in a given movement of experience. the test of validity of idea[ ] is its functional or instrumental use in effecting the transition from a relatively conflicting experience to a relatively integrated one. if lotze's view were correct, "blue" valid once would be valid always--even when red or green were actually called for to fulfil specific conditions. this is to say validity really refers to rightfulness or adequacy of performance in an asserting of connection--not to a meaning as contemplated in detachment. if we refer again to the fact that the genuine antecedent of thought is a situation which is disorganized in its structural elements, we can easily understand how certain contents may be detached and _held_ apart as meanings or references, actual or possible. we can understand how such detached contents may be of use in effecting a review of the entire experience, and as affording standpoints and methods of a reconstruction which will maintain the integrity of behavior. we can understand how validity of meaning is measured by reference to something which is not mere meaning; by reference to something which lies beyond it as such--viz., the reconstitution of an experience into which it enters as method of control. that paradox of ordinary experience and of scientific inquiry by which objectivity is given alike to matter of perception and to conceived relations--to facts and to laws--affords no peculiar difficulty because the test of objectivity is everywhere the same: anything is objective in so far as, through the medium of conflict, it controls the movement of experience in its reconstructive transition. there is not first an object, whether of sense perception or of conception, which afterward somehow exercises this controlling influence; but the objective is _any_ existence exercising the function of control. it may only control the act of inquiry; it may only set on foot doubt, but this is direction of subsequent experience, and, in so far, is a token of objectivity. it has to be reckoned with. so much for the thought-content or meaning as having a validity of its own. it does not have it as isolated or given or static; it has it in its dynamic reference, its use in determining further movement of experience. in other words, the "meaning," having been selected and made up with reference to performing a certain office in the evolution of a unified experience, can be tested in no other way than by discovering whether it does what it was intended to do and what it purports to do.[ ] . lotze has to wrestle with this question of validity in a further respect: what constitutes the objectivity of thinking as a total attitude, activity, or function? according to his own statement, the meanings or valid ideas are after all only building-stones for logical thought. validity is thus not a property of them in their independent existences, but of their mutual reference to each other. thinking is the process of instituting these mutual references; of building up the various scattered and independent building-stones into the coherent system of thought. what is the validity of the various forms of thinking which find expression in the various types of judgment and in the various forms of inference? categorical, hypothetical, disjunctive judgment; inference by induction, by analogy, by mathematical equation; classification, theory of explanation--all these are processes of reflection by which connection in an organized whole is given to the fragmentary meanings with which thought sets out. what shall we say of the validity of such processes? on one point lotze is quite clear. these various logical acts do not really enter into the constitution of the valid world. the logical forms as such are maintained _only_ in the process of thinking. the world of valid truth does not undergo a series of contortions and evolutions, paralleling in any way the successive steps and missteps, the succession of tentative trials, withdrawals, and retracings, which mark the course of our own thinking.[ ] lotze is explicit upon the point that only the thought-content in which the process of thinking issues has objective validity; the act of thinking is "purely and simply an inner movement of our own minds, made necessary to us by reason of the constitution of our nature and of our place in the world" (ii, ). here the problem of validity presents itself as the problem of the relation of the act of thinking to its own product. in his solution lotze uses two metaphors: one derived from building operations, the other from traveling. the construction of a building requires of necessity certain tools and extraneous constructions, stagings, scaffoldings, etc., which are necessary to effect the final construction, but which do not enter into the building as such. the activity has an instrumental, though not a constitutive, value as regards its product. similarly, in order to get a view from the top of a mountain--this view being the objective--the traveler has to go through preliminary movements along devious courses. these again are antecedent prerequisites, but do not constitute a portion of the attained view. the problem of thought as activity, as distinct from thought as content, opens up altogether too large a question to receive complete consideration at this point. fortunately, however, the previous discussion enables us to narrow the point which is in issue just here. the question is whether the activity of thought is to be regarded as an independent function supervening entirely from without upon antecedents, and directed from without upon data, or whether it marks the phase of the transformation which the course of experience (whether practical, or artistic, or socially affectional or whatever) undergoes for the sake of its deliberate control. if it be the latter, a thoroughly intelligent sense can be given to the proposition that the activity of thinking is instrumental, and that its worth is found, not in its own successive states as such, but in the result in which it comes to conclusion. but the conception of thinking as an independent activity somehow occurring after an independent antecedent, playing upon an independent subject-matter, and finally effecting an independent result, presents us with just one miracle the more. i do not question the strictly instrumental character of thinking. the problem lies not here, but in the interpretation of the nature of the instrument. the difficulty with lotze's position is that it forces us into the assumption of a means and an end which are simply and only external to each other, and yet necessarily dependent upon each other--a position which, whenever found, is thoroughly self-contradictory. lotze vibrates between the notion of thought as a tool in the external sense, a mere scaffolding to a finished building in which it has no part nor lot, and the notion of thought as an immanent tool, as a scaffolding which is an integral part of the very operation of building, and which is set up for the sake of the building-activity which is carried on effectively only with and through a scaffolding. only in the former case can the scaffolding be considered as a _mere_ tool. in the latter case the external scaffolding is _not_ the instrumentality; the actual tool is the _action_ of erecting the building, and this action involves the scaffolding as a constituent part of itself. the work of building is not set over against the completed building as mere means to an end; it _is_ the end taken in process or historically, longitudinally, temporally viewed. the scaffolding, moreover, is not an external means to the process of erecting, but an organic member of it. it is no mere accident of language that "building" has a double sense--meaning at once the process and the finished product. the outcome of thought is the thinking activity carried on to its own completion; the activity, on the other hand, _is_ the outcome taken anywhere short of its own realization, and thereby still going on. the only consideration which prevents easy and immediate acceptance of this view is the notion of thinking as something purely formal. it is strange that the empiricist does not see that his insistence upon a matter accidentally given to thought only strengthens the hands of the rationalist with his claim of thinking as an independent activity, separate from the actual make-up of the affairs of experience. thinking as a merely formal activity exercised upon certain sensations or images or objects sets forth an absolutely meaningless proposition. the psychological identification of thinking with the process of association is much nearer the truth. it is, indeed, on the way to the truth. we need only to recognize that association is of matters or meanings, not of ideas as existences or events; and that the type of association we call thinking differs from casual fancy and revery by control in reference to an end, to apprehend how completely thinking is a reconstructive movement of actual contents of experience in relation to each other. there is no miracle in the fact that tool and material are adapted to each other in the process of reaching a valid conclusion. were they external in origin to each other and to the result, the whole affair would, indeed, present an insoluble problem--so insoluble that, if this were the true condition of affairs, we never should even know that there was a problem. but, in truth, both material and tool have been secured and determined with reference to economy and efficiency in effecting the end desired--the maintenance of a harmonious experience. the builder has discovered that his building means building tools, and also building material. each has been slowly evolved with reference to its fit employ in the entire function; and this evolution has been checked at every point by reference to its own correspondent. the carpenter has not thought at large on his building and then constructed tools at large, but has thought of his building in terms of the material which enters into it, and through that medium has come to the consideration of the tools which are helpful. this is not a formal question, but one of the place and relations of the matters actually entering into experience. and they in turn determine the taking up of just those mental attitudes, and the employing of just those intellectual operations which most effectively handle and organize the material. thinking is adaptation _to_ an end _through_ the adjustment of particular objective contents. the thinker, like the carpenter, is at once stimulated and checked in every stage of his procedure by the particular situation which confronts him. a person is at the stage of wanting a new house: well, then, his materials are available resources, the price of labor, the cost of building, the state and needs of his family, profession, etc.; his tools are paper and pencil and compass, or possibly the bank as a credit instrumentality, etc. again, the work is beginning. the foundations are laid. this in turn determines its own specific materials and tools. again, the building is almost ready for occupancy. the concrete process is that of taking away the scaffolding, clearing up the grounds, furnishing and decorating rooms, etc. this specific operation again determines its own fit or relevant materials and tools. it defines the time and mode and manner of beginning and ceasing to use them. logical theory will get along as well as does the practice of knowing when it sticks close by and observes the directions and checks inherent in each successive phase of the evolution of the cycle of experience. the problem in general of validity of the thinking process as distinct from the validity of this or that process arises only when thinking is isolated from its historic position and its material context (see _ante_, p. ). . but lotze is not yet done with the problem of validity, even from his own standpoint. the ground shifts again under his feet. it is no longer a question of the validity of the idea or meaning with which thought is supposed to set out; it is no longer a question of the validity of the process of thinking in reference to its own product; it is the question of the validity of the product. supposing, after all, that the final meaning, or logical idea, is thoroughly coherent and organized; supposing it is an object for all consciousness as such. once more arises the question: what is the validity of even the most coherent and complete idea?--a question which arises and will not down. we may reconstruct the notion of the chimera until it ceases to be an independent idea and becomes a part of the system of greek mythology. has it gained in validity in ceasing to be an independent myth, in becoming an element in systematized myth? myth it was and myth it remains. mythology does not get validity by growing bigger. how do we know the same is not the case with the ideas which are the product of our most deliberate and extended scientific inquiry? the reference again to the content as the self-identical object of all consciousness proves nothing; the subject-matter of a hallucination does not gain validity in proportion to its social contagiousness. according to lotze, the final product is, after all, still thought. now, lotze is committed once for all to the notion that thought, in any form, is directed by and at an outside reality. the ghost haunts him to the last. how, after all, does even the ideally perfect valid thought apply or refer to reality? its genuine subject is still beyond itself. at the last lotze can dispose of this question only by regarding it as a metaphysical, not a logical, problem (ii, , ). in other words, _logically_ speaking, we are at the end just exactly where we were at the beginning--in the sphere of ideas, and of ideas only, plus a consciousness of the necessity of referring these ideas to a reality which is beyond them, which is utterly inaccessible to them, which is out of reach of any influence which they may exercise, and which transcends any possible comparison with their results. "it is vain," says lotze, "to shrink from acknowledging the circle here involved ... all we know of the external world depends upon the ideas of it which are within us" (ii, ). "it is then this varied world of ideas within us which forms the sole material directly given to us" (ii, ). as it is the only material given to us, so it is the only material with which thought can end. to talk about knowing the external world through ideas which are merely within us is to talk of an inherent self-contradiction. there is no common ground in which the external world and our ideas can meet. in other words, the original separation between an independent thought-material and an independent thought-function and purpose lands us inevitably in the metaphysics of subjective idealism, plus a belief in an unknown reality beyond, which although unknowable is yet taken as the ultimate test of the value of our ideas. at the end, after all our maneuvering we are where we began: with two separate disparates, one of meaning, but no existence, the other of existence, but no meaning. the other aspect of lotze's contradiction which completes the circle is clear when we refer to his original propositions, and recall that at the outset he was compelled to regard the origination and conjunctions of the impressions, the elements of ideas, as themselves the effects exercised by a world of things already in existence (see p. ). he sets up an independent world of thought, and yet has to confess that both at its origin and at its termination it points with absolute necessity to a world beyond itself. only the stubborn refusal to take this initial and terminal reference of thought beyond itself as having a _historic_ or temporal meaning, indicating a particular place of generation and a particular point of fulfilment, compels lotze to give such objective references a transcendental turn. when lotze goes on to say (ii, ) that the measure of truth of particular parts of experience is found in asking whether, when judged by thought, they are in harmony with other parts of experience; when he goes on to say that there is no sense in trying to compare the entire world of ideas with a reality which is non-existent (excepting as it itself should become an idea), he lands where he might better have frankly commenced.[ ] he saves himself from utter skepticism only by claiming that the explicit assumption of skepticism--the need of agreement of a ready-made idea as such with an extraneous ready-made material as such--is meaningless. he defines correctly the work of thought as consisting in harmonizing the various portions of experience with each other. in this case the test of thought is the harmony or unity of experience actually effected. the test of validity of thought is beyond thought, just as at the other limit thought originates out of a situation which is not dependent upon thought. interpret this before and beyond in a historic sense, as an affair of the place occupied and rôle played by thinking as a function in experience in relation to other non-intellectual experiences of things, and then the intermediate and instrumental character of thought, its dependence upon unreflective antecedents for its existence, and upon a consequent experience for its final test, becomes significant and necessary. taken at large, apart from temporal development and control, it plunges us in the depths of a hopelessly complicated and self-revolving metaphysic. footnotes: [ ] _philosophy of lotze_, chap. iii, "thought and the preliminary process of experience." [ ] i, . [ ] i, ; last italics mine. [ ] i, ; italics mine. [ ] see i, - . on p. this work is declared to be not only the first but the most indispensable of all thought's operations. [ ] i, . [ ] i, . [ ] i, ; see the strong statements already quoted, p. . what if this canon were applied in the first act of thought referred to above: the original objectification which transforms the mere state into an abiding quality or meaning? suppose, that is, it were said that the first objectifying act cannot make a substantial (or attached) quale out of a mere state of feeling; it must _find_ the distinction it makes there already! it is clear we should at once get a _regressus ad infinitum_. we here find lotze face to face with this fundamental dilemma: thought either arbitrarily forces in its own distinctions, or else just repeats what is already there--is either falsifying or futile. this same contradiction, so far as it affects the impression, has already been discussed. see p. . [ ] i, . [ ] as we have already seen, the concept, the meaning as such, is always a factor or status in a reflective situation; it is always a predicate of judgment, in use in interpreting and developing the logical subject, or datum of perception. [ ] royce, in his _world and individual_, i, chaps. vi and vii, has criticized the conception of meaning as valid, but in a way which implies that there is a difference between validity and reality, in the sense that the meaning or content of the valid idea becomes real only when it is experienced in direct _feeling_. the foregoing implies, of course, a difference between validity and reality, but finds the test of validity in exercise of the function of direction or control to which the idea makes pretension or claim. the same point of view would profoundly modify royce's interpretation of what he terms "inner" and "outer" meaning. see moore, _university of chicago decennial publications_, iii, on "existence, meaning, and reality." [ ] ii, , , and in general book iii, chap. iv. it is significant that thought itself, appearing as an act of thinking over against its own content, is here treated as psychical rather than as logical. consequently, as we see in the text, it gives him one more difficulty to wrestle with: how a process which is ex officio purely psychical and subjective can yet yield results which are valid in a logical, to say nothing of an ontological, sense. [ ] lotze even goes so far in this connection as to say that the antithesis between our ideas and the objects to which they are directed is itself a part of the world of ideas (ii, ). barring the phrase "world of _ideas_" (as against world of continuous experience), he need only have commenced at this point to have traveled straight and arrived somewhere. but it is absolutely impossible to hold both this view and that of the original independent existence of something given to and in thought and an independent existence of a thought-activity, thought-forms, and thought-contents. vi some stages of logical thought the man in the street, when asked what he thinks about a certain matter, often replies that he does not think at all; he knows. the suggestion is that thinking is a case of active uncertainty set over against conviction or unquestioning assurance. when he adds that he does not have to think, but knows, the further implication is that thinking, when needed, leads to knowledge; that its purpose or object is to secure stable equilibrium. it is the purpose of this paper to show some of the main stages through which thinking, understood in this way, actually passes in its attempt to reach its most effective working; that is, the maximum of reasonable certainty. i wish to show how a variety of modes of thinking, easily recognizable in the progress of both the race and the individual, may be identified and arranged as successive species of the relationship which doubting bears to assurance; as various ratios, so to speak, which the vigor of doubting bears to mere acquiescence. the presumption is that the function of questioning is one which has continually grown in intensity and range, that doubt is continually chased back, and, being cornered, fights more desperately, and thus clears the ground more thoroughly. its successive stations or arrests constitute stages of thinking. or to change the metaphor, just in the degree that what has been accepted as fact--the object of assurance--loses stable equilibrium, the tension involved in the questioning attitude increases, until a readjustment gives a new and less easily shaken equilibrium. the natural tendency of man is not to press home a doubt, but to cut inquiry as short as possible. the practical man's impatience with theory has become a proverb; it expresses just the feeling that, since the thinking process is of use only in substituting certainty for doubt, any apparent prolongation of it is useless speculation, wasting time and diverting the mind from important issues. to follow the line of least resistance is to cut short the stay in the sphere of doubts and suggestions, and to make the speediest return into the world where one can act. the result, of course, is that difficulties are evaded or surmounted rather than really disposed of. hence, in spite of the opposition of the would-be practical man, the needs of practice, of economy, and of efficiency have themselves compelled a continual deepening of doubt and widening of the area of investigation. it is within this evolution that we have to find our stages of thinking. the initial stage is where the doubt is hardly endured but not entertained; it is no welcome guest but an intruder, to be got rid of as speedily as possible. development of alternative and competitive suggestions, the forming of suppositions (of ideas), goes but a little way. the mind seizes upon the nearest or most convenient instrument of dismissing doubt and reattaining security. at the other end is the definitive and conscious search for problems, and the development of elaborate and systematized methods of investigation--the industry and technique of science. between these limits come processes which have started out upon the path of doubt and inquiry, and then halted by the way. in the first stage of the journey, beliefs are treated as something fixed and static. to those who are using them they are simply another kind of fact. they are used to settle doubts, but the doubts are treated as arising quite outside the ideas themselves. nothing is further from recognition than that ideas themselves are open to doubt, or need criticism and revision. indeed, the one who uses static meanings is not even aware that they originated and have been elaborated for the sake of dealing with conflicts and problems. the ideas are just "there," and they may be used like any providential dispensation to help men out of the troubles into which they have fallen. words are generally held responsible for this fixation of the idea, for this substantiation of it into a kind of thing. a long line of critics has made us familiar with the invincible habit "of supposing that wherever there is a name there is some reality corresponding to it"; of supposing that general and abstract words have their equivalent objects somewhere _in rerum natura_, as have also singular and proper names. we know with what simplicity of self-confidence the english empirical school has accounted for the ontological speculation of plato. words tend to fix intellectual contents, and give them a certain air of independence and individuality. that some truth is here expressed there can be no question. indeed, the attitude of mind of which we are speaking is well illustrated in the person who goes to the dictionary in order to settle some problem in morals, politics, or science; who would end some discussion regarding a material point by learning what meaning is attached to terms by the dictionary as authority. the question is taken as lying outside of the sphere of science or intellectual inquiry, since the meaning of the word--the idea--is unquestionable and fixed. but this petrifying influence of words is after all only a superficial explanation. there must be some meaning present or the word could not fix it; there must be something which accounts for the disposition to use names as a medium of fossilization. there is, in truth, a certain real fact--an existent reality--behind both the word and the meaning it stands for. this reality is social usage. the person who consults a dictionary is getting an established fact when he turns there for the definition of a term. he finds the sense in which the word is currently used. social customs are no less real than physical events. it is not possible to dispose of this fact of common usage by reference to mere convention, or any other arbitrary device. a form of social usage is no more an express invention than any other social institution. it embodies the permanent attitude, the habit taken toward certain recurring difficulties or problems in experience. ideas, or meanings fixed in terms, show the scheme of values which the community uses in appraising matters that need consideration and which are indeterminate or unassured. they are held up as standards for all its members to follow. here is the solution of the paradox. the fixed or static idea is a fact expressing an established social attitude, a custom. it is not merely verbal, because it denotes a force which operates, as all customs do, in controlling particular cases. but since it marks a mode of interpretation, a scheme for assigning values, a way of dealing with doubtful cases, it falls within the sphere of ideas. or, coming to the life of the individual, the fixed meaning represents, not a state of consciousness fixed by a name, but a recognition of a habitual way of belief: a habit of understanding. we find an apt illustration of fixed ideas in the rules prevalent in primitive communities, rules which minutely determine all acts in which the community as a whole is felt to have an interest. these rules are facts because they express customs, and carry with them certain sanctions. their meaning does not cease with judicial utterance. they are made valid at once in a practical way against anyone who departs from them. yet as rules they are ideas, for they express general ways of defining doubtful matters in experience and of re-establishing certainty. an individual may fail in acknowledgment of them and explicit reference is then necessary. for one who has lost himself in the notion that ideas are psychical and subjective, i know of no better way to appreciate the significance of an idea than to consider that a social rule of judgment is nothing but a certain way of viewing or interpreting facts; as such it is an idea. the point that is of special interest to us here, however, is that these ideas are taken as fixed and unquestionable, and that the cases to which they are to apply are regarded as in themselves equally fixed. so far as concerns the attitude of those who employ this sort of ideas, the doubt is simply as to what idea should be in a particular case. even the athenian greeks, for instance, long kept up the form of indicting and trying a tree or implement through which some individual had been killed. there was a rule--a fixed idea--for dealing with all who offended against the community by destroying one of its citizens. the fact that an inanimate object, a thing without intention or volition, offended was not a material circumstance. it made no difference in the case; that is, there was no doubt as to the nature of the fact. it was as fixed as was the rule. with advance in the complexity of life, however, rules accumulate, and discrimination--that is, a certain degree of inquiring and critical attitude--enters in. inquiry takes effect, however, in seeking among a collection of fixed ideas just the one to be used, rather than in directing suspicion against any rule or idea as such, or in an attempt to discover or constitute a new one. it is hardly necessary to refer to the development of casuistry, or to the multiplication of distinctions within dogmas, or to the growth of ceremonial law in cumbrous detail, to indicate what the outcome of this logical stage is likely to be. the essential thing is that doubt and inquiry are directed neither at the nature of the intrinsic fact itself, nor at the value of the idea as such, but simply at the manner in which one is attached to the other. thinking falls outside both fact and idea, and into the sphere of their external connection. it is still a fiction of judicial procedure that there is already in existence some custom or law under which every possible dispute--that is, every doubtful or unassured case--falls, and that the judge only declares which law is applicable in the particular case. this point of view has tremendously affected the theory of logic in its historic development. one of the chief, perhaps the most important, instrumentalities in developing and maintaining fixed ideas is the need of instruction and the way in which it is given. if ideas were called into play only when doubtful cases actually arise, they could not help retaining a certain amount of vitality and flexibility; but the community always instructs its new members as to its way of disposing of these cases before they present themselves. ideas are proffered, in other words, separated from present doubt and remote from application, in order to escape future difficulties and the need of any thinking. in primitive communities this is the main purport of instruction, and it remains such to a very considerable degree. there is a prejudgment rather than judgment proper. when the community uses its resources to fix certain ideas in the mind--that is, certain ways of interpreting and regarding experience--ideas are necessarily formulated so as to assume a rigid and independent form. they are doubly removed from the sphere of doubt. the attitude is uncritical and dogmatic in the extreme--so much so that one might question whether it is to be properly designated as a stage of thinking. in this form ideas become the chief instruments of social conservation. judicial decision and penal correction are restricted and ineffective methods of maintaining social institutions unchanged, compared with instilling in advance uniform ideas--fixed modes of appraising all social questions and issues. these set ideas thus become the embodiment of the values which any group has realized and intends to perpetuate. the fixation supports them against dissipation through attrition of circumstance, and against destruction through hostile attack. it would be interesting to follow out the ways in which such values are put under the protection of the gods and of religious rites, or themselves erected into quasi-divinities--as among the romans. this, however, would hardly add anything to the logic of the discussion, although it would indicate the importance attached to the fixation of ideas, and the thoroughgoing character of the means used to secure immobilization. the conserving value of the dogmatic attitude, the point of view which takes ideas as fixed, is not to be ignored. when society has no methods of science for protecting and perpetuating its achieved values, there is practically no other resort than such crystallization. moreover, with any possible scientific progress, some equivalent of the fixed idea must remain. the nearer we get to the needs of action the greater absoluteness must attach to ideas. the necessities of action do not await our convenience. emergencies continually present themselves where the fixity required for successful activity cannot be attained through the medium of investigation. the alternative to vacillation, confusion, and futility of action is importation to ideas of a positive and secured character, not in strict logic belonging to them. it is this sort of determination that hegel seems to have in mind in what he terms _verstand_--the understanding. "apart from _verstand_," he says, "there is no fixity or accuracy in the region either of theory or practice"; and, again, "_verstand_ sticks to fixity of characters and their distinctions from one another; it treats every meaning as having a subsistence of its own." in technical terminology, also, this is what is meant by "positing" ideas--hardening meanings. in recognizing, however, that fixation of intellectual content is a precondition of effective action, we must not overlook the modification that comes with the advance of thinking into more critical forms. at the outset fixity is taken as the rightful possession of the ideas themselves; it belongs to them and is their "essence." as the scientific spirit develops, we see that it is we who lend fixity to the ideas, and that this loan is for a purpose to which the meaning of the ideas is accommodated. fixity ceases to be a matter of intrinsic structure of ideas, and becomes an affair of security in using them. hence the important thing is the _way_ in which we fix the idea--the manner of the inquiry which results in definition. we _take_ the idea as if it were fixed, in order to secure the necessary stability of action. the crisis past, the idea drops its borrowed investiture, and reappears as surmise. when we substitute for ideas as uniform rules by which to decide doubtful cases that making over of ideas which is requisite to make them fit, the quality of thought alters. we may fairly say that we have come into another stage. the idea is now regarded as essentially subject to change, as a manufactured article needing to be made ready for use. to determine the conditions of this transition lies beyond my purpose, since i have in mind only a descriptive setting forth of the periods through which, as a matter of fact, thought has passed in the development of the inquiry function, without raising the problem of its "why" and "how." at this point we shall not do more than note that, as the scheduled stock of fixed ideas grows larger, their application to specific questions becomes more difficult, prolonged, and roundabout. there has to be a definite hunting for the specific idea which is appropriate; there has to be comparison of it with other ideas. this comes to involve a certain amount of mutual compromise and modification before selection is possible. the idea thus gets somewhat shaken. it has to be made over so that it may harmonize with other ideas possessing equal worth. often the very accumulation of fixed ideas commands this reconstruction. the dead weight of the material becomes so great that it cannot sustain itself without a readjustment of the center of gravity. simplification and systematization are required, and these call for reflection. critical cases come up in which the fiction of an idea or rule already in existence cannot be maintained. it is impossible to conceal that old ideas have to be radically modified before the situation can be dealt with. the friction of circumstance melts away their congealed fixity. judgment becomes legislative. seeking illustrations at large, we find this change typified in hebrew history in the growing importance of the prophet over the judge, in the transition from a justification of conduct through bringing particular cases into conformity with existent laws, into that effected by personal right-mindedness enabling the individual to see the law in each case for himself. profoundly as this changed conception of the relation between law and particular case affected moral life, it did not, among semites, directly influence the logical sphere. with the greeks, however, we find a continuous and marked departure from positive declaration of custom. we have assemblies meeting to discuss and dispute, and finally, upon the basis of the considerations thus brought to view, to decide. the man of counsel is set side by side with the man of deed. odysseus was much experienced, not only because he knew the customs and ways of old, but even more because from the richness of his experience he could make the pregnant suggestion to meet the new crisis. it is hardly too much to say that it was the emphasis put by the greek mind upon discussion--at first as preliminary to decision, and afterward to legislation--which generated logical theory. discussion is thus an apt name for this attitude of thought. it is bringing various beliefs together; shaking one against another and tearing down their rigidity. it is conversation of thoughts; it is dialogue--the mother of dialectic in more than the etymological sense. no process is more recurrent in history than the transfer of operations carried on between different persons into the arena of the individual's own consciousness. the discussion which at first took place by bringing ideas from different persons into contact, by introducing them into the forum of competition, and by subjecting them to critical comparison and selective decision, finally became a habit of the individual with himself. he became a miniature social assemblage, in which pros and cons were brought into play struggling for the mastery--for final conclusion. in some such way we conceive reflection to be born. it is evident that discussion, the agitation of ideas, if judged from the standpoint of the older fixed ideas, is a destructive process. ideas are not only shaken together and apart, they are so shaken in themselves that their whole validity becomes doubtful. mind, and not merely beliefs, becomes uncertain. the attempt to harmonize different ideas means that in themselves they are discrepant. the search for a conclusion means that accepted ideas are only points of view, and hence personal affairs. needless to say it was the sophists who emphasized and generalized this negative aspect--this presupposition of loss of assurance, of inconsistency, of "subjectivity." they took it as applying not only to this, that, and the other idea, but to ideas as ideas. since ideas are no longer fixed contents, they are just expressions of an individual's way of thinking. lacking inherent value, they merely express the interests that induce the individual to look this way rather than that. they are made by the individual's point of view, and hence will be unmade if he can be led to change his point of view. where all was fixity, now all is instability: where all was certitude, nothing now exists save opinion based on prejudice, interest, or arbitrary choice. the modern point of view, while condemning sophistry, yet often agrees with it in limiting the reflective attitude as such to self-involution and self-conceit. from bacon down, the appeal is to observation, to attention to facts, to concern with the external world. the sole genuine guaranty of truth is taken to be appeal to facts, and thinking as such is something different. if reflection is not considered to be merely variable matter, it is considered to be at least an endless mulling over of things. it is the futile attempt to spin truth out of inner consciousness. it is introspection, and theorizing, and mere speculation. such wholesale depreciation ignores the value inherent even in the most subjective reflection, for it takes the settled estate which is proof that thought is not needed, or that it has done its work, as if it supplied the standard for the occasions in which problems are hard upon us, and doubt is rife. it takes the conditions which come about after and because we have thought to measure the conditions which call out thinking. whenever we really need to reflect, we cannot appeal directly to the "fact," for the adequate reason that the stimulus to thinking arises just because "facts" have slipped away from us. the fallacy is neatly committed by mill in his discussion of whewell's account of the need of mental conception or hypothesis in "colligating" facts. he insists that the conception is "obtained" from the "facts" in which "it exists," is "impressed upon us from without," and also that it is the "darkness and confusion" of the facts that make us want the conception in order to create "light and order."[ ] reflection involves running over various ideas, sorting them out, comparing one with another, trying to get one which will unite in itself the strength of two, searching for new points of view, developing new suggestions; guessing, suggesting, selecting, and rejecting. the greater the problem, and the greater the shock of doubt and resultant confusion and uncertainty, the more prolonged and more necessary is the process of "mere thinking." it is a more obvious phase of biology than of physics, of sociology than of chemistry; but it persists in established sciences. if we take even a mathematical proposition, not _after_ it has been demonstrated--and is thus capable of statement in adequate logical form--but while in process of discovery and proof, the operation of this subjective phase is manifest, so much so, indeed, that a distinguished modern mathematician has said that the paths which the mathematical inquirer traverses in any new field are more akin to those of the experimentalist, and even to those of the poet and artist, than to those of the euclidean geometer. what makes the essential difference between modern research and the reflection of, say, the greeks, is not the absence of "mere thinking," but the presence of conditions for testing its results; the elaborate system of checks and balances found in the technique of modern experimentation. the thinking process does not now go on endlessly in terms of itself, but seeks outlet through reference to particular experiences. it is tested by this reference; not, however, as if a theory could be tested by directly comparing it with facts--an obvious impossibility--but through use in facilitating commerce with facts. it is tested as glasses are tested; things are looked at through the medium of specific meanings to see if thereby they assume a more orderly and clearer aspect, if they are less blurred and obscure. the reaction of the socratic school against the sophistic may serve to illustrate the third stage of thinking. this movement was not interested in the _de facto_ shaking of received ideas and a discrediting of all thinking. it was concerned rather with the virtual appeal to a common denominator involved in bringing different ideas into relation with one another. in their comparison and mutual modification it saw evidence of the operation of a standard permanent meaning passing judgment upon their conflict, and revealing a common principle and standard of reference. it dealt not with the shaking and dissolution, but with a comprehensive permanent idea finally to emerge. controversy and discussion among different individuals may result in extending doubt, manifesting the incoherency of accepted ideas, and so throwing an individual into an attitude of distrust. but it also involves an appeal to a single thought to be accepted by both parties, thus putting an end to the dispute. this appeal to a higher court, this possibility of attaining a total and abiding intellectual object, which should bring into relief the agreeing elements in contending thoughts, and banish the incompatible factors, animated the socratic search for the concept, the elaboration of the platonic hierarchy of ideas in which the higher substantiate the lower, and the aristotelian exposition of the systematized methods by which general truths may be employed to prove propositions otherwise doubtful. at least, this historic development will serve to illustrate what is involved in the transition from the second to the third stage; the transformation of discussion into reasoning, of subjective reflection into method of proof. discussion, whether with ourselves or others, goes on by suggestion of clues, as the uppermost object of interest opens a way here or there. it is discursive and haphazard. this gives it the devious tendency indicated in plato's remark that it needs to be tied to the post of reason. it needs, that is, to have the ground or basis of its various component statements brought to consciousness in such a way as to define the exact value of each. the socratic contention is the need of compelling the common denominator, the common subject, underlying the diversity of views to exhibit itself. it alone gives a sure standard by which the claims of all assertions may be measured. until this need is met, discussion is a self-deceiving play with unjudged, unexamined matters, which, confused and shifting, impose themselves upon us. we are familiar enough with the theory that the socratic universal, the platonic idea, was generated by an ignorant transformation of psychological abstractions into self-existent entities. to insist upon this as the key to the socratic logic is mere caricature. the objectivity of the universal stood for the sense of something decisive and controlling in all reflection, which otherwise is just manipulation of personal prejudices. this sense is as active in modern science as it was in the platonic dialectic. what socrates felt was the opinionated, conceited quality of the terms used in the moral and political discussion of his day, as that contrasted with the subject-matter, which, if rightly grasped, would put an end to mere views and argumentations. by aristotle's time the interest was not so much in the existence of standards of decision in cases of doubt and dispute as in the technique of their use. the judge was firmly seated on the bench. the parties in controversy recognized his jurisdiction, and their respective claims were submitted for adjudicature. the need was for rules of procedure by which the judge might, in an obvious and impartial way, bring the recognized universal or decisive law to bear upon particular matters. hence the elaboration of those rules of evidence, those canons of demonstrative force, which are the backbone of the aristotelian logic. there was a code by which to decide upon the admissibility and value of proffered testimony--the rules of the syllogism. the figures and terms of the syllogism provided a scheme for deciding upon the exact bearing of every statement propounded. the plan of arrangement of major and minor premises, of major, minor, and middle terms, furnished a manifesto of the exact procedure to be followed in determining the probative force of each element in reasoning. the judge knew what testimony to permit, when and how it should be introduced, how it could be impeached or have its competence lessened, and how the evidence was to be arranged so that a summary would also be an exhibit of its value in establishing a conclusion. this means that there now is a distinctive type of thinking marked off from mere discussion and reflection. it may be called either reasoning or proof. it is reasoning when we think of the regularity of the method for getting at and employing the unquestioned grounds which give validity to other statements. it is proof as regards the degree of logical desert thereby measured out to such propositions. proof is the acceptance or rejection justified through the reasoning. to quote from mill: "to give credence to a proposition as a conclusion from something else is to reason in the most extensive sense of the term. we say of a fact or statement, it is proved, when we believe its truth by reason of some other fact or statement from which it is said to follow."[ ] reasoning is marshaling a series of terms and propositions until we can bind some doubtful fact firmly to an unquestioned, although remote, truth; it is the regular way in which a certain proposition is brought to bear on a precarious one, clothing the latter with something of the peremptory quality of the former. so far as we reach this result, and so far as we can exhibit each step in the nexus and be sure it has been rightly performed, we have proof. but questions still face us. how about that truth upon which we fall back as guaranteeing the credibility of other statements--how about our major premise? whence does it derive its guaranty? _quis custodes custodiet?_ we may, of course, in turn subsume it under some further major premise, but an infinite regress is impossible, and on this track we are finally left hanging in the air. for _practical_ purposes the unquestioned principle may be taken as signifying mutual concession or agreement--it denotes that as a matter of fact its truth is not called in question by the parties concerned. this does admirably for settling arguments and controversies. it is a good way of amicably arranging matters among those already friends and fellow-citizens. but scientifically the widespread acceptance of an idea seems to testify to custom rather than to truth; prejudice is strengthened in influence, but hardly in value, by the number who share it; conceit is none the less self-conceit because it turns the heads of many. great interest was indeed afterward taken in the range of persons who hold truths in common. the _quod semper ubique omnibus_ became of great importance. this, however, was not, in theory at least, because common agreement was supposed to constitute the major premise, but because it afforded confirmatory evidence of its self-evident and universal character. hence the aristotelian logic necessarily assumes certain first or fundamental truths unquestioned and unquestionable, self-evident and self-evidencing, neither established nor modified by thought, but standing firm in their own right. this assumption was not, as modern dealers in formal logic would sometimes have it, an external psychological or metaphysical attachment to the theory of reasoning, to be omitted at will from logic as such. it was an essential factor of knowledge that there should be necessary propositions directly apprehended by reason and particular ones directly apprehended by sense. reasoning could then join them. without the truths we have only the play of subjective, arbitrary, futile opinion. _judgment_ has not taken place, and assertion is without warrant. hence the scheduling of first truths is an organic part of any reasoning which is occupied with securing demonstration, surety of assent, or valid conviction. to deny the necessary place of ultimate truths in the logical system of aristotle and his followers is to make them players in a game of social convention. it is to overlook, to invert, the fact that they were sincerely concerned with the question of attaining the grounds and process of assurance. hence they were obliged to assume primary intuitions, metaphysical, physical, moral, and mathematical axioms, in order to get the pegs of certainty to which to tie the bundles of otherwise contingent propositions. it would be going too far to claim that the regard for the authority of the church, of the fathers, of the scriptures, of ancient writers, of aristotle himself, so characteristic of the middle ages, was the direct outcome of this presupposition of truths fixed and unquestionable in themselves. but the logical connection is sure. the supply of absolute premises that aristotle was able to proffer was scant. in his own generation and situation this paucity made comparatively little difference; for to the mass of men the great bulk of values was still carried by custom, by religious belief, and social institution. it was only in the comparatively small sphere of persons who had come under the philosophic influence that need for the logical mode of confirmation was felt. in the mediaeval period, however, all important beliefs required to be concentrated by some fixed principle giving them stay and power, for they were contrary to obvious common-sense and natural tradition. the situation was exactly such as to call into active use the aristotelian scheme of thought. authority supplemented the meagerness of the store of universals known by direct intuition, the aristotelian plan of reasoning afforded the precise instrumentality through which the vague and chaotic details of life could be reduced to order by subjecting them to authoritative rules. it is not enough, however, to account for the ultimate major premises, for the unconditioned grounds upon which credibility is assigned. we have also to report where the other side comes from: matters so uncertain in themselves as to require that they have their grounds supplied from outside. the answer in the aristotelian scheme is an obvious one. it is the very nature of sense, of ordinary experience, to supply us with matters which in themselves are only contingent. there is a certain portion of the intellectual sphere, that derived from experience, which is infected throughout by its unworthy origin. it stands forever condemned to be merely empirical--particular, more or less accidental, inherently irrational. you cannot make gold from dross, and the best that can be done for and with material of this sort is to bring it under the protection of truth which has warrant and weight in itself. we may now characterize this stage of thinking with reference to our original remark that different stages denote various degrees in the evolution of the doubt-inquiry function. as compared with the period of fixed ideas, doubt is awake, and inquiry is active, but in itself it is rigidly limited. on one side it is bounded by fixed ultimate truths, whose very nature is that they cannot be doubted, which are not products or functions in inquiry, but bases that investigation fortunately rests upon. in the other direction all "matters of fact," all "empirical truths" belong to a particular sphere or kind of existence, and one intrinsically open to suspicion. the region is condemned in a wholesale way. in itself it exhales doubt; it cannot be reformed; it is to be shunned, or, if this is not possible, to be escaped from by climbing up a ladder of intermediate terms until we lay hold on the universal. the very way in which doubt is objectified, taken all in a piece, marks its lack of vitality. it is arrested and cooped up in a particular place. as with any doubtful character, the less of its company the better. uncertainty is not realized as a necessary instrument in compelling experienced matters to reveal their meaning and inherent order. this limitation upon inquiry settles the interpretation to be given thought at this stage--it is of necessity merely connective, merely mediating. it goes between the first principles--themselves, as to their validity, outside the province of thought--and the particulars of sense--also, as to their status and worth, beyond the dominion of thought. thinking is subsumption--just placing a particular proposition under its universal. it is inclusion, finding a place for some questioned matter within a region taken as more certain. it is use of general truths to afford support to things otherwise shaky--an application that improves their standing, while leaving their content unchanged. this means that thought has only a formal value. it is of service in exhibiting and arranging grounds upon which any particular proposition may be acquitted or condemned, upon which anything already current may be assented to, or upon which belief may reasonably be withheld. the metaphor of the law court is apt. there is assumed some matter to be either proved or disproved. as matter, as content, it is furnished. it is not to be found out. in the law court it is not a question of discovering what a man specifically is, but simply of finding reasons for regarding him as guilty or innocent. there is no all-around play of thought directed to the institution of something as fact, but a question of whether grounds can be adduced justifying acceptance of some proposition already set forth. the significance of such an attitude comes into relief when we contrast it with what is done in the laboratory. in the laboratory there is no question of proving that things are just thus and so, or that we must accept or reject a given statement; there is simply an interest in finding out what sort of things we are dealing with. any quality or change that presents itself may be an object of investigation, or may suggest a conclusion; for it is judged, not by reference to pre-existent truths, but by its suggestiveness, by what it may lead to. the mind is open to inquiry in any direction. or we may illustrate by the difference between the auditor and an actuary in an insurance company. one simply passes and rejects, issues vouchers, compares and balances statements already made out. the other investigates any one of the items of expense or receipt; inquires how it comes to be what it is, what facts, as regards, say, length of life, condition of money market, activity of agents, are involved, and what further researches and activities are indicated. the illustrations of the laboratory and the expert remind us of another attitude of thought in which investigation attacks matters hitherto reserved. the growth, for example, of freedom of thought during the renaissance was a revelation of the intrinsic momentum of the thought-process itself. it was not a mere reaction from and against mediaeval scholasticism. it was the continued operation of the machinery which the scholastics had set a-going. doubt and inquiry were extended into the region of particulars, of matters of fact, with the view of reconstituting them through discovery of their own structure, no longer with the intention of leaving that unchanged while transforming their claim to credence by connecting them with some authoritative principles. thought no longer found satisfaction in appraising them in a scale of values according to their nearness to, or remoteness from, fixed truths. such work had been done to a nicety, and it was futile to repeat it. thinking must find a new outlet. it was out of employment, and set to discover new lands. galileo and copernicus were travelers--as much so as the crusader, marco polo, and columbus. hence the fourth stage--covering what is popularly known as inductive and empirical science. thought takes the form of inference instead of proof. proof, as we have already seen, is accepting or rejecting a given proposition on the ground of its connection or lack of connection with some other proposition conceded or established. but inference does not terminate in any given proposition; it is after precisely those not given. it wants more facts, different facts. thinking in the mode of inference insists upon terminating in an intellectual advance, in a consciousness of truths hitherto escaping us. our thinking must not now "pass" certain propositions after challenging them, must not admit them because they exhibit certain credentials, showing a right to be received into the upper circle of intellectual society. thinking endeavors to compel things as they present themselves, to yield up something hitherto obscure or concealed. this advance and extension of knowledge through thinking seems to be well designated by the term "inference." it does not certify what is otherwise doubtful, but "goes from the known to the unknown." it aims at pushing out the frontiers of knowledge, not at marking those already attained with signposts. its technique is not a scheme for assigning status to beliefs already possessed, but is a method for making friends with facts and ideas hitherto alien. inference reaches out, fills in gaps. its work is measured not by the patents of standing it issues, but by the material increments of knowledge it yields. _inventio_ is more important than _judicium_, discovery than "proof." with the development of empirical research, uncertainty or contingency is no longer regarded as infecting in a wholesale way an entire region, discrediting it save as it can be brought under the protecting aegis of universal truths as major premises. uncertainty is now a matter of detail. it is the question whether the particular fact is really what it has been taken to be. it involves contrast, not of a fact as a fixed particular over against some fixed universal, but of the existing mode of apprehension with another possible better apprehension. from the standpoint of reasoning and proof the intellectual field is absolutely measured out in advance. certainty is located in one part, intellectual indeterminateness or uncertainty in another. but when thinking becomes research, when the doubt-inquiry function comes to its own, the problem is just: what is the fact? hence the extreme interest in details as such; in observing, collecting, and comparing particular causes, in analysis of structure down to its constituent elements, interest in atoms, cells, and in all matters of arrangement in space and time. the microscope, telescope, and spectroscope, the scalpel and microtome, the kymograph and the camera are not mere material appendages to thinking; they are as integral parts of investigative thought as were _barbara_, _celarent_, etc., of the logic of reasoning. facts must be discovered, and to accomplish this, apparent "facts" must be resolved into their elements. things must be readjusted in order to be held free from intrusion of impertinent circumstance and misleading suggestion. instrumentalities of extending and rectifying research are, therefore, of themselves organs of thinking. the specialization of the sciences, the almost daily birth of a new science, is a logical necessity--not a mere historical episode. every phase of experience must be investigated, and each characteristic aspect presents its own peculiar problems which demand, therefore, their own technique of investigation. the discovery of difficulties, the substitution of doubt for quiescent acceptance, are more important than the sanctioning of belief through proof. hence the importance of noting apparent exceptions, negative instances, extreme cases, anomalies. the interest is in the discrepant because that stimulates inquiry, not in the fixed universal which would terminate it once for all. hence the roaming over the earth and through the skies for new facts which may be incompatible with old theories, and which may suggest new points of view. to illustrate these matters in detail would be to write the history of every modern science. the interest in multiplying phenomena, in increasing the area of facts, in developing new distinctions of quantity, structure, and form, is obviously characteristic of modern science. but we do not always heed its logical significance--that it makes thinking to consist in the extension and control of contact with new material so as to lead regularly to the development of new experience. the elevation of the region of facts--the formerly condemned region of the inherently contingent and variable--to something that invites and rewards inquiry, defines the import, therefore, of the larger aspects of modern science. this spirit prides itself upon being positivistic--it deals with the observed and the observable. it will have naught to do with ideas that cannot verify themselves by showing themselves _in propria persona_. it is not enough to present credentials from more sovereign truths. these are hardly acceptable even as letters of introduction. refutation of newton's claim, that he did not make hypotheses, by pointing out that no one was busier in this direction than he, and that scientific power is generally in direct ratio to ability to imagine possibilities, is as easy as it is irrelevant. the hypotheses, the thoughts, that newton employed were of and about fact; they were for the sake of exacting and extending what can be apprehended. instead of being sacrosanct truths affording a redemption by grace to facts otherwise ambiguous, they were the articulating of ordinary facts. hence the notion of law changes. it is no longer something governing things and events from on high; it is the statement of their own order. thus the exiling of occult forces and qualities is not so much a specific achievement as it is a demand of the changed attitude. when thinking consists in the detection and determination of observable detail, forces, forms, qualities at large, are thrown out of employment. they are not so much proved non-existent as rendered nugatory. disuse breeds their degeneration. when the universal is but the order of the facts themselves, the mediating machinery disappears along with the essences. there is substituted for the hierarchical world in which each degree in the scale has its righteousness imputed from above a world homogeneous in structure and in the scheme of its parts; the same in heaven, earth, and the uttermost parts of the sea. the ladder of values from the sublunary world with its irregular, extravagant, imperfect motion up to the stellar universe, with its self-returning perfect order, corresponded to the middle terms of the older logic. the steps were graduated, ascending from the indeterminate, unassured matter of sense up to the eternal, unquestionable truths of rational perception. but when interest is occupied in finding out what anything and everything is, any fact is just as good as its fellow. the observable world is a democracy. the difference which makes a fact what it is is not an exclusive distinction, but a matter of position and quantity, an affair of locality and aggregation, traits which place all facts upon the same level, since all other observable facts also possess them and are, indeed, conjointly responsible for them. laws are not edicts of a sovereign binding a world of subjects otherwise lawless; they are the agreements, the compacts of facts themselves, or, in the familiar language of mill, the common attributes, the resemblances. the emphasis of modern science upon control flows from the same source. interest is in the new, in extension, in discovery. inference is the advance into the unknown, the use of the established to win new worlds from the void. this requires and employs regulation--that is, method--in procedure. there cannot be a blind attack. a plan of campaign is needed. hence the so-called practical applications of science, the baconian "knowledge is power," the comteian "science is prevision," are not extra-logical addenda or supererogatory benefits. they are intrinsic to the logical method itself, which is just the orderly way of approaching new experiences so as to grasp and hold them. the attitude of research is necessarily toward the future. the application of science to the practical affairs of life, as in the stationary engine, or telephone, does not differ in principle from the determination of wave-lengths of light through the experimental control of the laboratory. science lives only in arranging for new contacts, new insights. the school of kant agrees with that of mill in asserting that judgment must, in order to be judgment, be synthetic or instructive; it must extend, inform, and purvey. when we recognize that this service of judgment in effecting growth of experience is not accidental, but that judgment means exactly the devising and using of suitable instrumentalities for this end, we remark that the so-called practical uses of science are only the further and freer play of the intrinsic movement of discovery itself. * * * * * we began with the assumption that thought is to be interpreted as a doubt-inquiry function, conducted for the purpose of arriving at that mental equilibrium known as assurance or knowledge. we assumed that various stages of thinking could be marked out according to the amount of play which they give to doubt, and the consequent sincerity with which thinking is identified with free inquiry. modern scientific procedure, as just set forth, seems to define the ideal or limit of this process. it is inquiry emancipated, universalized, whose sole aim and criterion is discovery, and hence it marks the terminus of our description. it is idle to conceal from ourselves, however, that scientific procedure as a practical undertaking, has not as yet reflected itself into any coherent and generally accepted theory of thinking, into any accepted doctrine of logic which is comparable to the aristotelian. kant's conviction that logic is a "complete and settled" science, which with absolutely "certain boundaries has gained nothing and lost nothing since aristotle," is startlingly contradicted by the existing state of discussion of logical doctrine. the simple fact of the case is that there are at least three rival theories on the ground, each claiming to furnish the sole proper interpretation of the actual procedure of thought. the aristotelian logic is far from having withdrawn its claim. it still offers its framework as that into which the merely "empirical" results of observation and experimental inquiry must be fitted if they are to be regarded as really "proved." another school of logicians, starting professedly from modern psychology, discredits the whole traditional industry and reverses the aristotelian theory of validity; it holds that only particular facts are self-supporting, and that the authority allowed to general principles is derivative and second hand. a third school of philosophy claims, by analysis of science and experience, to justify the conclusion that the universe itself is a construction of thought, giving evidence throughout of the pervasive and constitutive action of reason, and holds, consequently, that our logical processes are simply the reading off or coming to consciousness of the inherently rational structure already possessed by the universe in virtue of the presence within it of this pervasive and constitutive action of thought. it thus denies both the claim of the traditional logic, that matters of experienced fact are mere particulars having their rationality in an external ground, and the claim of the empirical logic, that thought is just a gymnastic by which we vault from one presented fact to another remote in space and time. which of the three doctrines is to be regarded as the legitimate exponent of the procedure of thought manifested in modern science? while the aristotelian logic is willing to waive a claim to be regarded as expounder of the actual procedure, it still insists upon its right to be regarded as the sole ultimate umpire of the validity or _proved_ character of the results reached. but the empirical and transcendental logics stand face to face as rivals, each asserting that it alone tells the story of what science does and how it does it. with the consciousness of this conflict my discussion in its present, or descriptive, phase must cease. its close, however, suggests a further question. in so far as we adopt the conception that thinking is itself a doubt-inquiry process, must we not deny the claims of all of the three doctrines to be the articulate voicing of the methods of experimental science? do they not all agree in setting up something fixed outside inquiry, supplying both its material and its limit? that the first principle and the empirical matters of fact of the aristotelian logic fall outside the thinking process, and condemn the latter to a purely external and go-between agency, has been already sufficiently descanted upon. but it is also true that the fixed particulars, given facts, or sensations--whatever the empirical logician starts from--are material given ready-made to the thought-process, and externally limiting inquiry, instead of being distinctions arising within and because of search for truth. nor, as regards this point, is the transcendental in any position to throw stones at the empirical logic. thought "in itself" is so far from a process of inquiry that it is taken to be the eternal, fixed structure of the universe; _our_ thinking, involving doubt and investigation, is due wholly to our "finite," imperfect character, which condemns us to the task of merely imitating and reinstating "thought" in itself, once and forever complete, ready-made, fixed. the practical procedure and practical assumptions of modern experimental science, since they make thinking essentially and not merely accidentally a process of discovery, seem irreconcilable with both the empirical and transcendental interpretations. at all events there is here sufficient discrepancy to give occasion for further search: does not an account of thinking, basing itself on modern scientific procedure, demand a statement in which all the distinctions and terms of thought--judgment, concept, inference, subject, predicate, and copula of judgment, etc., _ad infinitum_--shall be interpreted simply and entirely as distinctive functions or divisions of labor within the doubt-inquiry process? footnotes: [ ] _logic_, book iv, chap. ii, § . [ ] _logic_, book ii, chap. i, § . i have changed the order of the sentences quoted, and have omitted some phrases. vii the logical character of ideas said john stuart mill: "to draw inferences has been said to be the great business of life.... it is the only occupation in which the mind never ceases to be engaged." if this be so, it seems a pity that mill did not recognize that this business identifies what we mean when we say "mind." if he had recognized this, he would have cast the weight of his immense influence not only against the conception that mind is a substance, but also against the conception that it is a collection of existential states or attributes without any substance in which to inhere; and he would thereby have done much to free logic from epistemological metaphysics. in any case, an account of intellectual operations and conditions from the standpoint of the rôle played and position occupied by them in the business of drawing inferences is a different sort of thing from an account of them as having an existence _per se_, from treating them as making up some sort of existential material distinct from the _things_ which figure in inference-drawing. this latter type of treatment is that which underlies the psychology which itself has adopted uncritically the remnants of the metaphysics of soul substance: the idea of accidents without the substance.[ ] this assumption from metaphysical psychology--the assumption of consciousness as an existent stuff or existent process--is then carried over into an examination of knowledge, so as to make the theory of knowledge not logic (an account of the ways in which valid inferences or conclusions from things to other things are made), but epistemology. we have, therefore, the result (so unfortunate for logic) that logic is not free to go its own way, but is compromised by the assumption that knowledge goes on not in terms of things (i use "things" in the broadest sense, as equaling _res_, and covering affairs, concerns, acts, as well as "things" in the narrower sense), but in terms of a relation _between_ things and a peculiar existence made up of consciousness, or else between things and functional operations of this existence. if it could be shown that psychology is essentially not a science of states of consciousness, but of behavior, conceived as a process of continuous readjustment, then the undoubted facts which go by the name of sensation, perception, image, emotion, concept, would be interpreted to mean peculiar (i.e., specifically qualitative) epochs, phases, and crises in the scheme of behavior. the supposedly scientific basis for the belief that states of consciousness inherently define a separate type of existence would be done away with. inferential knowledge, knowledge involving reflection, _psychologically_ viewed, would be assimilated to a certain mode of readaptation of functions, involving shock and the need of control; 'knowledge' in the sense of direct non-reflective presence of things would be identified (psychologically) with relatively stable or completed adjustments. i can not profess to speak for psychologists, but it is an obvious characteristic of the contemporary status of psychology that one school (the so-called functional or dynamic) operates with nothing more than a conventional and perfunctory reference to "states of consciousness"; while the orthodox school makes constant concessions to ideas of the behavior type. it introduces the conceptions of fatigue, practice, and habituation. it makes its fundamental classifications on the basis of physiological distinctions (e.g., the centrally initiated and the peripherally initiated), which, from a biological standpoint, are certainly distinctions of structures involved in the performance of acts. one of the aims of the _studies in logical theory_ was to show, on the negative or critical side, that the type of logical theory which professedly starts its account of knowledge from mere states of consciousness is compelled at every crucial juncture to assume _things_, and to define its so-called mental states in terms of things;[ ] and, on the positive side, to show that, logically considered, such distinctions as sensation, image, etc., mark instruments and crises in the development of controlled judgment, i.e., of inferential conclusions. it was perhaps not surprising that this effort should have been criticized not on its own merits, but on the assumption that this correspondence of the (functional) psychological and the logical points of view was intended in terms of the psychology which obtained in the _critic's_ mind--to wit, the psychology based on the assumption of consciousness as a separate existence or process. these considerations suggest that before we can intelligently raise the question of the truth of ideas we must consider their status in judgment, judgment being regarded as the typical expression of the inferential operation. ( ) do ideas present themselves except in situations which are doubtful and inquired into? do they exist side by side with the facts when the facts are themselves known? do they exist except when judgment is in suspense? ( ) are "ideas" anything else except the suggestions, conjectures, hypotheses, theories (i use an ascending scale of terms) tentatively entertained during a suspended conclusion? ( ) do they have any part to play in the conduct of inquiry? do they serve to direct observation, colligate data, and guide experimentation, or are they otiose?[ ] ( ) if the ideas have a function in directing the reflective process (expressed in judgment), does success in performing the function (that is, in directing to a conclusion which is stable) have anything to do with the logical worth or validity of the ideas? ( ) and, finally, does validity have anything to do with truth? does "truth" mean something inherently different from the fact that the conclusion of one judgment (the known fact, previously unknown, in which judging terminates) is itself applicable in further situations of doubt and inquiry? and is judgment properly more than tentative save as it terminates in a known fact, i.e., a fact present without the intermediary of reflection? when these questions--i mean, of course, questions which are exemplified in these queries--are answered, we shall, perhaps, have gone as far as it is possible to go with reference to the _logical_ character of ideas. the question may then recur as to whether the "ideas" of the epistemologist (that is, existences in a purely "private stream of consciousness") remain as something over and above, not yet accounted for; or whether they are perversions and misrepresentations of logical characters. i propose to give a brief dogmatic reply in the latter sense. where, and in so far as, there are unquestioned objects, there is no "consciousness." there are just things. when there is uncertainty, there are dubious, suspected objects--things hinted at, guessed at. such objects have a distinct status, and it is the part of good sense to give them, as occupying that status, a distinct caption. "consciousness" is a term often used for this purpose; and i see no objection to that term, _provided_ it is recognized to mean such objects as are problematic, plus the fact that in their problematic character they may be used, as effectively as accredited objects, to direct observations and experiments which finally relieve the doubtful features of the situation. such "objects" may turn out to be valid, or they may not. but, in any case, they may be used. they may be internally manipulated and developed through ratiocination into explicit statement of their implications; they may be employed as standpoints for selecting and arranging data, and as methods for conducting experiments. in short, they are not merely hypothetical; they are _working_ hypotheses. meanwhile, their aloofness from accredited objectivity may lead us to characterize them as merely ideas, or even as "mental states," provided once more we mean by mental state just this logical status. we have examples of such ideas in symbols. a symbol, i take it, is always itself, existentially, a particular object. a word, an algebraic sign, is just as much a concrete existence as is a horse, a fire-engine, or a flyspeck. but its value resides in its representative character: in its suggestive and directive force for operations that when performed lead us to non-symbolic objects, which without symbolic operations would not be apprehended, or at least would not be so easily apprehended. it is, i think, worth noting that the capacity (_a_) for regarding objects as mere symbols and (_b_) for employing symbols instrumentally furnishes the only safeguard against dogmatism, i.e., uncritical acceptance of any suggestion that comes to us vividly; and also that it furnishes the only basis for intelligently controlled experiments. i do not think, however, that we should have the tendency to regard ideas as _private_, as personal, if we stopped short at this point. if we had only words or other symbols uttered by others, or written, or printed, we might call them, when in objective suspense, mere ideas. but we should hardly think of these ideas as our own. such extra-organic stimuli, however, are not adequate logical devices. they are too rigid, too "objective" in their own existential status. their meaning and character are too definitely fixed. for effective discovery we need things which are more easily manipulated, which are more transitive, more easily dropped and changed. intra-organic events, adjustments _within_ the organism, that is, adjustments of the organism considered not with reference to the environment but with reference to one another, are much better suited to stand as representatives of genuinely dubious objects. an object which is _really_ doubted is by its nature precarious and inchoate, vague. what _is_ a thing when it is not yet discovered and yet is tentatively entertained and tested? ancient logic never got beyond the conception of an object whose logical _place_, whose subsumptive position as a particular with reference to some universal, was doubtful. it never got to the point where it could search for particulars which in themselves as particulars are doubtful. hence it was a logic of proof, of deduction, not of inquiry, of discovery, and of induction. it was hard up against its own dilemma: how can a man inquire? for either he knows that for which he seeks, and hence does not seek: or he does not know, in which case he can not seek, nor could he tell if he found. the individualistic movement of modern life detached, as it were, the individual, and allowed personal (i.e., intra-organic) events to have, transitively and temporarily, a worth of their own. these events are continuous with extra-organic events (in origin and eventual outcome); but they may be considered in temporary displacement as uniquely existential. in this capacity they serve as means for the elaboration of a delayed but more adequate response in a radically different direction. so treated, they are tentative, dubious but experimental, anticipations of an object. they are "subjective" (i.e., individualistic) surrogates of public, cosmic things, which may be so manipulated and elaborated as to terminate in public things which without them would not exist as empirical objects.[ ] the recognition then of intra-organic events, which are not merely effects nor distorted refractions of cosmic objects, but inchoate _future_ cosmic objects in process of experimental construction, resolves, to my mind, the paradox of so-called subjective and private things that have objective and universal reference, and that operate so as to lead to objective consequences which test their own value. when a man can say: this color is not necessarily the color of the glass nor the picture nor even of an object reflected but is at least an event in my nervous system, an event which i may refer to my organism till i get _surety of other reference_--he is for the first time emancipated from the dogmatism of unquestioned reference, and is set upon a path of experimental inquiry. i am not here concerned with trying to demonstrate that this is the correct mode of interpretation. i am only concerned with pointing out its radical difference from the view of a critic who, holding to the two-world theory of existences which from the start are divided into the fixedly objective and the fixedly psychical, interprets in terms of his own theory the view that the distinction between the objective and the subjective is a logical-practical distinction. whether the logical, as against the ontological, theory be true or false, it can hardly be fruitfully discussed without a preliminary apprehension of it as a logical conception. footnotes: [ ] this conception of "consciousness" as a sort of reduplicate world of things comes to us, i think, chiefly from hume's conception that the "_mind_ is nothing but a heap, a collection of different perceptions, united together by certain relations."--_treatise of human nature_, book i, part iv, sec. . for the evolution of this sort of notion out of the immaterial substance notion, see bush, "a factor in the genesis of idealism," in the james _festschrift_. [ ] see, for example, p. . "thus that which is 'nothing but a state of our consciousness' turns out straightway to be a specifically determined objective fact in a system of facts," and, p. , "actual sensation is determined as an event in a world of events." [ ] when it is said that an idea is a "plan of action," it must be remembered that the term "plan of action" is a formal term. it throws no light upon _what_ the action is with respect to which an idea is the plan. it may be chopping down a tree, finding a trail, or conducting a scientific research in mathematics, history, or chemistry. [ ] i owe this idea, both in its historical and in its logical aspects, to my former colleague, professor mead, of the university of chicago. viii the control of ideas by facts i there is something a little baffling in much of the current discussion regarding the reference of ideas to facts. the not uncommon assumption is that there was a satisfactory and consistent theory of their relation in existence prior to the somewhat impertinent intrusion of a functional and practical interpretation of them. the way the instrumental logician has been turned upon by both idealist and realist is suggestive of the way in which the outsider who intervenes in a family jar is proverbially treated by both husband and wife, who manifest their unity by berating the third party. i feel that the situation is due partly to various misapprehensions, inevitable perhaps in the first presentation of a new point of view[ ] and multiplied in this instance by the coincidence of the presentation of this logical point of view with that of the larger philosophical movements, humanism and pragmatism. i wish here to undertake a summary statement of the logical view on its own account, hoping it may receive clearer understanding on its own merits. in the first place it was (apart from the frightful confusion of logical theories) precisely the lack of an adequate and generally accepted theory of the nature of fact and idea, and of the kind of agreement or correspondence between them which constitutes the truth of the idea, that led to the development of a functional theory of logic. a brief statement of the difficulties in the traditional views may therefore be pertinent. that fruitful thinking--thought that terminates in valid knowledge--goes on in terms of the distinction of facts and judgment, and that valid knowledge is precisely genuine correspondence or agreement, _of some sort_, of fact and judgment, is the common and undeniable assumption. but the discussions are largely carried on in terms of an epistemological dualism, rendering the solution of the problem impossible in virtue of the very terms in which it is stated. the distinction is at once identified with that between mind and matter, consciousness and objects, the psychical and the physical, where each of these terms is supposed to refer to some fixed order of existence, a world in itself. then, of course, there comes up the question of the nature of the agreement, and of the recognition of it. what is the experience in which the survey of both idea and existence is made and their agreement recognized? is it an idea? is the agreement ultimately a matter of self-consistency of ideas? then what has become of the postulate that truth is agreement of idea with existence beyond idea? is it an absolute which transcends and absorbs the difference? then, once more, what is the test of any specific judgment? what has become of the correspondence of fact and thought? or, more urgently, since the pressing problem of life, of practice and of science, is the discrimination of the _relative_, or _superior_, validity of this or that theory, plan, or interpretation, what is the criterion of truth within present non-absolutistic experience, where the distinction between factual conditions and thoughts and the necessity of some working adjustment persist? putting the problem in yet another way, either both fact and idea are present all the time or else only one of them is present. but if the former, why should there be an idea at all, and why should it have to be tested by the fact? when we already have what we want, namely, existence, reality, why should we take up the wholly supernumerary task of forming more or less imperfect ideas of those facts, and then engage in the idle performance of testing them by what we already know to be? but if only ideas are present, it is idle to speak of comparing an idea with facts and testing its validity by its agreement. the elaboration and refinement of ideas to the uttermost still leaves us with an idea, and while a self-consistent idea stands a show of being true in a way in which an incoherent one does not, a self-consistent idea is still but a hypothesis, a candidate for truth. ideas are not made true by getting bigger. but if only 'facts' are present, the whole conception of agreement is once more given up--not to mention that such a situation is one in which there is by definition no thinking or reflective factor at all. this suggests that a strictly monistic epistemology, whether idealistic or realistic, does not get rid of the problem. suppose for example we take a sensationalistic idealism. it does away with the ontological gulf between ideas and facts, and by reducing both terms to a common denominator seems to facilitate fruitful discussion of the problem. but the problem of the distinction and reference (agreement, correspondence) of two types or sorts of sensations still persists. if i say the box there is square, and call "box" one of a group of ideas or sensations and "square" another sensation or "idea," the old question comes up: is "square" already a part of the "facts" of the box, or is it not? if it is, it is a supernumerary, an idle thing, both as an idea and as an assertion of fact; if it is not, how can we compare the two ideas, and what on earth or in heaven does their agreement or correspondence mean? if it means simply that we experience the two "sensations" in juxtaposition, then the same is true, of course, of any casual association or hallucination. on the sensational basis, accordingly, there is still a distinction of something "given," "there," brutally factual, the box, and something else which stands on a different level, ideal, absent, intended, demanded, the "square," which is asserted to hold good or be true of the thing "box." the fact that both are sensations throws no light on the logical validity of any proposition or belief, because by theory a like statement holds of every possible proposition.[ ] the same problem recurs on a realistic basis. for example, there has recently been propounded[ ] the doctrine of the distinction between relations of space and time and relations of meaning or significance, as a key to the problem of knowledge. things exist in their own characters, in their temporal and spatial relations. when knowledge intervenes, there is nothing new of a subjective or psychical sort, but simply a new relation of the things--the suggesting or signifying of one thing by another. now this seems to be an excellent way of stating the logical problem, but, i take it, it states and does not solve. for the characteristic of such situations, claiming to terminate in knowledge, is precisely that the meaning-relation is predicated _of_ the other relations; it is referred to them; it is not simply a supervention existing side by side with them, like casual suggestions or the play of phantasy. it is something which the facts, the qualitative space and time things, must bear the burden of, must accept and take unto themselves as part of themselves. until this happens, we have only "thinking," not accomplished knowledge. hence, logically, the existential relations play the rôle of fact, and the relation of signification that of idea,[ ] distinguished from fact and yet, if valid, to hold _of_ fact. this appears quite clearly in the following quotation: "it is the ice which means that it will cool the water, just as much as it is the ice which does cool the water when put into it." there is, however, a possible ambiguity in the statement, to which we shall return later. that the "ice" (the thing regarded as ice) _suggests_ cooling is as real as is a case of actual cooling. but, of course, not every suggestion is valid. the "ice" may be a crystal, and it will not cool water at all. so far as it is already certain that this _is_ ice, and also certain that ice, under all circumstances, cools water, the meaning-relation stands on the same level as the physical, being not merely suggested, but part of the facts ascertained. it is not a meaning-relation as such at all. we already have truth; the entire work of knowing as logical is done; we have no longer the relation characteristic of reflective situations. here again the implication of the thinking situation is of some "correspondence" or "agreement" between two sets of distinguished relations; the problem of valid determination remains the central question of any theory of knowing in its relation to facts and truth.[ ] ii i hope this statement of the difficulty, however inadequate, will serve at least to indicate that a functional logic inherits the problem in question and does not create it; that it has never for a moment denied the prima facie working distinction between "ideas," "thoughts," "meanings," and "facts," "existences," "the environment," nor the necessity of a control of meaning by facts. it is concerned not with denying, but with understanding. what is denied is not the genuineness of the problem of the terms in which it is stated, but the reality and value of the orthodox interpretation. what is insisted upon is the relative, instrumental, or working character of the distinction--that it _is_ a _logical_ distinction, instituted and maintained in the interests of intelligence, with all that intelligence imports in the exercise of the life functions. to this positive side i now turn. in the analysis it may prove convenient to take an illustration of a man lost in the woods, taking this case as typical of any reflective situation in so far as it involves perplexity--a problem to be solved. the problem is to find a correct idea of the way home--a practical idea or plan of action which will lead to success, or the realization of the purpose to get home. now the critics of the experimental theory of logic make the point that this practical idea, the truth of which is evidenced in the successful meeting of a need, is dependent for its success upon a purely presentative idea, that of the existent environment, whose validity has nothing to do with success but depends on agreement with the given state of affairs. it is said that what makes a man's idea of his environment true is its agreement with the actual environment, and "generally a true idea in any situation consists in its agreement with reality." i have already indicated my acceptance of this formula. but it was long my misfortune not to be possessed offhand of those perfectly clear notions of just what is meant in this formula by the terms "idea," "existence," and "agreement" which are possessed by other writers on epistemology; and when i analyzed these notions i found the distinction between the practical idea and the theoretical not fixed nor final, and i found a somewhat startling similarity between the notions of "success" and "agreement." just what is the environment of which an idea is to be formed: i.e., what is the intellectual content or objective detail to be assigned to the term "environment"? it can hardly mean the actual visible environment--the trees, rocks, etc., which a man is actually looking at. these things are there and it seems superfluous to form an idea of them; moreover, the wayfaring man, though lost, would have to be an unusually perverse fool if under such circumstances he were unable to form an idea (supposing he chose to engage in this luxury) in agreement with these facts. the environment must be a larger environment than the visible facts; it must include things not within the direct ken of the lost man; it must, for instance, extend from where he is now to his home, or to the point from which he started. it must include unperceived elements in their contrast with the perceived. otherwise the man would not be lost. now we are at once struck with the facts that the lost man has no alternative except either to wander aimlessly or else to _conceive_ this inclusive environment; and that this conception is just what is meant by idea. it is not some little psychical entity or piece of consciousness-stuff, but is _the interpretation of the locally present environment in reference to its absent portion_, that part to which it is referred as another part so as to give a view of a whole. just how such an idea would differ from one's plan of action in finding one's way, i do not know. for one's plan (if it be really a plan, a method) is a conception of what is given in its hypothetical relations to what is not given, employed as a guide to that act which results in the absent being also given. it is a map constructed with one's self lost and one's self found, whether at starting or at home again, as its two limits. if this map in its specific character is not also the only guide to the way home, one's only plan of action, then i hope i may never be lost. it is the _practical_ facts of being lost and desiring to be found which constitute the limits and the content of the "environment." then comes the test of _agreement_ of the idea and the environment. supposing the individual stands still and attempts to compare his idea with the reality, with what reality is he to compare it? not with the presented reality, for _that_ reality is the reality of himself lost; not with the complete reality, for at this stage of proceedings he has only the idea to stand for the complete theory. what kind of comparison is possible or desirable then, save to treat the mental layout of the whole situation as a working hypothesis, as a plan of action, and proceed to _act_ upon it, to use it as a director and controller of one's divagations instead of stumbling blindly around until one is either exhausted or accidentally gets out? now suppose one uses the idea--that is to say, the present facts projected into a whole in the light of absent facts--as a guide of action. suppose, by means of its specifications, one works one's way along until one comes upon familiar ground--finds one's self. _now_, one may say, my idea was right, it was in accord with facts; it agrees with reality. that is, acted upon sincerely, it has led to the desired conclusion; it has, _through action_, worked out the state of things which it contemplated or intended. the agreement, correspondence, is between purpose, plan, and its own execution, fulfillment; between a map of a course constructed for the sake of guiding behavior and the result attained in acting upon the indications of the map. just how does such agreement differ from success? iii if we exclude acting upon the idea, no conceivable amount or kind of intellectualistic procedure can confirm or refute an idea, or throw any light upon its validity. how does the non-pragmatic view consider that verification takes place? does it suppose that we first look a long while at the facts and then a long time at the idea, until by some magical process the degree and kind of their agreement become visible? unless there is some such conception as this, what conception of agreement is possible except the experimental or practical one? and if it be admitted that verification involves action, how can that action be relevant to the truth of an idea, unless the idea is itself already relevant to action? if by acting in accordance with the experimental definition of facts, viz., as obstacles and conditions, and the experimental definition of the end or intent, viz., as plan and method of action, a harmonized situation effectually presents itself, we have the adequate and the only conceivable verification of the intellectual factors. if the action indicated be carried out and the disordered or disturbed situation persists, then we have not merely confuted the tentative positions of intelligence, but we have in the very process of acting introduced new data and eliminated some of the old ones, and thus afforded an opportunity for the resurvey of the facts and the revision of the plan of action. by acting faithfully upon an inadequate reflective presentation, we have at least secured the elements for its improvement. this, of course, gives no absolute guaranty that the reflection will at any time be so performed as to prove its validity in fact. but the self-rectification of intellectual content through acting upon it in good faith is the "absolute" of knowledge, loyalty to which is the religion of intellect. the intellectual definition or delimitation assigned to the "given" is thus as tentative and experimental as that ascribed to the idea. in form both are categorical, and in content both are hypothetical. facts really exist just as facts, and meanings exist as meanings. one is no more superfluous, more subjective, or less necessitated than the other. in and of themselves as existences both are equally realistic and compulsive. but on the basis of existence, there is no element in either which may be strictly described as intellectual or cognitional. there is only a practical situation in its brute and unrationalized form. what is uncertain about the facts as given at any moment is whether the right exclusions and selections have been made. since that is a question which can be decided finally only by the experimental issue, this ascription of character is itself tentative and experimental. if it works, the characterization and delineation are found to be proper ones; but every admission prior to inquiry, of unquestioned, categorical, rigid objectivity, compromises the probability that it will work. the character assigned to the datum must be taken as hypothetically as possible in order to preserve the elasticity needed for easy and prompt reconsideration. any other procedure virtually insists that all facts and details anywhere happening to exist and happening to present themselves (all being equally real) must all be given equal status and equal weight, and that their outer ramifications and internal complexities must be indefinitely followed up. the worthlessness of this sheer accumulation of realities, its total irrelevancy, the lack of any way of judging the significance of the accumulations, are good proofs of the fallacy of any theory which ascribes objective logical content to facts wholly apart from the needs and possibilities of a situation. the more stubbornly one maintains the _full_ reality of either his facts or his ideas, just as they stand, the more accidental is the discovery of relevantly significant facts and of valid ideas--the more accidental, the less rational, is the issue of the knowledge situation. due progress is reasonably probable in just the degree in which the meaning, categorical in its existing imperativeness, and the fact, equally categorical in its brute coerciveness, are assigned only a provisional and tentative nature with reference to control of the situation. that this surrender of a rigid and final character for the content of knowledge on the sides both of fact and of meaning, in favor of experimental and functioning estimations, is precisely the change which has marked the development of modern from mediaeval and greek science, seems undoubted. to learn the lesson one has only to contrast the rigidity of phenomena and conceptions in greek thought (platonic ideas, aristotelian forms) with the modern experimental selection and determining of facts and experimental employment of hypotheses. the former have ceased to be ultimate realities of a nondescript sort and have become provisional data; the latter have ceased to be eternal meanings and have become working theories. the fruitful application of mathematics and the evolution of a technique of experimental inquiry have coincided with this change. that realities exist independently of their use as intellectual data, and that meanings exist apart from their utilization as hypotheses, are the permanent truths of greek realism as against the exaggerated subjectivism of modern philosophy; but the conception that this existence is to be defined in the same way as are contents of knowledge, so that perfect being is object of perfect knowledge and imperfect being object of imperfect knowledge, is the fallacy which greek thought projected into modern. science has advanced in its methods in just the degree in which it has ceased to assume that prior realities and prior meanings retain fixedly and finally, when entering into reflective situations, the characters they had prior to this entrance, and in which it has realized that their very presence within the knowledge situation signifies that they have to be redefined and revalued from the standpoint of the new situation. iv this conception does not, however, commit us to the view that there is any conscious situation which is totally non-reflective. it may be true that any experience which can properly be termed such comprises something which is _meant_ over and against what is given or there. but there are many situations into which the rational factor--the mutual distinction and mutual reference of fact and meaning--enters only incidentally and is slurred, not accentuated. many disturbances are relatively trivial and induce only a slight and superficial redefinition of contents. this passing tension of facts against meaning may suffice to call up and carry a wide range of meaningful facts which are quite irrelevant to the intellectual problem. such is the case where the individual is finding his way through any field which is upon the whole familiar, and which, accordingly, requires only an occasional resurvey and revaluation at moments of slight perplexity. we may call these situations, if we will, knowledge situations (for the reflective function characteristic of knowledge is present), but so denominating them does not do away with their sharp difference from those situations in which the critical qualification of facts and definition of meanings constitute the main business. to speak of the passing attention which a traveler has occasionally to give to the indications of his proper path in a fairly familiar and beaten highway as knowledge, in just the same sense in which the deliberate inquiry of a mathematician or a chemist or a logician is knowledge, is as confusing to the real issue involved as would be the denial to it of _any_ reflective factor. if, then, one bears in mind these two considerations--( ) the unique problem and purpose of every reflective situation, and ( ) the difference as to range and thoroughness of logical function in different types of reflective situations--one need have no difficulty with the doctrine that the great obstacle in the development of scientific knowing is that facts and meanings enter such situations with stubborn and alien characteristics imported from other situations. this affords an opportunity to speak again of the logical problem to which reference and promise of return were made earlier in this paper. facts may be regarded as existing qualitatively and in certain spatial and temporal relations; when there is knowledge another relation is added, that of one thing meaning or signifying another. water exists, for example, as water, in a certain place, in a certain temporal sequence. but it may signify the quenching of thirst; and this signification-relation constitutes knowledge.[ ] this statement may be taken in a way congruous with the account developed in this paper. but it may also be taken in another sense, consideration of which will serve to enforce the point regarding the tentative nature of the characterization of the given, as distinct from the intended and absent. water means quenching thirst; it is drunk, and death follows. it was not water, but a poison which "looked like" water. or it is drunk, and is water, but does not quench thirst, for the drinker is in an abnormal condition and drinking water only intensifies the thirst. or it is drunk and quenches thirst; but it also brings on typhoid fever, being not merely water, but water plus germs. now all these events demonstrate that error may appertain quite as much to the characterization of existing things, suggesting or suggested, as to the suggestion _qua_ suggestion. there is no ground for giving the "things" any superior reality. in these cases, indeed, it may fairly be said that the mistake is made because qualitative thing and suggested or meaning-relation were _not_ discriminated. the "signifying" force was regarded as a part of the direct quality of the given fact, quite as much as its color, liquidity, etc.; it is only in another situation that it is discriminated as a relation instead of being regarded as an element. it is quite as true to say that a thing is called water because it suggests thirst-quenching as to say that it suggests thirst-quenching because it is characterized as water. _the knowledge function becomes prominent or dominant in the degree in which there is a conscious discrimination between the fact-relations and the meaning-relations._ and this inevitably means that the "water" ceases to be _surely_ water, just as it becomes doubtful or hypothetical whether this thing, whatever it is, really means thirst-quenching. if it really means thirst-quenching, it is water; so far as it may not mean it, it perhaps is not water. it is now just as much a question _what_ this _is_ as what it means. whatever will resolve one question will resolve the other. in just the degree, then, in which an existence or thing gets intellectualized force or function, it becomes a fragmentary and dubious thing, to be circumscribed and described for the sake of operating as _sign_, or clue of a _future_ reality to be realized through action. only as "reality" is reduced to a sign, and questions of its nature as sign are considered, does it get intellectual or cognitional status. the bearing of this upon the question of practical character of the distinctions of fact and idea is obvious. no one, i take it, would deny that action of some sort _does_ follow upon judgment; no one would deny that this action _does_ somehow serve to test the value of the intellectual operations upon which it follows. but if this subsequent action is _merely_ subsequent, if the intellectual categories, operations, and distinctions are complete in themselves, without inherent reference to it, what guaranty is there that they pass into relevant action, and by what miracle does the action manage to test the worth of the idea? but if the intellectual identification and description of the thing are as tentative and instrumental as is the ascription of significance, then the exigencies of the active situation are operative in all the categories of the knowledge situation. action is not a more or less accidental appendage or afterthought, but is undergoing development and giving direction in the entire knowledge function. in conclusion, i remark that the ease with which the practical character of these fundamental logical categories, fact, meaning, and agreement, may be overlooked or denied is due to the organic way in which practical import is incarnate in them. it can be overlooked because it is so involved in the terms themselves that it is assumed at every turn. the pragmatist is in the position of one who is charged with denying the existence of something because, in pointing out a certain fundamental feature of it, he puts it in a strange light. such confusion always occurs when the familiar is brought to definition. the difficulties are more psychological--difficulties of orientation and mental adjustment--than logical, and in the long run will be done away with by our getting used to the different viewpoint, rather than by argument. footnotes: [ ] _studies in logical theory_, university of chicago press, . [ ] mill's doctrine of the ambiguity of the copula (_logic_, book i, chap. iv, § ) is an instance of one typical way of evading the problem. after insisting with proper force and clearness upon the objective character of our intellectual beliefs and propositions, viz., that when we say fire causes heat we mean actual phenomena, not our ideas of fire and heat (book i, chap. ii and chap. xi, § , and chap. v, § ), he thinks to dispose of the whole problem of the "is" in judgment by saying that it is only a sign of affirmation (chap. i, § , and chap. iv, § ). of course it is. but unless the affirmation (the sign of thought) "agrees" or "corresponds with" the relations of the phenomena, what becomes of the doctrine of the objective import of propositions? how otherwise shall we maintain with mill (and with common-sense and science) the difference between asserting "a fact of external nature" and "a fact in my mental history"? [ ] _studies in philosophy and psychology_, article by woodbridge on "the problem of consciousness," especially pp. - . [ ] in other words, "ideas" is a term capable of assuming any definition which is logically appropriate--say, meaning. it need not have anything to do with the conception of little subjective entities or psychical stuffs. [ ] of course, the monistic epistemologies have an advantage in the statement of the problem over the dualistic--they do not state it in terms which presuppose the impossibility of the solution. [ ] this view was originally advanced in the discussion of quite another problem than the one here discussed, viz., the problem of consciousness; and it may not be quite just to dissever it from that context. but as a formula for knowledge it has enough similarity with the one brought out in this paper to suggest further treatment; it is not intended that the results reached here shall apply to the problem of consciousness as such. ix naÏve realism vs. presentative realism[ ] i in spite of the elucidations of contemporary realists, a number of idealists continue to adduce in behalf of idealism certain facts having an obvious physical nature and explanation. the visible convergence of the railway tracks, for example, is cited as evidence that what is seen is a mental "content." yet this convergence follows from the physical properties of light and a lens, and is physically demonstrated in a camera. is the photograph, then, to be conceived as a psychical somewhat? that the time of the visibility of a light does not coincide with the time at which a distant body emitted the light is employed to support a similar idealistic conclusion, in spite of the fact that the exact difference in time may be deduced from a physical property of light--its rate. the dislocation in space of the light seen and the astronomical star is used as evidence of the mental nature of the former, though the exact angular difference is a matter of simple computation from purely physical data. the doubling of images of, say, the finger when the eyeball is pressed, is frequently proffered as a clincher. yet it is a simple matter to take any body that reflects light, and by a suitable arrangement of lenses to produce not only two but many images, projected into space. if the fact that under definite _physical_ conditions (misplacement of lenses), a finger yields two images proves the psychical character of the latter, then the fact that under certain conditions a sounding body yields one or more echoes is, by parity of reasoning, proof that the echo is made of mental stuff.[ ] if, once more, the differences in form and color of a table to different observers, occupying different physical positions, is proof that what each sees is a psychical, private, isolated somewhat, then the fact that one and the same physical body has different effects upon, or relations with, different physical media is proof of the mental nature of these effects. take a lump of wax and subject it to the same heat, located at different positions; now the wax is solid, now liquid--it might even be gaseous. how "psychical" these phenomena! it almost seems as if the transformation of the physical into the mental in the cases cited exemplifies an interesting psychological phenomenon. in each case the beginning is with a real and physical existence. taking "the real object," the astronomical star, on the basis of its physical reality, the idealist concludes to a psychical object, radically different! taking the _single_ object, the finger, from the premise of its real singleness, he concludes to a double mental content, which then takes the place of the original single thing! taking one-and-the-same-object, the table, presenting _its_ different surfaces and reflections of light to different real organisms, he eliminates the one-table-in-its-different-relations in behalf of a multiplicity of totally separate psychical tables! the logic reminds us of the story of the countryman who, after gazing at the giraffe, remarked, "there ain't no such animal." it almost seems, i repeat, as if this self-contradiction in the argument creates in some minds the impression that the object--not the argument--is undergoing the extraordinary reversal of form. however this may be, the problem indicated in the foregoing cases is simply the good old problem of the many in one, or, less cryptically, the problem of the maintenance of a continuity of process throughout differences. i do not pretend that this situation, though the most familiar thing in life, is wholly without difficulties. but its difficulty is not one of epistemology, that is, of the relation of known to a knower; to take it as such, and then to use it as proof of the psychical nature of a final term, is also to prove that the trail the rocket stick leaves behind is psychical, or that the flower which comes in a continuity of process from a seed is mental. ii contemporary realists have so frequently and clearly expounded the physical explanation of such cases as have been cited that one is at a loss as to why idealists go on repeating the cases without even alluding to the realistic explanation. one is moved to wonder whether this neglect is just one of those circumstances which persistently dog philosophical discussions, or whether something in the realistic position gives ground (from at least an _ad hominem_ point of view) for the neglect. there is a reason for adopting the latter alternative. many realists, in offering the type of explanation adduced above, have treated the cases of seen light, doubled imagery, as perception in a way that ascribes to perception an inherent cognitive status. they have treated the perceptions as _cases of knowledge_, instead of as simply natural events having, in themselves (apart from a _use_ that may be made of them), no more knowledge status or worth than, say, a shower or a fever. what i intend to show is that if "perceptions" are regarded as cases of knowledge, the gate is opened to the idealistic interpretation. the physical explanation holds of them as long as they are regarded simply as natural events--a doctrine i shall call naïve realism; it does not hold of them considered as cases of knowledge--the view i call presentative realism. the idealists attribute to the realists the doctrine that "the perceived object is the real object." please note the wording; it assumes that there is _the_ real object, something which stands in a contrasting relation with objects not real or else less real. since it is easily demonstrable that there is a numerical duplicity between the astronomical star and its effect of visible light, between the single finger and the doubled images, the latter evidently, when the former is dubbed "_the_" real object, stands in disparaging contrast to its reality. _if_ it is a case of knowledge, the knowledge refers to the star; and yet not the star, but something more or less unreal (that is, if the star be "the" real object), is known. consider how simply the matter stands in what i have called naïve realism. the astronomical star is _a_ real object, but not "the" real object; the visible light is another real object, found, when knowledge supervenes, to be an occurrence standing in a process continuous with the star. since the seen light is an event within a continuous process, there is no point of view from which its "reality" contrasts with that of the star. but suppose that the realist accepts the traditionary psychology according to which every event in the way of a perception is also a case of knowing something. is the way out now so simple? in the case of the doubled fingers or the seen light, the thing known in perception contrasts with the physical source and cause of the knowledge. there _is_ a numerical duplicity. moreover the thing known by perception is by this hypothesis in relation to a knower, while the physical cause is not. is not the most plausible account of the difference between the physical cause of the perceptive knowledge and what the latter presents precisely this latter difference--namely, presentation to a knower? if perception is a case of knowing, it must be a case of knowing the star; but since the "real" star is not known in the perception, the knowledge relation must somehow have changed the "object" into a "content." thus when the realist conceives the perceptual occurrence as an intrinsic case of knowledge or of presentation to a mind or knower, he lets the nose of the idealist camel into the tent. he has then no great cause for surprise when the camel comes in--and devours the tent. perhaps it will seem as if in this last paragraph i had gone back on what i said earlier regarding the physical explanation of the difference between the visible light and the astronomical star. on the contrary, my point is that this explanation, though wholly adequate as long as we conceive the perception to be itself simply a natural event, is not at all available when we conceive it to be an attempt at knowing its cause. in the former case, we are dealing with a relation between natural events. in the latter case, we are dealing with the difference between an object as a cause of knowledge and an object as known, and hence in relation to mind. by the "method of difference" the sole explanation of the difference between the two objects is then the absence or presence of relation to a knower. in the case of the seen light,[ ] reference to the velocity of light is quite adequate to account for its time and space differences from the star. but viewed as a case of what is known (on the supposition that perception is knowing), reference to it only increases the contrast between the real object and the object known in perception. for, being just as much a part of the object that causes the perception as is the star itself, it (the velocity of light) _ought_ logically to be part of what is known in the perception, while it is not. since the velocity of light is a constituent element in the star, it should be known in the perception; since it is not so known, reference to it only increases the discrepancy between the object of the perception--the seen light--and the real, astronomical star. the same is true of any physical condition that might be referred to: _the very things that, from the standpoint of perception as a natural event, are conditions that account for its happening are, from the standpoint of perception as a case of knowledge, part of the object which, if knowledge is to be valid, ought to be known, but is not._ in this fact we have, perhaps, the ground of the idealist's disregard of the oft-proffered physical explanation of the difference between the perceptual event and _the_ (so-called) real object. and it is quite possible that some realists who read these lines will feel that in my last paragraphs i have been making a covert argument for idealism. not so, i repeat; they are an argument for a truly naïve realism. the presentative realist, in his appeal to "common-sense" and the "plain man," first sophisticates the umpire and then appeals. he stops a good way short of a genuine naïveté. the plain man, for a surety, does not regard noises heard, lights seen, etc., as mental existences; but neither does he regard them as things _known_. that they are just things is good enough for him. that they are in relation to mind, or in relation to mind as their "knower," no more occurs to him than that they are mental. by this i mean much more than that the formulae of epistemology are foreign to him; i mean that his attitude to these things _as_ things involves their _not_ being in relation to him as a mind or a knower. he is in the attitude of a liker or hater, a doer or an appreciator. when he takes the attitude of a knower he begins to inquire. once depart from thorough naïveté, and substitute for it the psychological theory that perception is a cognitive presentation to a mind of a causal object, and the first step is taken on the road which ends in an idealistic system. iii for simplicity's sake, i have written as if my main problem were to show how, in the face of a supposed difficulty, a strictly realistic theory of the perceptual event may be maintained. but my interest is primarily in the facts, and in the theory only because of the facts it formulates. the significance of the facts of the case may, perhaps, be indicated by a consideration which has thus far been ignored. in regarding a perception as a case of knowledge, the presentative realist does more than shove into it a relation to mind which then, naturally and inevitably, becomes the explanation of any differences that exist between its subject-matter and some causal object with which it contrasts. in many cases--very important cases, too, in the physical sciences--the contrasting "real object" becomes known by a logical process, by inference--as the contemporary position of the star is determined by calculations from data, not by perception. this, then, is the situation of the presentative realist: if perception is knowledge of its cause, it stands in unfavorable contrast with another indirect mode of knowledge; _its_ object is less valid than the object of inference. i do not adduce these considerations as showing that the case is hopeless for the presentative realist;[ ] i am willing to concede he can find a satisfactory way out. but the difficulty exists; and in existing it calls emphatic attention to a case which is certainly and indisputably a case of knowledge--namely, propositions arrived at through inference, judgments as logical assertions. with relation to the unquestionable case of knowledge, the logical or inferential case, perceptions occupy a unique status, one which readily accounts for their being regarded as cases of knowledge, although in themselves they are natural events. ( ) they are the sole ultimate data, the sole media, of inference to all natural objects and processes. while we do not, in any intelligible or verifiable sense, know _them_, we know all things that we do know _with_ or _by_ them. they furnish the only ultimate evidence of the existence and nature of the objects which we infer, and they are the sole ultimate checks and tests of the inferences. the visible light is a necessary part of the evidence on the basis of which we infer the existence, place, and structure of the astronomical star, and some other perception is the verifying check on the value of the inference. because of this characteristic use of perceptions, the perceptions themselves acquire, by "second intention," a knowledge status. they _become_ objects of minute, accurate, and experimental scrutiny. since the body of propositions that forms natural science hangs upon them, _for scientific purposes_ their nature _as_ evidence, _as_ signs, entirely overshadows their natural status, that of being simply natural events. the scientific man, as scientific, cares for perceptions not in themselves, but as they throw light upon the nature of some object reached by evidence. and since every such inference tries to terminate in a further perception (as its test of validity), the value of inferential knowing depends on perception. ( ) independently of science, daily life uses perceptions as signs of other perceptions. when a perception of a certain kind frequently recurs and is constantly used as evidence of some other impending perceptual event, the function of habit (a natural function, be it noted, not a psychical or epistemological function) often brings it about that the perception loses its original quality in acquiring a sign-value. language is, of course, the typical case. noises, in themselves mere natural events, through habitual use as signs of other natural events become integrated with what they mean. what they stand for is telescoped, as it were, into what they are. this happens also with other natural events, colors, tastes, etc. thus, _for practical purposes_, many perceptual events are cases of knowledge; that is, they have been _used_ as such so often that the habit of so using them is established or automatic. in this brief reference to facts that are perfectly familiar, i have tried to suggest three points of crucial importance for a naïve realism: first, that inferential or evidential knowledge (that involving logical relation) is in the field as an obvious and undisputed case of knowledge; second, that this function, although embodying the logical relation, is itself a natural and specifically detectable process among natural things--it is not a non-natural or epistemological relation; third, that the _use_, practical and scientific, of perceptual events in the evidential or inferential function is such as to make them _become_ objects of inquiry and limits of knowledge, and to such a degree that this acquired characteristic quite overshadows, in many cases, their primary nature. if we add to what has been said the fact that, like every natural function, the inferential function turns out better in some cases and worse in others, we get a naturalistic or naïvely realistic conception of the "_problem_ of knowledge": control of the conditions of inference--the only type of knowledge detectable in direct existence--so as to guide it toward better conclusions. iv i do not flatter myself that i will receive much gratitude from realists for attempting to rescue them from that error of fact which exposes their doctrine to an idealistic interpretation. the superstition, growing up in a false physics and physiology and perpetuated by psychology, that sensations-perceptions are cases of knowledge, is too ingrained. but--_crede experto_--let them try the experiment of conceiving perceptions as pure natural events, not as cases of awareness or apprehension, and they will be surprised to see how little they miss--save the burden of carrying traditionary problems. meantime, while philosophic argument, such as this, will do little to change the state of belief regarding perceptions, the development of biology and the refinement of physiology will, in due season, do the work. in concluding my article, i ought to refer, in order to guard against misapprehension, to a reply that the presentative realist might make to my objection. he might say that while the seen light is a case of knowledge or presentative awareness, it is not a case of knowledge of the star, but simply of the seen light, just as it is. in this case the appeal to the physical explanations of the difference of the seen light from its objective source is quite legitimate. at first sight, such a position seems innocent and tenable. even if innocent, it would, however, be ungrounded, since there is no evidence of the existence of a knower, and of its relation to the seen light. but further consideration will reveal that there is a most fundamental objection. if the notion of perception as a case of adequate knowledge of its own object-matter be accepted, the knowledge relation is absolutely ubiquitous; it is an all-inclusive net. the "ego-centric predicament" is inevitable. this result of making perception a case of knowing will now occupy us. footnotes: [ ] i am indebted to dr. bush's article on "knowledge and perception," _journal of philosophy, psychology, and scientific methods_, vol. vi, p. , and to professor woodbridge's article on "perception and epistemology" in the _james memorial volume_, as well as to his paper on "sensations," read at the meeting of the american philosophical association. since my point of departure and aim are somewhat different, i make this general acknowledgment in lieu of more specific references. [ ] plato's use of shadows, of reflections in the water, and other "images" or "imitations" to prove the presence in nature of non-being was, considering the state of physical science in his day, a much more sensible conclusion than the modern use of certain images as proof that the object in perception is a psychical content. hobbes expressly treats all images as physical, as on the same plane as reflections in the water and echoes; the comparison is his. [ ] it is impossible, in this brief treatment, to forestall every misapprehension and objection. yet to many the use of the term "seen" will appear to be an admission that a case of knowledge is involved. but is smelling a case of knowledge? or (if the superstition persists as to smell) is gnawing or poking a case of knowledge? my point, of course, is that "seen" involves a relation to organic activity, not to a knower, or mind. [ ] this is the phase of the matter, of course, which the rationalistic or objective realist, the realist of the type of t. h. green, emphasizes. put in terms of systems, the difficulty is that in escaping the subjectivism latent in treating perception as a case of knowledge, the realist runs into the waiting arms of the objective idealist. x epistemological realism: the alleged ubiquity of the knowledge relation i have pointed out that if perception be treated as a case of knowledge, knowledge of every form and kind must be treated as a case of a presentation to a knower. the alleged discipline of epistemology is then inevitable. in common usage, the term "knowledge" tends to be employed eulogistically; its meaning approaches the connotation of the term "science." more loosely, it is used, of course, to designate all beliefs and propositions that are held with assurance, especially with the implication that the assurance is reasonable, or grounded. in its practical sense, it is used as the equivalent of "knowing _how_," of skill or ability involving such acquaintance with things and persons as enables one to anticipate how they behave under certain conditions and to take steps accordingly. such usages of the term are all differential; they all involve definite contrasts--with ungrounded conviction, or with doubt and mere guesswork, or with the inexpertness that accompanies lack of familiarity. in its epistemological use, the term "knowledge" has a blanket value which is absolutely unknown in common life. it covers any and every "presentation" of any and every thing to a knower, to an "awarer," if i may coin a word for the sake of avoiding some of the pitfalls of the term "consciousness." and, i repeat, this indiscriminate use of the term "knowledge," so foreign to science and daily life, is absolutely unavoidable if perception be regarded as, in itself, a mode of knowledge. and then--and only then--the problem of "the possibility, nature, and extent of knowledge _in general_" is also inevitable. i hope i shall not be regarded as offensively pragmatic if i suggest that this undesirable consequence is a good reason for not accepting the premise from which it follows, unless that premise be absolutely forced upon us. at all events, upon the supposition of the ubiquity of the knowledge relation in respect to a self, presentative realism is compelled to accept the genuineness of the epistemological problem, and thus to convert itself into an epistemological realism, getting one more step away from both naïve and naturalistic realism. the problem is especially acute for a presentative realism because idealism has made precisely this ubiquity of relationship its axiom, its short-cut. one sample is as good as a thousand. says bain: "there is no possible knowledge of a world except in relation to our minds. knowledge means a state of mind; the notion of material things is a mental fact. we are incapable even of discussing the existence of an independent material world; the very act is a contradiction. we can speak only of a world presented to our own minds." on the supposition of the ubiquity of the relation, realism and idealism exhaust the alternatives; if the ubiquity of the relation is a myth, both doctrines are unreal, because there is no problem of which they are the solution. my first step in indicating the unreality of both "solutions" is formal. i shall try to show that _if_ the knowledge relation of things to a self is the exhaustive and inclusive relation, there is no intelligible point at issue between idealism and realism; the differences between them are either verbal or else due to a failure on the part of one or the other to stick to their _common_ premise. i to my mind, professor perry rendered philosophic discussion a real service when he coined the phrase "ego-centric predicament." the phrase designated something which, whether or no it be real in itself, is very real in current discussion, and designating it rendered it more accessible to examination. in terming the alleged uniform complicity of a knower a predicament, it is intended, i take it, to suggest, among other things, that we have here a difficulty with which all schools of thought alike must reckon, so that it is a difficulty that cannot be used as an argument in behalf of one school and against another. if the relation be ubiquitous, it affects alike every view, every theory, every object experienced; it is no respecter of persons, no respecter of doctrines. since it cannot make any difference to any particular object, to any particular logical assertion, or to any particular theory, it does not support an idealistic as against a realistic theory. being a universal common denominator of all theories, it cancels out of all of them alike. it leaves the issue one of _subject-matter_, to be decided on the basis of that subject-matter, not on the basis of an unescapable attendant consideration that the subject-matter must be known in order to be discussed. in short, the moral is quite literally, "forget it," or "cut it out." but the idealist may be imagined to reply somewhat as follows: "if the ubiquity were of any kind other than precisely the kind it is, the advice to disregard it as a mere attendant circumstance of discussion would be relevant. thus, for example, we disregard gravitation when we are considering a particular chemical reaction; there is no ground for supposing that it affects a reaction in any way that modifies it as a chemical reaction. and if the 'ego-centric' relation were cited when the point at issue is something about one group of facts in distinction from another group, it ought certainly to be canceled from any statement about them. but since the point at issue is precisely the most universally defining trait of existence as known, the invitation deliberately to disregard the most universal trait is nothing more or less than an invitation to philosophic suicide." if the idealist i have imagined as making the foregoing retort were up in recent realistic literature, he might add the following argument _ad hominem_: "you, my realistic opponent, say that the doctrine of the external relation of terms expresses a ubiquitous mark of every genuine proposition or relational complex, and that this ubiquity is a strong presumption in favor of realism. why so uneven, so partial, in your attitude toward ubiquitous relations? is it perchance that you were so uneasy at our possession of a ubiquitous relation that gives a short cut to idealism that you felt you must also have a short cut to realism?" if i terminate the controversy at this point, it is not because i think the realist is unable to "come back." on the contrary, i stop here because i believe (for reasons that will come out shortly) that both realist and idealist, having the same primary assumption, can come back at each other indefinitely. consequently, i wish to employ the existence of this _tu quoque_ controversy to raise the question: under what conditions is the relation of knower to known an intelligible question? and i wish to show that it is _not_ intelligible, if the knowledge relation be ubiquitous and homogeneous. the controversy back and forth is in fact a warning of each side by the other not to depart from their _common_ premise. if the idealist begins to argue (as he constantly does) as if the relation to "mind" or to "consciousness" made some difference of a specific sort, like that between error and fact, or between sound perception and hallucination, he may be reminded that, since this relation is uniform, it substantiates and nullifies all things alike. and the realist is quite within the common premise when he points out that every special fact must be admitted for what it is specifically known to be; no idealistic doctrine can turn the edge of the fact that knowledge has evolved historically out of a state in which there was no mind, or of the fact that knowledge is even now dependent on the brain, provided that specific evidence shows these to be facts. the realist, on the other hand, must admit that, after all, the entire body of known facts, or of science, including such facts as the above, is held fast and tight in the net of relation to a mind or consciousness. in specific cases this relation may be ignored, but the exact ground for such an ignoring is precisely that the relation is not a specific fact, but a uniform relation of facts. and to call it an external relation makes no practical difference if it is universal and uniform. so the idealist might reply. imagine a situation like the following: the sole relation an organism bears to things is that of eater; the sole relation the environment bears to the organism is that of food, that is, things-to-eat. this relation, then, is exhaustive. it defines, or identifies, each term in relation to the other. but this means that there are not, as respects organism and environment, two terms at all. eater-of-food and food-being-eaten are two names for one and the same situation. could there be imagined a greater absurdity than to set to work to discuss the relation _of_ eater _to_ food, _of_ organism _to_ the environment, or to argue as to whether one modifies the other or not? given the premise, the statements in such a discussion could have only a verbal difference from one another. suppose, however, the discussion has somehow got under way. sides have been taken; the philosophical world is divided into two great camps, "foodists" and "eaterists." the eaterists (idealists) contend that no object exists except in relation to eating; hence that everything is constituted a thing by its relation to eating. special sciences exist indeed which discuss the nature of various sorts of things in relation to _one another_, and hence in legitimate abstraction from the fact that they are all foods. but the discussion of their nature _an sich_ depends upon "eatology," which deals primarily with the problem of the possibility, nature, and extent (or limits) of eating food in general, and thereby determines what food in general, _überhaupt_, is and means. nay, replies the foodist (realist). since the eating relation is uniform, it is negligible. all propositions which have any intelligible meaning are about objects just as they are, and in the relations they bear to one another. foods pass in and out of the relation to eater with no change in their own traits. moreover, the position of the eaterists is self-contradictory. how can a thing be eaten unless it is, in and of itself, a food? to suppose that a food is constituted by eating is to presuppose that eating eats eating, and so on in infinite regress. in short, to be an eater is to be an eater of food; take away the independent existence of foods, and you deny the existence and the possibility of an eater. i respectfully submit that there is no terminus to such a discussion. for either both sides are saying the same thing in different words, or else both of them depart from their common premise, and unwittingly smuggle in some relations between the organism and environment other than that of food-eater. if to be an eater means that an organism which is more and other than an eater is doing something _distinctive_, because contrasting with its other functions, in eating then, and then only, is there an issue. in this latter case, the thing which is food may, of course, be _proved_ to be something besides food, because of some different relation to the organism than that of eating. but if both stick consistently to their common premise, we get the following trivial situation. the idealist says: "every philosophy purports to be knowledge, knowledge of objects; all knowledge implies relation to mind; therefore every object with which philosophy deals is object-in-relation-to-mind." the realist says: "to be a mind is to be a knower; to be a knower is to be a knower-of-objects. without the objects to be known, mind, the knower, is and means nothing." the difficulties attending the discussion of epistemology are in no way attendant upon the special subject-matter of "epistemology." they are found wherever any reciprocal relation is taken to define, exclusively and exhaustively, all the connections between any pair of things. if there are two things that stand solely as buyer and seller to each other, or as husband and wife, then that relation is "unique," and undefinable; to discuss the relation _of_ the relation _to_ the terms of which it is the relation, is an obvious absurdity; to assert that the relation does _not_ modify the "seller," the "wife," or the "object known," is to discuss the relation _of_ the relation just as much as to assert the opposite. the only reason, i think, why anyone has ever supposed the case of knower-known to differ from any case of an alleged exhaustive and exclusive correlation is that while the knower is only one--just knower--the objects known are obviously many, and sustain many relations to one another which vary independently of their relation to the knower. this is the undoubted fact at the bottom of epistemological realism. but the idealist is entitled to reply that the objects in their variable relations to one another nevertheless fall within a relation to a knower, _as long as_ that relation is regarded by both as exhaustive or ubiquitous. ii nevertheless, i do not conceive that the realistic assertion and the idealistic assertion in this dilemma stand on the same level, or have the same value. the fact that objects vary in relation to one another independently of their relation to the "knower" _is_ a fact, and a fact recognized by all schools. the idealistic assertion rests simply upon the presupposition of the ubiquity of the knowledge relation, and consequently has only an _ad hominem_ force, that is a force as against epistemological realists--against those who admit that the sole and exhaustive relation of the "self" or "ego" to objects is that of knower of them.[ ] the relation of buyer and seller is a discussable relation; for buyer does not exhaust one party and seller does not exhaust the other. each is a man or a woman, a consumer or a producer or a middleman, a green-grocer or a dry-goods merchant, a taxpayer or a voter, and so on indefinitely. nor is it true that such additional relations are borne merely to _other_ things; the buyer-sellers are more than and other than buyer-seller to _each other_. they may be fellow-clubmen, belong to opposite political parties, dislike each other's looks, and be second cousins. hence the buyer-seller relation stands in intelligent connection and contrast with other relations, so that it can be discriminated, defined, analyzed. moreover, there are specific differences _in_ the buying-selling relation. because it is not ubiquitous, it is not homogeneous. if wealthy and a householder, the one who buys is a different buyer--i.e., buys differently--than if poor and a boarder. consequently, the seller sells differently, has more or less goods left to sell, more or less income to expend on other things, and so on indefinitely. moreover, in order to be a buyer the man has to _have been_ other things; i.e., he is not a buyer _per se_, but _becomes_ a buyer because he is an eater, wears clothes, is married, etc. it is also quite clear that the organism is something else than an eater, or something in relation to food alone. i will not again call the roll of perfectly familiar facts; i will lessen my appeal to the reader's patience by confining my reiteration to one point. even in relation to the things that are food, the organism is something more than their eater. he is their acquirer, their pursuer, their cultivator, their beholder, taster, etc.; he _becomes_ their eater _only_ because he is so many other things, and his becoming an eater is a natural episode in the natural unfolding of these other things. precisely the same sort of assertions may be made about the knower-known relation. if the one who is knower is something else and more than the knower of objects, and if objects are, _in relation to the one who knows them_, something else and other than things in a knowledge relation, there is somewhat to define and discuss; otherwise we are raising, as we have already seen, the quite foolish question as to what is the relation of a relation to itself, or the equally foolish question of whether being a thing modifies the thing that it is. and, moreover, epistemological realism and idealism both say the same thing: realism that a thing does not modify itself, idealism that, since the thing is what it is, it stands in the relation that it does stand in. there are many facts which, prima facie, support the claim that knowing is a connection of things which depends upon other and more primary connections between a self and things; a connection which grows out of these more fundamental connections and which operates in their interests at specifiable crises. i will not repeat what is so generally admitted and so little taken into account, that knowing is, biologically, a differentiation of organic behavior, but will cite some facts that are even more obvious and even more neglected. . if we take a case of perception, we find upon analysis that, so far as a self or organism is concerned in it at all, the self is, so to say, inside of it rather than outside of it. it would be much more correct to say that a self is contained in a perception than that a perception is presented to a self. that is to say, the organism is involved in the occurrence of the perception in the same sort of way that hydrogen is involved in the happening--producing--of water. we might about as well talk of the production of a specimen of water as a presentation of water to hydrogen as talk in the way we are only too accustomed to talk about perceptions and the organism. when we consider a perception as a case of "apperception," the same thing holds good. habits enter into the _constitution_ of the situation; they are in and of it, not, so far as it is concerned, something outside of it. here, if you please, is a unique relation of self and things, but it is unique not in being wholly incomparable to all natural relations among events, but in the sense of being distinctive or just the relation that it is. . taking the many cases where the self may be said, in an intelligible sense, to lie _outside_ a thing and hence to have dealings with it, we find that they are extensively and primarily cases where the self is agent-patient, doer, sufferer, and enjoyer. this means, of course, that things, the things that later come to be known, are primarily not objects of awareness, but causes of weal and woe, things to get and things to avoid, means and obstacles, tools and results. to a naïve spectator, the ordinary assumption that a thing is "in" experience only when it is an object of awareness (or even only when a perception), is nothing less than extraordinary. the self experiences whatever it undergoes, and there is no fact about life more assured or more tragic than that what we are aware of is determined by things that we are undergoing but of which we are not conscious and which we cannot be conscious of under the particular conditions. . so far as the question of the relation of the self to known objects is concerned, knowing is but one special case of the agent-patient, of the behaver-enjoyer-sufferer situation. it is, however, the case constantly increasing in relative importance. the connections of the self with things by way of weal or woe are progressively found to depend upon the connections established in knowing things; on the other hand, the progress, the advance, of science is found to depend more and more upon the courage and patience of the agent in making the widening and buttressing of knowledge a business. it is impossible to overstate the significance, the reality, of the relation of self as knower to things when it is thought of as a _moral_ relation, a deliberate and responsible undertaking of a self. ultimately the modern insistence upon the self in reference to knowledge (in contrast with the classic greek view) will be found to reside precisely here. my purpose in citing the foregoing facts is not to prove a positive point, viz., that there are many relations of self and things, of which knowing is but one differentiated case. it concerns something less obvious: viz., showing what is meant by saying that the problems at issue concern matters of fact, and are not matters to be decided by assumption, definition, and deduction. i mean also to suggest what kind of matters of fact would naturally be adduced as evidential in such a discussion. negatively put, my point is that the whole question of the relation of knower to known is radically misconceived in what passes as epistemology, because of an underlying unexamined assumption, an assumption which, moreover, when examined, makes the controversy verbal or absurd. positively put, my point is that since, prima facie, plenty of connections other than the knower-known one exist between self and things, there is a context in which the "problem" of their relation concerns matters of fact capable of empirical determination by matter-of-fact inquiry. the point about a difference being made (or rather making) in things when known is precisely of this sort. iii that question is not, _save upon the assumption of the ubiquity of the knowledge relation_, the absurd question of whether knowledge makes any difference to things already known or to things _as_ knowledge-objects, _as_ facts or truths. until the epistemological realists have seriously considered the main propositions of the pragmatic realists, viz., that knowing is something that happens to things in the natural course of their career, not the sudden introduction of a "unique" non-natural type of relation--that to a mind or consciousness--they are hardly in a position to discuss the second and derived pragmatic proposition that, in this natural continuity, things in becoming known undergo a specific and detectable qualitative change. i had occasion earlier to remark that if one identifies "knowledge" with situations involving the function of inference, the _problem_ of knowledge means the art of guiding this function most effectively. that statement holds when we take knowledge as a relation of the things _in_ the knowledge situation. if we are once convinced of the artificiality of the notion that the knowledge relation is ubiquitous, there will be an existential problem as to the self and knowledge; but it will be a radically different problem from that discussed in epistemology. the relation of knowing to existence will be recognized to form the subject-matter of no problem, because involving an ungrounded and even absurd preconception. but the problem of the relation of an existence in the way of knowing to other existences--or events--with which it forms a continuous process will then be seen to be a natural problem to be attacked by natural methods. footnote: [ ] professor perry says (_the new realism_, p. ): "professor dewey is mistaken in supposing that realism assumes 'the _ubiquity of the knowledge-relation_.' realism does not argue from the 'ego-centric predicament,' i.e., from the bare presence of the knowledge-relation in all cases of knowledge." if the text has not made my point clear, it is probably too much to expect that a footnote will do so. but i have not accused the realist of arguing from the ego-centric predicament. i have said that _if_ any realist holds that the sole and exclusive relation of the one who is knower to things is that of being their knower, then the realist cannot _escape_ the impact of the predicament. but if the one who knows things also stands in other connections with them, then it is possible to make an intelligible contrast between things as known and things as loved or hated or appreciated, or seen or heard or whatever. the argument, it should be noted, stands in connection with that of the last section as to whether hearing a sound and seeing a color are of themselves (apart from the use made of them in inference) cases of knowledge. it is significant that perry holds (_new realism_, p. ) that "sensing" is _per se_ a case of knowing. hence it must be in relation to a knower; it must fall within the "predicament," for "it makes the mind aware of a characteristic of the environment." that it is _used_ (or may be used) to make us aware of some characteristic of the environment, i of course hold. to say that it _is_ an awareness by the mind of a characteristic of the environment is at once to involve a philosopher immediately in the discussion of whether red qualities, or only certain vibrations, are "really" characteristics of the environment. then, when the authority of physics is invoked in behalf of the latter proposition, the epistemologist (however realistic in his intention) is forced to consider color as a misapprehension of the environment, a case of error or illusion, while the idealist triumphantly flourishes it as a case of the transformative or constitutive efficacy of "mind" in knowing. but if the color is simply a natural event, and if "mind" does not enter except when color is made the basis of inference to some characteristic of the environment, then there is no predicament; and there is no problem of error save as a false inference is made. moreover, since errors in inference are an undoubted fact, the principle that entities are not to be multiplied beyond need gives a prima facie superiority to any theory which connects all error with inference till adequate evidence to the contrary is produced. xi the existence of the world as a logical problem of the two parts of this paper the first is a study in formal analysis. it attempts to show that there is no problem, logically speaking, of the existence of an external world. its point is to show that the very attempt to state the problem involves a self-contradiction: that the terms cannot be stated so as to generate a problem without assuming what is professedly brought into question. the second part is a summary endeavor to state the actual question which has given rise to the unreal problem and the conditions which have led to its being misconstrued. so far as subject-matter is concerned, it supplements the first part; but the argument of the first part in no way depends upon anything said in the second. the latter may be false and its falsity have no implications for the first. i there are many ways of stating the problem of the existence of an external world. i shall make that of mr. bertrand russell the basis of my examinations, as it is set forth in his recent book _our knowledge of the external world as a field for scientific method in philosophy_. i do this both because his statement is one recently made in a book of commanding importance, and because it seems to me to be a more careful statement than most of those in vogue. if my point can be made out for his statement, it will apply, a fortiori, to other statements. even if there be those to whom this does not seem to be the case, it will be admitted that my analysis must begin somewhere. i cannot take the space to repeat the analysis in application to differing modes of statement with a view to showing that the method employed will yield like results in all cases. but i take the liberty of throwing the burden upon the reader and asking him to show cause why it does not so apply. after rejecting certain familiar formulations of the question because they employ the not easily definable notions of the self and independence, mr. russell makes the following formulation: can we "know that objects of sense ... exist at times when we are not perceiving them?" (_op. cit._, p. ). or, in another mode of statement: "can the existence of anything other than our own[ ] hard data be inferred from the existence of those data?" (pp. and ). i shall try to show that identification of the "data of sense" as the sort of term which will generate the problem involves an affirmative answer to the question--that it must have been answered in the affirmative before the question can be asked. and this, i take it, is to say that it is not a question at all. a point of departure may be found in the following passage: "i think it must be admitted as probable that the immediate objects of sense depend for their existence upon physiological conditions in ourselves, and that, for example, the colored surfaces which we see cease to exist when we shut our eyes" (p. ). i have not quoted the passage for the sake of gaining an easy victory by pointing out that this statement involves the existence of physiological conditions. for mr. russell himself affirms that fact. as he points out, such arguments assume precisely the "common sense world of stable objects" professedly put in doubt (p. ). my purpose is to ask what justification there is for calling immediate data "objects of sense." statements of this type always call color visual, sound auditory, and so on. if it were merely a matter of making certain admissions for the sake of being able to play a certain game, there would be no objection. but if we are concerned with a matter of serious analysis, one is bound to ask, whence come these adjectives? that color is visual in the sense of being an object of vision is certainly admitted in the common-sense world, but this is the world we have left. that color is visual is a proposition about color and it is a proposition which color itself does not utter. visible or visual color is already a "synthetic" proposition, not a term nor an analysis of a single term. that color is seen, or is visible, i do not call in question; but i insist that fact already assumes an answer to the question which mr. russell has put. it presupposes existence beyond the color itself. to call the color a "sensory" object involves another assumption of the same kind but even more complex--involving, that is, even more existence beyond the color. i see no reply to this statement except to urge that the terms "visual" and "sensory" as applied to the object are pieces of verbal supererogation having no force in the statement. this supposititious answer brings the matter to a focus. is it possible to institute even a preliminary disparaging contrast between immediate objects and a world external to them unless the term "sensory" has a definite effect upon the meaning assigned to immediate data or objects? before taking up this question i shall, however, call attention to another implication of the passage quoted. it appears to be implied that existence of color and "being seen" are equivalent terms. at all events, in similar arguments the identification is frequently made. but by description all that is required for the existence of color is certain physiological conditions. they may be present and color exist and yet not be seen. things constantly act upon the optical apparatus in a way which fulfils the conditions of the existence of color without color being seen. this statement does not involve any dubious psychology about an act of attention. i only mean that the argument implies over and above the existence of color something called seeing or perceiving--noting is perhaps a convenient neutral term. and this clearly involves an assumption of something beyond the existence of the datum--and this datum is by definition an external world. without this assumption the term "immediate" could not be introduced. is the _object_ immediate or is it the object of an immediate noting? if the latter, then the hard datum already stands in connection with something beyond itself. and this brings us to a further point. the sense objects are repeatedly spoken of as "known." for example: "it is obvious that since the senses give knowledge of the latter kind [believed on their own account, without the support of any outside evidence] the immediate facts perceived by sight or touch or hearing do not need to be proved by argument but are completely self-evident" (p. ). again, they are spoken of as "facts of sense"[ ] (p. ), and as facts going along, for knowledge, with the laws of logic (p. ). i do not know what belief or knowledge means here: nor do i understand what is meant by a _fact_ being evidence for itself.[ ] but obviously mr. russell knows, and knows their application to the sense object. and here is a further assumption of what, by definition, is a world external to the datum. again, we have assumed in getting a question stated just what is professedly called into question. and the assumption is not made the less simple in that mr. russell has defined belief as a case of a triadic relation, and said that without the recognition of the three-term relation the difference between perception and belief is inexplicable (p. ). we come to the question passed over. can such terms as "visual," "sensory," be neglected without modifying the force of the question--that is, without affecting the implications which give it the force of a problem? can we "know that objects of sense, or very similar objects, exist at times when we are not perceiving them? secondly, if this cannot be known, can we know that other objects, inferable from objects of sense but not necessarily resembling them, exist either when we are perceiving the objects of sense or at any other time" (p. )? i think a little reflection will make it clear that without the limitation of the term "perceiving" by the term "sense" no _problem_ as to existence _at other times_ can possibly arise. for neither (_a_) reference to time nor (_b_) limitation to a particular time is given either in the fact of existence of color or of perceiving color. mr. russell, for example, makes allusion to "a patch of color which is momentarily seen" (p. ). this is the sort of thing that may pass without challenge in the common-sense world, but hardly in an analysis which professes to call that world in question. mr. russell makes the allusion in connection with discriminating between sensation as signifying "the mental event of our being aware" and the sensation as object of which we are aware--the sense object. he can hardly be guilty, then, in the immediate context, of proceeding to identify the momentariness of the event with the momentariness of the object. there must be some grounds for assuming the temporal quality of the object--and that "immediateness" belongs to it in any other way than as an object of immediate seeing. what are these grounds? how is it, moreover, that even the act of being aware is describable as "momentary"? i know of no way of so identifying it except by discovering that it is delimited in a time continuum. and if this be the case, it is surely superfluous to bother about _inference_ to "other times." they are assumed in stating the question--which thus turns out again to be no question. it may be only a trivial matter that mr. russell speaks of "that patch of color which is momentarily seen when we _look at the table_" (p. , italics mine). i would not attach undue importance to such phrases. but the frequency with which they present themselves in discussions of this type suggests the question whether as matter of fact "the patch of color" is not determined by reference to an object--the table--and not vice versa. as we shall see later, there is good ground for thinking that mr. russell is really engaged, not in bringing into question the existence of an object beyond the datum, but in _re_defining the nature of an object, and that the reference to the patch of color as something more primitive than the table is really relevant to this reconstruction of traditional metaphysics. in other words, it is relevant to defining an object as a constant correlation of variations in qualities, instead of defining it as a substance in which attributes inhere--or a subject of predicates. _a_) if anything is an eternal essence, it is surely such a thing as color taken by itself, as by definition it must be taken in the statement of the question by mr. russell. anything more simple, timeless, and absolute than a red can hardly be thought of. one might question the eternal character of the received statement of, say, the law of gravitation on the ground that it is so complex that it may depend upon conditions not yet discovered and the discovery of which would involve an alteration in the statement. if plus equal be taken as an isolated statement, it might be conceived to depend upon hidden conditions and to be alterable with them. but by conception we are dealing in the case of the colored surface with an ultimate, simple datum. it can have no implications beyond itself, no concealed dependencies. how then can its existence, even if its perception be but momentary, raise a question of "other times" at all? _b_) suppose a perceived blue surface to be replaced by a perceived red surface--and it will be conceded that the change, or replacement, is also perceived. there is still no ground for a belief in the temporally limited duration of either the red or the blue surface. anything that leads to this conclusion would lead to the conclusion that the number two ceases when we turn to think of an atom. there is no way then of escaping the conclusion that the adjective "sense" in the term "sense object" is not taken innocently. it is taken as qualifying (for the purposes of statement of the problem) the nature of the object. aside from reference to the momentariness of the _mental_ event--a reference which is expressly ruled out--there is no way of introducing delimited temporal existence into the object save by reference to one and the same object which is perceived at different times to have different qualities. if the same object--however object be defined--is perceived to be of one color at one time and of another color at another time, then as a matter of course the color-datum of either the earlier or later time is identified as of transitory duration. but equally, of course, there is no question of _inference_ to "other times." other times have already been used to describe, define, and delimit _this_ (brief) time. a moderate amount of unbiased reflection will, i am confident, convince anyone that apart from a reference to the same existence perduring through different times while changing in _some_ respect, no temporal delimitation of the existence of such a thing as sound or color can be made. even plato never doubted the eternal nature of red; he only argued from the fact that a _thing_ is red at one time and blue at another to the unstable, and hence phenomenal, character of the _thing_. or, put in a different way, we can know that a red is a momentary or transitory existence only if we know of other things which determine its beginning and cessation. mr. russell gives a specific illustration of what he takes to be the correct way of stating the question in an account of what, in the common-sense universe of discourse, would be termed walking around a table. if we exclude considerations to which we have (apart from assuming just the things which are doubtful) no right, the datum turns out to be something to be stated as follows: "what is really known[ ] is a correlation of muscular and other bodily sensations with changes in visual sensations" (p. ). by "sensations" must be meant sensible objects, not mental events. this statement repeats the point already dealt with: "muscular," "visual," and "other bodily" are all terms which are indispensable and which also assume the very thing professedly brought into question: the external world as that was defined. "really known" assumes both noting and belief, with whatever complex implications they may involve--implications which, for all that appears to the contrary, may be indefinitely complex, and which, by mr. russell's own statement, involve relationship to at least two other terms besides the datum. but in addition there appears the new term "correlation." i cannot avoid the conclusion that this term involves an _explicit_ acknowledgment of the external world. note, in the first place, that the correlation in question is not simple: it is threefold, being a correlation of correlations. the "changes in visual sensations" (objects) must be correlated in a temporal continuum; the "muscular and other bodily sensations" (objects) must also constitute a connected series. one set of changes belongs to the serial class "visual"; the other set to the serial class "muscular." and these two classes sustain a point-to-point correspondence to each other--they are correlated. i am not raising the old question of how such complex correlations can be said to be either "given" or "known" in sense, though it is worth a passing notice that it was on account of this sort of phenomenon that kant postulated his threefold intellectual synthesis of apprehension, reproduction, and recognition in conception; and that it is upon the basis of necessity for such correlations that the rationalists have always criticized sensationalist empiricism. personally i agree that temporal and spatial qualities are quite as much given in experience as are particulars--in fact, as i have been trying to show, particulars can be identified _as_ particulars only in a relational complex. my point is rather (i) that any such given is already precisely what is meant by the "world"; and (ii) that such a highly specified correlation as mr. russell here sets forth is in no case a psychological, or historical, primitive, but is a _logical_ primitive arrived at by an analysis of an empirical complex. (i) the statement involves the assumption of two temporal "spreads" which, moreover, are determinately specified as to their constituent elements and as to their order. and these sustain to each other a correlation, element to element. the elements, moreover, are all specifically qualitative and some of them, at least, are spatial. how this differs from the external world of common-sense i am totally unable to see. it may not be a very big external world, but having begged a small external world, i do not see why one should be too squeamish about extending it over the edges. the reply, i suppose, is that this complex defined and ordered object is by conception the object of a single perception, so that the question remains as to the possibility of inferring from it to something beyond.[ ] but the reply only throws us back upon the point previously made. a particular or single event of perceptual awareness can be _determined_ as to its ingredients and structure only in a continuum of objects. that is, the series of changes in color and shape can be determined as just such and such an ordered series of specific elements, with a determinate beginning and end, only in respect to a temporal continuum of things anteceding and succeeding. moreover, the determination involves an analysis which disentangles qualities and shapes from contemporaneously given objects which are irrelevant. in a word, mr. russell's object already extends beyond itself; it already belongs to a larger world. (ii) a sensible object which can be described as a correlation of an ordered series of shapes and colors with an ordered series of muscular and other bodily objects presents a definition of an object, not a psychological datum. what is stated is the definition of an object, of any object in the world. barring ambiguities[ ] in the terms "muscular" and "bodily," it seems to be an excellent definition. but good definition or poor, it states what a datum is _known_ to be as an object in a known system; viz., definite correlations of specified and ordered elements. as a definition, it is general. it is not made from the standpoint of any particular percipient. it says: _if_ there be any percipient at a specified position in a space continuum, _then_ the object may be perceived as such and such. and this implies that a percipient at any _other_ position in the space continuum can deduce from the known system of correlations just what the series of shapes and colors will be from another position. for, as we have seen, the correlation of the series of changes of shape assumes a spatial continuum; hence one perspective projection may be correlated with that of any position in the continuum. i have no direct concern with mr. russell's solution of his problem. but if the prior analysis is correct, one may anticipate in advance that it will consist simply in making explicit the assumptions which have tacitly been made in stating the problem--subject to the conditions involved in failure to recognize that they have been made. and i think an analytic reading of the solution will bear out the following statement. his various "peculiar," "private" points of view and their perspectives are nothing but names for the positions and projectional perspectives of the ordinary space of the public worlds. their correlation by likeness is nothing but the explicit recognition that they are all defined and located, from the start, in one common spatial continuum. one quotation must suffice. "if two men are sitting in a room, two somewhat similar worlds are perceived by them; if a third man enters and sits between them, a third world, intermediate between the two others, begins to be perceived" (pp. - ). pray what is this room and what defines the position (standpoint and perspective) of the two men and the standpoint "intermediate" between them? if the room and all the positions and perspectives which they determine are only within, say, mr. russell's private world, that private world is interestingly complex, but it gives only the original problem over again, not a "solution" of it. it is a long way from likenesses _within_ a private world to likenesses _between_ private worlds. and if the worlds are all private, pray who judges their likeness or unlikeness? this sort of thing makes one conclude that mr. russell's actual procedure is the reverse of his professed one. he really starts with one room as a spatial continuum within which different positions and projections are determined, and which are readily correlated with one another just because they are projections from positions within one and the same space-room. having employed this, he, then, can assign different positions to different percipients and institute a comparison between what each perceives and pass upon the extent of the likeness which exists between them. what is the bearing of this account upon the "empirical datum"? just this: the correlation of correlative series of changes which defines the object of sense perception is in no sense an original historic or psychologic datum. it signifies the result of an analysis of the usual crude empirical data, and an analysis which is made possible only by a very complex knowledge of the world. it marks not a primitive psychologic datum but an outcome, a limit, of analysis of a vast amount of empirical objects. the definition of an object as a correlation of various subcorrelations of changes represents a great advance--so it seems to me--over the definition of an object as a number of adjectives stuck into a substantive; but it represents an improved definition made possible by the advance of scientific knowledge about the common-sense world. it is a definition not only wholly independent of the context in which mr. russell arrives at it, but is one which (once more and finally) assumes extensive and accurate knowledge of just the world professedly called into question. ii i have come to the point of transition to the other part of my paper. a formal analysis is necessarily dialectical in character. as an empiricist i share in the dissatisfaction which even the most correct dialectical discussion is likely to arouse when brought to bear on matters of fact. i do not doubt that readers will feel that some _fact_ of an important character in mr. russell's statement has been left untouched by the previous analysis--even upon the supposition that the criticisms are just. particularly will it be felt, i think, that psychology affords to his statement of the problem a support of fact not affected by any logical treatment. for this reason i append a summary statement as to the facts which are misconstrued by any statement which makes the existence of the world problematic. i do not believe a psychologist would go as far as to admit that a definite correlation of elements as specific and ordered as that of mr. russell's statement is a primitive psychological datum. many would doubtless hold that patches of colored extensity, sounds, kinaesthetic qualities, etc., are psychologically much more primitive than, say, a table, to say nothing of a group of objects in space or a series of events in time; they would say, accordingly, that there is a real problem as to how we infer or construct the latter on the basis of the former. at the same time i do not believe that they would deny that their own knowledge of the existence and nature of the ultimate and irreducible qualities of sense is the product of a long, careful, and elaborate analysis to which the sciences of physiology, anatomy, and controlled processes of experimental observation have contributed. the ordinary method of reconciling these two seemingly inconsistent positions is to assume that the original sensible data of experience, as they occurred in infancy, have been overlaid by all kinds of associations and inferential constructions so that it is now a work of intellectual art to recover them in their innocent purity. now i might urge that as matter of fact the reconstruction of the experience of infancy is itself an inference from present experience of an objective world, and hence cannot be employed to make a problem out of the knowledge of the existence of that world. but such a retort involves just the dialectic excursus which i am here anxious to avoid. i am on matter-of-fact ground when i point out that the assumption that even infancy begins with such highly discriminated particulars as those enumerated is not only highly dubious but has been challenged by eminent psychologists. according to mr. james, for example, the original datum is large but confused, and specific sensible qualities represent the result of discriminations. in this case, the elementary data, instead of being primitive empirical data, are the last terms, the limits, of the discriminations we have been able to make. that knowledge grows from a confusedly experienced external world to a world experienced as ordered and specified would then be the teaching of psychological science, but at no point would the mind be confronted with the problem of inferring a world. into the arguments in behalf of such a psychology of original experience i shall not go, beyond pointing out the extreme improbability (in view of what is known about instincts and about the nervous system) that the starting-point is a quality corresponding to the functioning of a single sense organ, much less of a single neuronic unit of a sense organ. if one adds, as a hypothesis, that even the most rudimentary conscious experience contains within itself the element of suggestion or expectation, it will be granted that the object of conscious experience even with an infant is homogeneous with the world of the adult. one may be unwilling to concede the hypothesis. but no one can deny that inference from one thing to another is itself an empirical event, and that just as soon as such inference occurs, even in the simplest form of anticipation and prevision, a world exists like in kind to that of the adult. i cannot think that it is a trivial coincidence that psychological analysis of sense perception came into existence along with that method of experimentally controlled observation which marks the beginning of modern science. modern science did not begin with discovery of any new kind of inference. it began with the recognition of the need of different data if inference is to proceed safely. it was contended that starting with the ordinary--or customary--objects of perception hopelessly compromised in advance the work of inference and classification. hence the demand for an experimental resolution of the common-sense objects in order to get data less ambiguous, more minute, and more extensive. increasing knowledge of the structure of the nervous system fell in with increased knowledge of other objects to make possible a discrimination of specific qualities in all their diversity; it brought to light that habits, individual and social (through influence on the formation of individual habits), were large factors in determining the accepted or current system of objects. it was brought to light, in other words, that factors of chance, habit, and other non-rational factors were greater influences than intellectual inquiry in determining what men currently believed about the world. what psychological analysis contributed was, then, not primitive historic data out of which a world had somehow to be extracted, but an analysis of the world which had been previously thought of and believed in, into data making possible better inferences and beliefs about the world. analysis of the influences customarily determining belief and inference was a powerful force in the movement to improve knowledge of the world. this statement of matters of fact bears out, it will be observed, the conclusions of the dialectical analysis. that brought out the fact that the ultimate and elementary data of sense perception are identified and described as limiting elements in a complex world. what is now added is that such an identification of elements marks a significant addition to the resources of the technique of inquiry devoted to improving knowledge of the world. when these data are isolated from their logical status and office, they are inevitably treated as self-sufficient, and they leave upon our hands the insoluble, because self-contradictory, problem of deriving from them the world of common-sense and science. taken for what they really are, they are elements detected _in_ the world and serving to guide and check our inferences about it. they are never self-inclosed particulars; they are always--even as crudely given--connected with other things in experience. but analysis gets them in the form where they are keys to much more significant relations. in short, the particulars of perception, taken as complete and independent, make nonsense. taken as objects discriminated for the purposes of improving, reorganizing, and testing knowledge of the world they are invaluable assets. the material fallacy lying behind the formal fallacy which the first part of this paper noted is the failure to recognize that what is doubtful is not the existence of the world but the validity of certain customary yet inferential beliefs about things in it. it is not the common-sense _world_ which is doubtful, or which is inferential, but _common-sense_ as a complex of beliefs about specific things and relations _in_ the world. hence never in any actual procedure of inquiry do we throw the existence of the world into doubt, nor can we do so without self-contradiction. we doubt some received piece of "knowledge" about some specific thing of that world, and then set to work, as best we can, to rectify it. the contribution of psychological science to determining unambiguous data and eliminating the irrelevant influences of passion and habit which control the inferences of common-sense is an important aid in the technique of such rectifications. footnotes: [ ] i shall pass over the terms "our own" so far as specific reference is concerned, but the method employed applies equally to them. who are the "we," and what does "own" mean, and how is ownership established? [ ] contrast the statement: "when i speak of a fact, i do not mean one of the simple things of the world, i mean that a certain thing has a certain quality, or that certain things have a certain relation" (p. ). [ ] in view of the assumption, shared by mr. russell, that there is such a thing as non-inferential knowledge, the conception that a thing offers evidence for itself needs analysis. self-evidence is merely a convenient term for disguising the difference between the indubitably given and the believed in. hypotheses, for example, are self-evident sometimes, that is, obviously present for just what they are, but they are still hypotheses, and to offer their self-evident character as "evidence" would expose one to ridicule. meanings may be self-evident (the cartesian "clear and distinct") and truth dubious. [ ] "really known" is an ambiguous term. it may signify _understood_, or it may signify known to be _there_ or _given_. either meaning implies reference beyond. [ ] the reply implies that the exhaustive, all-at-once perception of the entire universe assumed by some idealistic writers does not involve any external world. i do not make this remark for the sake of identifying myself with this school of thinkers, but to suggest that the limited character of empirical data is what occasions inference. but it is a fallacy to suppose that the nature of the limitations is psychologically given. on the contrary, they have to be determined by descriptive identifications which involve reference to the more extensive world. hence no matter how "self-evident" the existence of the data may be, it is never self-evident that they are rightly delimited with respect to the specific inference in process of making. [ ] the ambiguities reside in the possibility of treating the "muscular and other bodily sensations" as meaning something other than data of motion and corporealness--however these be defined. muscular sensation may be an awareness of motion of the muscles, but the phrase "of the muscles" does not alter the nature of motion as motion; it only specifies _what_ motion is involved. and the long controversy about the existence of immediate "muscular sensations" testifies to what a complex cognitive determination we are here dealing with. anatomical directions and long experimentation were required to answer the question. were they psychologically primitive data no such questions could ever have arisen. xii what pragmatism means by practical pragmatism, according to mr. james, is a temper of mind, an attitude; it is also a theory of the nature of ideas and truth; and, finally, it is a theory about reality. it is pragmatism as method which is emphasized, i take it, in the subtitle, "a new name for some old ways of thinking."[ ] it is this aspect which i suppose to be uppermost in mr. james's own mind; one frequently gets the impression that he conceives the discussion of the other two points to be illustrative material, more or less hypothetical, of the method. the briefest and at the same time the most comprehensive formula for the method is: "the attitude of looking away from first things, principles, 'categories,' supposed necessities; and of looking towards last things, fruits, consequences, facts" (pp. - ). and as the attitude looked "away from" is the rationalistic, perhaps the chief aim of the lectures is to exemplify some typical differences resulting from taking one outlook or the other. but pragmatism is "used in a still wider sense, as meaning also a certain theory of truth" (p. ); it is "a genetic theory of what is meant by truth" (p. ). truth means, as a matter of course, agreement, correspondence, of idea and fact (p. ), but what do agreement, correspondence, mean? with rationalism they mean "a static, inert relation," which is so ultimate that of it nothing more can be said. with pragmatism they signify the guiding or leading power of ideas by which we "dip into the particulars of experience again," and if by its aid we set up the arrangements and connections among experienced objects which the idea intends, the idea is verified; it corresponds with the things it means to square with (pp. - ). the idea is true which works in leading us to what it purports (p. ).[ ] or, "any idea that will carry us prosperously from any one part of experience to any other part, linking things satisfactorily, working securely, simplifying, saving labor, is true for just so much, true in so far forth" (p. ). this notion presupposes that ideas are essentially intentions (plans and methods), and that what they, as ideas, ultimately intend is _prospective_--certain changes in prior existing things. this contrasts again with rationalism, with its copy theory, where ideas, _as_ ideas, are ineffective and impotent, since they mean only to mirror a reality (p. ) complete without them. thus we are led to the third aspect of pragmatism. the alternative between rationalism and pragmatism "concerns the structure of the universe itself" (p. ). "the essential contrast is that reality ... for pragmatism is still in the making" (p. ). and in a recent number of the _journal of philosophy, psychology, and scientific methods_,[ ] he says: "i was primarily concerned in my lectures with contrasting the belief that the world is still in the process of making with the belief that there is an eternal edition of it ready-made and complete." i it will be following mr. james's example, i think, if we here regard pragmatism as primarily a method, and treat the account of ideas and their truth and of reality somewhat incidentally so far as the discussion of them serves to exemplify or enforce the method. regarding the attitude of orientation which looks to outcomes and consequences, one readily sees that it has, as mr. james points out, points of contact with historic empiricism, nominalism, and utilitarianism. it insists that general notions shall "cash in" as particular objects and qualities in experience; that "principles" are ultimately subsumed under facts, rather than the reverse; that the empirical consequence rather than the a priori basis is the sanctioning and warranting factor. but all of these ideas are colored and transformed by the dominant influence of experimental science: the method of treating conceptions, theories, etc., as working hypotheses, as directors for certain experiments and experimental observations. pragmatism as attitude represents what mr. peirce has happily termed the "laboratory habit of mind" extended into every area where inquiry may fruitfully be carried on. a scientist would, i think, wonder not so much at the method as at the lateness of philosophy's conversion to what has made science what it is. nevertheless it is impossible to forecast the intellectual change that would proceed from carrying the method sincerely and unreservedly into all fields of inquiry. leaving philosophy out of account, what a change would be wrought in the historical and social sciences--in the conceptions of politics and law and political economy! mr. james does not claim too much when he says: "the center of gravity of philosophy must alter its place. the earth of things, long thrown into shadow by the glories of the upper ether, must resume its rights.... it will be an alteration in the 'seat of authority' that reminds one almost of the protestant reformation" (p. ). i can imagine that many would not accept this method in philosophy for very diverse reasons, perhaps among the most potent of which is lack of faith in the power of the elements and processes of experience and life to guarantee their own security and prosperity; because, that is, of the feeling that the world of experience is so unstable, mistaken, and fragmentary that it must have an absolutely permanent, true, and complete ground. i cannot imagine, however, that so much uncertainty and controversy as actually exists should arise about the content and import of the doctrine on the basis of the general formula. it is when the method is applied to special points that questions arise. mr. james reminds us in his preface that the pragmatic movement has found expression "from so many points of view, that much unconcerted statement has resulted." and speaking of his lectures he goes on to say: "i have sought to unify the picture as it presents itself to my own eyes, dealing in broad strokes." the "different points of view" here spoken of have concerned themselves with viewing pragmatically a number of different things. and it is, i think, mr. james's effort to combine them, as they stand, which occasions misunderstanding among mr. james's readers. mr. james himself applied it, for example, in to philosophic controversies to indicate what they mean in terms of practical issues at stake. before that, mr. peirce himself (in ) had applied the method to the proper way of _conceiving_ and defining objects. then it has been applied to _ideas_ in order to find out what they mean in terms of what they intend, and what and how they must intend in order to be true. again, it has been applied to _beliefs_, to what men actually accept, hold to, and affirm. indeed, it lies in the nature of pragmatism that it should be applied as widely as possible; and to things as diverse as controversies, beliefs, truths, ideas, and objects. but yet the situations and problems _are_ diverse; so much so that, while the meaning of each may be told on the basis of "last things," "fruits," "consequences," "facts," _it is quite certain that the specific last things and facts will be very different in the diverse cases, and that very different types of meaning will stand out_. "meaning" will itself _mean_ something quite different in the case of "objects" from what it will mean in the case of "ideas," and for "ideas" something different from "truths." now the explanation to which i have been led of the unsatisfactory condition of contemporary pragmatic discussion is that in composing these "different points of view" into a single pictorial whole, the distinct type of consequence and hence of meaning of "practical" appropriate to each has not been sufficiently emphasized. . when we consider separately the subjects to which the pragmatic method has been applied, we find that mr. james has provided the necessary formula for each--with his never-failing instinct for the concrete. we take first the question of the significance of an object: the meaning which should properly be contained in its conception or definition. "to attain perfect clearness in our thoughts of an object, then, we need only consider what conceivable effects of a practical kind the object may involve--what sensations we are to expect from it and what reactions we must prepare" (pp. - ). or, more shortly, as it is quoted from ostwald, "all realities influence our practice, and that influence is their meaning for us" (p. ). here it will be noted that the start is from objects already empirically given or presented, existentially vouched for, and the question is as to their proper conception--what is the proper meaning, or idea, of an object? and the meaning is the effects _these given objects produce_. one might doubt the correctness of this theory, but i do not see how one could doubt its import, or could accuse it of subjectivism or idealism, since the object with its power to produce effects is assumed. meaning is expressly distinguished from objects, not confused with them (as in idealism), and is said to consist in the practical reactions objects exact of us or impose upon us. when, then, it is a question of an object, "meaning" signifies its _conceptual content or connotation, and "practical" means the future responses which an object requires of us or commits us to_. . but we may also start from a given idea, and ask what the _idea_ means. pragmatism will, of course, look to future consequences, but they will clearly be of a different sort when we start from an idea as idea, than when we start from an object. for what an idea as idea means, is precisely that an object is _not_ given. the pragmatic procedure here is to set the idea "at work within the stream of experience. it appears less as a solution than as a program for more work, and particularly as an indication of the ways in which existing realities may be changed. theories, thus, become instruments.... we don't lie back on them, we move forward, and, on occasion, make nature over again by their aid" (p. ). in other words, an idea is a draft drawn upon existing things, and intention to act so as to arrange them in a certain way. from which it follows that if the draft is honored, if existences, following upon the actions, rearrange or readjust themselves in the way the idea intends, the idea is true. when, then, it is a question of an idea, it is the idea itself which is practical (being an intent) and its _meaning_ resides in the existences which, as changed, it intends. while the meaning of an object is the changes it requires in our attitude,[ ] the meaning of an idea is the changes it, as our attitude, effects in objects. . then we have another formula, applicable not to objects nor ideas as objects and ideas, but to _truths_--to things, that is, where the meaning of the object and of the idea is assumed to be already ascertained. it reads: "what difference would it practically make to anyone if this notion rather than that notion were true? if no practical difference whatever can be traced, then the alternatives mean practically the same thing, and all dispute is idle" (p. ). there can be "no difference in abstract truth that doesn't express itself in a difference in concrete fact, and in conduct consequent upon the fact, imposed on somebody" (p. ).[ ] now when we start with something which is already a truth (or taken to be truth), and ask for its meaning in terms of its consequences, it is implied that the conception, or conceptual significance, is already clear, and that the existences it refers to are already in hand. meaning here, then, can be neither the connotative nor denotative reference of a term; they are covered by the two prior formulae. meaning here means _value_, importance. the practical factor is, then, the worth character of these consequences: they are good or bad; desirable or undesirable; or merely _nil_, indifferent, in which latter case belief is idle, the controversy a vain and conventional, or verbal, one. the term "meaning" and the term "practical" taken in isolation, and without explicit definition from their specific context and problem, are triply ambiguous. the meaning may be the conception or definition of an _object_; it may be the denotative existential reference of an _idea_; it may be actual value or _importance_. so practical in the corresponding cases may mean the attitudes and conduct exacted of us by objects; or the capacity and tendency of an idea to effect changes in prior existences; or the desirable and undesirable quality of certain ends. the general pragmatic attitude, none the less, is applied in all cases. if the differing problems and the correlative diverse significations of the terms "meaning" and "practical" are borne in mind, not all will be converted to pragmatism, but the present uncertainty as to what pragmatism is, anyway, and the present constant complaints on both sides of misunderstanding will, i think, be minimized. at all events, i have reached the conclusion that what the pragmatic movement just now wants is a clear and consistent bearing in mind of these different problems and of what is meant by practical in each. accordingly the rest of this paper is an endeavor to elucidate from the standpoint of pragmatic method the importance of enforcing these distinctions. ii first, as to the problems of philosophy when pragmatically approached, mr. james says: "the whole function of philosophy ought to be to find out what definite difference it will make to you and me, at definite instants of our life, if this world-formula or that world-formula be true" (p. ). here the world-formula is assumed as already given; it is there, defined and constituted, and the question is as to its import if believed. but from the second standpoint, that of idea as working hypothesis, the chief function of philosophy is not to find out what difference ready-made formulae make, _if true_, but to arrive at and to clarify their _meaning as programs of behavior for modifying the existent world_. from this standpoint, the meaning of a world-formula is practical and moral, not merely in the consequences which flow from accepting a certain conceptual content as true, but as regards that content itself. and thus at the very outset we are compelled to face this question: does mr. james employ the pragmatic method to discover the value in terms of consequences in life of some formula which has its logical content already fixed; or does he employ it to criticize and revise and, ultimately, to constitute the meaning of that formula? if it is the first, there is danger that the pragmatic method will be employed only to vivify, if not validate, doctrines which in themselves are pieces of rationalistic metaphysics, not inherently pragmatic. if the last, there is danger that some readers will think old notions are being confirmed, when in truth they are being translated into new and inconsistent notions. consider the case of design. mr. james begins with accepting a ready-made notion, to which he then applies the pragmatic criterion. the traditional notion is that of a "seeing force that runs things." this is rationalistically and retrospectively empty; its being there makes no difference. (this seems to overlook the fact that the past world may be just what it is in virtue of the difference which a blind force or a seeing force has already made in it. a pragmatist as well as a rationalist may reply that it makes no difference retrospectively only because we leave out the most important retrospective difference). but "returning with it into experience, we gain a more confiding outlook on the future. if not a blind force, but a seeing force, runs things, we may reasonably expect better issues. _this vague confidence in the future is the sole pragmatic meaning at present discernible in the terms design and designer_" (p. , italics mine). now is this meaning intended to _replace_ the meaning of a "seeing force which runs things"? or is it intended to superadd a pragmatic value and validation to that concept of a seeing force? or does it mean that, irrespective of the existence of any such object, a belief in it has that value? strict pragmatism would seem to require the first interpretation. the same difficulties arise in the discussion of spiritualistic theism _versus_ materialism. compare the two following statements: "the notion of god ... guarantees an ideal order that shall be permanently preserved" (p. ). "here, then, in these different emotional and practical appeals, in these adjustments of our attitudes of hope and expectation, and all the delicate consequences which their differences entail, _lie the real meanings of materialism and spiritualism_" (p. , italics mine). does the latter method of determining the meaning of, say, a spiritual god afford the substitute for the conception of him as a "superhuman power" effecting the eternal preservation of something; does it, that is, define god, supply the content for our notion of god? or does it merely superadd a value to a meaning already fixed? and, if the latter, does the object, god as defined, or the notion, or the belief (the acceptance of the notion) effect these consequent values? in either of the latter alternatives, the good or valuable consequences cannot clarify the meaning or conception of god; for, by the argument, they proceed from a prior definition of god. they cannot prove, or render more probable, the existence of such a being, for, by the argument, these desirable consequences depend upon accepting such an existence; and not even pragmatism can prove an existence from desirable consequences which themselves exist only when and if that other existence is there. on the other hand, if the pragmatic method is not applied simply to tell the value of a belief or controversy, but to fix the meaning of the terms involved in the belief, resulting consequences would serve to constitute the entire meaning, intellectual as well as practical, of the terms; and hence the pragmatic method would simply abolish the meaning of an antecedent power which will perpetuate eternally some existence. for that consequence flows not from the belief or idea, but from the existence, the power. it is not pragmatic at all. accordingly, when mr. james says: "other than this _practical_ significance, the words god, free will, design, _have none_. yet dark though they be in themselves, or intellectualistically taken, when we bear them on to life's thicket with us, the darkness then grows light about us" (p. , italics mine), what is meant? is it meant that when we take the intellectualistic notion and employ it, it gets value in the way of results, and hence then has some value of its own; or is it meant that the intellectual content itself must be determined in terms of the changes effected in the ordering of life's thicket? an explicit declaration on this point would settle, i think, not merely a point interesting in itself, but one essential to the determination of what is pragmatic method. for myself, i have no hesitation in saying that it seems unpragmatic for pragmatism to content itself with finding out the value of a conception whose own inherent significance pragmatism has not first determined; a fact which entails that it be taken not as a truth but simply as a working hypothesis. in the particular case in question, moreover, it is difficult to see how the pragmatic method could possibly be applied to a notion of "eternal perpetuation," which, by its nature, can never be empirically verified, or cashed in any particular case. this brings us to the question of truth. the problem here is also ambiguous in advance of definition. does the problem of what is truth refer to discovering the "true meaning" of something; or to discovering what an idea has to effect, and how, in order to be true; or to discovering what the value of truth is when it is an existent and accomplished fact? ( ) we may, of course, find the "true meaning" of a thing, as distinct from its incorrect interpretation, without thereby establishing the truth of the "true meaning"--as we may dispute about the "true meaning" of a passage in the classics concerning centaurs, without the determination of its true sense establishing the truth of the notion that there are centaurs. occasionally this "true meaning" seems to be what mr. james has in mind, as when, after the passage upon design already quoted, he goes on: "but if cosmic confidence is right, not wrong, better, not worse, that [vague confidence in the future] is a most important meaning. that much at least of possible 'truth' the terms will then have in them" (p. ). "truth" here seems to mean that design has a genuine, not merely conventional or verbal, meaning: that something is at stake. and there are frequently points where "truth" seems to mean just meaning that is genuine as distinct from empty or verbal. ( ) but the problem of the meaning of truth may also refer to the meaning or value of truths that already exist as truths. we have them; they exist; now what do they mean? the answer is: "true ideas lead us into useful verbal and conceptual quarters as well as directly up to useful sensible termini. they lead to consistency, stability, and flowing human intercourse" (p. ). this, referring to things already true, i do not suppose the most case-hardened rationalist would question; and even if he questions the pragmatic contention that these consequences define the meaning of truth, he should see that here is not given an account of what it means for an idea to _become true_, but only of what it means _after_ it has become true, truth as _fait accompli_. it is the meaning of truth as _fait accompli_ which is here defined. bearing this in mind, i do not know why a mild-tempered rationalist should object to the doctrine that truth is valuable not _per se_, but because, when given, it leads to desirable consequences. "the true thought is useful here because the home which is its object is useful. the practical value of true ideas is thus primarily derived from the practical importance of their objects to us" (p. ). and many besides confirmed pragmatists, any utilitarian, for example, would be willing to say that our duty to pursue "truth" is conditioned upon its leading to objects which upon the whole are valuable. "the concrete benefits we gain are what we mean by calling the pursuit a duty" (p. , compare p. ). ( ) difficulties have arisen chiefly because mr. james is charged with converting simply the foregoing proposition, and arguing that since true ideas are good, any idea if good in any way is true. certainly transition from one of these conceptions to the other is facilitated by the fact that ideas are tested as to their validity by a certain goodness, viz., whether they are good for accomplishing what they intend, for what they claim to be good for, that is, certain modifications in prior given existences. in this case, it is the idea which is practical, since it is essentially an intent and plan of altering prior existences in a specific situation, which is indicated to be unsatisfactory by the very fact that it needs or suggests a specific modification. then arises the theory that ideas as ideas are always working hypotheses concerning the attaining of particular empirical results, and are tentative programs (or sketches of method) for attaining them. if we stick consistently to this notion of ideas, only _consequences which are actually produced by the working of the idea in co-operation with, or application to, prior existences are good consequences in the specific sense of good which is relevant to establishing the truth of an idea_. this is, at times, unequivocally recognized by mr. james. (see, for example, the reference to veri-_fication_, on p. ; the acceptance of the idea that verification means the advent of the object intended, on p. .) but at other times any good which flows from acceptance of a belief is treated as if it were an evidence, _in so far_, of the truth of the idea. this holds particularly when theological notions are under consideration. light would be thrown upon how mr. james conceives this matter by statements on such points as these: if ideas terminate in good consequences, but yet the goodness of the consequences was no part of the intention of an idea, does the goodness have any verifying force? if the goodness of consequences arises from the context of the idea in belief rather than from the idea itself, does it have any verifying force?[ ] if an idea leads to consequences which are good in the _one_ respect only of fulfilling the intent of the idea (as when one drinks a liquid to test the idea that it is a poison), does the badness of the consequences in every other respect detract from the verifying force of consequences? since mr. james has referred to me as saying "truth is what gives satisfaction" (p. ), i may remark (apart from the fact that i do not think i ever said that truth is what _gives_ satisfaction) that i have never identified any satisfaction with the truth of an idea, save _that_ satisfaction which arises when the idea as working hypothesis or tentative method is applied to prior existences in such a way as to fulfil what it intends. my final impression (which i cannot adequately prove) is that upon the whole mr. james is most concerned to enforce, as against rationalism, two conclusions about the character of truths as _faits accomplis_: namely, that they are made, not a priori, or eternally in existence,[ ] and that their value or importance is not static, but dynamic and practical. the special question of _how_ truths are made is not particularly relevant to this anti-rationalistic crusade, while it is the chief question of interest to many. because of this conflict of problems, what mr. james says about the value of truth when accomplished is likely to be interpreted by some as a criterion of the truth of ideas; while, on the other hand, mr. james himself is likely to pass lightly from the consequences that determine the worth of a belief to those which decide the worth of an idea. when mr. james says the function of giving "satisfaction in marrying previous parts of experience with newer parts" is necessary in order to establish truth, the doctrine is unambiguous. the satisfactory character of consequences is itself measured and defined by the conditions which led up to it; the inherently satisfactory quality of results is not taken as validating the antecedent intellectual operations. but when he says (not of his own position, but of an opponent's[ ]) of the idea of an absolute, "so far as it affords such comfort it surely is not sterile, it has that amount of value; it performs a concrete function. as a good pragmatist i myself ought to call the absolute true _in so far forth_ then; and i unhesitatingly now do so" (p. ), the doctrine seems to be as unambiguous in the other direction: that any good, consequent upon acceptance of a belief is, in so far forth,[ ] a warrant of truth. in such passages as the following (which are of the common type) the two notions seem blended together: "ideas become true just in so far as they help us to get into satisfactory relations with other parts of our experience" (p. ); and, again, on the same page: "any idea that will carry us _prosperously_ from any one part of our experience to any other part, linking things _satisfactorily_, working securely, simplifying, saving labor, is true for just so much" (italics mine). an explicit statement as to whether the carrying function, the linking of things, is satisfactory and prosperous and hence true in so far as it executes the intent of an idea; or whether the satisfaction and prosperity reside in the material consequences on their own account and in that aspect make the idea true, would, i am sure, locate the point at issue and economize and fructify future discussion. at present pragmatism is accepted by those whose own notions are thoroughly rationalistic in make-up as a means of refurbishing, galvanizing, and justifying those very notions. it is rejected by non-rationalists (empiricists and naturalistic idealists) because it seems to them identified with the notion that pragmatism holds that the desirability of certain beliefs overrides the question of the meaning of the ideas involved in them and the existence of objects denoted by them. others (like myself), who believe thoroughly in pragmatism as a method of orientation, as defined by mr. james, and who would apply the method to the determination of the meaning of objects, the intent and worth of ideas as ideas, and to the human and moral value of beliefs, when these various problems are carefully distinguished from one another, do not know whether they are pragmatists in some other sense, because they are not sure whether the practical, in the sense of desirable facts which define the worth of a belief, is confused with the practical as an attitude imposed by objects, and with the practical as a power and function of ideas to effect changes in prior existences. hence the importance of knowing which one of the three senses of practical is conveyed in any given passage. it would do mr. james an injustice, however, to stop here. his real doctrine is that a belief is true when it satisfies both personal needs and the requirements of objective things. speaking of pragmatism, he says, "her only test of probable truth is what works best in the way of _leading us_, what fits every part of life best and _combines with the collectivity of experience's demands_, nothing being omitted" (p. , italics mine). and again, "that new idea is truest which performs most felicitously its function of satisfying _our double urgency_" (p. ). it does not appear certain from the context that this "double urgency" is that of the personal and the objective demands, respectively, but it is probable (see, also, p. , where "consistency with previous truth and novel fact" is said to be "always the most imperious claimant"). on this basis, the "in so far forth" of the truth of the absolute because of the comfort it supplies, means that one of the two conditions which need to be satisfied has been met, so that if the idea of the absolute met the other one also, it would be quite true. i have no doubt this is mr. james's meaning, and it sufficiently safeguards him from the charge that pragmatism means that anything which is agreeable is true. at the same time, i do not think, in logical strictness, that satisfying one of two tests, when satisfaction of both is required, can be said to constitute a belief true even "in so far forth." iii at all events this raises a question not touched so far: the place of the personal in the determination of truth. mr. james, for example, emphasizes the doctrine suggested in the following words: "we say this theory solves it [the problem] more satisfactorily than that theory; but that means more satisfactorily _to ourselves_, and individuals will emphasize their points of satisfaction differently" (p. , italics mine). this opens out into a question which, in its larger aspects--the place of the personal factor in the constitution of knowledge systems and of reality--i cannot here enter upon, save to say that a synthetic pragmatism such as mr. james has ventured upon will take a very different form according as the point of view of what he calls the "chicago school" or that of humanism is taken as a basis for interpreting the nature of the personal. according to the latter view, the personal appears to be ultimate and unanalyzable, the metaphysically real. associations with idealism, moreover, give it an idealistic turn, a translation, in effect, of monistic intellectualistic idealism into pluralistic, voluntaristic idealism. but, according to the former, the personal is not ultimate, but is to be analyzed and defined, biologically on its genetic side, ethically on its prospective and functioning side. there is, however, one phase of the teaching illustrated by the quotation which is directly relevant here. because mr. james recognizes that the personal element enters into judgments passed upon whether a problem has or has not been satisfactorily solved, he is charged with extreme subjectivism, with encouraging the element of personal preference to run rough-shod over all objective controls. now the question raised in the quotation is primarily one of fact, not of doctrine. is or is not a personal factor found in truth evaluations? if it is, pragmatism is not responsible for introducing it. if it is not, it ought to be possible to refute pragmatism by appeal to empirical fact, rather than by reviling it for subjectivism. now it is an old story that philosophers, in common with theologians and social theorists, are as sure that personal habits and interests shape their opponents' doctrines as they are that their own beliefs are "absolutely" universal and objective in quality. hence arises that dishonesty, that insincerity characteristic of philosophic discussion. as mr. james says (p. ), "the most potential of all our premises is never mentioned." now the moment the complicity of the personal factor in our philosophic valuations is recognized, is recognized fully, frankly, and generally, that moment a new era in philosophy will begin. we shall have to discover the personal factors that now influence us unconsciously, and begin to accept a new and moral responsibility for them, a responsibility for judging and testing them by their consequences. so long as we ignore this factor, its deeds will be largely evil, not because _it_ is evil, but because, flourishing in the dark, it is without responsibility and without check. the only way to control it is by recognizing it. and while i would not prophesy of pragmatism's future, i would say that this element which is now so generally condemned as intellectual dishonesty (perhaps because of an uneasy, instinctive recognition of the searching of hearts its acceptance would involve) will in the future be accounted unto philosophy for righteousness' sake. so much in general. in particular cases, it is possible that mr. james's language occasionally leaves the impression that the fact of the inevitable involution of the personal factor in every belief gives some special sanction to some special belief. mr. james says that his essay on the _right_ to believe was unluckily entitled the "_will_ to believe" (p. ). well, even the term "right" is unfortunate, if the personal or belief factor is inevitable--unfortunate because it seems to indicate a privilege which might be exercised in special cases, in religion, for example, though not in science; or, because it suggests to some minds that the fact of the personal complicity involved in belief is a warrant for this or that special personal attitude, instead of being a warning to locate and define it so as to accept responsibility for it. if we mean by "will" not something deliberate and consciously intentional (much less, something insincere), but an active personal participation, then belief _as_ will, rather than either the right or the will to believe seems to phrase the matter correctly. i have attempted to review not so much mr. james's book as the present status of the pragmatic movement which is expressed in the book; and i have selected only those points which seem to bear directly upon matters of contemporary controversy. even as an account of this limited field, the foregoing pages do an injustice to mr. james, save as it is recognized that his lectures were "popular lectures," as the title-page advises us. we cannot expect in such lectures the kind of explicitness which would satisfy the professional and technical interests that have inspired this review. moreover, it is inevitable that the attempt to compose different points of view, hitherto unco-ordinated, into a single whole should give rise to problems foreign to any one factor of the synthesis, left to itself. the need and possibility of the discrimination of various elements in the pragmatic meaning of "practical," attempted in this review, would hardly have been recognized by me were it not for by-products of perplexity and confusion which mr. james's combination has effected. mr. james has given so many evidences of the sincerity of his intellectual aims, that i trust to his pardon for the injustice which the character of my review may have done _him_, in view of whatever service it may render in clarifying the problem to which he is devoted. as for the book itself, it is in any case beyond a critic's praise or blame. it is more likely to take place as a philosophical classic than any other writing of our day. a critic who should attempt to appraise it would probably give one more illustration of the sterility of criticism compared with the productiveness of creative genius. even those who dislike pragmatism can hardly fail to find much of profit in the exhibition of mr. james's instinct for concrete facts, the breadth of his sympathies, and his illuminating insights. unreserved frankness, lucid imagination, varied contacts with life digested into summary and trenchant conclusions, keen perceptions of human nature in the concrete, a constant sense of the subordination of philosophy to life, capacity to put things into an english which projects ideas as if bodily into space till they are solid things to walk around and survey from different sides--these things are not so common in philosophy that they may not smell sweet even by the name of pragmatism. footnotes: [ ] william james, _pragmatism. a new name for some old ways of thinking._ (popular lectures on philosophy.) new york: longmans, green, & co., . pp. xiii[+] . [ ] certain aspects of the doctrine are here purposely omitted, and will meet us later. [ ] vol. iv, p. . [ ] only those who have already lost in the idealistic confusion of existence and meaning will take this to mean that the object is those changes in our reactions. [ ] i assume that the reader is sufficiently familiar with mr. james's book not to be misled by the text into thinking that mr. james himself discriminates as i have done these three types of problems from one another. he does not; but, none the less, the three formulae for the three situations are there. [ ] the idea of immortality, or the traditional theistic idea of god, for example, may produce its good consequences, not in virtue of the idea as idea, but from the character of the person who entertains the belief; or it may be the idea of the supreme value of ideal considerations, rather than that of their temporal duration, which works. [ ] "eternal truth" is one of the most ambiguous phrases that philosophers trip over. it may mean eternally in existence; or that a statement which is ever true is always true (if it is true a fly is buzzing, it is eternally true that just now a fly buzzed); or it may mean that some truths, _in so far as wholly conceptual_, are irrelevant to any particular time determination, since they are non-existential in import--e.g., the truth of geometry dialectically taken--that is, without asking whether any particular existence exemplifies them. [ ] such statements, it ought in fairness to be said, generally come when mr. james is speaking of a doctrine which he does not himself believe, and arise, i think, in that fairness and frankness of mr. james, so unusual in philosophers, which cause him to lean over backward--unpragmatically, it seems to me. as to the claim of his own doctrine, he consistently sticks to his statement: "pent in, as the pragmatist, more than any one, sees himself to be, between the whole body of funded truths squeezed from the past and the coercions of the world of sense about him, who, so well as he, feels the immense pressure of objective control under which our minds perform their operations? if anyone imagines that this law is lax, let him keep its commandments one day, says emerson" (p. ). [ ] of course, mr. james holds that this "in so far" goes a very small way. see pp. - . but even the slightest concession is, i think, non-pragmatic unless the satisfaction is relevant to the idea as intent. now the satisfaction in question comes not from the idea as _idea_, but from its acceptance as _true_. can a satisfaction dependent on an assumption that an idea is already true be relevant to testing the truth of an idea? and can an idea, like that of the absolute, which, if true, "absolutely" precludes any appeal to consequences as test of truth, be confirmed by use of the pragmatic test without sheer self-contradiction? in other words, we have a confusion of the test of an idea as idea, with that of the value of a belief as belief. on the other hand, it is quite possible that all mr. james intends by truth here is true (i.e., genuine) meaning at stake in the issue--true not as distinct from false, but from meaningless or verbal. xiii an added note as to the "practical" it is easier to start a legend than to prevent its continued circulation. no misconception of the instrumental logic has been more persistent than the belief that it makes knowledge merely a means to a practical end, or to the satisfaction of practical needs--practical being taking to signify some quite definite utilities of a material or bread-and-butter type. habitual associations aroused by the word "pragmatic" have been stronger than the most explicit and emphatic statements which any pragmatist has been able to make. but i again affirm that the term "pragmatic" means only the rule of referring all thinking, all reflective considerations, to _consequences_ for final meaning and test. nothing is said about the nature of the consequences; they may be aesthetic, or moral, or political, or religious in quality--anything you please. all that the theory requires is that they be in some way consequences of thinking; not, indeed, of it alone, but of it acted upon in connection with other things. this is no after-thought inserted to lessen the force of objections. mr. peirce explained that he took the term "pragmatic" from kant, in order to denote empirical consequences. when he refers to their practical character it is only to indicate a criterion by which to avoid purely verbal disputes. different consequences are alleged to constitute rival meanings of a term. is a difference more than merely one of formulation? the way to get an answer is to ask whether, if realized, these consequences would exact of us different modes of behavior. if they do not make such a difference in conduct the difference between them is conventional. it is not that consequences are themselves practical, but that practical consequences from them may at times be appealed to in order to decide the specific question of whether two proposed meanings differ save in words. mr. james says expressly that what is important is that the consequences should be specific, not that they should be active. when he said that general notions must "cash in," he meant of course that they must be translatable into verifiable specific things. but the words "cash in" were enough for some of his critics, who pride themselves upon a logical rigor unattainable by mere pragmatists. in the logical version of pragmatism termed instrumentalism, action or practice does indeed play a fundamental rôle. but it concerns not the nature of consequences but the nature of knowing. to use a term which is now more fashionable (and surely to some extent in consequence of pragmatism) than it was earlier, instrumentalism means a behaviorist theory of thinking and knowing. it means that knowing is literally something which we do; that analysis is ultimately physical and active; that meanings in their logical quality are standpoints, attitudes, and methods of behaving toward facts, and that active experimentation is essential to verification. put in another way it holds that thinking does not mean any transcendent states or acts suddenly introduced into a previously natural scene, but that the operations of knowing are (or are artfully derived from) natural responses of the organism, which constitute knowing in virtue of the situation of doubt in which they arise and in virtue of the uses of inquiry, reconstruction, and control to which they are put. there is no warrant in the doctrine for carrying over _this_ practical quality into the consequences in which action culminates, and by which it is tested and corrected. a knowing as an act is instrumental to the resultant controlled and more significant situation; this does not imply anything about the intrinsic or the instrumental character of the consequent situation. that is whatever it may be in a given case. there is nothing novel nor heterodox in the notion that thinking is instrumental. the very word is redolent of an _organum_--whether _novum_ or _veterum_. the term "instrumentality," applied to thinking, raises at once, however, the question of whether thinking as a tool falls within or without the subject-matter which it shapes into knowledge. the answer of formal logic (adopted moreover by kant and followed in some way by all neo-kantian logics) is unambiguous. to call logic "formal" means precisely that mind or thought supplies forms foreign to the original subject-matter, but yet required in order that it should have the appropriate form of knowledge. in this regard it deviates from the aristotelian _organon_ which it professes to follow. for according to aristotle, the processes of knowing--of teaching and learning--which lead up to knowledge are but the actualization through the potentialities of the human body of the _same_ forms or natures which are previously actualized in nature through the potentialities of extra-organic bodies. thinking which is not instrumental to truth, which is merely formal in the modern sense, would have been a monstrosity inconceivable to him. but the discarding of the metaphysics of form and matter, of cyclic actualizations and eternal species, deprived the aristotelian "thought" of any place within the scheme of things, and left it an activity with forms alien to subject-matter. to conceive of thinking as instrumental to truth or knowledge, and as a tool shaped out of the same subject-matter as that to which it is applied, is but to return to the aristotelian tradition about logic. that the practice of science has in the meantime substituted a logic of experimental discovery (of which definition and classification are themselves but auxiliary tools) for a logic of arrangement and exposition of what is already known, necessitates, however, a very different sort of _organon_. it makes necessary the conception that the object of knowledge is not something with which thinking sets out, but something with which it ends: something which the processes of inquiry and testing, that constitute thinking, themselves produce. thus the object of knowledge is practical in the sense that it depends upon a specific kind of practice for its existence--for its existence as an object of knowledge. how practical it may be in any other sense than this is quite another story. the _object of knowledge_ marks an achieved triumph, a secured control--that holds by the very nature of knowledge. what other uses it may have depends upon its own inherent character, not upon anything in the nature of knowledge. we do not know the origin and nature and the cure of malaria till we can both produce and eliminate malaria; the _value_ of either the production or the removal depends upon the character of malaria in relation to other things. and so it is with mathematical knowledge, or with knowledge of politics or art. their respective objects are not known till they are made in course of the process of experimental thinking. their usefulness when made is whatever, from infinity to zero, experience may subsequently determine it to be. xiv the logic of judgments of practice their nature in introducing the discussion, i shall first say a word to avoid possible misunderstandings. it may be objected that such a term as "practical judgment" is misleading; that the term "practical judgment" is a misnomer, and a dangerous one, since all judgments by their very nature are intellectual or theoretical. consequently, there is a danger that the term will lead us to treat as judgment and knowledge something which is not really knowledge at all and thus start us on the road which ends in mysticism or obscurantism. all this is admitted. i do not mean by practical judgment a type of judgment having a different organ and source from other judgments. i mean simply a kind of judgment having a specific type of subject-matter. propositions exist relating to _agenda_--to things to do or be done, judgments of a situation demanding action. there are, for example, propositions of the form: m. n. should do thus and so; it is better, wiser, more prudent, right, advisable, opportune, expedient, etc., to act thus and so. and this is the type of judgment i denote practical. it may also be objected that this type of subject-matter is not distinctive; that there is no ground for marking it off from judgments of the form _sp_, or _mrn_. i am willing, again, to admit that such may turn out to be the fact. but meanwhile the prima facie difference is worth considering, if only for the sake of reaching a conclusion as to whether or no there is a kind of subject-matter so distinctive as to imply a distinctive logical form. to assume in advance that the subject-matter of practical judgments _must_ be reducible to the form _sp_ or _mrn_ is assuredly as gratuitous as the contrary assumption. it begs one of the most important questions about the world which can be asked: the nature of time. moreover, current discussion exhibits, if not a complete void, at least a decided lacuna as to propositions of this type. mr. russell has recently said that of the two parts of logic the first enumerates or inventories the different kinds or forms of propositions.[ ] it is noticeable that he does not even mention this kind as a possible kind. yet it is conceivable that this omission seriously compromises the discussion of other kinds. additional specimens of practical judgments may be given: he had better consult a physician; it would not be advisable for you to invest in those bonds; the united states should either modify its monroe doctrine or else make more efficient military preparations; this is a good time to build a house; if i do that i shall be doing wrong, etc. it is silly to dwell upon the practical importance of judgments of this sort, but not wholly silly to say that their practical importance arouses suspicion as to the grounds of their neglect in discussion of logical forms in general. regarding them, we may say: . their subject-matter implies an incomplete situation. this incompleteness is not psychical. something is "there," but what is there does not constitute the entire objective situation. _as_ there, it requires something else. only after this something else has been supplied will the given coincide with the full subject-matter. this consideration has an important bearing upon the conception of the indeterminate and contingent. it is sometimes assumed (both by adherents and by opponents) that the validity of these notions entails that the _given_ is itself indeterminate--which appears to be nonsense. the logical implication is that of a subject-matter as yet _unterminated_, unfinished, or not wholly given. the implication is of future things. moreover, the incompleteness is not personal. i mean by this that the situation is not confined _within_ the one making the judgment; the practical judgment is neither exclusively nor primarily about one's self. on the contrary, it is a judgment about one's self only as it is a judgment about the situation in which one is included, and in which a multitude of other factors external to self are included. the contrary assumption is so constantly made about moral judgments that this statement must appear dogmatic. but surely the prima facie case is that when i judge that i should not give money to the street beggar i am judging the nature of an objective situation, and that the conclusion about myself is governed by the proposition about the situation in which i happen to be included. the full, complex proposition includes the beggar, social conditions and consequences, a charity organization society, etc., on exactly the same footing as it contains myself. aside from the fact that it seems impossible to defend the "objectivity" of moral propositions on any other ground, we may at least point to the fact that judgments of policy, whether made about ourselves or some other agent, are certainly judgments of a _situation_ which is temporarily unfinished. "now is a good time for me to buy certain railway bonds" is a judgment about myself only because it is primarily a judgment about hundreds of factors wholly external to myself. if the genuine existence of such propositions be admitted, the only question about moral judgments is whether or no they are cases of practical judgments as the latter have been defined--a question of utmost importance for moral theory, but not of crucial import for our logical discussion. . their subject-matter implies that the proposition is itself a factor in the completion of the situation, carrying it forward to its conclusion. according as the judgment is that this or that should be done, the situation will, when completed, have this or that subject-matter. the proposition that it is well to do this is a proposition to treat the given in a certain way. since the way is established by the proposition, the proposition is _a_ determining factor in the outcome. as a proposition about the supplementation of the given, it is a factor _in_ the supplementation--and this not as an extraneous matter, something subsequent to the proposition, but in its own logical force. here is found, prima facie at least, a marked distinction of the practical proposition from descriptive and narrative propositions, from the familiar _sp_ propositions and from those of pure mathematics. the latter imply that the proposition does not enter into the constitution of the subject-matter of the proposition. there also is a distinction from another kind of contingent proposition, namely, that which has the form: "he has started for your house"; "the house is still burning"; "it will probably rain." the unfinishedness of the given is implied in these propositions, but it is not implied that the proposition is a factor in determining their completion. . the subject-matter implies that it makes a difference how the given is terminated: that one outcome is better than another, and that the proposition is to be a factor in securing (as far as may be) the better. in other words, there is something objectively at stake in the forming of the proposition. a right or wrong _descriptive_ judgment (a judgment confined to the given, whether temporal, spatial, or subsistent) does not affect its subject-matter; it does not help or hinder its development, for by hypothesis it has no development. but a practical proposition affects the subject-matter for better or worse, for it is a judgment as to the condition (the thing to be done) of the existence of the complete subject-matter.[ ] . a practical proposition is binary. it is a judgment that the given is to be treated in a specified way; it is also a judgment that the given admits of such treatment, that it admits of a specified objective termination. it is a judgment, at the same stroke, of end--the result to be brought about--and of means. ethical theories which disconnect the discussion of ends--as so many of them do--from determination of means, thereby take discussion of ends out of the region of judgment. if there be such ends, they have no intellectual status. to judge that i should see a physician implies that the given elements of the situation should be completed in a specific way and also that they afford the conditions which make the proposed completion practicable. the proposition concerns both resources and obstacles--intellectual determination of elements lying in the way of, say, proper vigor, and of elements which can be utilized to get around or surmount these obstacles. the judgment regarding the need of a physician implies the existence of hindrances in the pursuit of the normal occupations of life, but it equally implies the existence of positive factors which may be set in motion to surmount the hindrances and reinstate normal pursuits. it is worth while to call attention to the reciprocal character of the practical judgment in its bearing upon the statement of means. from the side of the end, the reciprocal nature locates and condemns utopianism and romanticism: what is sometimes called idealism. from the side of means, it locates and condemns materialism and predeterminism: what is sometimes called mechanism. by materialism i mean the conception that the given contains exhaustively the entire subject-matter of practical judgment: that the facts in their givenness are all "there is to it." the given is undoubtedly just what it is; it is determinate throughout. but it is the given _of_ something to be done. the survey and inventory of present conditions (of facts) are not something complete in themselves; they exist for the sake of an intelligent determination of what is to be done, of what is required to complete the given. to conceive the given in any such way, then, as to imply that it negates in its given character the possibility of any doing, of any modification, is self-contradictory. as a part of a practical judgment, the discovery that a man is suffering from an illness is not a discovery that he must suffer, or that the subsequent course of events is determined by his illness; it is the indication of a needed and a possible course by which to restore health. even the discovery that the illness is hopeless falls within this principle. it is an indication not to waste time and money on certain fruitless endeavors, to prepare affairs with respect to death, etc. it is also an indication of search for conditions which will render in the future similar cases remediable, not hopeless. the whole case for the genuineness of practical judgments stands or falls with this principle. it is open to question. but decision as to its validity must rest upon empirical evidence. it cannot be ruled out of court by a dialectic development of the implications of propositions about what is already given or what has already happened. that is, its invalidity cannot be deduced from an assertion that the character of the scientific judgment as a discovery and statement of what is forbids it, much less from an analysis of mathematical propositions. for this method only begs the question. unless the facts are complicated by the surreptitious introduction of some preconception, the prima facie empirical case is that the scientific judgment--the determinate diagnosis--favors instead of forbidding the doctrine of a possibility of change of the given. to overthrow this presumption means, i repeat, to discover specific evidence which makes it impossible. and in view of the immense body of empirical evidence showing that we add to control of what is given (the subject-matter of scientific judgment) by means of scientific judgment, the likelihood of any such discovery seems slight. these considerations throw light upon the proper meaning of (practical) idealism and of mechanism. idealism in action does not seem to be anything except an explicit recognition of just the implications we have been considering. it signifies a recognition that the given is given _as_ obstacles to one course of active development or completion and _as_ resources for another course by which development of the situation directly blocked may be indirectly secured. it is not a blind instinct of hopefulness or that miscellaneous obscurantist emotionalism often called optimism, any more than it is utopianism. it is recognition of the increased liberation and redirection of the course of events achieved through accurate discovery. or, more specifically, it is this recognition operating as a ruling motive in extending the work of discovery and utilizing its results. "mechanism" means the reciprocal recognition on the side of means. it is the recognition of the import within the practical judgment, of the given, of fact, in its determinate character. the facts in their isolation, taken as complete in themselves, are not mechanistic. at most, they just are, and that is the end of them. they are mechanistic as indicating the mechanism, the means, of accomplishing the possibilities which they indicate. apart from a forward look (the anticipation of the future movement of affairs) mechanism is a meaningless conception. there is no sense in applying the conception to a finished world, to any scene which is simply and only done with. propositions regarding a past world, just as past (not as furnishing the conditions of what is to be done), might be complete and accurate, but they would be of the nature of a complex catalogue. to introduce, in addition, the conception of mechanism is to introduce the implication of possibilities of future accomplishment.[ ] . the judgment of what is to be done implies, as we have just seen, a statement of what the given facts of the situation are, taken as indications of the course to pursue and of the means to be employed in its pursuit. such a statement demands accuracy. completeness is not so much an additional requirement as it is a condition of accuracy. for accuracy depends fundamentally upon relevancy to the determination of what is to be done. completeness does not mean exhaustiveness _per se_, but adequacy as respects end and its means. to include too much, or what is irrelevant, is a violation of the demand for accuracy quite as well as to leave out--to fail to discover--what is important. clear recognition of this fact will enable one to avoid certain dialectic confusions. it has been argued that a judgment of given existence, or fact, cannot be hypothetical; that factuality and hypothetical character are contradictions in terms. they would be if the two qualifications were used in the same respect. but they are not. the hypothesis is that the facts which constitute the terms of the proposition of the given are relevant and adequate for the purpose in hand--the determination of a possibility to be accomplished in action. the data may be as factual, as absolute as you please, and yet in no way guarantee that they are the data _of_ this particular judgment. suppose the thing to be done is the formation of a prediction regarding the return of a comet. the prime difficulty is not in making observations, or in the mathematical calculations based upon them--difficult as these things may be. it is making sure that we have taken as data the observations really implicated in the doing rightly of this particular thing: that we have not left out something which is relevant, or included something which has nothing to do with the further movement of the comet. darwin's hypothesis of natural selection does not stand or fall with the correctness of his propositions regarding breeding of animals in domestication. the facts of artificial selection may be as stated--in themselves there may be nothing hypothetical about them. but their bearing upon the origin of species _is_ a hypothesis. logically, any factual proposition is a hypothetical proposition when it is made the basis of any inference. . the bearing of this remark upon the nature of the truth of practical judgments (including the judgment of what is given) is obvious. their truth or falsity is constituted by the issue. the determination of end-means (constituting the terms and relations of the practical proposition) is hypothetical until the course of action indicated has been tried. the event or issue of such action _is_ the truth or falsity of the judgment. this is an immediate conclusion from the fact that only the issue gives the complete subject-matter. in this case, at least, verification and truth completely coincide--unless there is some serious error in the prior analysis. this completes the account, preliminary to a consideration of other matters. but the account suggests another and independent question with respect to which i shall make an excursus. how far is it possible and legitimate to extend or generalize the results reached to apply to all propositions of facts? that is to say, is it possible and legitimate to treat all scientific or descriptive statements of matters of fact as implying indirectly if not directly, something to be done, future possibilities to be realized in action? the question as to legitimacy is too complicated to be discussed in an incidental way. but it cannot be denied that there is a possibility of such application, nor that the possibility is worth careful examination. we may frame at least a hypothesis that all judgments of fact have reference to a determination of courses of action to be tried and to the discovery of means for their realization. in the sense already explained all propositions which state discoveries or ascertainments, all categorical propositions, would be hypothetical, and their truth would coincide with their tested consequences effected by intelligent action. this theory may be called pragmatism. but it is a type of pragmatism quite free from dependence upon a voluntaristic psychology. it is not complicated by reference to emotional satisfactions or the play of desires. i am not arguing the point. but possibly critics of pragmatism would get a new light upon its meaning were they to set out with an analysis of ordinary practical judgments and then proceed to consider the bearing of its result upon judgments of facts and essences. mr. bertrand russell has remarked[ ] that pragmatism originated as a theory about the truth of theories, but ignored the "truths of fact" upon which theories rest and by which they are tested. i am not concerned to question this so far as the origin of pragmatism is concerned. philosophy, at least, has been mainly a matter of theories; and mr. james was conscientious enough to be troubled about the way in which the meaning of such theories is to be settled and the way in which they are to be tested. his pragmatism was in effect (as mr. russell recognizes) a statement of the need of applying to philosophic theories the same kinds of test as are used in the theories of the inductive sciences. but this does not preclude the application of a like method to dealing with so-called "truths of fact." facts may be facts, and yet not be the facts _of_ the inquiry in hand. in all scientific inquiry, however, to call them facts or data or truths of fact signifies that they are taken as the _relevant_ facts of the inference to be made. _if_ (as this would seem to indicate) they are then implicated however indirectly in a proposition about what is to be done, they are themselves theoretical in logical quality. accuracy of statement and correctness of reasoning would then be factors in truth, but so also would be verification. truth would be a triadic relation, but of a different sort from that expounded by mr. russell. for accuracy and correctness would both be functions of verifiability. judgments of value i it is my purpose to apply the conclusions previously drawn as to the implications of practical judgment to the subject of judgments of value. first, i shall try to clear away some sources of misunderstanding. unfortunately, however, there is a deep-seated ambiguity which makes it difficult to dismiss the matter of value summarily. the _experience_ of a good and the _judgment_ that something is a value of a certain kind and amount have been almost inextricably confused. the confusion has a long history. it is found in mediaeval thought; it is revived by descartes; recent psychology has given it a new career. the senses were regarded as modes of knowledge of greater or less adequacy, and the feelings were regarded as modes of sense, and hence as modes of cognitive apprehension. descartes was interested in showing, for scientific purposes, that the senses are not organs of apprehending the qualities of bodies as such, but only of apprehending their relation to the well-being of the sentient organism. sensations of pleasure and pain, along with those of hunger, thirst, etc., most easily lent themselves to this treatment; colors, tones, etc., were them assimilated. of them all he says: "these perceptions of sense have been placed within me by nature for the purpose of _signifying_ what things are beneficial or harmful."[ ] thus it was possible to identify the real properties of bodies with their geometrical ones, without exposing himself to the conclusion that god (or nature) deceives us in the perception of color, sound, etc. these perceptions are only intended to teach us what things to pursue and avoid, and as _such_ apprehensions they are adequate. his identification of any and every experience of good with a judgment or cognitive apprehension is clear in the following words: "when we are given news the mind first judges of it and if it is good it rejoices."[ ] this is a survival of the scholastic psychology of the _vis aestimativa_. lotze's theory that the emotions, as involving pleasure and pain, are organs of value judgments, or in more recent terminology, that they are cognitive appreciations of worth (corresponding to immediate apprehensions of sensory qualities) presents the same tradition in a new terminology. as against all this, the present paper takes its stand with the position stated by hume, in the following words: "a passion is an original existence, or, if you will, modification of existence; and contains not any representative quality, which renders it a copy of any other existence or modification. when i am angry i am actually possest with the passion, and in that emotion have no more a reference to any other object, than when i am thirsty, or sick, or more than five feet high."[ ] in so doing, i may seem to some to be begging the question at issue. but such is surely the prima facie fact of the matter. only a prior dogma to the effect that every conscious experience _is_, _ipso facto_, a form of cognition leads to any obscuration of the fact, and the burden of proof is upon those who uphold the dogma.[ ] a further word upon "appreciation" seems specially called for in view of the currency of the doctrine that "appreciation" is a peculiar kind of knowledge, or cognitive revelation of reality: peculiar in having a distinct type of reality for its object and in having for its organ a peculiar mental condition differing from the intelligence of everyday knowledge and of science. actually, there do not seem to be any grounds for regarding appreciation as anything but an intentionally enhanced or intensified experience of an object. its opposite is not descriptive or explanatory knowledge, but _de_preciation--a degraded realization of an object. a man may climb a mountain to get a better realization of a landscape; he may travel to greece to get a realization of the parthenon more full than that which he has had from pictures. intelligence, knowledge, may be involved in the steps taken to get the enhanced experience, but that does not make the landscape or the parthenon as fully savored a cognitive object. so the fulness of a musical experience may depend upon prior critical analysis, but that does not necessarily make the hearing of music a kind of non-analytic cognitive act. either appreciation means just an intensified experience, or it means a kind of criticism, and then it falls within the sphere of ordinary judgment, differing in being applied to a work of art instead of to some other subject-matter. the same mode of analysis may be applied to the older but cognate term "intuition." the terms "acquaintance" and "familiarity" and "recognition" (acknowledgment) are full of like pitfalls of ambiguity. in contemporary discussion of value-judgments, however, appreciation is a peculiarly treacherous term. it is first asserted (or assumed) that all experiences of good are modes of knowing: that good is a term of a proposition. then when experience forces home the immense difference between evaluation as a critical process (a process of inquiry for the determination of a good precisely similar to that which is undertaken in science in the determination of the nature of an event) and ordinary experience of good and evil, appeal is made to the difference between direct apprehension and indirect or inferential knowledge, and "appreciation" is called in to play the convenient rôle of an immediate cognitive apprehension. thus a second error is used to cover up and protect a primary one. to savor a thing fully--as arnold bennett's heroines are wont to do--is no more a knowing than is the chance savoring which arises when things smelled are found good, or than is being angry or thirsty or more than five feet high. all the language which we can employ is charged with a force acquired through reflection. even when i speak of a direct experience of a good or bad, one is only too likely to read in traits characterizing a thing which is found in consequence of thinking, to be good; one has to use language simply to stimulate a recourse to a direct experiencing in which language is not depended upon. if one is willing to make such an imaginative excursion--no one can be compelled--he will note that _finding_ a thing good apart from reflective judgment means simply treating the thing in a certain way, hanging on to it, dwelling upon it, welcoming it and acting to perpetuate its presence, taking delight in it. it is a way of behaving toward it, a mode of organic reaction. a psychologist may, indeed, bring in the emotions, but if his contribution is relevant it will be because the emotions which figure in his account are just part of the primary organic reaction to the object. in contrary fashion, to find a thing bad (in a direct experience as distinct from the result of a reflective examination) is to be moved to reject it, to try to get away from it, to destroy or at least to displace it. it connotes not an act of apprehension but an act of repugning, of repelling. to term the thing good or evil is to state the fact (noted in recollection) that it was actually involved in a situation of organic acceptance or rejection, with whatever qualities specifically characterize the act. all this is said because i am convinced that contemporary discussion of values and valuation suffers from confusion of the two radically different attitudes--that of direct, active, non-cognitive experience of goods and bads and that of valuation, the latter being simply a mode of judgment like any other form of judgment, differing in that its subject-matter happens to be a good or a bad instead of a horse or planet or curve. but unfortunately for discussions, "to value" means two radically different things: to prize and appraise; to esteem and to estimate: to find good in the sense described above, and to judge it to be good, to _know_ it as good. i call them radically different because to prize names a practical, non-intellectual attitude, and to appraise names a judgment. that men love and hold things dear, that they cherish and care for some things, and neglect and contemn other things, is an undoubted fact. to call these things values is just to repeat that they are loved and cherished; it is not to give a reason for their being loved and cherished. to call them values and then import into them the traits of objects of valuation; or to import into values, meaning valuated objects, the traits which things possess as held dear, is to confuse the theory of judgments of value past all remedy. and before coming to the more technical discussion, the currency of the confusion and the bad result consequences may justify dwelling upon the matter. the distinction may be compared to that between eating something and investigating the food properties of the thing eaten. a man eats something; it may be said that his very eating implies that he _took_ it to be food, that he judged it, or regarded it cognitively, and that the question is just whether he judged truly or made a false proposition. now if anybody will condescend to a concrete experience he will perceive how often a man eats _without_ thinking; that he puts into his mouth what is set before him from habit, as an infant does from instinct. an onlooker or anyone who reflects is justified in saying that he _acts as if_ he judged the material to be food. he is not justified in saying that any judgment or intellectual determination has entered in. he has acted; he has behaved toward something as food: that is only to say that he has put it in his mouth and swallowed it instead of spewing it forth. the object may then be called food. but this does not mean either that it _is_ food (namely, digestible and nourishing material) or that the eater judged it to be food and so formed a proposition which is true or false. the proposition would arise only in case he is in some doubt, or if he reflects that in spite of his immediate attitude of aversion the thing is wholesome and his system needs recuperation, etc. or later, if the man is ill, a physician may inquire what he ate, and pronounce that something not food at all, but poison. in the illustration employed, there is no danger of any harm arising from using the retroactive term "food"; there is no likelihood of confusing the two senses "actually eaten" and "nourishing article." but with the terms "value" and "good" there is a standing danger of just such a confusion. overlooking the fact that good and bad as _reasonable_ terms involve a _relationship to other things_ (exactly similar to that implied in calling a particular article food or poison), we suppose that when we are reflecting upon or inquiring into the good or value of some act or object, we are dealing with something as simple, as self-inclosed, as the simple act of immediate prizing or welcoming or cherishing performed without rhyme or reason, from instinct or habit. in truth just as determining a thing _to be_ food means considering its relations to digestive organs, to its distribution and ultimate destination in the system, so determining a thing found good (namely, treated in a certain way) _to be_ good means precisely ceasing to look at it as a direct, self-sufficient thing and considering it in its consequences--that is, in its relations to a large set of other things. if the man in eating consciously implies that what he eats is food, he anticipates or predicts certain consequences, with more or less adequate grounds for so doing. he passes a judgment or apprehends or knows--truly or falsely. so a man may not only enjoy a thing, but he may judge the thing enjoyed to be good, to be a value. but in so doing he is going beyond the thing immediately present and making an inference to other things, which, he implies, are connected with it. the thing taken into the mouth and stomach _has_ consequences whether a man thinks of them or not. but he does not _know_ the thing he eats--he does not make it a term of a certain character--unless he thinks of the consequences and connects them with the thing he eats. if he just stops and says "oh, how good this is," he is not saying anything about the object except the fact that he enjoys eating it. we may if we choose regard this exclamation as a reflection or judgment. but if it is intellectual, it is asserted for the sake of enhancing the enjoyment; it is a means to an end. a very hungry man will generally satisfy his appetite to some extent before he indulges in even such rudimentary propositions.[ ] ii but we must return to a placing of our problem in this context. my theme is that a judgment of value is simply a case of a practical judgment, a judgment about the doing of something. this conflicts with the assumption that it is a judgment about a particular kind of existence independent of action, concerning which the main problem is whether it is subjective or objective. it conflicts with every tendency to make the determination of the right or wrong course of action (whether in morals, technology, or scientific inquiry) dependent upon an independent determination of some ghostly things called value-objects--whether their ghostly character is attributed to their existing in some transcendental eternal realm or in some realm called states of mind. it asserts that value-objects mean simply objects as judged to possess a certain _force_ within a situation temporally developing toward a determinate result. to _find_ a thing good is, i repeat, to attribute or impute nothing to it. it is just to do something to it. but to consider _whether_ it is good and how good it is, is to ask how it, _as if acted upon_, will operate in promoting a course of action. hence the great contrast which may exist between a good or an immediate experience and an evaluated or judged good. the rain may be most uncomfortable (just _be_ it, as a man is more than five feet tall) and yet be "good" for growing crops--that is, favor or promote their movement in a given direction. this does not mean that two contrasting judgments of value are passed. it means that _no_ judgment has yet taken place. if, however, i am moved to pass a value-judgment i should probably say that in spite of the disagreeableness of getting wet, the shower is a good thing. i am now judging it as a _means_ in two contrasting situations, as a means with respect to two ends. i compare my discomfort as a _consequence_ of the rain with the prospective crops as another consequence, and say "let the latter consequence be." i identify myself as agent with it, rather than with the immediate discomfort of the wetting. it is quite true that in this case i cannot do anything about it; my identification is, so to speak, sentimental rather than practical so far as stopping the rain or growing the crops is concerned. but in effect it is an assertion that one would not on account of the discomfort of the rain stop it; that one would, if one could, encourage its continuance. go it, rain, one says. the specific intervention of action is obvious enough in plenty of other cases. it occurs to me that this agreeable "food" which i am eating isn't a food for me; it brings on indigestion. it functions no longer as an _immediate_ good; as something to be accepted. if i continue eating, it will be after i have deliberated. i have considered it as a means to two conflicting possible consequences, the present enjoyment of eating and the later state of health. one or other is possible, not both--though of course i may "solve" the problem by persuading myself that in this instance they are congruent. the value-object now means thing judged to be a means of procuring this or that end. as prizing, esteeming, holding dear denote ways of acting, so valuing denotes a passing judgment upon such acts with reference to their connection with other acts, or with respect to the continuum of behavior in which they fall. valuation means change of mode of behavior from direct acceptance and welcoming to doubting and looking into--acts which involve postponement of direct (or so-called overt) action and which imply a future act having a different _meaning_ from that just now occurring--for even if one decides to continue in the previous act its meaning-content is different when it is chosen after reflective examination. a practical judgment has been defined as a judgment of what to do, or what is to be done: a judgment respecting the future termination of an incomplete and in so far indeterminate situation. to say that judgments of value fall within this field is to say two things: one, that the judgment of value is never complete in itself, but always in behalf of determining what is to be done; the other, that judgments of value (as distinct from the direct experience of something as good) imply that value is not anything previously given, but is something to be given by future action, itself conditioned upon (varying with) the judgment. this statement may appear to contradict the recent assertion that a value-object for knowledge means one investigated as a means to competing ends. for such a means it already is; the lobster _will_ give me present enjoyment and future indigestion _if_ i eat it. but as long as i judge, _value_ is indeterminate. the question is not what the thing will do--i may be quite clear about that: it is whether to perform the act which will actualize its potentiality. what will i have the situation _become_ as between alternatives? and that means what force shall the thing as means be given? shall i take it as means to present enjoyment, or as a (negative) condition of future health? when its status in these respects is determined, its value is determined; judgment ceases, action goes on. practical judgments do not therefore primarily concern themselves with the value of _objects_; but with the course of action demanded to carry an incomplete situation to its fulfilment. the adequate control of such judgments may, however, be facilitated by judgment of the worth of objects which enter as ends and means into the action contemplated. for example, my primary (and ultimate) judgment has to do, say, with buying a suit of clothes: whether to buy and, if so, what? the question is of better and worse with respect to alternative courses of action, not with respect to various objects. but the judgment will be a judgment (and not a chance reaction) in the degree in which it takes for its intervening subject-matter the value-status of various objects. what are the prices of given suits? what are their styles in respect to current fashion? how do their patterns compare? what about their durability? how about their respective adaptability to the chief wearing use i have in mind? relative, or comparative, durability, cheapness, suitability, style, aesthetic attractiveness constitute value traits. they are traits of objects not _per se_, but _as entering into a possible and foreseen completing of the situation_. their value is their force in precisely this function. the decision of better and worse is the determination of their respective capacities and intensities _in this regard_. apart from their status in this office, they have no traits of value for knowledge. a determination of better value as found in some one suit is equivalent to (has the force of) a decision as to what it is better to do. it provided the lacking stimulus so that action occurs, or passes from its indeterminate-indecisive-state into decision. reference to the terms "subjective" and "objective" will, perhaps, raise a cloud of ambiguities. but for this very reason it may be worth while to point out the ambiguous nature of the term objective as applied to valuations. objective may be identified, quite erroneously, with qualities existing outside of and independently of the situation in which a decision as to a future course of action has to be reached. or, objective may denote the status of qualities of an object _in respect_ to the situation to be completed through judgment. independently of the situation requiring practical judgment, clothes already have a given price, durability, pattern, etc. these traits are not affected by the judgment. they exist; they are given. but as given they are _not_ determinate values. they are not _objects_ of valuation; they are _data for_ a valuation. we may have to take pains to discover that these given qualities are, but their discovery is in order that there may be a subsequent judgment of value. were they already definite values, they would not be estimated; they would be stimuli to direct response. if a man had already decided that cheapness constituted value, he would simply take the cheapest suit offered. what he judges is the value of cheapness, and this depends upon its weight or importance in the situation requiring action, as compared with durability, style, adaptability, etc. discovery of shoddy would not affect the _de facto_ durability of the goods, but it would affect the value of cheapness--that is, _the weight assigned that trait in influencing judgment_--which it would not do, if cheapness already had a definite value. a value, in short, means a _consideration_, and a consideration does not mean an existence merely, but an existence having a claim upon judgment. value judged is not existential quality noted, but is the influence attached by judgment to a given existential quality in determining judgment. the conclusion is not that value is subjective, but that it is practical. the situation in which judgment of value is required is not mental, much less fanciful. i can but think that much of the recent discussion of the objectivity of value and of value-judgments rests upon a false psychological theory. it rests upon giving certain terms meanings that flow from an introspective psychology which accepts a realm of purely private states of consciousness, private not in a social sense (a sense implying courtesy or mayhap secrecy toward others), but existential independence and separateness. to refer value to choice or desire, for example, is in that case to say that value is subjectively conditioned. quite otherwise, if we have steered clear from such a psychology. choice, decision, means primarily a certain act, a piece of behavior on the part of a particular thing. that a horse chooses to eat hay means only that it eats hay; that the man chooses to steal means (at least) that he tries to steal. this trial may come, however, _after_ an intervening act of reflection. it then has a certain intellectual or cognitive quality. but it may mean simply the bare fact of an action which is retrospectively called a choice: as a man, in spite of all temptation to belong to another nation, chooses to be born an englishman, which, if it has any sense at all, signifies a choice to continue in a line adopted without choice. taken in this latter sense (in which case, terms like choice and desire refer to ways of behavior), their use is only a specification of the general doctrine that all valuation has to do with the determination of a course of action. choice, preference, is originally only a bias in a given direction, a bias which is no more subjective or psychical than is the fact that a ball thrown is swerving in a particular direction rather than in some other curve. it is just a name for the differential character of the action. but let continuance in a certain line of action become questionable, let, that is to say, it be regarded as a means to a future consequence, which consequence has alternatives, and then choice gets a logical or intellectual sense; a _mental_ status if the term "mental" is reserved for acts having this intellectualized quality. choice still means the fixing of a course of action; it means at least a _set_ to be released as soon as physically possible. otherwise man has not chosen, but has quieted himself into a belief that he has chosen in order to relieve himself of the strain of suspense. exactly the same analysis applies to desire. diverse anticipated ends may provoke divided and competing present reactions; the organism may be torn between different courses, each interfering with the completion of the other. this intra-organic pulling and hauling, this strife of active tendencies, is a genuine phenomenon. the pull in a given direction measures the immediate hold of an anticipated termination or end upon us, as compared with that of some other. if one asked after the mechanism of the valuing process, i have no doubt that the answer would be in terms of desires thus conceived. but unless everything relating to the activity of a highly organized being is to be denominated subjective, i see no ground for calling it subjective. so far as i can make out, the emphasis upon a psychological treatment of value and valuation in a subjective sense is but a highly awkward and negative way of maintaining a positive truth: that value and valuation fall within the universe of _action_: that as welcoming, accepting, is an act, so valuation is a present act determining an act _to be_ done, a present act taking place because the future act is uncertain and incomplete. it does follow from this fact that valuation is not simply a _recognition_ of the force or efficiency of a means with respect to continuing a process. for unless there is _question_ about its continuation, about its termination, valuation will not occur. and there is no question save where activity is hesitant in direction because of conflict within it. metaphorically we may say that rain is good to lay the dust, identifying force or efficiency with value. i do not believe that valuations occur and values are brought into being save in a continuing situation where things have potency for carrying forward processes. there is a close relationship between prevailing, valiancy, valency, and value. but the term "value" is not a mere reduplication of the term "efficiency": it adds something. when we are moving toward a result and at the same time are stimulated to move toward something else which is incompatible with it (as in the case of the lobster as a cause of both enjoyment and indigestion), a thing has a dual potency. not until the end has been established is the value of the lobster settled, although there need be no doubt about its efficiencies. as was pointed out earlier, the practical judgment determines means and end at the same time. how then can value be given, as efficiency is given, until the end is chosen? the rain is (metaphorically) valuable for laying dust. whether it is valuable for us to have the dust laid--and if so, how valuable--we shall never know until some activity of our own which is a factor in dust-laying comes into conflict with an incompatible activity. its value is its force, indeed, but it is its force in moving us to one end _rather_ than to another. not every potency, in other words, but potency with the specific qualification of falling within judgment about future action, means value or valuable thing. consequently there is no value save in situations where desires and the need of deliberation in order to choose are found, and yet this fact gives no excuse for regarding desire and deliberation and decision as subjective phenomena. to use an irish bull, as long as a man _knows_ what he desires there is no desire; there is movement or endeavor in a given direction. desire is desires, and simultaneous desires are incompatible; they mark, as we have noted, competing activities, movements in directions, which cannot both be extended. reflection is a process of finding out what we want, what, as we say, we _really_ want, and this means the formation of new desire, a new direction of action. in this process, things _get_ values--something they did not possess before, although they had their efficiencies. at whatever risk of shock, this doctrine should be exposed in all its nakedness. to judge value is to engage in instituting a determinate value where none is given. it is not necessary that antecedently given values should be the data of the valuation; and where they are given data they are only terms in the determination of a not yet existing value. when a man is ill and after deliberation concludes that it be well to see a doctor, the doctor doubtless exists antecedently. but it is not the doctor who is judged to be the good of the situation, but the _seeing_ of the doctor: a thing which, by description, exists only because of an act dependent upon a judgment. nor is the health the man antecedently possessed (or which somebody has) the thing which he judges to be a value; the thing judged to be a value is the restoring of health--something by description not yet existing. the results flowing from his past health will doubtless influence him in reaching his judgment that it will be a good to have restored health, but they do not constitute the good which forms his subject-matter and object of his judgment. he may judge that they _were_ good without judging that they are now good, for to be judged now good means to be judged to be the object of a course of action still to be undertaken. and to _judge_ that they were good (as distinct from merely recalling certain benefits which accrued from health) is to judge that _if_ the situation had required a reflective determination of a course of action one would have judged health an existence to be attained or preserved by action. there are dialectic difficulties which may be raised about judgments of this sort. for they imply the seeming paradox of a judgment whose proper subject-matter is its own determinate formation. but nothing is gained by obscuring the fact that such is the nature of the practical judgment: it is a judgment of what and how to judge--of the weight to be assigned to various factors in the determination of judgment. it would be interesting to inquire into the question whether this peculiarity may not throw light upon the nature of "consciousness," but into that field we cannot now go. iii from what has been said, it immediately follows, of course, that a determinate value is instituted as a decisive factor with respect to what is to be done. wherever a determinate good exists, there is an adequate stimulus to action, and no judgment of what is to be done or of the value of an object is called for. it is frequently assumed, however, that valuation is a process of applying some fixed or determinate value to the various competing goods of a situation; that valuation implies a prior standard of value and consists in comparing various goods with the standard as the supreme value. this assumption requires examination. if it is sound it deprives the position which has been taken of any validity. for it renders the judgment of what to do a matter of applying a value existing ready-made, instead of making--as we have done--the valuation a determination within the practical judgment. the argument would run this way: every practical judgment depends upon a judgment of the value of the end to be attained; this end may be such only proximately, but that implies something else judged to be good, and so, logically, till we have arrived at the judgment of a supreme good, a final end or _summum bonum_. if this statement correctly describes the state of the case there can be no doubt that a practical judgment depends upon a prior recognition of value; consequently the hypothesis upon which we have been proceeding reverses the actual facts. the first thing by way of critical comment is to point out the ambiguity in the term "end." i should like to fall back upon what was said earlier about the thoroughly reciprocal character of means and end in the practical judgment. if this be admitted it is also admitted that only by a judgment of means--things having value in the carrying of an indeterminate situation to a completion--is the end determinately made out in judgment. but i fear i cannot count upon this as granted. so i will point out that "end" may mean either the _de facto_ limit to judgment, which by definition does not enter into judgment at all, or it may mean the last and completing object of judgment, the conception of that object in which a transitive incompletely given situation would come to rest. of end in the first sense, it is to be said that it is not a value at all; of end in the second sense, that it is identical with a finale of the kind we have just been discussing or that it is determined in judgment, not a value given by which to control the judgment. it may be asserted that in the illustration used some typical suit of clothes is the value which affords the standard of valuation of all the suits which are offered to the buyer; that he passes judgment on their value as compared with the standard suit as an end and supreme value. this statement brings out the ambiguity just referred to. the need of something to wear is the _stimulus_ to the judgment of the value of suits offered, and possession of a suit puts an end _to_ judgment. it is an end _of_ judgment in the objective, not in the possessive, sense of the preposition "of"; it is an end not in the sense of aim, but in the sense of a terminating limit. when possession begins, judgment has already ceased. and if argument _ad verucundiam_ has any weight i may point out that this is the doctrine of aristotle when he says we never deliberate about ends, but only about means. that is to say, in all deliberation (or practical judgment or inquiry) there is always something outside of judgment which fixes its beginning and end or terminus. and i would add that, according to aristotle, deliberation always ceases when we have come to the "first link in the chain of causes, which is last in the order of discovery," and this means "when we have traced back the chain of causes [means] to ourselves." in other words, the last end-in-view is always that which operates as the direct or immediate means of setting our own powers in operation. the end-in-view upon which judgment of action settles down is simply the adequate or complete means to the doing of something. we do deliberate, however, about _aims_, about ends-in-view--a fact which shows their radically different nature from ends as limits to deliberation. the aim in the present instance is not the suit of clothes, but the _getting of a proper_ suit. that is what is precisely estimated or valuated; and i think i may claim to have shown that the determination of this aim is identical with the determination of the value of a suit through comparison of the values of cheapness, durability, style, pattern of different suits offered. value is not determined by comparing various suits with an ideal model, but by comparing various suits with respect to cheapness, durability, adaptability _with one another_--involving, of course, reference also to length of purse, suits already possessed, etc., and other specific elements in the situation which demands that something be done. the purchaser may, of course, have settled upon something which serves as a model before he goes to buy; but that only means that his judging has been done beforehand; the model does not then function in judgment, but in his act as stimulus to immediate action. and there is a consideration here involved of the utmost importance as to practical judgments of the moral type: the more completely the notion of the model is formed outside and irrespective of the specific conditions which the situation of action presents, the less intelligent is the act. most men might have their ideals of the model changed somewhat in the face of the actual offering, even in the case of buying clothes. the man who is not accessible to such change in the case of moral situations has ceased to be a moral agent and become a reacting machine. in short, the standard of valuation is formed in the process of practical judgment or valuation. it is not something taken from outside and applied within it--such application means there is no judgment. iv nothing has been said thus far about a standard. yet the conception of a standard, or a measure, is so closely connected with valuation that its consideration affords a test of the conclusions reached. it must be admitted that the concepts of the nature of a standard pointed to by the course of the prior discussion is not in conformity with current conceptions. for the argument points to a standard which is determined within the process of valuation, not outside of it, and hence not capable of being employed ready-made, therefore, to settle the valuing process. to many persons, this will seem absurd to the point of self-contradiction. the prevailing conception, however, has been adopted without examination; it is a preconception. if accepted, it deprives judgment and knowledge of all significant import in connection with moral action. if the standard is already given, all that remains is its mechanical application to the case in hand--as one would apply a yard rule to dry-goods. genuine moral uncertainty is then impossible; where it seems to exist, it is only a name for a moral unwillingness, due to inherent viciousness, to recognize and apply the rules already made and provided, or else for a moral corruption which has enfeebled man's power of moral apprehension. when the doctrine of standards prior to and independent of moral judgments is accompanied by these other doctrines of original sin and corruption, one must respect the thoroughgoing logic of the doctrine. such is not, however, the case with the modern theories which make the same assumption of standards preceding instead of resulting from moral judgments, and which ignore the question of uncertainty and error in their apprehension. such considerations do not, indeed, decide anything, but they may serve to get a more unprejudiced hearing for a hypothesis which runs counter to current theories, since it but formulates the trend of current practices in their increasing tendency to make the act of intelligence the central factor in morals. let us, accordingly, consider the alternatives to regarding the standard of value as something evolved in the process of reflective valuation. how can such a standard be known? either by an a priori method of intuition, or by abstraction from prior cases. the latter conception throws us into the arms of hedonism. for the hedonistic theory of the standard of value derives its logical efficiency from the consideration that the notion of a prior and fixed standard (one which is not determined within the situation by reflection) forces us back upon antecedent irreducible pleasures and pains which alone are values definite and certain enough to supply standards. they alone are simple enough to be independent and ultimate. the apparently common-sense alternative would be to take the "value" of prior situations _in toto_, say, the value of an act of kindness to a sufferer. but any such good is a function of the total unanalyzed situation; it has, consequently, no application to a new situation unless the new exactly repeats the old one. only when the "good" is resolved into simple and unalterable units, in terms of which old situations can be equated to new ones on the basis of the number of units contained, can an unambiguous standard be found. the logic is unimpeachable, and points to irreducible pleasures and pains as the standard of valuation. the difficulty is not in the logic but in empirical facts, facts which verify our prior contention. conceding, for the sake of argument, that there are definite existences such as are called pleasures and pains, they are _not_ value-objects, but are only things to be valued. exactly the same pleasure or pain, as an existence, has different values at different times according to the way in which it is judged. what is the value of the pleasure of eating the lobster as compared with the pains of indigestion? the rule tells us, of course, to break up the pleasure and pain into elementary units and count.[ ] such ultimate simple units seem, however, to be about as much within the reach of ordinary knowledge as atoms or electrons are within the grasp of the man of the street. their resemblance to the ultimate, neutral units which analytic psychologists have postulated as a methodological necessity is evident. since the value of even such a definite entity as a toothache varies according to the organization constructed and presented in reflection, it is clear that ordinary empirical pleasures and pains are highly complex. this difficulty, however, may be waived. we may even waive the fact that a theory which set out to be ultra-empirical is now enmeshed in the need for making empirical facts meet dialectical requirements. another difficulty is too insuperable to be waived. in any case the quantity of elementary existences which constitutes the criterion of measurement is dependent upon the very judgment which is assumed to be regulated by it. the standard of valuation is the units which will _result_ from an act; they are future consequences. now the character of the agent judging is one of the conditions of the production of these consequences. a callous person not only will not foresee certain consequences, and will not be able to give them proper weight, but he does not afford the same condition of their occurrence which is constituted by a sensitive man. it is quite possible to employ judgment so as to produce acts which will increase this organic callousness. the analytic conception of the moral criterion provides--logically--for deliberate blunting of susceptibilities. if the matter at issue is simply one of number of units of pleasure over pain, arrange matters so that certain pains will not, as matter of fact, be felt. while this result may be achieved by manipulation of extra-organic conditions, it may also be effected by rendering the organism insensitive. persistence in a course which in the short run yields uneasiness and sympathetic pangs, will in the long run eliminate these pains and leave a net pleasure balance. this is a time-honored criticism of hedonism. my present concern with it is purely logical. it shows that the attempt to bring over from past objects the elements of a standard for valuing future consequences is a hopeless one. the express object of a valuation-judgment is to release factors which being new, cannot be measured on the basis of the past alone. this discussion of the analytic logic as applied in morals would, however, probably not be worth while did it not serve to throw into relief the significance of any appeal to fulfilment of a system or organization as _the_ moral good--the standard. such an appeal, if it is wary, is an appeal to the present situation as _undergoing that reorganization that will confer upon it the unification which it lacks_; to organization as something to be brought about, to be made. and it is clear that this appeal meets all the specifications of judgments of practice as they have been described. the organization which is to be fulfilled through action is an organization which, at the time of judging, is present in conception, in idea--in, that is, reflective inquiry as a phase of reorganizing activity. and since its presence in conception is both a condition of the organization aimed at _and_ a function of the adequacy of the reflective inquiry, it is evident that there is here a confirmation of our statement that the practical judgment is a judgment of what and how to judge as an integral part of the completion of an incomplete temporal situation. more specifically, it also appears that the standard is a rule for conducting inquiry to its completion: it is a counsel to make examination of the operative factors complete, a warning against suppressing recognition of any of them. however a man may impose upon himself or upon others, a man's real measure of value is exhibited in what he _does_, not in what he consciously thinks or says. for the doing is the _actual_ choice. it is the completed reflection. it is comparatively easy at the present time in moral theory to slam both hedonism and apriorism. it is not so easy to see the logical implications of the alternative to them. the conception of an organization of interests or tendencies is often treated as if it were a conception which is definite in subject-matter as well as clear-cut in form. it is taken not as a rule for procedure in inquiry, a direction and a warning (which it is), but as something all of whose constituents are already given for _knowledge_, even though not given in fact. the act of fulfilling or realizing must then be treated as devoid of intellectual import. it is a mere doing, not a learning and a testing. but how can a situation which is incomplete in fact be completely known until it _is_ complete? short of the fulfilment of a conceived organization, how can the conception of the proposed organization be anything more than a working hypothesis, a method of treating the given elements in order to see what happens? does not every notion which implies the possibility of an apprehension of knowledge of the end to be reached[ ] also imply either an a priori revelation of the nature of that end, or else that organization is nothing but a whole composed of elementary parts already given--the logic of hedonism? the logic of subsumption in the physical sciences meant that a given state of things could be compared with a ready-made concept as a model--the phenomena of the heavens with the implications of, say, the circle. the methods of experimental science broke down this motion; they substituted for an alleged regulative model a formula which was the integrated function of the particular phenomena themselves, a formula to be used as a method of further observations and experiments and thereby tested and developed. the unwillingness to believe that, in a similar fashion, moral standards or models can be trusted to develop out of the specific situations of action shows how little the general logical force of the method of science has been grasped. physical knowledge did not as matter of fact advance till the dogma of models or forms as standards of knowledge had been ousted. yet we hang tenaciously to a like doctrine in morals for fear of moral chaos. it once seemed to be impossible that the disordered phenomena of perception could generate a knowledge of law and order; it was supposed that independent principles of order must be supplied and the phenomena measured by approach to or deviation from the fixed models. the ordinary conception of a standard in practical affairs is a precise analogue. physical knowledge started on a secure career when men had courage to start from the irregular scene and to treat the suggestions to which it gave rise as methods for instituting new observations and experiences. acting upon the suggested conceptions analyzed, extended, and ordered phenomena and thus made improved conceptions--methods of inquiry--possible. it is reasonable to believe that what holds moral knowledge back is above all the conception that there are standards of good given to knowledge apart from the work of reflection in constructing methods of action. as the bringer of bad news gets a bad name, being made to share in the production of the evil which he reports, so honest acknowledgment of the uncertainty of the moral situation and of the hypothetical character of all rules of moral mensuration prior to acting upon them, is treated as if it originated the uncertainty and created the skepticism. it may be contended, however, that all this does not justify the earlier statement that the limiting situation which occasions and cuts off judgment is not itself a value. why, it will be asked, does a man buy a suit of clothes unless that is a value, or at least a proximate means to a further value? the answer is short and simple: because he has to; because the situation in which he lives demands it. the answer probably seems too summary. but it may suggest that while a man lives, he never is called upon to judge whether he shall act, but simply _how_ he shall act. a decision not to act is a decision to act in a certain way; it is never a judgment not to act, unqualifiedly. it is a judgment to do something else--to wait, for example. a judgment that the best thing to do is to retire from active life, to become a simon stylites, is a judgment to act in a certain way, conditioned upon the necessity that, irrespective of judging, a man will have to act somehow anyway. a decision to commit suicide is not a decision to be dead; it is a decision to perform a certain act. the act may depend upon reaching the conclusion that life is not worth living. but as a judgment, this is a conclusion to act in a way to terminate the possibility of further situations requiring judgment and action. and it does not imply that a judgment about life as a supreme value and standard underlies all judgments as to how to live. more specifically, it is not a judgment upon the value of life _per se_, but a judgment that one does not find at hand the specific means of making life worth while. as an act to be done, it falls within and assumes life. as a judgment upon the value of life, by definition it evades the issue. no one ever influenced a person considering committing suicide by arguments concerning the value of life, but only by suggesting or supplying conditions and means which make life worth living; in other words, by furnishing _direct_ stimuli to living. however, i fear that all this argument may only obscure a point obvious without argument, namely, that all deliberation upon what to do is concerned with the completion and determination of a situation in some respect incomplete and so indeterminate. every such situation is specific; it is not _merely_ incomplete; the incompleteness is _of_ a specific situation. hence the situation sets limits to the reflective process; what is judged has reference to it and that which limits never is judged in the particular situation in which it is limiting. now we have in ordinary speech a word which expresses the nature of the conditions which limit the judgments of value. it is the word "invaluable." the word does not mean something of supreme value as compared with other things any more than it means something of zero value. it means something out of the scope of valuation--something out of the range of judgment; whatever in the situation at hand is not and cannot be any part of the subject-matter of judgment and which yet instigates and cuts short the judgment. it means, in short, that judgment at some point runs against the brute act of holding something dear as its limit. v the statement that values are determined in the process of judgment of what to do (that is, in situations where preference depends upon reflection upon the conditions and possibilities of a situation requiring action) will be met by the objection that our practical deliberations usually assume precedent specific values and also a certain order or grade among them. there is a sense in which i am not concerned to deny this. our deliberate choices go on in situations more or less like those in which we have previously chosen. when deliberation has reached a valuation, and action has confirmed or verified the conclusion, the result remains. situations overlap. the _m_ which is judged better than _n_ in one situation is found worse than _l_ in another, and so on; thus a certain order of precedence is established. and we have to broaden the field to cover the habitual order of reflective preferences in the community to which we belong. the valu-eds or valuables thus constituted present themselves as facts in subsequent situations. moreover, by the same kind of operation, the dominating objects of past valuations present themselves as standardized values. but we have to note that such value-standards are only presumptive. their status depends, on one hand, upon the extent in which the present situation is like the past. in a progressive or rapidly altering social life, the presumption of identical present value is weakened. and while it would be foolish not to avail one's self of the assistance in present valuations of the valuables established in other situations, we have to remember that habit operates to make us overlook differences and presume identity where it does not exist--to the misleading of judgment. on the other hand, the contributory worth of past determinations of value is dependent upon the extent in which _they_ were critically made; especially upon the extent in which the consequences brought about through acting upon them have been carefully noted. in other words, the presumptive force of a past value in present judgment depends upon the pains taken with its verification. in any case, so far as judgment takes place (instead of the reminiscence of a prior good operating as a direct stimulus to present action) all valuation is in some degree a revaluation. nietzsche would probably not have made so much of a sensation, but he would have been within the limits of wisdom, if he had confined himself to the assertion that all judgment, in the degree in which it is critically intelligent, is a transvaluation of prior values. i cannot escape recognition that any allusion to modification or transformation of an object through judgment arouses partisan suspicion and hostility. to many it appears to be a survival of an idealistic epistemology. but i see only three alternatives. either there are no practical judgments--as judgments they are wholly illusory; or the future is bound to be but a repetition of the past or a reproduction of something eternally existent in some transcendent realm (which is the same thing logically),[ ] or the object of a practical judgment is some change, some alteration, to be brought about in the given, the nature of the change depending upon the judgment and yet constituting its subject-matter. unless the epistemological realist accepts one of the two first alternatives, he seems bound, in accepting the third, to admit not merely that practical judgments make a difference in things as an after-effect (this he seems ready enough to admit), but that the import and validity of judgments is a matter of the difference thus made. one may, of course, hold that this is just what marks the distinction of the practical judgment from the scientific judgment. but one who admits this fact as respects a practical judgment can no longer claim that it is fatal to the very idea of judgment to suppose that its proper object is some difference to be brought about in things, and that the truth of the judgment is constituted by the differences in consequences actually made. and a logical realist who takes seriously the notion that moral good is a fulfilment of an organization or integration must admit that any proposition about such an object is prospective (for it is something _to be_ attained through action), and that the proposition is made for the sake of furthering the fulfilment. let one start at this point and carry back the conception into a consideration of other kinds of propositions, and one will have, i think, the readiest means of apprehending the intent of the theory that all propositions are but the propoundings of possible knowledge, not knowledge itself. for unless one marks off the judgment of good from other judgment by means of an arbitrary division of the organism from the environment, or of the subjective from the objective, no ground for any sharp line of division in the propositional-continuum will appear. but (to obviate misunderstanding) this does not mean that some psychic state or act makes the difference in things. in the first place, the subject-matter of the judgment is a change to be brought about; and, in the second place, this subject-matter does not become an _object_ until the judgment has issued in act. it is the act which makes the difference, but nevertheless the act is but the complete object of judgment and the judgment is complete as a judgment only in the act. the anti-pragmatists have been asked (notably by professor a. w. moore) how they sharply distinguish between judgment--or knowledge--and act and yet freely admit and insist that knowledge makes a difference in action and hence in existence. this is the crux of the whole matter. and it is a logical question. it is not a query (as it seems to have been considered) as to how the mental can influence a physical thing like action--a variant of the old question of how the mind affects the body. on the contrary, the implication is that the relation of knowledge to action becomes a problem of the action of a mental (or logical) entity upon a physical one only when the logical import of judgment has been misconceived. the positive contention is that the realm of logical propositions presents in a realm of _possibility_ the specific rearrangement of things which overt action presents in actuality. hence the passage of a proposition into action is not a miracle, but the realization of its own character--its own meaning as logical. i do not profess, of course, to have shown that such is the case for _all_ propositions; that is a matter which i have not discussed. but in showing the tenability of the hypothesis that practical judgments are of that nature, i have at least ruled out any purely dialectic proof that the _nature_ of knowledge as such forbids entertaining the hypothesis that the import--indirect if not direct--of all logical propositions is some difference to be brought about. the road is at least cleared for a more unprejudiced consideration of this hypothesis on its own merits. sense perception as knowledge i mentioned incidentally in the first section that it is conceivable that failure to give adequate consideration to practical judgments may have a compromising effect upon the consideration of other types. i now intend to develop this remark with regard to sense perception as a form of knowledge. the topic is so bound up with a multitude of perplexing psychological and epistemological traditions that i have first to make it reasonably clear what it is and what it is not which i propose to discuss. i endeavored in an earlier series of papers[ ] to point out that the question of the _material_ of sense perception is not, as such, a problem of the theory of knowledge at all, but simply a problem of the occurrence of a certain material--a problem of causal conditions and consequences. that is to say, the problem presented by an image[ ] of a bent stick, or by a dream, or by "secondary" sensory qualities is properly a problem of physics--of conditions of occurrence, and not of logic, of truth or falsity, fact or fiction. that the existence of a red _quale_ is dependent upon disturbances of a certain velocity of a medium in connection with certain changes of the organism is not to be confused with the notion that red is a way of knowing, in some more or less adequate fashion, some more "real" object or else of knowing itself. the fact of causation--or functional dependence--no more makes the _quale_ an "appearance" to the mind of something more real than itself or of itself than it makes bubbles on the water a real fish transferred by some cognitive distortion into a region of appearance. with a little stretching we may use the term appearance in either case, but the term only means that the red _quale_ or the water-bubble is an _obvious_ or conspicuous thing from which we infer something else not so obvious. this position thus freely resumed here needs to be adequately guarded on all sides. it implies that the question of the existence or presence of the _subject-matter_ of even a complex sense perception may be treated as a question of physics. it also implies that the _existence_ of a sense perception may be treated as a problem of physics. but the position is not that _all_ the problems of sense perception are thereby exhausted. there is still, on the contrary, the problem of the cognitive status of sense perception. so far from denying this fact, i mean rather to emphasize it in holding that this knowledge aspect is not to be identified--as it has been in both realistic and idealistic epistemologies--with the simple _occurrence_ of presented subject-matter and with the _occurrence_ of a perceptive act. it is often stated, for example, that primitive sense objects when they are stripped of all inferential material cannot possibly be false--but with the implication that they, therefore, must be true. well, i meant to go this statement one better--to state that they are neither true nor false--that is, that the distinction of true-or-false is as irrelevant and inapplicable as to any other existence, as it is, say, to being more than five feet high or having a low blood pressure. this position when taken leaves over the question of sense perception as knowledge, as capable of truth or falsity. it is this question, then, which i intend to discuss in this paper. i my first point is that some sense perceptions at least (as matter of fact the great bulk of them), are without any doubt forms of practical judgment--or, more accurately, are terms in practical judgments as propositions of what to do. when in walking down a street i see a sign on the lamp-post at the corner, i assuredly see a sign. now in ordinary context (i do not say always or necessarily) this is a sign of what to do--to continue walking or to turn. the other term of the proposition may not be stated or it may be; it is probably more often tacit. of course, i have taken the case of the sign purposely. but the case may be extended. the lamp-post as perceived is to a lamp-lighter a sign of something else than a turn, but still a sign of something to be done. to another man, it may be a sign of a possible support. i am anxious not to force the scope of cases of this class beyond what would be accepted by an unbiased person, but i wish to point out that certain features of the perceived object, as a cognitive term, which do not seem at first sight to fall within this conception of the object, as, an intellectual sign of what to do, turn out upon analysis to be covered by it. it may be said, for example, that our supposed pedestrian perceives much besides that which serves as evidence of the thing to be done. he perceives the lamp-_post_, for example, and possibly the carbons of the arc. and these assuredly do not enter into the indication of what to do or how to do it. the reply is threefold. in the first place, it is easy--and usual--to read back into the sense perception more than was actually in it. it is easy to _recall_ the familiar features of the lamp-post; it is practically impossible--or at least very unusual--to recall what was actually perceived. so we read the former into the latter. the _tendency_ is for actual perception to limit itself to the minimum which will serve as sign. but, in the second place, since it is never wholly so limited, since there is always a surplusage of perceived object, the fact stated in the objection is admitted. but it is precisely this surplusage which has not _cognitive_ status. it does not serve as a sign, but neither is it _known_, or a term in knowledge. a child, walking by his father's side, with no aim and hence no reason for securing indications of what to do, will probably see more in his idle curiosity than his parent. he will have more presented material. but this does not mean that he is making more propositions, but only that he is getting more material for possible propositions. it means, in short, that he is in an aesthetic attitude of realization rather than in a cognitive attitude. but even the most economical observer has some aesthetic, non-cognitive surplusage.[ ] in the third place, surplusage is necessary for the operation of the signifying function. independently of the fact that surplusage may be required to render the sign specific, action is free (its variation is under control) in the degree in which _alternatives_ are present. the pedestrian has probably the two alternatives in mind: to go straight on or to turn. the perceived object might indicate to him another alternative--to stop and inquire of a passer-by. and, as is obvious in a more complicated case, it is the extent of the perceived object which both multiplies alternative ways of acting and gives the grounds for selecting among them. a physician, for example, deliberately avoids such hard-and-fast alternatives as have been postulated in our instance. he does not observe simply to get an indication of whether the man is well or ill; but in order to determine what to do he extends his explorations over a wide field. much of his perceived object field is immaterial to what he finally does; that is, does not serve as sign. but it is all relevant to _judging_ what he is to do. sense perception as a term in practical judgment _must_ include more than the element which finally serves as sign. if it did not, there would be no perception, but only a direct stimulus to action.[ ] the conclusion that such perceptions as we have been considering are terms in an inference is to be carefully discriminated from the loose statement that sense perceptions are unconscious inferences. there is a great difference between saying that the perception of a shape affords an indication for an inference and saying that the perception of shape is itself an inference. that definite shapes would not be perceived, were it not for neural changes brought about in prior inferences, is a possibility; it may be, for aught i know, an ascertained fact. such telescoping of a perceived object with the object inferred from it may be a constant function; but in any case the telescoping is not a matter of a present inference going on unconsciously, but is the result of an organic modification which has occurred in consequence of prior inferences. in similar fashion, to say that to see a table is to get an indication of something to write on is in no way to say that the perception of a table is an inference from sensory data. to say that certain earlier perceived objects not having as perceived the character of a table have now "fused" with the results of inferences drawn from them is not to say that the perception of the table is now an inference. suppose we say that the first perception was of colored patches; that we inferred from this the possibility of reaching and touching, and that on performing these acts we secured certain qualities of hardness, smoothness, etc., and that these are now all fused with the color-patches. at most this only signifies that certain _previously_ inferred qualities have now become consolidated with qualities from which they were formerly inferred. and such fusion or consolidation is precisely _not inference_. as matter of fact, such "fusion" of qualities, given and _formerly_ inferred, is but a matter of speaking. what has really happened is that _brain_ processes which formerly happened successively now happen simultaneously. what we are dealing with is not a fact of cognition, but a fact of the organic conditions of the occurrence of an act of perception. let us apply the results to the question of sense "illusions." the bent reed in the water comes naturally to mind. purely physical considerations account for the refraction of the light which produces an optical image of a bent stick. this has nothing to do with knowledge or with sense perception--with seeing. it is simply and wholly a matter of the properties of light and a lens. such refractions are constantly produced without our noting them. in the past, however, light refracted and unrefracted has been a constant stimulus to responsive actions. it is a matter of the native constitution of the organism that light stimulates the eyes to follow and the arms to reach and the hands to clutch and handle. as a consequence, certain arrangements of reflected and refracted light have become a sign to perform certain specific acts of handling and touching. as a rule, stimuli and reactions occur in an approximately homogeneous medium--the air. the system of signs or indexes of action set up has been based upon this fact and accommodated to it. a habit or bias in favor of a certain kind of inference has been set up. we infer from a bent ray of light that the hand, in touching the reflecting object, will, at a certain point, have to change its direction. this habit is carried over to a medium in which the conclusion does not hold. instead of saying that light is bent--which it is--we _infer_ that the stick is bent: we infer that the hand could not protract a straight course in handling the object. but an expert fisherman never makes such an error in spearing fish. reacting in media of different refractive capacities, he bases his signs and inferences upon the conditions and results of his media. i see no difference between these cases and that of a man who can read his own tongue. he sees the word "pain" and infers it means a certain physical discomfort. as matter of fact, the thing perceived exists in an unfamiliar medium and signifies bread. to the one accustomed to the french language the right inference occurs.[ ] there is neither error nor truth in the optical image: it just exists physically. but we take it for something else, we behave to it as if it were something else. we _mis_-take it. ii so far as i can see, the pronounced tendency to regard the perceived object as itself the object of a peculiar kind of knowledge instead of as a term in knowledge of the practical kind has two causes. one is the confirmed habit of neglecting the wide scope and import of practical judgments. this leads to overlooking the responsive act as the other term indicated by the perception, and to taking the perceived object as the whole of the situation just by itself. the other cause is the fact that because perceived objects are constantly employed as evidence of what is to be done--or how to do something--they themselves become the objects of prolonged and careful scrutiny. we pass naturally and inevitably from recognition to _observation_. inference will usually take care of itself if the datum is properly determined. at the present day, a skilled physician will have little difficulty in inferring typhoid instead of malaria from certain symptoms provided he can make certain observations--that is, secure certain data from which to infer. the labor of intelligence is thus transferred from inference to the determination of data, the data being determined, however, in the interests of inference and as parts of an inference. at this point, a significant complication enters in. the ordinary assumption in the discussion of the relation of perceived objects to knowledge is that "the" object--the real object--of knowledge in perception is the thing which _caused_ the qualities which are given. it is assumed, that is, that the other term of a proposition in which a sense datum is one term must be the thing which produced it. since this producing object does not for the most part appear in ordinary sense perception, we have on our hands perception as an epistemological problem--the relation of an appearance to some reality which it, somehow, conceals rather than indicates. hence also the difficulties of "reconciling" scientific knowledge in physics where these causes are the terms of the propositions with "empirical" or sense perception knowledge where they do not even appear. here is where the primary advantage of recognizing that ordinary sense perceptions are forms of practical judgment comes in. in practical judgments, the other term is as open and aboveboard as is the sensory quality: it is the thing to be done, the response to be selected. to borrow an illustration of professor woodbridge's: a certain sound indicates to the mother that her baby needs attention. if she turns out to be in error, it is not because sound ought to mean so many vibrations of the air, and as matter of fact doesn't even suggest air vibrations, but because there is wrong inference as to the act to be performed. i imagine that if error never occurred in inferences of this practical sort the human race would have gone on quite contented with them. however that may be, errors _do_ occur and the endeavor to control inference as to consequences (so as to reduce their likelihood of error) leads to propositions where the knowledge-object of the perceived thing is not something to be done, but the cause which produced it. the mother finds her baby peacefully sleeping and says the baby didn't _make_ the noise. she investigates and decides a swinging door _made_ it. instead of inferring a consequence, she infers a cause. if she had identified the noise in the first place, she would have concluded that the hinges needed oiling. now where does the argument stand? the proper control of inference in specific cases is found (_a_) to lie in the proper identification of the datum. if the perception is of a certain kind, the inference takes place as a matter of course; or else inference can be suspended until more adequate data are found, and thus error is avoided even if truth be not found. furthermore (_b_) it is discovered that the most effective way of identifying datum (and securing adequate data) is by inference to its cause. the mother stops short with the baby and the door as causes. but the same motives which made her transfer her inference from consequences to conditions are the motives which lead others to inferring from sounds to vibrations of air. hence our scientific propositions about sensory data. they are not, as such, about things to do, but about things which have been done, have happened--"facts." but they have reference, nevertheless, to inferences regarding consequences to be effected. they are the means of securing data which will prevent errors which would otherwise occur, and which facilitate an entirely new crop of inferences as to possibilities--means and ends--of action. that scientific men should be conscious of this reference or even interested in it is not at all necessary, for i am talking about the logic of propositions, not about biography nor psychology. if i reverted to psychology, it would be to point out that there is no reason in the world why the practical activity of some men should not be predominantly directed into the pursuits connected with discovery. the extent in which they actually are so directed depends upon social conditions. iii we are brought to a consideration of the notion of "primitive" sense data. it was long customary to treat the attempt to define true knowledge in terms derived from sense data as a confusion of psychology--or the history of the growth of knowledge--with logic, the theory of the character of knowledge as knowledge. as matter of fact, there _is_ confusion, but in the opposite direction. the attempt involved a confusion of logic with psychology--that is, it treated a phase of the technique of inference as if it were a natural history of the growth of ideas and beliefs. the chief source of error in ordinary inference is an unrecognized complexity of data. perception which is not experimentally controlled fails to present sufficiently wide data to secure differentia of possible inferences, and it fails to present, even in what is given, lines of cleavage which are important for proper inference. this is only an elaborate way of saying what scientific inquiry has made clear, that, for purposes of inference as to conditions of production of what is present, _ordinary_ sense perception is too narrow, too confused, too vivid as to some _quales_ and too blurred as to some others. let us confine our attention for the moment to confusion. it has often been pointed out that sense qualities being just what they are, it is illegitimate to introduce such notions as obscurity or confusion into them: a slightly illuminated color is just as irretrievably what it is, as clearly itself, as an object in the broad glare of noonday. but the case stands otherwise when the _quale_ is taken as a datum for inference. it is not so easy to identify a perceived object _for purposes of inference_ in the dusk as in bright light. from the standpoint of an inference to be effected, the confusion is the same as an unjustifiable simplification. this over-simplification has the effect of making the _quale_, as a term of inference, ambiguous. to infer from it is to subject ourselves to the danger of all fallacies of ambiguity which are expounded in the textbooks. the remedy is clearly the resolution, by experimental means, of what seems to be a simple datum into its "elements." this is a case of analysis; it differs from other modes of analysis only in the subject-matter upon which it is directed, viz., something which had been previously accepted as a simple whole. the result of this analysis is the existence as objects of perception of isolated qualities like the colors of the spectrum scientifically determined, the tones of the scale in all their varying intensities, etc., in short, the "sensations" or sense qualities of contemporary psychology textbooks or the "simple ideas" of sensation of locke or the "objects of sense" of russell. they are the material of sense perception discriminated for the purpose of better inferences. note that these simple data or elements are not original, psychologically or historically; they are _logical_ primitives--that is, irreducible for purposes of inference. they are simply the most unambiguous and best defined objects of perception which can be secured to serve as _signs_. they are experimentally determined, with great art, precisely because the naturally given, the customary, objects in perception have been ambiguous or confused terms in inference. hence they are replaced, through experimental means involving the use of wide scientific knowledge deductively employed, by simpler sense objects. stated in current phraseology, "sensations" (i.e., qualities present to sense) are not the elements out of which perceptions are composed, constituted, or constructed; they are the finest, most carefully discriminated objects of perception. we do not first perceive a single, thoroughly defined shade, a tint and hue of red; its perception is the last refinement of observation. such things are the limits of perception, but they are final, not initial, limits. they are what is perceived to be given under the most favorable possible conditions; conditions, moreover, which do not present themselves accidentally, but which have to be intentionally and experimentally established, and detection of which exacts the use of a vast body of scientific propositions. i hope it is now evident what was meant by saying that current logic presents us not with a confusion of psychology with logic, but with a wholesale mistaking of logical determinations for facts of psychology. the confusion was begun by locke--or rather made completely current through the enormous influence exercised by locke--and some reference to locke may be of aid in clearing up the point. locke's conception of knowledge was logical, not psychological. he meant by knowledge thoroughly justified beliefs or propositions, "certainty," and carefully distinguished it from what passed current as knowledge at a given time. the latter he called "assent," opinion, belief, or judgment. moreover, his interest in the latter was logical. he was after an art of controlling the proper degree of assent to be given in matters of probability. in short, his sole aim was to determine certainty where certainty is possible and to determine the due degree of probability in the much vaster range of cases where only probability is attainable. a natural history of the growth of "knowledge" in the sense of what happens to pass for knowledge was the last of his interests. but he was completely under the domination of the ruling idea of his time; namely, that _nature_ is the norm of truth. now the earliest period of human life presents the "work of nature" in its pure and unadulterated form. the normal is the original, and the original is the normative. nature is both beneficent and truthful in its work; it retains all the properties of the supreme being whose vice-regent it is. to get the logical ultimates we have only, therefore, to get back to the natural primitives. under the influence of such deistic ideas, locke writes a mythology of the history of knowledge, starting from clear and distinct meanings, each simple, well defined, sharply and unambiguously just what it is on its face, without concealments and complications, and proceeds by "natural" compoundings up to the store of complex ideas, and to the perception of simple relations of agreement among ideas: a perception always certain if the ideas are simple, and always controllable in the case of complex ideas if we consider the simple ideas and their compoundings. thus he established the habit of taking logical discriminations as historical or psychological primitives--as "sources" of beliefs and knowledge instead of as checks upon inference and as means of knowing. i hope reference to locke will not make a scapegoat. i should not have mentioned him if it were not that this way of looking at things found its way over into orthodox psychology and then back again into the foundations of logical theory. it may be said to be the stock in trade of the school of empiricist logicians, and (what is even more important) of the other schools of logic whenever they are dealing with propositions of perception and observation: _vide_ russell's trusting confidence in "atomic" propositions as psychological primitives. it led to the supposition that there is a kind of _knowledge_ or simple apprehension (or sense acquaintance) implying no inference and yet basic to inference. note, if you please, the multitude of problems generated by thinking of whatever is present in experience (as sensory qualities are present) as if it were intrinsically and apart from the use made of its subject-matter of knowledge. _a_) the mind-body problem becomes an integral part of the problem of knowledge. sense organs, neurones, and neuronic connections are certainly involved in the occurrence of a sense quality. if the occurrence of the latter is in and of itself a mode of knowledge, it becomes a matter of utmost importance to determine just how the sense organs take part in it. if one is an idealist he responds with joy to any intimation that the "process of apprehension" (that is, speaking truly, the physical conditions of the occurrence of the sensory datum) transforms the extra-organic stimulus: the alteration is testimony somehow to the constitutive nature of mind! but if he is a realist he conceives himself under obligation to show that the external stimulus is transmitted without any alteration and is apprehended just as it is; color must be shown to be simply, after all, a compacting of vibrations--or else the validity of knowledge is impugned! recognize that knowledge is something _about_ the color, whether about its conditions or causes or consequences or whatever, and that we don't have to identify color itself with a mode of knowing, and the situation changes. we know a color when we understand, just as we know a thunder-storm when we understand. more generally speaking, the relation of brain-change to consciousness is thought to be an essential part of the problem of knowledge. but if the brain is involved in knowing simply as part of the mechanism of acting, as the mechanism for co-ordinating partial and competing stimuli into a single scheme of response, as part of the mechanism of actual experimental inquiry, there is no miracle about the participation of the brain in knowing. one might as well make a problem of the fact that it takes a hammer to drive a nail and takes a hand to hold the hammer as to make a problem out of the fact that it also requires a physical structure to discover and to adapt the particular acts of holding and striking which are needed. _b_) the propositions of physical science are not found among the data of apprehension. mathematical propositions may be disposed of by making them purely a priori; propositions about sense objects by making them purely a posteriori.[ ] but physical propositions, such as make up physics, chemistry, biology, to say nothing of propositions of history, anthropology, and society, are neither one nor the other. i cannot state the case better than mr. russell has stated it, although, i am bound to add, the stating did not arouse in mr. russell any suspicion of the premises with which he was operating. "men of science, for the most part, are willing to condemn immediate data as 'merely subjective,' while yet maintaining the truth of the physics inferred from those data. but such an attitude, though it may be _capable_ of justification, obviously stands in need of it; and the only justification possible must be one which exhibits matter as a logical construction from sense data.... it is therefore necessary to find some way of bridging the gulf between the world of physics and the world of sense."[ ] i do not see how anyone familiar with the two-world schemes which have played such a part in the history of humanity can read this statement without depression. and if it occurred to one that the sole generating condition of _these_ two worlds is the assumption that sense objects are modes of apprehension or knowledge (are so intrinsically and not in the use made of them), he might think it a small price to pay to inquire into the standing of this assumption. for it was precisely the fact that sense perception and physical science appeared historically (in the seventeenth century) as rival modes of knowing the same world which led to the conception of sense objects as "subjective"--since they were so different from the objects of science. unless sense and science had both first been thought of as modes of knowing and then as modes of knowing the same things, there would not have been the slightest reason for regarding immediate data, as "merely subjective." they would have been natural phenomena, like any other. that they are phenomena which involve the interaction of an organism with other things is just an important discovery about them, as is also a discovery about starch in plants. physical science is the _knowledge_ of the world by their means. it is a rival, not of them, but of the medley of prior dogmas, superstitions, and chance opinions about the world--a medley which grew up and nourished precisely because of absence of a will to explore and of a technique for detecting unambiguous data. that mr. russell, who is a professed realist, can do no better with the problem (once committed to the notion that sense objects are of themselves _objects_ of knowledge) than to hold that although the world of physics is not a legitimate inference from sense data, it is a permissible logical construction from them--permissible in that it involves no logical inconsistencies--suggests that the pragmatic difference between idealist and realist--of this type--is not very great. from necessary ideal constructions to permissible logical constructions involves considerable difference in technique but no perceptible practical difference. and the point of this family likeness is that both views spring from regarding sense perception and science as ways of knowing the same objects, and hence as rivals until some scheme of conciliation has been devised. _c_) it is but a variant of this problem to pass to what may be called either the ego-centric predicament or the private-public problem. sense data differ from individual to individual. if they are recognized to be natural events, this variation is no more significant than any change depending upon variation of generating conditions. one does not expect two lumps of wax at different distances from a hot body to be affected exactly alike; the upsetting thing would be if they were. neither does one expect cast-iron to react exactly as does steel. that organisms, because of different positions or different internal structures, should introduce differences in the phenomena which they respectively have a share in producing is a fact of the same nature. but make the sense qualities thus produced not natural events (which may then be made either objects of inquiry or means of inquiry into something else) but modes of knowing, and every such deviation marks a departure from true knowing: it constitutes an anomaly. taken _en masse_ the deviations are so marked as to lead to the conclusion (even on the part of a realist like mr. russell) that they constitute a world of private existences, which, however, may be correlated without logical inconsistency with other such worlds. not all realists are leibnizian monadists as is mr. russell; i do not wish to leave the impression that all come to just this solution. but all who regard sense data as apprehensions have on their hands in some form the problem of the seemingly distorting action exercised by the individual knower upon a public or common thing known or believed in. iv i am not trying to discuss or solve these problems. on the contrary, i am trying to show that these problems exist only because of the identification of a datum determined with reference to control of inference with a self-sufficient knowledge-object. as against this assumption i point to the following facts. what is actually given as matter of empirical fact may be indefinitely complicated and diffused. as empirically existent, perceived objects never constitute the whole scope of the given; they have a context of indefinite extent in which they are set. to control inference it is necessary to analyze this complex situation--to determine what is data for inference and what is irrelevant. this analysis involves discriminative resolution into more ultimate simples. the resources of experimentation, all sorts of microscopic, telescopic, and registering apparatus, are called in to perform that analysis. as a result we differentiate not merely visual data from auditory--a discrimination effected by experiments within the reach of everybody--but a vast multitude of visual and auditory data. physics and physiology and anatomy all play a part in the analysis. we even carry the analysis to the point of regarding, say, a color as a self-included object unreferred to any other object. we may avoid a false inference by conceiving it, not as a quality of any object, but as merely a product of a nervous stimulation and reaction. instead of referring it to a ribbon or piece of paper we may refer it to the organism. but this is only as a part of the technique of suspended inference. we avoid some habitual inference in order to make a more careful inference. thus we escape, by a straightening out of our logic (by avoiding erecting a system of logical distinctions and checks into a mythological natural history), the epistemological problems. we also avoid the contradiction which haunts every epistemological scheme so far propounded. as matter of fact every proposition regarding what is "given" to sensation or perception is dependent upon the assumption of a vast amount of scientific knowledge which is the result of a multitude of prior analyses, verifications, and inferences. what a combination of tantalus and sisyphus we get when we fancy that we have cleared the slate of all these material implications, fancy that we have really started with simple and independent givens, and then try to show how from these original givens we can arrive at the very knowledge which we have all the time employed in the discovery and fixation of the simple sense data![ ] science as a practical art no one will deny that, as seen from one angle science is a pursuit, an enterprise--a mode of practice. it is at least that, no matter how much more or else it is. in course of the practice of knowing distinctive practical judgments will then naturally be made. especially does this hold good when an intellectual class is developed, when there is a body of persons working at knowing as another body is working at farming or engineering. moreover, the instrumentalities of this inquiring class gain in importance for all classes in the degree in which it is realized that success in the conduct of the practice of farming or engineering or medicine depends upon use of the successes achieved in the business of knowing. the importance of the latter is thrown into relief from another angle if we consider the enterprises, like diplomacy, politics, and, to a considerable extent, morals, which do not acknowledge a thoroughgoing and constant dependence upon the practice of science. as hobbes was wont to say, the advantages of a science of morals are most obvious in the evils which we suffer from its lack. to say that something is to be learned, is to be found out, is to be ascertained or proved or believed, is to say that something is to be done. every such proposition in the concrete is a practical proposition. every such proposition of inquiry, discovery and testing will have then the traits assigned to the class of practical propositions. they imply an incomplete situation going forward to completion, and the proposition as a specific organ of carrying on the movement. i have not the intention of dwelling at length upon this theme. i wish to raise in as definite and emphatic a way as possible a certain question. suppose that the propositions arising within the _practice_ of knowing and functioning as agencies in its conduct could be shown to present all the distinctions and relations characteristic of the subject-matter of logic: what would be the conclusion? to an unbiased mind the question probably answers itself: all purely logical terms and propositions fall within the scope of the class of propositions of inquiry as a special form of propositions of practice. my further remarks are not aimed at _proving_ that the case accords with the hypothesis propounded, but are intended to procure hospitality for the hypothesis. if thinking is the art by which knowledge is practiced, then the materials with which thinking deals may be supposed, by analogy with the other arts, to take on in consequence special shapes. the man who is making a boat will give wood a form which it did not have, in order that it may serve the purposes to which it is to be put. thinking may then be supposed to give its material the form which will make it amenable to its purpose--attaining knowledge, or, as it is ordinarily put, going from the unknown to the known. that physical analysis and synthesis are included in the processes of investigation of natural objects makes them a part of the practice of knowing. and it makes any general traits which result in consequence of such treatment characters of _objects as they are involved in knowledge-getting_. that is to say, if there are any features which natural existences assume in order that inference may be more fertile and more safe than it would otherwise be, those features correspond to the special traits which would be given to wood in process of constructing a boat. they are manufactured, without being any worse because of it. the question which i raised in the last paragraph may then be restated in this fashion: are there such features? if there are, are they like those characters which books on logic talk about? comparison with language may help us. language--i confine myself for convenience to spoken language--consists of sounds. but it does not consist simply of those sounds which issue from the human organs prior to the attempt to communicate. it has been said that an american baby before talking makes almost every sound found in any language. but elimination takes place. and so does intensification. certain sounds originally slurred over are made prominent; the baby has to work for them and the work is one which he neither undertakes nor accomplishes except under the incitation of others. language is chiefly marked off, however, by articulation; by the arrangement of what is selected into an orderly sequence of vowels and consonants with certain rules of stress, etc. it may fairly be said that speech is a manufactured article: it consists of natural ebullitions of sound which have been shaped for the sake of being effective instrumentalities of a purpose. for the most part the making has gone on under the stress of the necessities of communication with little deliberate control. works on phonetics, dictionaries, grammars, rhetorics, etc., mark some participation of deliberate intention in the process of manufacture. if we bring written language into the account, we should find the conscious factor extended somewhat. but making, shaping for an end, there is, whether with or without conscious control. now while there is something in the antecedent properties of sound which enters into the determination of speech, the _worth_ of speech is in no way measured by faithfulness to these antecedent properties. it is measured only by its efficiency and economy in realizing the special results for which it is constructed. written language need not look like sounds any more than sounds look like objects. it must _represent_ articulate sounds, but faithful representation is wholly a matter of carrying the mind to the same outcome, of exercising the same function, not of resemblance or copying. original structure _limits_ what may be made out of anything: one cannot (at least at present) make a silk purse out of pigs' bristles. but this conditioning relationship is very different from one in which the antecedent existences are a model or prototype to which the consequent must be servilely faithful. the boatmaker must take account of the grain and strength of his wood. to take account of, to reckon with, is a very different matter, however, from repetition or literal loyalty. the measure is found in the consequences for which existences are used. i wish, of course, to suggest that logical traits are just features of original existences as they have been worked over for use in inference, as the traits of manufactured articles are qualities of crude materials modified for specific purposes. upon the whole, past theories have vibrated between treating logical traits as "subjective," something resident in "mind" (mind being thought of as an immaterial or psychical existence independent of natural things and events), and ascribing ontological pre-existence to them. thus far in the history of thought, each method has flourished awhile and then called out a reaction to its opposite. the reification (i use the word here without prejudice) of logical traits has taken both an idealistic form (because of emphasis upon their spiritual or ideal nature and stuff) and a realistic one, due to emphasis upon their immediate apprehension and givenness. that mathematics have been from plato to descartes and contemporary analytic realism the great provocative of realistic idealisms is a familiar fact. the hypothesis here propounded is a _via media_. what has been overlooked is the reality and importance of art and its works. the tools and works of art are neither mental, subjective things, nor are they antecedent entities like crude or raw material. they are the latter shaped for a purpose. it is impossible to overstate their objectivity from the standpoint of their existence and their efficacy within the operations in question; nor their objectivity in the sense of their dependence upon prior natural existences whose traits have to be taken account of, or reckoned with, by the operations of art. in the case of the art of inference, the art securely of going from the given to the absent, the dependence of mind upon inference, the fact that wherever inference occurs we have a conscious agent--one who recognizes, plans, invents, seeks out, deliberates, anticipates, and who, reacting to anticipations, fears, hates, desires, etc.--explains the theories which, because of misconception of the nature of mind and consciousness, have labeled logical distinctions psychical and subjective. in short, the theory shows why logical features have been made into ontological entities and into mental states. to elaborate this thesis would be to repeat what has been said in all the essays of this volume. i wish only to call attention to certain considerations which may focus other discussions upon this hypothesis. . the existence of inference is a fact, a fact as certain and unquestioned as the existence of eyes or ears or the growth of plants, or the circulation of the blood. one observes it taking place everywhere where human beings exist. a student of the history of man finds that history is composed of beliefs, institutions, and customs which are inexplicable without acts of inference. this fact of inference is as much a datum--a hard fact--for logical theory as any sensory quality whatsoever. it is something men do as they walk, chew, or jump. there is nothing a priori or ideological about it. it is just a brute empirically observable event. . its importance is almost as conspicuous as its existence. every act of human life, not springing from instinct or mechanical habit, contains it; most habits are dependent upon some amount of it for their formation, as they are dependent upon it for their readaptation to novel circumstances. from the humblest act of daily life to the most intricate calculations of science and the determination and execution of social, legal, and political policies, things are used as signs, indications, or evidence from which one proceeds to something else not yet directly given. . the act of inferring takes place naturally, i.e., without intention. it is at first something we do, not something which we _mean_ to do. we do it as we breathe or walk or gesture. only after it is done do we notice it and reflect upon it--and the great mass of men no more reflect upon it after its occurrence than they reflect upon the process of walking and try to discover its conditions and mechanism. that an individual, an animal organism, a man or a woman performs the acts is to say something capable of direct proof through appeal to observation; to say that something called mind, or consciousness does it is itself to employ inference and dubious inference. the fact of inference is much surer, in other words, than that of a particular inference, such as that to something called reason or consciousness, in connection with it; save as mind is but another word for the fact of inference, in which case of course it cannot be re-referred to as its cause, source, or author. moreover, by all principles of science, inference cannot be referred to mind or consciousness as its condition, unless there is _independent_ proof of the existence of that mind to which it is referred. prima facie we are conscious or aware _of_ inference precisely as we are of anything else, not by introspection of something within the very consciousness which is supposed to be its source, but by observation of something taking place in the world--as we are conscious of walking _after_ we have walked. after it has been done naturally--or "unconsciously"--it may be done "consciously," that is, with intent or on purpose. but this means that it is done _with_ consciousness (whatever consciousness may be discovered to mean), not that it is done _by_ consciousness. now if other natural events characteristic only (so far as can be ascertained) of highly organized beings are marked by unique or by distinctive traits, there is good ground for the assumption that inference will be so marked. as we do not find the circulation of blood or the stimulation of nerves in a stone, and as we expect as a matter of course to find peculiar conditions, qualities, and consequences in the being where such operations occur, so we do not find the act of inference in a stone, and we expect peculiar conditions, qualities, and consequences in whatever beings perform the act. unless, in other words, all the ordinary canons of inquiry are suspended, inference is not an isolated nor a merely formal event. as against the latter, it has its own distinctive structure and properties; as against the former, it has specific generating conditions and specific results. . possibly all this seems too obvious for mention. but there is often a virtual conspiracy in philosophy, not to mention obvious things nor to dwell upon them: otherwise remote speculations might be brought to a sudden halt. the point of these commonplaces resides in the push they may give anyone to engage in a search for _distinctive features in the act of inference_. the search may perhaps be best initiated by noting the seeming inconsistency between what has been said about inference as an art and inference as a natural, unpremeditated occurrence. the obvious function of spontaneous inference is to bring before an agent absent considerations to which he may respond as he otherwise responds to the stimulating force of the given situation. to infer rain is to enable one to behave _now_ as given conditions would not otherwise enable him to conduct himself. this instigation to behave toward the remote in space or time is the primary trait of the inferential act; descriptively speaking, the act consists in taking up an attitude of response to an absent thing as if it were present. but just because the thing is absent, the attitude taken may be either irrelevant and positively harmful or extremely pertinent and advantageous. we may infer rain when rain is not going to happen, and acting upon the inference be worse off than if there had been no inference. or we may make preparations, which we would not otherwise have made; the rain may come, and the inference save our lives--as the ark saved noah. inference brings, in short, truth and falsity into the world, just as definitely as the circulation of the blood brings its distinctive consequences, both advantages and liabilities into the world, or as the existence of banking brings with it consequences of business extension and of bankruptcy not previously existent. if the reader objects to the introduction of the terms "truth" and "falsity", i am perfectly willing to leave the choice of words to him, provided the fact is recognized that through inference men are capable of a kind of success and exposed to a kind of failure not otherwise possible: dependent upon the fact that inference takes absent things as being in a certain real continuum with present things, so that our attitude toward the latter is bound up with our reaction to the former as parts of the same situation. and in any event, i wish to protest against a possible objection to the introduction of the terms "false" and "true." it may be said that inference is not responsible for the occurrence of errors and truths, because these accompany simple apprehensions where there is no inference: as when i see a snake which isn't there--or any other case which may appear to the objector to afford an illustration of his point. the objection illustrates my point. to affirm a snake is to affirm potentialities going beyond what is actually given; it says that what is given is _going_ to do something--the doing characteristic of a snake, so that we are to react to the given as to a snake. or if we take the case of a face in the cloud recognized as a phantasy; then (to say nothing of "in the cloud" which involves reference beyond the given) "phantasy," "dream," equally means a reference to objects and considerations _not_ given as the actual datum is given. we have not got very far with our question of distinctive, unique traits called into existence by inference, but we have got far enough to have light upon what is called the "transcendence" of knowledge. all inference is a _going beyond_ the assuredly present to an absent. hence it is a more or less precarious journey. it is transcending limits of security of immediate response. the stone which reacts only to stimuli of the present, not of the future, cannot make the mistakes which a being reacting to a future taken to be connected with the present is sure to make. but it is important to note just what this transcendence consists in. it has nothing to do with transcending mental states to arrive at an external object. _it is behaving to the given situation as involving something not given._ it is robinson crusoe going from a seen foot to an unseen man, not from a mental state to something unmental. . the mistakes and failures resulting from inference constitute the ground for transition from natural spontaneous performance to a technique or deliberate art of inference. there is something humorous about the discussion of the problem of error as if it were a rare or exceptional thing--an anomaly--when the barest glance at human history shows that mistakes have been the rule, and that truth lies at the bottom of a well. as to inferences bound up with barely keeping alive, man has had to effect a considerable balance of good guesses over bad. aside from this somewhat narrow field, the original appearance of inference upon the scene probably added to the interest of life rather than to its efficiency. if the classic definition of man as a rational animal means simply an inferring or guessing animal, it applies to the natural man, for it allows for the guesses being mostly wrong. if it is used with its customary eulogistic connotations, it applies only to man chastened to the use of a hardly won and toilsome art. if it alleges that man has any natural preference for a reasonable inference or that the rationality of an inference is a measure of its hold upon him, it is grotesquely wrong. to propagate this error is to encourage man in his most baleful illusion, and to postpone the day of an effective and widespread adoption of a perfected art of knowing. summarily put, the waste and loss consequent upon the natural happening of inference led man, slowly and grudgingly, to the adoption of safeguards in its performance. in some part, the scope of which is easily exaggerated, man has come to attribute many of the ills from which he suffers to his own premature, inept, and unguarded performing of inference, instead of to fate, bad luck, and accident. in some things, and to some extent in all things, he has invented and perfected an art of inquiry: a system of checks and tests to be used before the conclusion of inference is categorically affirmed. its nature has been considered in many other places in these pages, but it may prove instructive to restate it in this context. _a_) nothing is less adapted to a successful accomplishing of an inference than the subject-matter from which it ordinarily fares forth. that subject-matter is a nest of obscurities and ambiguities. the ordinary warnings against trusting to imagination, the bad name which has come intellectually to attach to fancy, are evidences that anything may suggest anything. regarding most of the important happenings in life no inference has been too extravagant to obtain followers and influence action, because subject-matter was so variegated and complex that any objects which it suggested had a prima facie plausibility. that every advance in knowledge has been effected by using agencies which break up a complex subject-matter into independent variables (from each of which a distinct inference may be drawn), and by attacking each one of these things by every conceivable tool for further resolution so as to make sure we are dealing with something so simple as to be unambiguous, is the report of the history of science. it is sometimes held that knowledge comes ultimately to a necessity of belief, or acceptance, which is the equivalent of an incapacity to think otherwise than so and so. well, even in the case of such an apparently simple "self-evident" thing as a red, this inability, if it is worth anything, is a residuum from experimental analysis. we do not believe in the thing as red (whenever there is a need of scientific testing) till we have exhausted all kinds of active attack and find the red still resisting and persisting. ordinarily we move the head; we shade the eyes; we turn the thing over; we take it to a different light. the use of lens, prism, or whatever device, is simply carrying farther the use of like methods as of physical resolution. whatever endures all these active (not mental) attacks, we accept--pending invention of more effective weapons. to make sure that a given fact _is_ just and such a shade of red is, one may say, a final triumph of scientific method. to turn around and treat it as something naturally or psychologically given is a monstrous superstition. when assured, such a simple datum is for the sake of guarding the act of inference. color may mean a lot of things; any red may mean a lot of things; such things are ambiguous; they afford unreliable evidence or signs. to get the color down to the last touch of possible discrimination is to limit its range of testimony; ideally, it is to secure a voice which says but one thing and says that unmistakably. its simplicity is not identical with isolation, but with _specified_ relationship. thus the hard "facts," the brute data, the simple qualities or ideas, the sense elements of traditional and of contemporary logic, get placed and identified within the art of controlling inference. the allied terms "self-evident," "sensory truths," "simple apprehensions" have their meanings unambiguously determined in this same context; while apart from it they are the source of all kinds of error. they are no longer notions to conjure with. they express the last results attainable by present physical methods of discriminative analysis employed in the search for dependable data for inference. improve the physical means of experimentation, improve the microscope or the registering apparatus or the chemical reagent, and they may be replaced tomorrow by new, simple apprehensions of simple and ultimate data. _b_) natural or spontaneous inference depends very largely upon the habits of the individual in whom inferring takes place. these habits depend in turn very largely upon the customs of the social group in which he has been brought up. an eclipse suggests very different things according to the rites, ceremonies, legends, traditions, etc., of the group to which the spectator belongs. the average layman in a civilized group may have no more personal science than an australian bushman, but the legends which determine his reactions are different. his inference is better, neither because of superior intellectual capacity, nor because of more careful personal methods of knowing, but because his instruction has been superior. the instruction of a scientific inquirer in the best scientific knowledge of his day is just as much a part of the control (or art) of inference as is the technique of observational analysis which he uses. as the bulk of prior ascertainments increases, the tendency is to identify this stock of learning, this store of achieved truth, with knowledge. there is no objection to this identification save as it leads the logician or epistemologist to ignore that which _made_ it "knowledge" (that which gives it a right to the title), and as a consequence to fall into two errors: one, overlooking its function in the guidance and handling of future inferences; the other, confusing the mere act of reference to what is known (known so far as it has accrued from prior tested inquiries) with knowing. to remind myself of what is known as to the topic with which i am dealing is an indispensable performance, but to call this reminder "knowing" (as the presentative realist usually does) is to confuse a psychological event with a logical achievement. it is from misconception of this act of reminding one's self of what is known, as a check in some actual inquiry, that arise most of the fallacies about simple acquaintance, mere apprehension, etc.--the fallacies which eliminate inquiry and inferring from knowledge. _c_) the art of inference gives rise to specific features characterizing the _inferred_ thing. the natural man reacts to the suggested thing as he would to something present. that is, he tends to accept it uncritically. the man called up by the footprint on the sand is just as real a man as the footprint is a real footprint. it is a _man_, not the idea of a man, which is indicated. what a thing means is another _thing_; it doesn't mean a meaning. the only difference is that the thing indicated is farther off, or more concealed, and hence (probably) more mysterious, more powerful and awesome, on that account. the man indicated to crusoe by the footprints was like a man of menacing powers seen at a distance through a telescope. things naturally inferred are accepted, in other words, by the natural man on altogether too realistic a basis for adequate control; they impose themselves too directly and irretrievably. there are no alternatives save either acceptance or rejection _in toto_. what is needed for control is some device by which they can be treated for just what they are, namely, _inferred_ objects which, however assured as objects of _prior_ experiences, are uncertain as to their existence in connection with the object from which present inference sets out. while more careful inspection of the given object--to see if it be really a footprint, how fresh, etc.--may do much for safe-guarding inference; and while forays into whatever else is known may help, there is still need for something else. we need some method of freely examining and handling the object in its status as an inferred object. this means some way of detaching it, as it were, from the particular act of inference in which it presents itself. without some such detachment, crusoe can never get into a free and effective relation with the man indicated by the footprint. he can only, so to speak, go on repeating, with continuously increasing fright, "there's a man about, there's a man about." the "man" needs to be treated, not as man, but as something having a merely inferred and hence potential status; as a meaning or thought, or "idea." there is a great difference between meaning and _a_ meaning. meaning is simply a function of the situation: this thing means that thing: meaning is this relationship. a meaning is something quite different; it is not a function, but a specific entity, a peculiar thing, namely the man _as_ suggested. words are the great instrument of translating a relation of inference existing between two things into a new kind of thing which can be operated with on its own account; the term of discourse or reflection is the solution of the requirement for greater flexibility and liberation. let me repeat: crusoe's inquiry can play freely around and about the man inferred from the footprint only as he can, so to say, get away from the immediate suggestive force of the footprint. as it originally stands, the man suggested is on the same coercive level as the suggestive footprint. they are related, tied together. but a gesture, a sound, may be used as a _substitute_ for the thing inferred. it exists independently of the footprint and may therefore be thought about and ideally experimented with irrespective of the footprint. it at once preserves the meaning-force of the situation and detaches it from the immediacy of the situation. it is a meaning, an idea. here we have, i submit, the explanation of notions, forms, essences, terms, subsistences, ideas, meanings, etc. they are surrogates of the objects of inference of such a character that they may be elaborated and manipulated exactly as primary things may be, so far as inference is concerned. they can be brought into relation with one another, quite irrespective of the things which originally suggested them. without such free play reflective inquiry is mockery, and control of inference an impossibility. when a speck of light suggests to the astronomer a comet, he would have nothing to do but either to accept the inferred object as a real one, or to reject it as a mere fancy unless he could treat "comet" for the time being not as a thing at all, but as a meaning, a conception; a meaning having, moreover, by connection with other meanings, implications--meanings consequent from it. unless a meaning is an inferred object, detached and fixed as a term capable of independent development, what sort of a ghostly being is it? except on the basis stated, what is the transition from the function of meaning to _a_ meaning as an entity in reasoning? and, once more, unless there is such a transition, is reasoning possible? cats have claws and teeth and fur. they do not have implications. no physical thing has implications. the _term_ "cat" has implications. how can this difference be explained? on the ground that we cannot use the "cat" object inferred from given indications in such a way as will test the inference and make it fruitful, helpful, unless we can detach it from its existential dependence upon the particular things which suggest it. we need to know what a cat would be _if_ it were there; what other things would also be indicated if the cat is really indicated. we therefore create a _new_ object: we take something to stand for the cat-in-its-status-as-inferred in contrast with the cat as a live thing. a sound or a visible mark is the ordinary mechanism for producing such a new object. whatever the physical means employed, we now have a new object; a term, a meaning, a notion, an essence, a form or species, according to the terminology which may be in vogue. it is as much a specific existence as any sound or mark is. but it is a mark which notes, concentrates, and records an outcome of an inference which is not yet accepted and affirmed. that is to say, it designates an object which is _not yet_ to be reacted to as one reacts to the given stimulus, but which is an object of further examination and inquiry, a medium of a postponed conclusion and of investigation continued till better grounds for affirming an object (making a definite, unified response) are given. _a term is an object so far as that object is undergoing shaping in a directed act of inquiry._ it may be called a possible object or a hypothetical object. such objects do not walk or bite or scratch, but they are nevertheless actually present as the vital agencies of reflection. if we but forget where they live and operate--within the event of controlled inference--we have on our hands all the mysteries of the double world of existence and essence, particular and universal, thing and idea, ordinary life and science. for the world of science, especially of mathematical science, is the world of considerations which have approved themselves to be effectively regulative of the operations of inference. it is easier to wash with ordinary water than with h{ }o, and there is a marked difference between falling off a building and / _gt_^{ }. but h{ }o and / _gt_^{ } are as potent for the distinctive act of inference--as genuine and distinctive an act as washing the hands or rolling down hill--as ordinary water and falling are impotent. scientific men can handle these things-of-inference precisely as the blacksmith handles his tools. they are not thoughts as they are ordinarily used, not even in the logical sense of thought. they are rather things whose manipulation (as the blacksmith manipulates his tools) yield knowledge--or methods of knowledge--with a minimum of recourse to thinking and a maximum of efficiency. when one considers the importance of the enterprise of knowledge, it is not surprising that appropriate tools have been devised for carrying it on, and that these tools have no prototypes in pre-existent materials. they are real objects, but they are just the real objects which they are and not some other objects. theory and practice our last paragraphs have touched upon the nature of science. they contain, by way of intimation, an explanation of the distance which lies between the things of daily intercourse and the terms of science. controlled inference is science, and science is, accordingly, a highly specialized industry. it is such a specialized mode of practice that it does not appear to be a mode of practice at all. this high specialization is part of the reason for the current antithesis of theory and practice, knowledge and conduct, the other part being the survival of the ancient conception of knowledge as intuitive and dialectical--the conception which is set forth in the aristotelian logic. starting from the hypothesis that the art of controlled inference requires for its efficient exercise specially adapted entities, it follows that the various sciences are the various forms which the industry of controlled inquiry assumes. it follows that the conceptions and formulations of the sciences--physical and mathematical--concern things which have been reshaped in view of the exigencies of regulated and fertile inference. to get things into the estate where such inference is practicable, many qualities of the water and air, cats and dogs, stones and stars, of daily intercourse with the world have been dropped or depressed. much that was trivial or remote has been elevated and exaggerated. neither the omissions nor the accentuations are arbitrary. they are purposeful. they represent the changes in the things of ordinary life which are needed to safeguard the important business of inference. there is then a great difference between the entities of science and the things of daily life. this may be fully acknowledged. but unless the admission is accompanied by an ignoring of the function of inference, it creates no problem of conciliation, no need of apologizing for either one or the other. it generates no problem of the real and the apparent. the "real" or "true" objects of science are those which best fulfil the demands of secure and fertile inference. to arrive at them is such a difficult operation, there are so many specious candidates clamoring for the office, that it is no wonder that when the objects suitable for inference are constituted, they tend to impose themselves as _the_ real objects, in comparison with which the things of ordinary life are but impressions made upon us (according to much modern thought), or defective samples of being--according to much of ancient thought. but one has only to note that their genuinely characteristic feature is fitness for the aims of inference to awaken from the nightmare of all such problems. they differ from the things of the common world of action and association as the means and ends of one occupation differ from those of another. the difference is not that which exists between reality and appearance, but is that between the subject-matter of crude occupations and of a highly specialized and difficult art, upon the success of which (so it is discovered) the progress of other occupations ultimately depends. the entities of science are not only _from_ the scientist; they are also _for_ him. they express, that is, not only the outcome of reflective inquiries, but express them in the particular form in which they can enter most directly and efficiently into subsequent inquiries. the fact that they are sustained within the universe of inquiry accounts for their remoteness from the things of daily life, the latter being promptly precipitated out of suspense in such solutions. that most of the immediate qualities of things (including the so-called secondary qualities) are dropped signifies that such qualities have not turned out to be fruitful for inference. that mathematical, mechanical, and "primary" distinctions and relations have come to constitute the proper subject-matter of science signifies that they represent such qualities of original things as are most manipular for knowledge-getting or assured and extensive inference. consider what a hard time the scientific man had in getting away from other qualities, and how the more immediate qualities have been pressed upon him from all quarters, and it is not surprising that he inclines to think of the intellectually useful properties as alone "real" and to relegate all others to a quasi-illusory field. but his victory is now sufficiently achieved so that this tension may well relax; it may be acknowledged that the difference between scientific entities and ordinary things is one of function, the former being selected and arranged for the successful conduct of inferential knowings. i conclude with an attempt to show how bootless the ordinary antithesis between knowledge (or theory) and practice becomes when we recognize that it really involves only a contrast between the kinds of judgments appropriate to ordinary modes of practice and those appropriate to the specialized industry of knowledge-getting. it is not true that to insist that scientific propositions fall within the domain of practice is to depreciate them. on its face, the insistence means simply that all knowledge involves experimentation, with whatever appliances are suited to the problem in hand, of an active and physical type. instead of this doctrine leading to a low estimate of knowledge, the contrary is the case. this art of experimental thinking turns out to give the key to the control and development of other modes of practice. i have touched elsewhere in these essays upon the way in which knowledge is the instrument of regulation of our human undertakings, and i have also pointed out that intrinsic increments of meaning accrue in consequence of thinking. i wish here to point how that mode of practice which is called theorizing emancipates experience--how it makes for steady progress. no matter how much specialized skill improves, we are restricted in the degree in which our ends remain constant or fixed. significant progress, progress which is more than technical, depends upon ability to foresee new and different results and to arrange conditions for their effectuation. science is the instrument of increasing our technique in attaining results already known and cherished. more important yet, it is the method of emancipating us from enslavement to customary ends, the ends established in the past. let me borrow from political philosophy a kind of caricature of the facts. as social philosophers used to say that the state came into existence when individuals agreed to surrender some of their native personal rights for the sake of getting the advantages of non-interference and aid from others who made a like surrender, so we might say that science began when men gave up the claim to form the structure of knowledge each from himself as a center and measure of meaning--when there was an agreement to take an impersonal standpoint. non-scientific modes of practice, left to their natural growth, represent, in other words, arrangements of objects which cluster about the self, and which are closely tied down to the habits of the self. science or theory means a system of objects detached from any particular personal standpoint, and therefore available for any and every possible personal standpoint. even the exigencies of ordinary social life require a slight amount of such detachment or abstraction. i must neglect my own peculiar ends enough to take some account of my neighbor if i am going to be intelligible to him. i must at least find common ground. science systematizes and indefinitely extends this principle. it takes its stand, not with what is common with some particular neighbor living at this especial date in this particular village, but with any possible neighbor in the wide stretches of time and space. and it does so by the mere fact that it is continually reshaping its peculiar objects with an eye single to availability in inference. the more abstract, the more impersonal, the more impartially objective are _its_ objects, the greater the variety and scope of inference made possible. every street of experience which is laid out by science has its tracks for transportation, and every line issues transfer checks to every other line. you and i may keep running in certain particular ruts, but conditions are provided for somebody else to foresee--or infer--new combinations and new results. the depersonalizing of the things of everyday practice becomes the chief agency of their repersonalizing in new and more fruitful modes of practice. the paradox of theory and practice is that theory is with respect to all other modes of practice the most practical of all things, and the more impartial and impersonal it is, the more truly practical it is. and this is the sole paradox. but lest the man of science, the man of dominantly reflective habits, be puffed up with his own conceits, he must bear in mind that practical application--that is, experiment--is a condition of his own calling, that it is indispensable to the institution of knowledge or truth. consequently, in order that he keep his own balance, it is needed that his findings be everywhere applied. the more their application is confined within his own special calling, the less meaning do the conceptions possess, and the more exposed they are to error. the widest possible range of application is the means of the deepest verification. as long as the specialist hugs his own results they are vague in meaning and unsafe in content. that individuals in every branch of human endeavor should be experimentalists engaged in testing the findings of the theorist is the sole final guaranty for the sanity of the theorist. footnotes: [ ] _scientific method in philosophy_, p. . [ ] the analytic realists have shown a peculiar disinclination to discuss the nature of future consequences as terms of propositions. they certainly are not identical with the mental act of referring to them; they are "objective" to it. do they, therefore, already subsist in some realm of subsistence? or is subsistence but a name for the fact of logical reference, leaving the determination of the meaning of "subsistence" dependent upon a determination of the meaning of "logical"? more generally, what is the position of analytic realism about the future? [ ] supposing the question to be that of some molten state of the earth in past geologic ages. taken as the complete subject-matter of a proposition--or science--the facts discovered cannot be regarded as causative of, or a mechanism of, the appearance of life. for by definition they form a closed system; to introduce reference to a future event is to deny the definition. contrariwise, a statement of that past condition of the earth as a mechanical condition of the later emergence of life means that that past stage is taken not merely as past, but as in process of transition to its future, as in process of alteration in the direction of life. change in this direction is an integral part of a statement of the early stage of the earth's history. a purely geologic statement may be quite accurate in its own universe of discourse and yet quite incomplete and hence inaccurate in another universe of discourse. that is to say, a geologist's propositions may accurately set forth a prior state of things, while ignoring any reference to a later state entailed by them. but a would-be philosophy may not ignore the implied future. [ ] _philosophical essays_, pp. , . [ ] _sixth meditation._ [ ] _principles of philosophy_, p. . [ ] _treatise of human nature_, part iii, sec. iii. [ ] it is perhaps poor tactics on my part to complicate this matter with anything else. but it is evident that "passions" and pains and pleasures may be used as _evidences_ of something beyond themselves (as may the fact of being more than five feet high) and so get a representative or cognitive status. is there not also a prima facie presumption that all sensory qualities are of themselves bare existences or occurrences without cognitive pretension, and that they acquire the latter status as signs or evidence of something else? epistemological idealists or realists who admit the non-cognitive character of pleasure and pain would seem to be under special obligations carefully to consider the thesis of the non-cognitive nature of all sensory qualities except as they are employed as indications or indexes of some other thing. this recognition frees logic from the epistemological discussion of secondary qualities. [ ] to readers who have grasped the thought of my argument, it may not be meaningless to say that the typical idealistic fallacy is to import into the direct experience the results of the intellectual or reflective examination, while that of realism is to treat the reflective operation as dealing with precisely the same subject-matter as the original act was concerned with--taking the good of "reason" and the good of immediate behavior to be the same sort of things. and both fallacies will result from any assimilation of two different acts to one another through giving them both the title "knowledge," and hence treating the difference between them as simply the difference between a direct apprehension and a mediated one. [ ] analytic realism ought to be favorable to such a hedonism; the fact that present-day analytic realists are not favorable would seem to indicate that they have not taken their logic seriously enough, but have been restrained, by practical motives, from applying it thoroughly. to say that the moral life presents a high degree of organization and integration is to say something which is true, but is also to say something which by the analytic logic calls for its resolution into ultimate and independent simples. unless they accept the pleasures and pains of bentham as such ultimates, they are bound to present acceptable substitutes. but here they tend to shift their logic and to make the fulfilment of some _organization_ (variously defined) the standard good. consistency would then admit the hypothesis that in _all_ cases an eventual organization rather than antecedent simples supply the standard of knowledge. meanwhile the term "fulfilment" (or any similar term) stands as an acknowledgment that the organization in question is not something ontologically prior but is one yet to be achieved. [ ] it must not be overlooked that a mere reminder of an end previously settled upon may operate as a sufficient stimulus to action. it is probably this act of calling the end to mind which the realist confuses with knowledge, and therefore terms apprehension. but there is nothing cognitive about it, any more than there is in pressing a button to give the signal for an act already decided upon. [ ] upholders of this view generally disguise the assumption of repetition by the notion that what is judged is progress in the direction of approximation to an eternal value. but as matter of fact, progress is never judged (as i have had repeated occasion to point out) by reference to a transcendent eternal value, but in reference to the success of the end-in-view in meeting the needs and conditions of the specific situation--a surrender of the doctrine in favor of the one set forth in the text. logically, the notion of progress as approximation has no place. the thesis should read that we always try to repeat a given value, but always fail as a matter of fact. and constant failure is a queer name for progress. [ ] see ix and x _ante_. [ ] i use the term "image" in the sense of optics, not of psychology. [ ] that something of the cognitive, something of the sign or term function, enters in as a catalyzer, so to speak, in even the most aesthetic experiences, seems to be altogether probable, but that question it is not necessary to raise here. [ ] the superstition that whatever influences the action of a conscious being must be an unconscious sensation or perception, if it is not a conscious one, should be summarily dismissed. we are active beings from the start and are naturally, wholly apart from consciousness, engaged in redirecting our action in response to changes in our surroundings. _alternative_ possibilities, and hence an indeterminate situation, change direct response into a response mediated by a perception as a sign of possibilities, that is, a physiological stimulus into a perceived quality: a sensory datum. [ ] compare woodbridge, _journal of philosophy and psychology_, x, . [ ] see russell, _scientific method in philosophy_, p. . [ ] _ibid._, p. . [ ] see the essay on _the existence of the world as a logical problem_. index analysis, ff., ff. _see also_ data; sensations. appreciation, ff., . apprehension, simple (also acquaintance), , , , , , . _see also_ inference; perception; presentationalism. behavior, , , . _see also_ consequences; practical. bosanquet, b., n. bush, w. t., n., n. conflict, as stimulus to thinking, ff., , , iii, ff., , , . _see also_ practical. consciousness, , , , , . consequences, , , , ff., ff. constitutive thought, . data, ff., , iv, viii, xi, , , . _see also_ sensations. deduction, , ff. descartes, . design, ff. desire, ff. dialectic, . doubt, , , , , , , . _see also_ conflict. ego-centric predicament, , , . _see also_ subjectivity. ends and means, ff., ff., ff. error, ff. essence, , , , , ff. _see also_ meaning. evidence, , ff., , , , . _see also_ inference. experience, ff., n., ff., ff., , , n., , , , , . experiment. _see_ experience. facts. _see_ data. genetic, , , . hedonism, ff. hegel, . holt, e. b., n. hume, n., . hypothesis. _see_ idea; meaning. idea, , , , , ff., vii, viii, ff., , . _see also_ meaning. idealism, ff., ff., ff., ff., , n. illusions, ff. image, n., , . implication, n., . _see also_ inference. indeterminate, . inference, , ff., , , n., , , - , ff., . _see also_ data; evidence; ideas; thinking. instrumentalism, , , , , , , , , . invaluable, . james, william, , xii, , . jones, h., n., , n. klyce, s., - n. knowledge, ff., , ff., v, , ff., , , ff. _see also_ apprehension; perception; thinking. language, , , , , . locke, ff. logical theory, , ff., ff., , , , , , . lotze, ii-v, . mathematics, , , , , . mead, g. h., . meaning, ff., , , , , , , iv, ff., , , , ff. _see also_ essence; idea. mechanism, . montague, w. p., n. moore, a. w., . mill, j. s., , , , , n. nature as norm, . organization, , , , . peirce, c. s., , . perception, ff., , - . perry, r. b., , n. philosophy, ff. practical, xii, xiii, xiv. pragmatism, xii, . _see also_ conflict; consequences; purpose. presentationalism, ix. privacy, , . _see also_ subjectivity. psychology, , , , , , , ff., . _see also_ logical theory. purpose, , , , ff., . realism, ff., ff., , , , ix, x, , n. reality, ff. royce, j., n. russell, b., xi, , , ff. santayana, g., , . self. _see_ subjectivity. sensation, ff., ff., , xi, ff., . _see also_ data. sidgwick, a., n. sign. _see_ evidence. subjectivity, ff., , , , , , , , , , . suggestion, ff., ff. temporal place, , , , ff., , ff., . terms, ff., ff. thinking, ff., , ff., ff., , , , ii-vi. transcendence, . truth, , , , , , , , , , , , , . two worlds, , . value, - . woodbridge, f. j. e., n., n., n., . * * * * * transcriber's notes: obvious printer's errors were repaired. otherwise retained spellings and punctuation (including hypenation variations) as in the original. p. : "philosophic disciplines"; original reads "philosophic disciples." p. : "(in a direct experience"; original reads "in direct a experience." transposition corrected. ten cases of lettered paragraph labels with closing but no opening parentheses were retained--"a)" on p. , , and , "b)" on p. , , and , and "c)" on p. and . transcriber's note: . text enclosed by underscores is in italics (_italics_). . in the mathematical expressions in this text the carat character represents 'raised to the power' (example: + = ^ ). . the original text includes greek characters. for this text file version these letters have been replaced with their transliterations, with the exception of greek letter 'pi' which is represented as [pi]. studies in logical theory by john dewey professor of philosophy with the co-operation of members and fellows of the department of philosophy the decennial publications second series volume xi chicago the university of chicago press copyright, by the university of chicago preface this volume presents some results of the work done in the matter of logical theory in the department of philosophy of the university of chicago in the first decade of its existence. the eleven studies are the work of eight different hands, all, with the exception of the editor, having at some period held fellowships in this university, dr. heidel in greek, the others in philosophy. their names and present pursuits are indicated in the table of contents. the editor has occasionally, though rarely, added a footnote or phrase which might serve to connect one study more closely with another. the pages in the discussion of hypothesis, on mill and whewell, are by him. with these exceptions, each writer is individually and completely responsible for his own study. the various studies present, the editor believes, about the relative amount of agreement and disagreement that is natural in view of the conditions of their origin. the various writers have been in contact with one another in seminars and lecture courses in pursuit of the same topics, and have had to do with shaping one another's views. there are several others, not represented in this volume, who have also participated in the evolution of the point of view herein set forth, and to whom the writers acknowledge their indebtedness. the disagreements proceed from the diversity of interests with which the different writers approach the logical topic; and from the fact that the point of view in question is still (happily) developing and showing no signs of becoming a closed system. if the studies themselves do not give a fair notion of the nature and degree of the harmony in the different writers' methods, a preface is not likely to succeed in so doing. a few words may be in place, however, about a matter repeatedly touched upon, but nowhere consecutively elaborated--the more ultimate philosophical bearing of what is set forth. all agree, the editor takes the liberty of saying, that judgment is the central function of knowing, and hence affords the central problem of logic; that since the act of knowing is intimately and indissolubly connected with the like yet diverse functions of affection, appreciation, and practice, it only distorts results reached to treat knowing as a self-inclosed and self-explanatory whole--hence the intimate connections of logical theory with functional psychology; that since knowledge appears as a function within experience, and yet passes judgment upon both the processes and contents of other functions, its work and aim must be distinctively reconstructive or transformatory; that since reality must be defined in terms of experience, judgment appears accordingly as the medium through which the consciously effected evolution of reality goes on; that there is no reasonable standard of truth (or of success of the knowing function) in general, except upon the postulate that reality is thus dynamic or self-evolving, and, in particular, except through reference to the specific offices which knowing is called upon to perform in readjusting and expanding the means and ends of life. and all agree that this conception gives the only promising basis upon which the working methods of science, and the proper demands of the moral life, may co-operate. all this, doubtless, does not take us very far on the road to detailed conclusions, but it is better, perhaps, to get started in the right direction than to be so definite as to erect a dead-wall in the way of farther movement of thought. in general, the obligations in logical matters of the writers are roughly commensurate with the direction of their criticisms. upon the whole, most is due to those whose views are most sharply opposed. to mill, lotze, bosanquet, and bradley the writers then owe special indebtedness. the editor acknowledges personal indebtedness to his present colleagues, particularly to mr. george h. mead, in the faculty of philosophy, and to a former colleague, dr. alfred h. lloyd, of the university of michigan. for both inspiration and the forging of the tools with which the writers have worked there is a pre-eminent obligation on the part of all of us to william james, of harvard university, who, we hope, will accept this acknowledgment and this book as unworthy tokens of a regard and an admiration that are coequal. table of contents i. thought and its subject-matter by john dewey ii. thought and its subject-matter: the antecedents of thought by john dewey iii. thought and its subject-matter: the datum of thinking by john dewey iv. thought and its subject-matter: the content and object of thought by john dewey v. bosanquet's theory of judgment by helen bradford thompson, ph.d., director of the psychological laboratory of mount holyoke college vi. typical stages in the development of judgment by simon fraser mclennan, ph.d., professor of philosophy in oberlin college vii. the nature of hypothesis by myron lucius ashley, ph.d., instructor, american correspondence school viii. image and idea in logic by willard clark gore, ph.d., assistant professor of psychology in the university of chicago ix. the logic of the pre-socratic philosophy by william arthur heidel, ph.d., professor of latin in iowa college x. valuation as a logical process by henry waldgrave stuart, ph.d., instructor in philosophy in the state university of iowa xi. some logical aspects of purpose by addison webster moore, ph.d., assistant professor of philosophy in the university of chicago i thought and its subject-matter: the general problem of logical theory no one doubts that thought, at least reflective, as distinct from what is sometimes called constitutive, thought, is derivative and secondary. it comes after something and out of something, and for the sake of something. no one doubts that the thinking of everyday practical life and of science is of this reflective type. we think about; we reflect over. if we ask what it is which is primary and radical to thought; if we ask what is the final objective for the sake of which thought intervenes; if we ask in what sense we are to understand thought as a derived procedure, we are plunging ourselves into the very heart of the logical problem: the relation of thought to its empirical antecedents and to its consequent, truth, and the relation of truth to reality. yet from the naïve point of view no difficulty attaches to these questions. the antecedents of thought are our universe of life and love; of appreciation and struggle. we think about anything and everything: snow on the ground; the alternating clanks and thuds that rise from below; the relation of the monroe doctrine to the embroglio in venezuela; the relation of art to industry; the poetic quality of a painting by botticelli; the battle of marathon; the economic interpretation of history; the proper definition of cause; the best method of reducing expenses; whether and how to renew the ties of a broken friendship; the interpretation of an equation in hydrodynamics; etc. through the madness of this miscellaneous citation there appears so much of method: anything--event, act, value, ideal, person, or place--may be an object of thought. reflection busies itself alike with physical nature, the record of social achievement, and the endeavors of social aspiration. it is with reference to _such_ affairs that thought is derivative; it is with reference to them that it intervenes or mediates. taking some part of the universe of action, of affection, of social construction, under its special charge, and having busied itself therewith sufficiently to meet the special difficulty presented, thought releases that topic and enters upon further more direct experience. sticking for a moment to this naïve standpoint, we recognize a certain rhythm of direct practice and derived theory; of primary construction and of secondary criticism; of living appreciation and of abstract description; of active endeavor and of pale reflection. we find that every more direct primary attitude passes upon occasion into its secondary deliberative and discursive counterpart. we find that when the latter has done its work it passes away and passes on. from the naïve standpoint such rhythm is taken as a matter of course. there is no attempt to state either the nature of the occasion which demands the thinking attitude, nor to formulate a theory of the standard by which is judged its success. no general theory is propounded as to the exact relationship between thinking and what antecedes and succeeds it. much less do we ask how empirical circumstances can generate rationality of thought; nor how it is possible for reflection to lay claim to power of determining truth and thereby of constructing further reality. if we were to ask the thinking of naïve life to present, with a minimum of theoretical elaboration, its conception of its own practice, we should get an answer running not unlike this: thinking is a kind of activity which we perform at specific need, just as at other need we engage in other sorts of activity: as converse with a friend; draw a plan for a house; take a walk; eat a dinner; purchase a suit of clothes; etc., etc. in general, its material is anything in the wide universe which seems to be relevant to this need--anything which may serve as a resource in defining the difficulty or in suggesting modes of dealing effectively with it. the measure of its success, the standard of its validity, is precisely the degree in which the thinking actually disposes of the difficulty and allows us to proceed with more direct modes of experiencing, that are forthwith possessed of more assured and deepened value. if we inquire why the naïve attitude does not go on to elaborate these implications of its own practice into a systematic theory, the answer, on its own basis, is obvious. thought arises in response to its own occasion. and this occasion is so exacting that there is time, as there is need, only to do the thinking which is needed in that occasion--not to reflect upon the thinking itself. reflection follows so naturally upon its appropriate cue, its issue is so obvious, so practical, the entire relationship is so organic, that once grant the position that thought arises in reaction to specific demand, and there is not the particular type of thinking called logical theory because there is not the practical demand for reflection of that sort. our attention is taken up with particular questions and specific answers. what we have to reckon with is not the problem of, how can i think _überhaupt_? but, how shall i think right _here and now_? not what is the test of thought at large, but what validates and confirms _this_ thought? in conformity with this view, it follows that a generic account of our thinking behavior, the generic account termed logical theory, arises at historic periods in which the situation has lost the organic character above described. the general theory of reflection, as over against its concrete exercise, appears when occasions for reflection are so overwhelming and so mutually conflicting that specific adequate response in thought is blocked. again, it shows itself when practical affairs are so multifarious, complicated, and remote from control that thinking is held off from successful passage into them. anyhow (sticking to the naïve standpoint), it is true that the stimulus to that particular form of reflective thinking termed logical theory is found when circumstances require the act of thinking and nevertheless impede clear and coherent thinking in detail; or when they occasion thought and then prevent the results of thinking from exercising directive influence upon the immediate concerns of life. under these conditions we get such questions as the following: what is the relation of rational thought to crude or unreflective experience? what is the relation of thought to reality? what is the barrier which prevents reason from complete penetration into the world of truth? what is it that makes us live alternately in a concrete world of experience in which thought as such finds not satisfaction, and in a world of ordered thought which is yet only abstract and ideal? it is not my intention here to pursue the line of historical inquiry thus suggested. indeed, the point would not be mentioned did it not serve to fix attention upon the nature of the logical problem. it is in dealing with this latter type of questions that logical theory has taken a turn which separates it widely from the theoretical implications of practical deliberation and of scientific research. the two latter, however much they differ from each other in detail, agree in a fundamental principle. they both assume that every reflective problem and operation arises with reference to some _specific_ situation, and has to subserve a _specific_ purpose dependent upon its own occasion. they assume and observe distinct limits--limits from which and to which. there is the limit of origin in the needs of the particular situation which evokes reflection. there is the limit of terminus in successful dealing with the particular problem presented--or in retiring, baffled, to take up some other question. the query that at once faces us regarding the nature of logical theory is whether reflection upon reflection shall recognize these limits, endeavoring to formulate them more exactly and to define their relationships to each other more adequately; or shall it abolish limits, do away with the matter of specific conditions and specific aims of thought, and discuss thought and its relation to empirical antecedents and rational consequents (truth) at large? at first blush, it might seem as if the very nature of logical theory as generalization of the reflective process must of necessity disregard the matter of particular conditions and particular results as irrelevant. how, the implication runs, could reflection become generalized save by elimination of details as irrelevant? such a conception in fixing the central problem of logic fixes once for all its future career and material. the essential business of logic is henceforth to discuss the relation of thought as such to reality as such. it may, indeed, involve much psychological material, particularly in the discussion of the processes which antecede thinking and which call it out. it may involve much discussion of the concrete methods of investigation and verification employed in the various sciences. it may busily concern itself with the differentiation of various types and forms of thought--different modes of conceiving, various conformations of judgment, various types of inferential reasoning. but it concerns itself with any and all of these three fields, not on their own account or as ultimate, but as subsidiary to the main problem: the relation of thought as such, or at large, to reality as such, or at large. some of the detailed considerations referred to may throw light upon the terms under which thought transacts its business with reality; upon, say, certain peculiar limitations it has to submit to as best it may. other considerations throw light upon the ways in which thought gets at reality. still other considerations throw light upon the forms which thought assumes in attacking and apprehending reality. but in the end all this is incidental. in the end the one problem holds: how do the specifications of thought as such hold good of reality as such? in fine, logic is supposed to grow out of the epistemological inquiry and to lead up to its solution. from this point of view various aspects of logical theory are well stated by an author whom later on we shall consider in some detail. lotze[ ] refers to "universal forms and principles of thought which hold good everywhere both in judging of reality and in weighing possibility, _irrespective of any difference in the objects_." this defines the business of _pure_ logic. this is clearly the question of thought as such--of thought at large or in general. then we have the question "of how far the most complete structure of thought ... can claim to be an adequate account of that which we seem compelled to assume as the object and occasion of our ideas." this is clearly the question of the relation of thought at large to reality at large. it is epistemology. then comes "applied logic," having to do with the actual employment of concrete forms of thought with reference to investigation of specific topics and subjects. this "applied" logic would, if the standpoint of practical deliberation and of scientific research were adopted, be the sole genuine logic. but the existence of thought _in itself_ having been agreed upon, we have in this "applied" logic only an incidental inquiry of how the particular resistances and oppositions which "pure" thought meets from particular matters may best be discounted. it is concerned with methods of investigation which obviate defects in the relationship of thought at large to reality at large, as these present themselves under the limitations of human experience. it deals merely with hindrances, and with devices for overcoming them; it is directed by considerations of utility. when we reflect that this field includes the entire procedure of practical deliberation and of concrete scientific research, we begin to realize something of the significance of the theory of logic which regards the limitations of specific origination and specific outcome as irrelevant to its main problem, which assumes an activity of thought "pure" or "in itself," that is, "irrespective of any difference in its objects." this suggests, by contrast, the opposite mode of stating the problem of logical theory. generalization of the nature of the reflective process certainly involves elimination of much of the specific material and contents of the thought-situations of daily life and of critical science. quite compatible with this, however, is the notion that it seizes upon _certain_ specific conditions and factors, and aims to bring them to clear consciousness--not to abolish them. while eliminating the particular material of particular practical and scientific pursuits, ( ) it may strive to hit upon the common denominator in the various situations which are antecedent or primary to thought and which evoke it; ( ) it may attempt to show how typical features in the specific antecedents of thought call out to diverse typical modes of thought-reaction; ( ) it may attempt to state the nature of the specific consequences in which thought fulfils its career. ( ) it does not eliminate dependence upon specific occasions as provocative of thought; but endeavors to define _what_ in the various situations constitutes them thought-provoking. the specific occasion is not eliminated, but insisted upon and brought into the foreground. consequently psychological considerations are not subsidiary incidents, but of essential importance so far as they enable us to trace the generation of the thought-situation. ( ) so from this point of view the various types and modes of conceiving, judging, and inference are treated, not as qualifications of thought per se or at large, but of thought engaged in its specific, most economic, effective response to its own particular occasion; they are adaptations for control of stimuli. the distinctions and classifications that have been accumulated in "formal" logic are relevant data; but they demand interpretation from the standpoint of use as organs of adjustment to material antecedents and stimuli. ( ) finally the question of validity, or ultimate objective of thought, is relevant; but is such as a matter of the specific issue of the specific career of a thought-function. all the typical investigatory and verificatory procedures of the various sciences are inherently concerned as indicating the ways in which thought actually brings itself to its own successful fulfilment in dealing with various types of problems. while the epistemological type of logic may, as we have seen, leave (under the name of applied logic), a subsidiary place open for the instrumental type, the type which deals with thinking as a specific procedure relative to a specific antecedent occasion and to a subsequent specific fulfilment, is not able to reciprocate the favor. from its point of view, an attempt to discuss the antecedents, data, forms, and objective of thought, apart from reference to particular position occupied, and particular part played in the growth of experience is to reach results which are not so much either true or false as they are radically meaningless--because they are considered apart from limits. its results are not only abstractions (for all theorizing ends in abstractions), but abstractions without possible reference or bearing. from this point of view, the taking of something, whether that something be thinking activity, its empirical condition, or its objective goal, apart from the limits of a historic or developing situation, is the essence of _metaphysical_ procedure--in the sense of metaphysics which makes a gulf between it and science. as the reader has doubtless anticipated, it is the object of this chapter to present the problem and industry of reflective thought from this latter point of view. i recur again to the standpoint of naïve experience, using the term in a sense wide enough to cover both practical procedure and concrete scientific research. i resume by saying that this point of view knows no fixed distinction between the empirical values of unreflective life and the most abstract process of rational thought. it knows no fixed gulf between the highest flight of theory and control of the details of practical construction and behavior. it passes, according to the occasion and opportunity of the moment, from the attitude of loving and struggling and doing to that of thinking and the reverse. its contents or material shift their values back and forth from technological or utilitarian to æsthetic, ethic, or affectional. it utilizes data of perception or of discursive ideation as need calls, just as an inventor now utilizes heat, now mechanical strain, now electricity, according to the demands set by his aim. from this point of view, more definite logical import is attached to our earlier statements (p. ) regarding the possibility of taking anything in the universe of experience as subject-matter of thought. anything from past experience may be taken which appears to be an element in either the statement or the solution of the present problem. thus we understand the coexistence without contradiction of an indeterminate possible field and a limited actual field. the undefined set of means becomes specific through reference to an end. in all this, there is no difference of kind between the methods of science and those of the plain man. the difference is the greater control in science of the statement of the problem, and of the selection and use of relevant material, both sensible or ideational. the two are related to each other just as the hit-or-miss, trial-and-error inventions of uncivilized man stand to the deliberate and consecutively persistent efforts of a modern inventor to produce a certain complicated device for doing a comprehensive piece of work. neither the plain man nor the scientific inquirer is aware, as he engages in his reflective activity, of any transition from one sphere of existence to another. he knows no two fixed worlds--reality on one side and mere subjective ideas on the other; he is aware of no gulf to cross. he assumes uninterrupted, free, and fluid passage from ordinary experience to abstract thinking, from thought to fact, from things to theories and back again. observation passes into development of hypothesis; deductive methods pass to use in description of the particular; inference passes into action with no sense of difficulty save those found in the particular task in question. the fundamental assumption is _continuity_ in and of experience. this does not mean that fact is confused with idea, or observed datum with voluntary hypothesis, theory with doing, any more than a traveler confuses land and water when he journeys from one to the other. it simply means that each is placed and used with reference to service rendered the other, and with reference to future use of the other. only the epistemological spectator is aware of the fact that the everyday man and the scientific man in this free and easy intercourse are rashly assuming the right to glide over a cleft in the very structure of reality. this fact raises a query not favorable to the epistemologist. why is it that the scientific man, who is constantly plying his venturous traffic of exchange of facts for ideas, of theories for laws, of real things for hypotheses, should be so wholly unaware of the radical and generic (as distinct from specific) difficulty of the undertakings in which he is engaged? we thus come afresh to our inquiry: does not the epistemological logician unwittingly transfer the specific difficulty which always faces the scientific man--the difficulty in detail of correct and adequate translation back and forth of _this_ set of facts and _this_ group of ideas--into a totally different problem of the wholesale relation of thought at large with reality in general? if such be the case, it is clear that the very way in which the epistemological type of logic states the problem of thinking, in relation both to empirical antecedents and to objective truth, makes that problem insoluble. working terms, terms which as working are flexible and historic, relative, are transformed into absolute, fixed, and predetermined forms of being. we come a little closer to the problem when we recognize that every scientific inquiry passes historically through at least four stages. (_a_) the first of these stages is, if i may be allowed the bull, that in which scientific inquiry does not take place at all, because no problem or difficulty in the quality of the experience has presented itself to provoke reflection. we have only to cast our eye back from the existing status of any science, or back from the status of any particular topic in any science, to discover a time when no reflective or critical thinking busied itself with the matter--when the facts and relations were taken for granted and thus were lost and absorbed in the value which accrued from the experience. (_b_) after the dawning of the problem, there comes a period of occupation with relatively crude and unorganized facts--the hunting for, locating, and collecting of raw material. this is the empiric stage, which no existing science, however proud in its attained rationality, can disavow as its own progenitor. (_c_) then there is also a speculative stage: a period of guessing, of making hypotheses, of framing ideas which later on are labeled and condemned as only ideas. there is a period of distinction and classification-making which later on is regarded as only mentally-gymnastic in character. and no science, however proud in its present security of experimental assurance, can disavow a scholastic ancestor. (_d_) finally, there comes a period of fruitful interaction between the mere ideas and the mere facts: a period when observation is determined by experimental conditions depending upon the use of certain guiding conceptions; when reflection is directed and checked at every point by the use of experimental data, and by the necessity of finding such form for itself as will enable it to serve as premise in a deduction leading to evolution of new meanings, and ultimately to experimental inquiry, which brings to light new facts. in the emerging of a more orderly and significant region of fact, and of a more coherent and self-luminous system of meaning, we have the natural limit of evolution of the logic of a given science. but consider what has happened in this historic record. unanalyzed experience has broken up into distinctions of facts and ideas; the factual side has been developed by indefinite and almost miscellaneous descriptions and cumulative listings; the conceptual side has been developed by unchecked and speculative elaboration of definitions, classifications, etc. there has been a relegation of accepted meanings to the limbo of mere ideas; there has been a passage of some of the accepted facts into the region of mere hypothesis and opinion. conversely, there has been a continued issuing of ideas from the region of hypotheses and theories into that of facts, of accepted objective and meaningful contents. out of a world of only _seeming_ facts, and of only _doubtful_ ideas, there emerges a universe continually growing in definiteness, order, and luminosity. this progress, verified in every record of science, is an absolute monstrosity from the standpoint of the epistemology which assumes a thought in general, on one side, and a reality in general, on the other. the reason that it does not present itself as such a monster and miracle to those actually concerned with it is because there is a certain _homogeneity_ or _continuity_ of reference and of use which controls all diversities in both the modes of existence specified and the grades of value assigned. the distinction of thought and fact is treated in the growth of a science, or of any particular scientific problem, as an _induced_ and _intentional_ practical division of labor; as relative assignments of position with reference to performance of a task; as deliberate distribution of forces at command for their more economic use. the interaction of bald fact and hypothetical idea into the outcome of a single world of scientific apprehension and comprehension is but the successful achieving of the aim on account of which the distinctions in question were instituted. thus we come back to the problem of logical theory. to take the distinctions of thought and fact, etc., as ontological, as inherently fixed in the make-up of the structure of being, is to treat the actual development of scientific inquiry and scientific control as a mere subsidiary topic ultimately of only utilitarian worth. it is also to state the terms upon which thought and being transact business in a way so totally alien to the use made of these distinctions in concrete experience as to create a problem which can be discussed only in terms of itself--not in terms of the conduct of life--metaphysics again in the bad sense of that term. as against this, the problem of a logic which aligns itself with the origin and employ of reflective thought in everyday life and in critical science, is to follow the natural history of thinking as a life-process having its own generating antecedents and stimuli, its own states and career, and its own specific objective or limit. this point of view makes it possible for logical theory to come to terms with psychology.[ ] when logic is considered as having to do with the wholesale activity of thought per se, the question of the historic process by which this or that particular thought came to be, of how its object happens to present itself as sensation, or perception, or conception, is quite irrelevant. these things are mere temporal accidents. the psychologist (not lifting his gaze from the realm of the changeable) may find in them matters of interest. his whole industry is just with natural history--to trace series of psychical events as they mutually excite and inhibit one another. but the logician, we are told, has a deeper problem and an outlook of more unbounded horizon. he deals with the question of the eternal nature of thought and its eternal validity in relation to an eternal reality. he is concerned, not with genesis, but with value, not with a historic cycle, but with absolute distinctions and relations. still the query haunts us: is this so in truth? or has the logician of a certain type arbitrarily made it thus by taking his terms apart from reference to the specific occasions in which they arise and situations in which they function? if the latter, then the very denial of historic relationship and of the significance of historic method, is indicative only of the unreal character of his own abstraction. it means in effect that the affairs under consideration have been isolated from the conditions in which alone they have determinable meaning and assignable worth. it is astonishing that, in the face of the advance of the evolutionary method in natural science, any logician can persist in the assertion of a rigid difference between the problem of origin and of nature; between genesis and analysis; between history and validity. such assertion simply reiterates as final a distinction which grew up and had meaning in pre-evolutionary science. it asserts against the most marked advance which scientific method has yet made a survival of a crude period of logical scientific procedure. we have no choice save either to conceive of thinking as a response to a specific stimulus, or else to regard it as something "in itself," having just in and of itself certain traits, elements, and laws. if we give up the last view, we must take the former. the entire significance of the evolutionary method in biology and social history is that every distinct organ, structure, or formation, every grouping of cells or elements, has to be treated as an instrument of adjustment or adaptation to a particular environing situation. its meaning, its character, its value, is known when, and only when, it is considered as an arrangement for meeting the conditions involved in some specific situation. this analysis of value is carried out in detail by tracing successive stages of development--by endeavoring to locate the particular situation in which each structure has its origin, and by tracing the successive modifications through which, in response to changing media, it has reached its present conformation.[ ] to persist in condemning natural history from the standpoint of what natural history meant before it identified itself with an evolutionary process is not so much to exclude the natural-history standpoint from philosophic consideration as it is to evince ignorance of what it signifies. psychology as the natural history of the various attitudes and structures through which experiencing passes, as an account of the conditions under which this or that state emerges, and of the way in which it influences, by stimulation or inhibition, production of other states or conformations of consciousness, is indispensable to logical evaluation, the moment we treat logical theory as an account of thinking as a mode of adaptation to its own generating conditions, and judge its validity by reference to its efficiency in meeting its problems. the historical point of view describes the sequence; the normative follows the sequence to its conclusion, and then turns back and judges each historical step by viewing it in reference to its own outcome.[ ] in the course of changing experience we keep our balance as we move from situations of an affectional quality to those which are practical or appreciative or reflective, because we bear constantly in mind the context in which any particular distinction presents itself. as we submit each characteristic function and situation of experience to our gaze, we find it has a dual aspect. wherever there is striving there are obstacles; wherever there is affection there are persons who are attached; wherever there is doing there is accomplishment; wherever there is appreciation there is value; wherever there is thinking there is material-in-question. we keep our footing as we move from one attitude to another, from one characteristic quality to another, because we know the position occupied in the whole growth by the particular function in which we are engaged, and the position within the function of the particular element that engages us. the distinction _between_ each attitude and function and its predecessor and successor is serial, dynamic, operative. the distinctions _within_ any given operation or function are structural, contemporaneous, and distributive. thinking follows, we will say, striving, and doing follows thinking. each in the fulfilment of its own function inevitably calls out its successor. but coincident, simultaneous, and correspondent _within_ doing, is the distinction of doer and of deed; _within_ the function of thought, of thinking and material thought upon; within the function of striving, of obstacle of aim, of means and end. we keep our paths straight because we do not confuse the sequential, efficient, and functional relationship of types of experience with the contemporaneous, correlative, and structural distinctions of elements within a given function. in the seeming maze of endless confusion and unlimited shiftings, we find our way by the means of the stimulations and checks occurring within the process we are actually engaged with. we do not contrast or confuse a condition or state which is an element in the formation of one operation with the status or element which is one of the distributive terms of another function. if we do, we have at once an insoluble, because meaningless, problem upon our hands. now the epistemological logician deliberately shuts himself off from those cues and checks upon which the plain man instinctively relies, and which the scientific man deliberately searches for and adopts as constituting his technique. consequently he is likely to set the sort of object or material which has place and significance only in one of the serial functional situations of experience, over against the active attitude which describes part of the structural constitution of another situation; or with equal lack of justification to assimilate terms characteristic of different stages to one another. he sets the agent, as he is found in the intimacy of love or appreciation, over against the externality of the fact, as that is defined within the reflective process. he takes the material which thought selects as its own basis for further procedure to be identical with the significant content which it secures for itself in the successful pursuit of its aim; and this in turn he regards as the material which was presented at the outset, and whose peculiarities were the express means of awakening thought. he identifies the final deposit of the thought-function with its own generating antecedent, and then disposes of the resulting surd by reference to some metaphysical consideration, which remains when logical inquiry, when science (as interpreted by him), has done its work. he does this, not because he prefers confusion to order, or error to truth, but simply because, when the chain of historic sequence is cut, the vessel of thought is afloat to veer upon a sea without soundings or moorings. there are but two alternatives: either there is an object "in itself" of thought "in itself," or else there are a series of values which vary with the varying functions to which they belong. if the latter, the only way these values can be defined is by discriminating the functions to which they belong. it is only conditions relative to a specific period or epoch of development in a cycle of experience which-enables one to tell what to do next, or to estimate the value and meaning of what is already done. and the epistemological logician, in choosing to take his question as one of thought which has its own form just as "thought," apart from the limits of the special work it has to do, has deprived himself of these supports and stays. the problem of logic has a more general and a more specific phase. in its generic form, it deals with this question: how does one type of functional situation and attitude in experience pass out of and into another; for example, the technological or utilitarian into the æsthetic, the æsthetic into the religious, the religious into the scientific, and this into the socio-ethical and so on? the more specific question is: how does the particular functional situation termed the reflective behave? how shall we describe it? what in detail are its diverse contemporaneous distinctions, or divisions of labor, its correspondent _statuses_; in what specific ways do these operate with reference to each other so as to effect the specific aim which is proposed by the needs of the affair? this chapter may be brought to conclusion by reference to the more alternate value of the logic of experience, of logic taken in its wider sense; that is, as an account of the sequence of the various typical functions or situations of experience in their determining relations to one another. philosophy, defined as such a logic, makes no pretense to be an account of a closed and finished universe. its business is not to secure or guarantee any particular reality or value. _per contra_, it gets the significance of a method. the right relationship and adjustment of the various typical phases of experience to one another is a problem felt in every department of life. intellectual rectification and control of these adjustments cannot fail to reflect itself in an added clearness and security on the practical side. it may be that general logic can not become an instrument in the immediate direction of the activities of science or art or industry; but it is of value in criticising and in organizing the tools of immediate research in these lines. it also has direct significance in the valuation for social or life-purposes of results achieved in particular branches. much of the immediate business of life is badly done because we do not know in relation to its congeners the organic genesis and outcome of the work that occupies us. the manner and degree of appropriation of the values achieved in various departments of social interest and vocation are partial and faulty because we are not clear as to the due rights and responsibilities of one function of experience in reference to others. the value of research for social progress; the bearing of psychology upon educational procedure; the mutual relations of fine and industrial art; the question of the extent and nature of specialization in science in comparison with the claims of applied science; the adjustment of religious aspirations to scientific statements; the justification of a refined culture for a few in face of economic insufficiency for the mass--such are a few of the many social questions whose _final_ answer depends upon the possession and use of a general logic of experience as a method of inquiry and interpretation. i do not say that headway cannot be made in such questions apart from the method indicated: a logic of genetic experience. but unless we have a critical and assured view of the juncture in which and with reference to which a given attitude or interest arises, unless we know the service it is thereby called upon to perform and hence the organs or methods by which it best functions in that service, our progress is impeded and irregular. we take a part for a whole, a means for an end, or attack wholesale some other interest because it interferes with the deified sway of the one we have selected as ultimate. a clear and comprehensive consensus of social conviction, and a consequent concentrated and economical direction of effort, are assured only as there is some way of locating the position and rôle of each typical interest and occupation in experience. the domain of opinion is one of conflict; its rule is arbitrary and costly. only intellectual method affords a substitute for opinion. the general logic of experience can alone do for the region of social values and aims what the natural sciences after centuries of struggle are doing for activity in the physical realm. this does not mean that systems of philosophy which have attempted to state the nature either of thought and of reality at large, apart from limits of particular crises in the growth of experience, have been worthless--though it does mean that their industry has been somewhat misapplied. the unfolding of metaphysical theory has made large contributions to positive evaluations of the typical situations and relationships of experience--even when its conscious intention has been quite otherwise. every system of philosophy is itself a mode of reflection; consequently (if our main contention be true), it too has been evoked out of specific social antecedents, and has had its use as a response to them. it has effected something in modifying the situation within which it found its origin. it may not have solved the problem which it consciously put itself; in many cases we may freely admit that the question put has afterward been found to be so wrongly put as to be insoluble. yet exactly the same thing is true, in precisely the same sense, in the history of science. for this reason, if for no other, it is impossible for the scientific man to cast the first stone at the philosopher. the progress of science in any branch continually brings with it a realization that problems in their previous form of statement are insoluble because put in terms of unreal conditions; because the real conditions have been mixed up with mental artifacts or misconstructions. every science is continually learning that its supposed solutions are only apparent, because the "solution" solves, not the actual problem, but one which has been made up. but the very putting of the question, the very giving of the wrong answer, induces modification of existing intellectual habits, standpoints, and aims. wrestling with the problem, there is evolution of new forms of technique to control its treatment, there is search for new facts, institution of new types of experimentation; there is gain in the methodic control of experience. and all this is progress. it is only the worn-out cynic, the devitalized sensualist, and the fanatical dogmatist who interpret the continuous change of science as proving that, since each successive statement is wrong, the whole record is error and folly; and that the present truth is only the error not yet found out. such draw the moral of caring naught for all these things, or of flying to some external authority which will deliver once for all the fixed and unchangeable truth. but historic philosophy even in its aberrant forms has proved a factor in the valuation of experience; it has brought problems to light, it has provoked intellectual conflicts without which values are only nominal; even through its would-be absolutistic isolations, it has secured recognition of mutual dependencies and reciprocal reinforcements. yet if it can define its work more clearly, it can concentrate its energy upon its own characteristic problem: the genesis and functioning in experience of various typical interests and occupations with reference to one another. ii thought and its subject-matter: the antecedent conditions and cues of the thought-function we have discriminated logic in its wider sense, concerned with the sequence of characteristic functions and attitudes in experience, from logic in its stricter meaning, concerned in particular with description and interpretation of the function of reflective thought. we must avoid yielding to the temptation of identifying logic with either of these to the exclusion of the other; or of supposing that it is possible to isolate one finally from the other. the more detailed treatment of the organs and methods of reflection cannot be carried on with security save as we have a correct idea of the historic position of reflection in the evolving of experience. yet it is impossible to determine this larger placing, save as we have a defined and analytic, as distinct from a merely vague and gross, view of what we mean by reflection--what is its actual constitution. it is necessary to work back and forth between the larger and the narrower fields, transforming every increment upon one side into a method of work upon the other, and thereby testing it. the apparent confusion of existing logical theory, its uncertainty as to its own bounds and limits, its tendency to oscillate from larger questions of the inherent worth of judgment and validity of inference over to details of scientific technique, and to translation of distinctions of formal logic into terms of an investigatory or verificatory process, are indications of the need of this double movement. in the next three chapters it is proposed to take up some of the considerations that lie on the borderland between the larger and the narrower conceptions of logical theory. i shall discuss the _locus_ of the function of thought, so far as such _locus_ enables us to select and characterize some of the most fundamental distinctions, or divisions of labor, within the reflective process. in taking up the problem of the subject-matter of thought, i shall try to make clear that it assumes three quite distinct forms according to the epochal moment reached in transformation of experience; and that continual confusion and inconsistency are introduced when these respective meanings are not identified and described according to their respective geneses and places. i shall attempt to show that we must consider subject-matter from the standpoint, first, of the _antecedents_ or conditions that evoke thought; second, of the _datum_ or _immediate material_ presented to thought; and, third, of the _proper content_ of thought. of these three distinctions the first, that of antecedent and stimulus, clearly refers to the situation that is immediately prior to the thought-function as such. the second, that of datum or immediately given matter, refers to a distinction which is made within the thought-process as a part of and for the sake of its own _modus operandi_. it is a status in the scheme of thinking. the third, that of content or object, refers to the progress actually made in any thought-function; the material which is organized into the thought-situation, so far as this has fulfilled its purpose. it goes without saying that these are to be discriminated as stages of a life-process in the natural history of experience, not as ready-made or ontological; it is contended that, save as they are differentiated in connection with well-defined historical stages, they are either lumped off as equivalents, or else treated as absolute divisions--or as each by turns, according to the exigencies of the particular argument. in fact, this chapter will get at the matter of preliminary conditions of thought indirectly rather than directly, by indicating the contradictory positions into which one of the most vigorous and acute of modern logicians, lotze, has been forced through failing to define logical distinctions in terms of the history of readjustment of experience, and therefore endeavoring to interpret certain notions as absolute instead of as periodic and methodological. before passing directly to the exposition and criticism of lotze, it will be well, however, to take the matter in a somewhat freer way. we cannot approach logical inquiry in a wholly direct and uncompromised manner. of necessity we bring to it certain distinctions--distinctions partly the outcome of concrete experience; partly due to the logical theory which has got embodied in ordinary language and in current intellectual habits; partly results of deliberate scientific and philosophic inquiry. these more or less ready-made results are resources; they are the only weapons with which we can attack the new problem. yet they are full of unexamined assumptions; they commit us to all sorts of logically predetermined conclusions. in one sense our study of the new subject-matter, let us say logical theory, is in truth only a review, a re-testing and criticising of the intellectual standpoints and methods which we bring with us to the study. everyone comes with certain distinctions already made between the subjective and the objective, between the physical and the psychical, between the intellectual and the factual. ( ) we have learned to regard the region of emotional disturbance, of uncertainty and aspiration, as belonging somehow peculiarly to ourselves; we have learned to set over against this a world of observation and of valid thought as something unaffected by our moods, hopes, fears, and opinions. ( ) we have also come to distinguish between what is immediately present in our experience and the past and the future; we contrast the realms of memory and anticipation of sense-perception; the given with the ideal. ( ) we are confirmed in a habit of distinguishing between what we call actual fact and our mental attitude toward that fact--the attitude of surmise or wonder or reflective investigation. while one of the aims of logical theory is precisely to make us critically conscious of the significance and bearing of these various distinctions, to change them from ready-made assumptions into controlled constructs, our mental habits are so set that they tend to have their own way with us; and we read into logical theory conceptions that were formed before we had even dreamed of the logical undertaking which after all has for its business to assign to the terms in question their proper meaning. we find in lotze an unusually explicit inventory of these various preliminary distinctions; and an unusually serious effort to deal with the problems which arise from introducing them into the structure of logical theory. ( ) he expressly separates the matter of logical worth from that of psychological genesis. he consequently abstracts the subject-matter of logic as such wholly from the question of historic _locus_ and _situs_. ( ) he agrees with common-sense in holding that logical thought is reflective and thus presupposes a given material. he occupies himself with the nature of the antecedent conditions. ( ) he wrestles with the problem of how a material formed prior to thought and irrespective of it can yet afford it stuff upon which to exercise itself. ( ) he expressly raises the question of how thought working independently and from without upon a foreign material can shape the latter into results which are valid--that is, objective. if his discussion is successful; if lotze can provide the intermediaries which span the gulf between an independent thought-material and an independent thought-activity; if he can show that the question of the origin of thought-material and of thought-activity is irrelevant to the question of its worth, we shall have to surrender the position already taken. but if we find that lotze's elaborations only elaborate the same fundamental difficulty, presenting it now in this light and now in that, but never effecting more than presenting the problem as if it were its own solution, we shall be confirmed in our idea of the need of considering logical questions from a different point of view. if we find that, whatever his formal treatment, he always, as matter of fact, falls back upon some organized situation or function as the source of both the specific thought-material and the specific thought-activity in correspondence with each other, we shall have in so far an elucidation and even a corroboration of our theory. . we begin with the question of the material antecedents of thought--antecedents which condition reflection, and which call it out as reaction or response, by giving it its cue. lotze differs from many logicians of the same type in affording us an explicit account of these antecedents. the ultimate material antecedents of thought are found in impressions, which are due to external objects as stimuli. taken in themselves, these impressions are mere psychical states or events. they exist in us side by side, or one after the other, according as the objects which excite them operate simultaneously or successively. the occurrence of these various psychical states is not, however, entirely dependent upon the presence of the exciting thing. after a state has once been excited, it gets the power of reawakening other states which have accompanied it or followed it. the associative mechanism of revival plays a part. if we had a complete knowledge of both the stimulating object and its effects, and of the details of the associative mechanism, we should be able from given data to predict the whole course of any given train or current of ideas (for the impressions as conjoined simultaneously or successively become ideas and a current of ideas). taken in itself, a sensation or impression is nothing but a "state of our consciousness, a mood of ourselves." any given current of ideas is a necessary sequence of existences (just as necessary as any succession of material events), happening in some particular sensitive soul or organism. "just because, under their respective conditions, every such series of ideas hangs together by the same necessity and law as every other, there would be no ground for making any such distinction of value as that between truth and untruth, thus placing one group in opposition to all the others."[ ] . thus far, as the last quotation clearly indicates, there is no question of reflective thought, and hence no question of logical theory. but further examination reveals a peculiar property of the current of ideas. some ideas are merely coincident, while others may be termed coherent. that is to say, the exciting causes of some of our simultaneous and successive ideas really belong together; while in other cases they simply happen to act at the same time, without there being a real connection between them. by the associative mechanism, however, both the coherent and the merely coincident combinations recur. the first type of recurrence supplies positive material for knowledge; the second gives occasion for error. . it is a peculiar mixture of the coincident and the coherent which sets the peculiar problem of reflective thought. the business of thought is to recover and confirm the coherent, the really connected, adding to its reinstatement an accessory justifying notion of the real ground of coherence, while it eliminates the coincident as such. while the mere current of ideas is something which just happens within us, the process of elimination and of confirmation by means of statement of real ground and basis of connection is an activity which mind as such exercises. it is this distinction which marks off thought as activity from any psychical event and from the associative mechanism as receptive happenings. one is concerned with mere _de facto_ coexistences and sequences; the other with the _worth_ of these combinations.[ ] consideration of the peculiar work of thought in going over, sorting out, and determining various ideas according to a standard of value will occupy us in our next chapter. here we are concerned with the material antecedents of thought as they are described by lotze. at first glance, he seems to propound a satisfactory theory. he avoids the extravagancies of transcendental logic, which assumes that all the matter of experience is determined from the very start by rational thought; and he also avoids the pitfall of purely empirical logic, which makes no distinction between the mere occurrence and association of ideas and the real worth and validity of the various conjunctions thus produced. he allows unreflective experience, defined in terms of sensations and their combinations, to provide material conditions for thinking, while he reserves for thought a distinctive work and dignity of its own. sense-experience furnishes the antecedents; thought has to introduce and develop systematic connection--rationality. a further analysis of lotze's treatment may, however, lead us to believe that his statement is riddled through and through with inconsistencies and self-contradictions; that, indeed, any one part of it can be maintained only by the denial of some other portion. . the impression is the ultimate antecedent in its purest or crudest form (according to the angle from which one views it). it is that which has never felt, for good or for bad, the influence of thought. combined into ideas, these impressions stimulate or arouse the activities of thought, which are forthwith directed upon them. as the recipient of the activity which they have excited and brought to bear upon themselves, they furnish also the material content of thought--its actual stuff. as lotze says over and over again: "it is the relations themselves already subsisting between impressions, when we become conscious of them, by which the action of thought which is never anything but reaction, is attracted; and this action consists merely in interpreting relations which we find existing between our passive impressions into aspects of the matter of impressions."[ ] and again:[ ] "thought can make no difference where it finds none already in the matter of the impressions." and again:[ ] "the possibility and the success of thought's procedure depends upon this original constitution and organization of the whole world of ideas, a constitution which, though not necessary in thought, is all the more necessary to make thinking possible." the impressions and ideas play a versatile rôle; they now assume the part of ultimate antecedents and provocative conditions; of crude material; and somehow, when arranged, of content for thought. this very versatility awakens suspicion. while the impression is merely subjective and a bare state of our own consciousness, yet it is determined, both as to its existence and as to its relation to other similar existences, by external objects as stimuli, if not as causes. it is also determined by a psychical mechanism so thoroughly objective or regular in its workings as to give the same necessary character to the current of ideas that is possessed by any physical sequence. thus that which is "nothing but a state of our consciousness" turns out straightway to be a specifically determined objective fact in a system of facts. that this absolute transformation is a contradiction is no clearer than that just such a contradiction is indispensable to lotze. if the impressions were nothing but states of consciousness, moods of ourselves, bare psychical existences, it is sure enough that we should never even know them to be such, to say nothing of conserving them as adequate conditions and material for thought. it is only by treating them as real facts in a real world, and only by carrying over into them, in some assumed and unexplained way, the capacity of representing the cosmic facts which arouse them, that impressions or ideas come in any sense within the scope of thought. but if the antecedents are really impressions-in-their-objective-setting, then lotze's whole way of distinguishing thought-worth from _mere_ existence or event without objective significance must be radically modified. the implication that impressions have actually a matter or quality or meaning of their own becomes explicit when we refer to lotze's theory that the immediate antecedent of thought is found in the _matter_ of ideas. when thought is said to "take cognizance of _relations_ which its own activity does not originate, but which have been prepared for it by the unconscious mechanism of the psychic states,"[ ] the attribution of objective content, of reference and meaning to ideas, is unambiguous. the idea forms a most convenient half-way house for lotze. on one hand, as absolutely prior to thought, as material antecedent condition, it is merely psychical, a bald subjective event. but as subject-matter for thought, as antecedent which affords stuff for thought's exercise, it is _meaning_, characteristic quality of content. although we have been told that the impression is a mere receptive irritation without participation of mental activity, we are not surprised, in view of this capacity of ideas, to learn that the mind actually has a determining share in both the reception of stimuli and in their further associative combinations. the subject always enters into the presentation of any mental object, even the sensational, to say nothing of the perceptional and the imaged. the perception of a given state of things is possible only on the assumption that "the perceiving subject is at once enabled and compelled by its own nature to combine the excitations which reach it from objects into those forms which it is to perceive in the objects, and which it supposes itself simply to _receive_ from them."[ ] it is only by continual transition from impression and ideas as mental states and events to ideas as cognitive (or logical) _objects or contents_, that lotze bridges the gulf from bare exciting antecedent to concrete material conditions of thought. this contradiction, again, is necessary to lotze's standpoint. to set out frankly with "meanings" as antecedents would demand reconsideration of the whole view-point, which supposes that the difference between the logical and its antecedent is a matter of the difference between _worth_ and mere _existence_ or _occurrence_. it would indicate that since meaning or value is already there, the task of thought must be that of the transformation or _reconstruction of worth_ through an intermediary process of valuation. on the other hand, to stick by the standpoint of _mere_ existence is not to get anything which can be called even antecedent of thought. . why is there a task of transformation? consideration of the material in its function of evoking thought, giving it its cue, will serve to complete the picture of the contradiction and of the real facts. it is the conflict between ideas as merely coincident and ideas as coherent that constitutes the need which provokes the response of thought. here lotze vibrates (_a_) between considering coincidence and coherence as both affairs of existence of psychical events; (_b_) considering coincidence as purely psychical and coherence as at least quasi-logical, and (_c_) the inherent logic which makes them both determinations within the sphere of reflective thought. in strict accordance with his own premises, coincidence and coherence both ought to be mere peculiarities of the current of ideas as events within ourselves. but so taken the distinction becomes absolutely meaningless. events do not cohere; at the most certain sets of them happen more or less frequently than other sets; the only intelligible difference is one of repetition of coincidence. and even this attributes to an event the supernatural trait of reappearing after it has disappeared. even coincidence has to be defined in terms of relation of the _objects_ which are supposed to excite the psychical events that happen together. as recent psychological discussion has made clear enough, it is the matter, meaning, or content, of ideas that is associated, not the ideas as states or existences. take such an idea as sun-revolving-about-earth. we may say it means the conjunction of various sense-impressions, but it is conjunction, or mutual reference, of _attributes_ that we have in mind in the assertion. it is absolutely certain that our psychical image of the sun is not psychically engaged in revolving about our psychical image of the earth. it would be amusing if such were the case; theaters and all dramatic representations would be at a discount. in truth, sun-revolving-about-earth is a single meaning or idea; it is a unified subject-matter within which certain distinctions of reference appear. it is concerned with what we intend when we think earth and sun, and think them in their relation to each other. it is really a specification or direction of how to think when we have occasion to think a certain subject-matter. to treat the origin of this mutual reference as if it were simply a case of conjunction of ideas produced by conditions of original psycho-physical irritation and association is a profound case of the psychological fallacy. we may, indeed, analyze an experience and find that it had its origin in certain conditions of the sensitive organism, in certain peculiarities of perception and of association, and hence conclude that the belief involved in it was not justified by the facts themselves. but the significance of the belief in sun-revolving-about-earth as an item of the experience of those who meant it, consisted precisely in the fact that it was taken not as a mere association of feelings, but as a definite portion of the whole structure of objective experience, guaranteed by other parts of the fabric, and lending its support and giving its tone to them. it was to them part of the experience-frame of things--of the real universe. put the other way, if such an instance meant a mere conjunction of psychical states, there would be in it absolutely nothing to evoke thought. each idea as event, as lotze himself points out (vol. i, p. ), may be regarded as adequately and necessarily determined to the place it occupies. there is absolutely no question on the side of events of mere coincidence _versus_ genuine connection. as event, it is there and it belongs there. we cannot treat something as at once bare fact of existence and as problematic subject-matter of logical inquiry. to take the reflective point of view is to consider the matter in a totally new light; as lotze says, it is to raise the question of rightful claims to a position or relation. the point becomes clearer when we contrast coincidence with connection. to consider coincidence as simply psychical, and coherence as at least quasi-logical, is to put the two on such different bases that no question of contrasting them can arise. the coincidence which precedes a valid or grounded coherence (the conjunction which as coexistence of objects and sequence of acts is perfectly adequate) never is, as antecedent, the coincidence which is set over against coherence. the side-by-sideness of books on my bookshelf, the succession of noises that rise through my window, do not as such trouble me logically. they do not appear as errors or even as problems. one coexistence is just as good as any other until some new point of view, or new end, presents itself. if it is a question of the convenience of arrangement of books, then the value of their present collocation becomes a problem. then i may contrast their present bare conjunction with a scheme of possible coherence. if i regard the sequence of noises as a case of articulate speech, their order becomes important--it is a problem to be determined. the inquiry whether a given combination means only apparent or real connection, shows that reflective inquiry is already going on. does this phase of the moon really mean rain, or does it just happen that the rain-storm comes when the moon has reached this phase? to ask such questions shows that a certain portion of the universe of experience is subjected to critical analysis for purposes of definitive restatement. the tendency to regard one combination as bare conjunction or mere coincidence is absolutely a _part_ of the movement of mind in its search for the real connection. if coexistence as such is to be set over against coherence as such, as the non-logical against the logical, then, since our whole spatial universe is one of collocation, and since thought in this universe can never get farther than substituting one collocation for another, the whole realm of space-experience is condemned off-hand and in perpetuity to anti-rationality. but, in truth, coincidence as over against coherence, conjunction as over against connection, is just _suspected_ coherence, one which is under the fire of active inquiry. the distinction is one which arises only within the grasp of the logical or reflective function. . this brings us explicitly to the fact that there is no such thing as either coincidence or coherence in terms of the elements or meanings contained in any couple or pair of ideas taken by itself. it is only when they are co-factors in a situation or function which includes more than either the "coincident" or the "coherent" and more than the arithmetical sum of the two, that thought's activity can be evoked. lotze is continually in this dilemma: thought either shapes its own material or else just accepts it. in the first case (since lotze cannot rid himself of the presumption that thought must have a fixed ready-made antecedent) its activity can only alter this stuff and thus lead the mind farther away from reality. but if thought just accepts its material, how can there be any distinctive aim or activity of thought at all? as we have seen, lotze endeavors to escape this dilemma by supposing that, while thought receives its material, it yet checks it up: it eliminates certain portions of it and reinstates others, plus the stamp and seal of its own validity. lotze objects most strenuously to the notion that thought awaits its subject-matter with certain ready-made modes of apprehension. this notion would raise the insoluble question of how thought contrives to bring the matter of each impression under that particular form which is appropriate to it (vol. i, p. ). but he has not really avoided the difficulty. how does thought know which of the combinations are merely coincident and which are merely coherent? how does it know which to eliminate as irrelevant and which to confirm as grounded? either this evaluation is an imposition of its own, or else gets its cue and clue from the subject-matter. now, if the coincident and the coherent taken in and of themselves are competent to give this direction, they are already practically labeled. the further work of thought is one of supererogation. it has at most barely to note and seal the material combinations that are already there. such a view clearly renders thought's work as unnecessary in form as it is futile in force. but there is no alternative in this dilemma except to recognize that an entire situation of experience, within which are both that afterward found to be mere coincidence and that found to be real connection, actually provokes thought. it is only as an experience previously accepted comes up in its wholeness against another one equally integral; and only as some larger experience dawns which requires each as a part of itself and yet within which the required factors show themselves mutually incompatible, that thought arises. it is not bare coincidence, or bare connection, or bare addition of one to the other, that excites thought. it is a situation which is organized or constituted as a whole, and which yet is falling to pieces in its parts--a situation which is in conflict within itself--that arouses the search to find what really goes together and a correspondent effort to shut out what only seemingly belongs together. and real coherence means precisely capacity to exist within the comprehending whole. it is a case of the psychologist's fallacy to read back into the preliminary situation those distinctions of mere conjunction of material and of valid relationship which get existence, to say nothing of fixation, only within the thought-process. we must not leave this phase of the discussion, however, until it is quite clear that our objection is not to lotze's position that reflective thought arises from an antecedent which is not reflectional in character; nor yet to his idea that this antecedent has a certain structure and content of its own setting the peculiar problem which evokes thought and gives the cue to its specific activities. on the contrary, it is this latter point upon which we would insist; and, by insisting, point out, negatively, that this view is absolutely inconsistent with lotze's theory that psychical impressions and ideas are the true antecedents of thought; and, positively, that it is the _situation as a whole_, and not any one isolated part of it, or distinction within it, that calls forth and directs thinking. we must beware the fallacy of assuming that some one element in the prior situation in isolation or detachment induces the thought which in reality comes forth only from the whole disturbed situation. on the negative side, characterizations of impression and idea (whether as mental contents or as psychical existences) are distinctions which arise only within reflection upon the situation which is the genuine antecedent of thought; while the distinction of psychical existences from external existences arises only within a highly elaborate technical reflection--that of the psychologist as such.[ ] positively, it is the whole dynamic experience with its qualitative and pervasive identity of value, and its inner distraction, its elements at odds with each other, in tension against each other, contending each for its proper placing and relationship, that generates the thought-situation. from this point of view, at this period of development, the distinctions of objective and subjective have a characteristic meaning. the antecedent, to repeat, is a situation in which the various factors are actively incompatible with each other, and which yet in and through the striving tend to a re-formation of the whole and to a restatement of the parts. this situation as such is clearly objective. it is there; it is there as a whole; the various parts are there; and their active incompatibility with one another is there. nothing is conveyed at this point by asserting that any particular part of the situation is illusory or subjective, or mere appearance; or that any other is truly real. it is the further work of _thought_ to exclude some of the contending factors from membership in experience, and thus to relegate them to the sphere of the merely subjective. but just at this epoch the experience exists as one of vital and active confusion and conflict. the conflict is not only objective in a _de facto_ sense (that is, really existent), but is objective in a logical sense as well; it is just this conflict which effects the transition into the thought-situation--this, in turn, being only a constant movement toward a defined equilibrium. the conflict has objective logical value because it is the antecedent condition and cue of thought. every reflective attitude and function, whether of naïve life, deliberate invention, or controlled scientific research, has risen through the medium of some such total objective situation. the abstract logician may tell us that sensations or impressions, or associated ideas, or bare physical things, or conventional symbols, are antecedent conditions. but such statements cannot be verified by reference to a single instance of thought in connection with actual practice or actual scientific research. of course, by extreme mediation symbols may become conditions of evoking thought. they get to be objects in an active experience. but they are stimuli only in case their manipulation to form a new whole occasions resistance, and thus reciprocal tension. symbols and their definitions develop to a point where dealing with them becomes itself an experience, having its own identity; just as the handling of commercial commodities, or arrangement of parts of an invention, is an individual experience. there is always as antecedent to thought an experience of some subject-matter of the physical or social world, or organized intellectual world, whose parts are actively at war with each other--so much so that they threaten to disrupt the entire experience, which accordingly for its own maintenance requires deliberate re-definition and re-relation of its tensional parts. this is the reconstructive process termed thinking: the reconstructive situation, with its parts in tension and in such movement toward each other as tends to a unified experience, is the thought-situation. this at once suggests the subjective phase. the situation, the experience as such, is objective. there is an experience of the confused and conflicting tendencies. but just _what in particular_ is objective, just _what_ form the situation shall take as an organized harmonious whole, is unknown; that is the problem. it is the uncertainty as to the _what_ of the experience together with the certainty _that_ there is such an experience, that evokes the thought-function. viewed from this standpoint of uncertainty, the situation as a whole is subjective. no particular content or reference can be asserted off-hand. definite assertion is expressly reserved--it is to be the outcome of the procedure of reflective inquiry now undertaken. this holding off of contents from definitely asserted position, this viewing them as candidates for reform, is what we mean at this stage of the natural history of thought by the subjective. we have followed lotze through his tortuous course of inconsistencies. it is better, perhaps, to run the risk of vain repetition, than that of leaving the impression that these are _mere_ self-contradictions. it is an idle task to expose contradictions save we realize them in relation to the fundamental assumption which breeds them. lotze is bound to differentiate thought from its antecedents. he is intent to do this, however, through a preconception that marks off the thought-situation radically from its predecessor, through a difference that is complete, fixed, and absolute, or at large. it is a total contrast of thought as such to something else as such that he requires, not a contrast within experience of one phase of a process, one period of a rhythm, from others. this complete and rigid difference lotze finds in the difference between an experience which is _mere existence_ or occurrence, and one which has to do with worth, truth, right relationship. now things, objects, have already, implicitly at least, determinations of worth, of truth, reality, etc. the same is true of deeds, affections, etc., etc. only states of feelings, bare impressions, etc., seem to fulfil the prerequisite of being given as existence, and yet without qualification as to worth, etc. then the current of ideas offers itself, a ready-made stream of events, of existences, which can be characterized as wholly innocent of reflective determination, and as the natural predecessor of thought. but this stream of existences is no sooner there than its total incapacity to officiate as material condition and cue of thought appears. it is about as relevant as are changes that may be happening on the other side of the moon. so, one by one, the whole series of determinations of value or worth already traced are introduced _into_ the very make-up, the inner structure, of what was to be _mere_ existence: viz., ( ) value as determined by things of whose spatial and temporal relations the things are somehow _representative_; ( ) hence, value in the shape of _meaning_--the idea as significant, possessed of quality, and not a mere event; ( ) distinguished values of coincidence and coherence within the stream. all these kinds of value are explicitly asserted, as we have seen; underlying and running through them all is the recognition of the supreme value of a situation which is organized as a whole, yet conflicting in its inner constitution. these contradictions all arise in the attempt to put thought's work, as concerned with value or validity over against experience as a mere antecedent happening, or occurrence. since this contrast arises because of the deeper attempt to consider thought as an independent somewhat in general which yet, in _our_ experience, is specifically dependent, the sole radical avoiding of the contradictions can be found in the endeavor to characterize thought as a specific mode of valuation in the evolution of significant experience, having its own specific occasion or demand, and its own specific place. the nature of the organization and value that the antecedent conditions of the thought-function possess is too large a question here to enter upon in detail. lotze himself suggests the answer. he speaks of the current of ideas, just as a current, supplying us with the "mass of well-grounded information which _regulates_ daily life" (vol. i, p. ). it gives rise to "_useful combinations_," "_correct expectations_," "_seasonable reactions_" (vol. i, p. ). he speaks of it, indeed, as if it were just the ordinary world of naïve experience, the so-called empirical world, as distinct from the world as critically revised and rationalized in scientific and philosophic inquiry. the contradiction between this interpretation and that of a mere stream of psychical impressions is only another instance of the difficulty already discussed. but the phraseology suggests the type of value possessed by it. the unreflective world is a world of practical values; of ends and means, of their effective adaptations; of control and regulation of conduct in view of results. even the most purely utilitarian of values are nevertheless values; not _mere_ existences. but the world of uncritical experience is saved from reduction to just material uses and worths; for it is a world of social aims and means, involving at every turn the values of affection and attachment, of competition and co-operation. it has incorporate also in its own being the surprise of æsthetic values--the sudden joy of light, the gracious wonder of tone and form. i do not mean that this holds in gross of the unreflective world of experience over against the critical thought-situation--such a contrast implies the very wholesale, at large, consideration of thought which i am striving to avoid. doubtless many and many an act of thought has intervened in effecting the organization of our commonest practical-affectional-æsthetic region of values. i only mean to indicate that thought does take place in such a world; not _after_ a world of bare existences lacking value-specifications; and that the more systematic reflection we call organized science, may, in some fair sense, be said to come _after_, but to come after affectional, artistic, and technological interests which have found realization and expression in building up a world of values. having entered so far upon a suggestion which cannot be followed out, i venture one other digression. the notion that value or significance as distinct from mere existentiality is the product of thought or reason, and that the source of lotze's contradictions lies in the effort to find _any_ situation prior or antecedent to thought, is a familiar one--it is even possible that my criticisms of lotze have been interpreted by some readers in this sense.[ ] this is the position frequently called neo-hegelian (though, i think, with questionable accuracy), and has been developed by many writers in criticising kant. this position and that taken in this chapter do indeed agree in certain general regards. they are at one in denial of the factuality and the possibility of developing fruitful reflection out of antecedent bare existence or mere events. they unite in denying that there is or can be any such thing as mere existence--phenomenon unqualified as respects meaning, whether such phenomenon be psychic or cosmic. they agree that reflective thought grows organically out of an experience which is already organized, and that it functions within such an organism. but they part company when a fundamental question is raised: is all organized meaning the work of thought? does it therefore follow that the organization out of which reflective thought grows is the work of thought of some other type--of pure thought, creative or constitutive thought, intuitive reason, etc.? i shall indicate briefly the reasons for divergence at this point. to cover all the practical-social-æsthetic values involved, the term "thought" has to be so stretched that the situation might as well be called by any other name that describes a typical value of experience. more specifically, when the difference is minimized between the organized and arranged scheme of values out of which reflective inquiry proceeds, and reflective inquiry itself (and there can be no other reason for insisting that the antecedent of reflective thought is itself somehow thought), exactly the same type of problem recurs that presents itself when the distinction is exaggerated into one between bare unvalued existences and rational coherent meanings. for the more one insists that the antecedent situation is constituted by thought, the more one has to wonder why another type of thought is required; what need arouses it, and how it is possible for it to improve upon the work of previous constitutive thought. this difficulty at once forces us from a logic of experience as it is concretely experienced into a metaphysic of a purely hypothetical experience. constitutive thought precedes _our_ conscious thought-operations; hence it must be the working of some absolute universal thought which, unconsciously to our reflection, builds up an organized world. but this recourse only deepens the difficulty. how does it happen that the absolute constitutive and intuitive thought does such a poor and bungling job that it requires a finite discursive activity to patch up its products? here more metaphysic is called for: the absolute reason is now supposed to work under limiting conditions of finitude, of a sensitive and temporal organism. the antecedents of reflective thought are not, therefore, determinations of thought pure and undefiled, but of what thought can do when it stoops to assume the yoke of change and of feeling. i pass by the metaphysical problem left unsolved by this flight into metaphysic: why and how should a perfect, absolute, complete, finished thought find it necessary to submit to alien, disturbing, and corrupting conditions in order, in the end, to recover through reflective thought in a partial, piecemeal, wholly inadequate way what it possessed at the outset in a much more satisfactory way? i confine myself to the logical difficulty. how can thought relate itself to the fragmentary sensations, impressions, feelings, which, in their contrast with and disparity from the workings of constitutive thought, mark it off from the latter; and which in their connection with its products give the cue to reflective thinking? _here we have again exactly the problem with which lotze has been wrestling_: we have the same insoluble question of the reference of thought-activity to a wholly indeterminate unrationalized, independent, prior existence. the absolute rationalist who takes up the problem at this point will find himself forced into the same continuous seesaw, the same scheme of alternate rude robbery and gratuitous gift, that lotze engaged in. the simple fact is that here _is_ just where lotze himself began; he saw that previous transcendental logicians had left untouched the specific question of relation of _our_ supposedly finite, reflective thought to its own antecedents, and he set out to make good the defect. if reflective thought is required because constitutive thought works under externally limiting conditions of sense, then we have some elements which are, after all, mere existences, events, etc. or, if they have organization from some other source, and induce reflective thought not as bare impressions, etc., but through their place in some whole, then we have admitted the possibility of organic unity in experience, apart from reason, and the ground for assuming pure constitutive thought is abandoned. the contradiction appears equally when viewed from the side of thought-activity and its characteristic forms. all our knowledge, after all, of thought as constitutive is gained by consideration of the operations of reflective thought. the perfect system of thought is so perfect that it is a luminous, harmonious whole, without definite parts or distinctions--or, if there are such, it is only reflection that brings them out. the categories and methods of constitutive thought itself must therefore be characterized in terms of the _modus operandi_ of reflective thought. yet the latter takes place just because of the peculiar problem of the peculiar conditions under which it arises. its work is progressive, reformatory, reconstructive, synthetic, in the terminology made familiar by kant. we are not only _not_ justified, accordingly, in transferring its determinations over to constitutive thought, but we are absolutely prohibited from attempting any such transfer. to identify logical processes, states, devices, results that are conditioned upon the primary fact of resistance to thought as constitutive with the structure of such thought is as complete an instance of the fallacy of recourse from one genus to another as could well be found. constitutive and reflective thought are, first, defined in terms of their dissimilarity and even opposition, and then without more ado the forms of the description of the latter are carried over bodily to the former![ ] this is not meant for a merely controversial criticism. it is meant to point positively toward the fundamental thesis of these chapters: all the distinctions of the thought-function, of conception as over against sense-perception, of judgment in its various modes and forms, of inference in its vast diversity of operation--all these distinctions come within the thought-situation as growing out of a characteristic antecedent typical formation of experience; and have for their purpose the solution of the peculiar problem with respect to which the thought-function is generated or evolved: the restoration of a deliberately integrated experience from the inherent conflict into which it has fallen. the failure of transcendental logic has the same origin as the failure of the empiristic (whether taken pure or in the mixed form in which lotze presents it). it makes absolute and fixed certain distinctions of existence and meaning, and of one kind of meaning and another kind, which are wholly historic and relative in their origin and their significance. it views thought as attempting to represent or state reality once for all, instead of trying to determine some phases or contents of it with reference to their more effective and significant reciprocal employ--instead of as reconstructive. the rock against which every such logic splits is that either reality already has the statement which thought is endeavoring to give it, or else it has not. in the former case, thought is futilely reiterative; in the latter, it is falsificatory. the significance of lotze for critical purposes is that his peculiar effort to combine a transcendental view of thought (_i. e._, of thought as active in forms of its own, pure in and of themselves) with certain obvious facts of the dependence of our thought upon specific empirical antecedents, brings to light fundamental defects in both the empiristic and the transcendental logics. we discover a common failure in both: the failure to view logical terms and distinctions with respect to their necessary function in the redintegration of experience. iii thought and its subject-matter: the datum of thinking we have now reached a second epochal stage in the evolution of the thought-situation, a crisis which forces upon us the problem of the distinction and mutual reference of the datum or presentation, and the ideas or "thoughts." it will economize and perhaps clarify discussion if we start from the relatively positive and constructive result just reached, and review lotze's treatment from that point of regard. we have reached the point of conflict in the matters or contents of an experience. it is _in_ this conflict and because of it that the matters or contents, or significant quales, stand out as such. as long as the sun revolves about earth without tension or question, this "content," or fact, is not in any way abstracted _as_ content or object. its very distinction as content from the form or mode of experience as such is the result of post-reflection. the same conflict makes other experiences assume conscious objectification; they, too, cease to be ways of living, and become distinct objects of observation and consideration. the movements of planets, eclipses, etc., are cases in point.[ ] the maintenance of a unified experience has become a problem, an end. it is no longer secure. but this involves such restatement of the conflicting elements as will enable them to take a place somewhere in the new experience; they must be disposed of somehow, and they can be disposed of finally only as they are provided for. that is, they cannot be simply denied or excluded or eliminated; they must be taken into the fold of the new experience; such introduction, on the other hand, clearly demands more or less modification or transformation on their part. the thought-situation is the conscious maintenance of the unity of experience, with a critical consideration of the claims of the various conflicting contents to a place within itself, and a deliberate final assignment of position. the conflicting situation inevitably polarizes or dichotomizes itself. there is somewhat which is untouched in the contention of incompatibles. there is something which remains secure, unquestioned. on the other hand, there are elements which are rendered doubtful and precarious. this gives the framework of the general distribution of the field into "facts," the given, the presented, the datum; and ideas, the ideal, the conceived, the thought. for there is always something unquestioned in any problematic situation at any stage of its process,[ ] even if it be only the fact of conflict or tension. for this is never _mere_ tension at large. it is thoroughly qualified, or characteristically toned and colored, by the particular elements which are in strife. hence it is _this_ conflict, unique and irreplaceable. that it comes now means precisely that it has never come before; that it is now passed in review and some sort of a settlement reached, means that just _this_ conflict will never recur. in a word, the conflict as such is immediately expressed, or felt, as of just this and no other sort, and this immediately apprehended quality is an irreducible datum. _it_ is fact, even if all else be _doubtful_. as it is subjected to examination, it loses vagueness and assumes more definite form. only in very extreme cases, however, does the assured, unquestioned element reduce to as low terms as we have here imagined. certain things come to stand forth as facts, no matter what else may be doubted. there are certain _apparent_ diurnal changes of the sun; there is a certain annual course or track. there are certain nocturnal changes in the planets, and certain seasonal rhythmic paths. the significance of these may be doubted: do they _mean_ real change in the sun or in the earth? but change, and change of a certain definite and numerically determinate character is there. it is clear that such out-standing facts (ex-istences) constitute the data, the given or presented, of the thought-function. it is obvious that this is only one correspondent, or status, in the total situation. with the consciousness of _this_ as certain, as given to be reckoned with, goes the consciousness of uncertainty as to _what it means_--of how it is to be understood or interpreted. the facts _qua_ presentation or existences are sure; _qua_ meaning (position and relationship in an experience yet to be secured) they are doubtful. yet doubt does not preclude memory or anticipation. indeed, it is possible only through them. the memory of past experience makes sun-revolving-about-earth an object of attentive regard. the recollection of certain other experiences suggests the idea of earth-rotating-daily-on-axis and revolving-annually-about-sun. these contents are as much present as is the observation of change, but as respects worth, they are only possibilities. accordingly, they are categorized or disposed of as just ideas, meanings, thoughts, ways of conceiving, comprehending, interpreting facts. correspondence of reference here is as obvious as correlation of existence. in the logical process, the datum is not just real existence, and the idea mere psychical unreality. both are modes of existence--one of _given_ existence, the other of _mental_ existence. and if the mental existence is in such cases regarded, from the standpoint of the unified experience aimed at, as having only _possible_ value, the datum also is regarded, from the value standpoint, as incomplete and unassured. the very existence of the idea or meaning as separate _is_ the partial, broken up, and hence objectively unreal (from the validity standpoint) character of the datum. or, as we commonly put it, while the ideas are impressions, suggestions, guesses, theories, estimates, etc., the facts are crude, raw, unorganized, brute. they lack relationship, that is, assured place in the universe; they are deficient as to continuity. mere change of apparent position of sun, which is absolutely unquestioned as datum, is a sheer abstraction from the standpoint either of the organized experience left behind, or of the reorganized experience which is the end--the objective. it is impossible as a persistent object in experience or reality. in other words, datum and ideatum are divisions of labor, co-operative instrumentalities, for economical dealing with the problem of the maintenance of the integrity of experience. once more, and briefly, both datum and ideatum may (and positively, veritably, do) break up, each for itself, into physical and psychical. in so far as the conviction gains ground that the earth revolves about the sun, the old fact is broken up into a new cosmic existence, and a new psychological condition--the recognition of a mental process in virtue of which movements of smaller bodies in relation to very remote larger bodies are interpreted in a reverse sense. we do not just eliminate as false the source of error in the old content. we reinterpret it as valid in its own place, viz., a case of the psychology of apperception, although invalid as a matter of cosmic structure. in other words, with increasing accuracy of determination of the given, there comes a distinction, for methodological purposes, between the _quality_ or matter of the sense-experience and its _form_--the sense-perceiving, as itself a psychological fact, having its own place and laws or relations. moreover, the old experience, that of sun-revolving, abides. but it is regarded as belonging to "me"--to this experiencing individual, rather than to the cosmic world. it is _psychic_. here, then, _within_ the growth of the thought-situation and as a part of the process of determining _specific_ truth under _specific_ conditions, we get for the first time the clue to that distinction with which, as ready-made and prior to all thinking, lotze started out, namely, the separation of the matter of impression from impression as psychical event. the separation which, taken at large, engenders an insoluble problem, appears within a particular reflective inquiry, as an inevitable differentiation of a scheme of values. the same sort of thing occurs on the side of thought, or meaning. the meaning or idea which is growing in acceptance, which is gaining ground as meaning-of-datum, gets logical or intellectual or objective force; that which is losing standing, which is increasingly doubtful, gets qualified as just a notion, a fancy, a pre-judice, mis-conception--or finally just an error, a mental slip. evaluated as fanciful in validity it becomes mere image--subjective;[ ] and finally a psychical existence. it is not eliminated, but receives a new reference or meaning. thus the distinction between subjectivity and objectivity is not one between meaning as such and datum as such. it is a specification that emerges, correspondently, in _both_ datum and ideatum, as affairs of the direction of logical movement. that which is left behind in the evolution of accepted meaning is characterized as real, but only in a psychical sense; that which is moved toward is regarded as real in an objective, cosmic sense.[ ] the implication of the psychic and the logical within both the given presentation and the thought about it, appears in the continual shift to which logicians of lotze's type are put. when the psychical is regarded as existence over against meaning as just ideal, reality seems to reside in the psychical; it is _there_ anyhow, and meaning is just a curious attachment--curious because as _mere meaning_ it is non-existent as event or state--and there seems to be nothing by which it can be even tied to the psychical state as its bearer or representative. but when the emphasis falls on thought as _content_, as significance, then the psychic event, the idea as image[ ] (as distinct from idea as meaning) appears as an accidental but necessary evil, the unfortunate irrelevant medium through which _our_ thinking has to go on.[ ] . _the data of thought._--when we turn to lotze, we find that he makes a clear distinction between the presented material of thought, its datum, and the typical characteristic modes of thinking in virtue of which the datum gets organization or system. it is interesting to note also that he states the datum in terms different from those in which the antecedents of thought are defined. from the point of view of the material upon which ideas exercise themselves, it is not coincidence, collocation, or succession that counts; but gradation of degrees in a scale. it is not things in spatial or temporal grouping that are emphasized, but qualities as mutually distinguished, yet classed--as differences of a common somewhat. there is no inherent inconceivability in the idea that every impression should be as incomparably different from every other as sweet is from warm. but by a remarkable circumstance such is not the case. we have series, and networks of series. we have diversity of a common--diverse colors, sounds, smells, tastes, etc. in other words, the datum is sense-qualities which, fortunately for thought, are given arranged, as shades, degrees, variations, or qualities of somewhat that is identical.[ ] all this is given, presented, to our ideational activities. even the universal, the common-color which runs through the various qualities of blue, green, white, etc., is not a product of thought, but something which thought finds already in existence. it conditions comparison and reciprocal distinction. particularly all mathematical determinations, whether of counting (number), degree (more or less), and quantity (greatness and smallness), come back to this peculiarity of the datum of thought. here lotze dwells at considerable length upon the fact that the very possibility, as well as the success, of thought is due to this peculiar universalization or _prima facie_ ordering with which its material is given to it. such pre-established fitness in the meeting of two things that have nothing to do with each other is certainly cause enough for wonder and congratulation. it should not be difficult to see why lotze uses different categories in describing the given material of thought from those employed in describing its antecedent conditions, even though, according to him, the two are absolutely the same.[ ] he has different _functions_ in mind. in one case, the material must be characterized as evoking, as incentive, as stimulus--from this point of view the peculiar combination of coincidence and coherence is emphasized. but in the other case the material must be characterized as affording stuff, actual subject-matter. data are not only what is given _to_ thought, but they are also the food, the raw material, _of_ thought. they must be described as, on the one hand, wholly outside of thought. this clearly puts them into the region of sense-perception. they are matter of _sensation_ given free from all inferring, judging, relating influence. sensation is just what is _not_ called up in memory or in anticipated projection--it is the immediate, the irreducible. on the other hand, sensory-_matter_ is qualitative, and quales are made up on a common basis. they are degrees or grades of a common quality. thus they have a certain ready-made setting of mutual distinction and reference which is already almost, if not quite, the effect of comparing, of relating, and these are the express traits of thinking. it is easy to interpret this miraculous gift of grace in the light of what has been said. the data are in truth precisely that which is selected and set aside _as_ present, as immediate. thus they are _given_ to _further_ thought. but the selection has occurred in view of the need for thought; it is a listing of the capital in the way of the undisturbed, the undiscussed, which thought can count upon in this particular problem. hence it is not strange that it has a peculiar fitness of adaptation for thought's further work. having been selected with precisely that end in view, the wonder would be if it were not so fitted. a man may coin counterfeit money for use upon others, but hardly with the intent of passing it off upon himself. our only difficulty here is that the mind flies away from the logical interpretation of sense-datum to a ready-made notion of it brought over from abstract psychological inquiry. the belief in sensory quales as somehow forced upon us, and forced upon us at large, and thus conditioning thought wholly _ab extra_, instead of determining it as instrumentalities or elements in its own scheme, is too fixed. such qualities _are_ forced upon us, but _not_ at large. the sensory data of experience, as distinct from the psychologists' constructs, always come _in a context_; they always appear as variations in a continuum of values. even the thunder which breaks in upon me (to take the extreme of apparent discontinuity and irrelevancy) disturbs me because it is taken as a part of the same space-world as that in which my chair and room and house are located; and it is taken as an influence which interrupts and disturbs, _because_ it is part of my common world of causes and effects. the solution of continuity is itself practical or teleological, and thus presupposes and affects continuity of purpose, occupations, and means in a life-process. it is not metaphysics, it is biology which enforces the idea that actual sensation is not only determined as an event in a world of events,[ ] but is an occurrence occurring at a certain period in the evolution of experience, marking a certain point in its cycle, and, consequently--having always its own conscious context and bearings--is a characteristic function of reconstruction in experience.[ ] . _forms of thinking data._--as sensory datum is material set for the work of thought, so the ideational forms with which thought does its work are apt and prompt to meet the needs of the material. the "accessory"[ ] notion of ground of coherence turns out, in truth, not to be a formal, or external, addition to the data, but a requalification of them. thought is accessory as accomplice, not as addendum. "thought" is to eliminate mere coincidence, and to assert grounded coherence. lotze makes it absolutely clear that he does not at bottom conceive of "thought" as an activity "in itself" imposing a form of coherence; but that the organizing work of "thought" is only the progressive realization of an inherent unity, or system, in the material experience. the specific modes in which thought brings its "accessory" power to bear--names, conception, judgment, and inference--are successive stages in the adequate organization of the matter which comes to us first as datum; they are successive stages of the effort to overcome the original defects of the datum. conception starts from the given universal (the common element) of sense. yet (and this is the significant point) it does not simply abstract this common element, and consciously generalize it as over against its own differences. such a "universal" is _not_ coherence, just because it does not _include_ and dominate the temporal and local heterogeneity. the _true_ concept (see vol. i, p. ) is a system of attributes, held together on the basis of some ground, or determining, dominating principle--a ground which so controls all its own instances as to make them into an inwardly connected whole, and so specifies its own limits as to be exclusive of all else. if we abstract color as the common element of various colors, the result is not a scientific idea or concept. discovery of a process of light-waves whose various rates constitute the various colors of the spectrum gives the concept. and when we get such a concept, the former mere temporal abruptness of color experiences gives way to organic parts of a color system. the logical product--the concept, in other words--is not a formal seal or stamp; it is a thoroughgoing transformation of data in a given sense. the form or mode of thought which marks the continued transformation of the data and the idea in reference to each other is judgment. judgment makes explicit the assumption of a principle which determines connection within an individualized whole. it definitely states red as _this_ case or instance of the law or process of color, and thus overcomes further the defect in _subject-matter_ or data still left by conception.[ ] now judgment logically terminates in disjunction. it gives a universal which may determine any one of a number of alternative defined particulars, but which is arbitrary as to _what_ one is selected. systematic _inference_ brings to light the material conditions under which the law, or dominating universal, applies to this, rather than that alternative particular, and so completes the ideal organization of the subject-matter. if this act were complete, we should finally have present to us a whole on which we should know the determining and effective or authorizing elements, and the order of development or hierarchy of dependence, in which others follow from them.[ ] in this account by lotze of the operations of the forms of thought, there is clearly put before us the picture of a continuous correlative determination of datum on one side and of idea or meaning on the other, till experience is again integral, data thoroughly defined and corrected, and ideas completely incarnate as the relevant meaning of subject-matter. that we have here in outline a description of what actually occurs there can be no doubt. but there is as little doubt that it is thoroughly inconsistent with lotze's supposition that the material or data of thought is precisely the same as the antecedents of thought; or that ideas, conceptions, are purely mental somewhats brought to bear, as the sole essential characteristics of thought, extraneously upon a material provided ready-made. it means but one thing: the maintenance of unity and wholeness in experience through conflicting contents occurs by means of a strictly correspondent setting apart of fact to be accurately described and properly related, and meaning to be adequately construed and properly referred. the datum is given _in_ the thought-situation, and _to_ further qualification of ideas or meanings. but even in this aspect it presents a problem. to find out _what is_ given is an inquiry which taxes reflection to the uttermost. every important advance in scientific method means better agencies, more skilled technique for simply detaching and describing what is barely there, or given. to be able to find out what can safely be taken as _there_, as given in any particular inquiry, and hence be taken as material for orderly and verifiable thinking, for fruitful hypothesis-making, for entertaining of explanatory and interpretative ideas, is one phase of the effort of systematic scientific inquiry. it marks its inductive phase. to take what is given _in_ the thought-situation, for the sake of accomplishing the aim of thought (along with a correlative discrimination of ideas or meanings), as if it were given absolutely, or apart from a particular historic situs and context, is the fallacy of empiricism as a logical theory. to regard the thought-forms of conception, judgment, and inference as qualifications of "pure thought, apart from any difference in objects," instead of as successive dispositions in the progressive organization of the material (or objects) is the fallacy of rationalism. lotze attempts to combine the two, thinking thereby to correct each by the other. lotze recognizes the futility of thought if the sense-data are final, if they alone are real, the truly existent, self-justificatory and valid. he sees that, if the empiricist were right in his assumption as to the real worth of the given data, thinking would be a ridiculous pretender, either toilfully and poorly doing over again what needs no doing, or making a wilful departure from truth. he realizes that thought really is evoked because it is needed, and that it has a work to do which is not merely formal, but which effects a modification of the subject-matter of experience. consequently he assumes a thought-in-itself, with certain forms and modes of action of its own, a realm of meaning possessed of a directive and normative worth of its own--the root-fallacy of rationalism. his attempted compromise between the two turns out to be based on the assumption of the indefensible ideas of both--the notion of an independent matter of thought, on one side, and of an independent worth or value of thought-forms, on the other. this pointing out of inconsistencies becomes stale and unprofitable save as we bring them back into connection with their root-origin--the erection of distinctions that are genetic and historic, and working or instrumental divisions of labor, into rigid and ready-made differences of structural reality. lotze clearly recognizes that thought's nature is dependent upon its aim, its aim upon its problem, and this upon the situation in which it finds its incentive and excuse. its work is cut out for it. it does not what it would, but what it must. as lotze puts it, "logic has to do with thought, not as it would be under hypothetical conditions, but as it is" (vol. i, p. ), and this statement is made in explicit combination with statements to the effect that the peculiarity of the material of thought conditions its activity. similarly he says in a passage already referred to: "the possibility and the success of thought's production in general depends upon this original constitution and organization of the whole world of ideas, a constitution which, though not necessary in thought, is all the more necessary to make thought possible."[ ] as we have seen, the essential nature of conception, judgment, and inference is dependent upon peculiarities of the propounded material, they being forms dependent for their significance upon the stage of organization in which they begin. from this only one conclusion is suggested. if thought's nature is dependent upon its actual conditions and circumstances, the primary logical problem is to study thought-in-its-conditioning; it is to detect the crisis within which thought and its subject-matter present themselves in their mutual distinction and cross-reference. but lotze is so thoroughly committed to a ready-made antecedent of some sort, that this genetic consideration is of no account to him. the historic method is a mere matter of psychology, and has no logical worth (vol. i, p. ). we must presuppose a psychological mechanism and psychological material, but logic is concerned not with origin or history, but with authority, worth, value (vol. i, p. ). again: "logic is not concerned with the manner in which the elements utilized by thought come into existence, but their value _after_ they have somehow come into existence, for the carrying out of intellectual operations" (vol. i, p. ). and finally: "i have maintained throughout my work that logic cannot derive any serious advantage from a discussion of _the conditions under which thought as a psychological process comes about_. the significance of logical forms ... is to be found in the utterances of thought, the laws which it imposes, after or during the act of thinking, not in the conditions which lie back of and which produce thought."[ ] lotze, in truth, represents a halting-stage in the evolution of logical theory. he is too far along to be contented with the reiteration of the purely formal distinctions of a merely formal thought-by-itself. he recognizes that thought as formal is the form of some matter, and has its worth only as organizing that matter to meet the ideal demands of reason; and that "reason" is in truth only an ideal systematization of the matter or content. consequently he has to open the door to admit "psychical processes" which furnish this material. having let in the material, he is bound to shut the door again in the face of the processes from which the material proceeded--to dismiss them as impertinent intruders. if thought gets its data in such a surreptitious manner, there is no occasion for wonder that the legitimacy of its dealings with the material remains an open question. logical theory, like every branch of the philosophic disciplines, waits upon a surrender of the obstinate conviction that, while the work and aim of thought is conditioned by the material supplied to it, yet the _worth_ of its performances is something to be passed upon in complete abstraction from conditions of origin and development. iv thought and its subject-matter: the content and object of thought in the foregoing discussion, particularly in the last chapter, we were led repeatedly to recognize that thought has its own content. at times lotze gives way to the tendency to define thought entirely in terms of modes and forms of activity which are exercised by it upon a strictly foreign material. but two motives continually push him in the other direction. ( ) thought has a distinctive work to do, one which involves a qualitative transformation of (at least) the _relationships_ of the presented matter; as fast as it accomplishes this work, the subject-matter becomes somehow thought's own. as we have just seen, the data are progressively organized to meet thought's ideal of a complete whole, with its members interconnected according to a determining principle. such progressive organization throws backward doubt upon the assumption of the original total irrelevancy of the data and thought-form to each other. ( ) a like motive operates from the side of the subject-matter. as merely foreign and external, it is too heterogeneous to lend itself to thought's exercise and influence. the idea, as we saw in the first chapter, is the convenient medium through which lotze passes from the purely heterogeneous psychical impression or event, which is totally irrelevant to thought's purpose and working, over to a state of affairs which can reward thought. idea as meaning forms the bridge from the brute factuality of the psychical impression over to the coherent value of thought's own content. we have, in this chapter, to consider the question of the idea or content of thought from two points of view: first, the _possibility_ of such a content--its consistency with lotze's fundamental premises; secondly, its _objective_ character--its validity and test. i. the question of the possibility of a specific content of thought is the question of the nature of the idea as meaning. meaning is the characteristic content of thought as such. we have thus far left unquestioned lotze's continual assumption of meaning as a sort of thought-unit; the building-stone of thought's construction. in his treatment of meaning, lotze's contradictions regarding the antecedents, data, and content of thought reach their full conclusion. he expressly makes meaning to be the product of thought's activity and also the unreflective material out of which thought's operations grow. this contradiction has been worked out in accurate and complete detail by professor jones.[ ] he summarizes it as follows (p. ): "no other way was left to him [lotze] excepting this of first attributing all to sense and afterwards attributing all to thought, and, finally of attributing it to thought only because it was already in its material. this _seesaw_ is essential to his theory; the elements of knowledge as he describes them can subsist only by the alternate robbery of each other." we have already seen how strenuously lotze insists upon the fact that the given subject-matter of thought is to be regarded wholly as the work of a physical mechanism, "without any action of thought."[ ] but lotze also states that if the products of the psychical mechanism "are to admit of combination in the definite form of a _thought_, they each require some previous shaping to make them into logical building-stones and to convert them from _impressions_ into _ideas_. nothing is really more familiar to us than this first operation of thought; the only reason why we usually overlook it is that in the language which we inherit, it is already carried out, and it seems, therefore, to belong to the self-evident presuppositions of thought, _not to its own specific work_."[ ] and again (vol. i, p. ) judgments "can consist of nothing but combinations of ideas which are no longer mere impressions: every such idea must have undergone at least the simple formation mentioned above." such ideas are, lotze goes on to urge, already rudimentary concepts--that is to say, logical determinations. the obviousness of the logical contradiction of attributing to a preliminary specific work of thought exactly the condition of affairs which is elsewhere explicitly attributed to a psychical mechanism prior to any thought-activity, should not blind us to its meaning and relative necessity. the impression, it will be recalled, is a mere state of our own consciousness--a mood of ourselves. as such it has simply _de facto_ relations as an event to other similar events. but reflective thought is concerned with the relationship of a content or matter to other contents. hence the impression must have a matter before it can come at all within the sphere of thought's exercise. how shall it secure this? why, by a preliminary activity of thought which objectifies the impression. blue as a mere sensuous irritation or feeling is given a quality, the meaning "blue"--blueness; the sense-impression is objectified; it is presented "no longer as a condition which we undergo, but as a something which has its being and its meaning in itself, and which continues to be what it is, and to mean what it means whether we are conscious of it or not. it is easy to see here the _necessary beginning of that activity which we above appropriated to thought as such_: it has not yet got so far as converting coexistence into coherence. it has first to perform the previous task of investing each single impression with an independent validity, without which the later opposition of their real coherence to mere coexistence could not be made in any intelligible sense."[ ] this objectification, which converts a sensitive state into a sensible matter to which the sensitive state is referred, also gives this matter "position," a certain typical character. it is not objectified in a merely general way, but is given a specific sort of objectivity. of these kinds of objectivity there are three mentioned: that of a substantive content; that of an attached dependent content; that of an active relationship connecting the various contents with each other. in short, we have the types of meaning embodied in language in the form of nouns, adjectives, and verbs. it is through this preliminary formative activity of thought that reflective or _logical_ thought has presented to it a world of meanings ranged in an order of relative independence and dependence, and ranged as elements in a complex of meanings whose various constituent parts mutually influence each other's meanings.[ ] as usual, lotze mediates the contradiction between material constituted _by_ thought and the same material just presented _to_ thought, by a further position so disparate to each that, taken in connection with each in a pair, and by turns, it seems to bridge the gulf. after describing the prior constitutive work of thought as above, he goes on to discuss a _second_ phase of thought which is intermediary between this and the third phase, viz., reflective thought proper. this second activity is that of arranging experienced quales in series and groups, thus ascribing a sort of universal or common somewhat to various instances (as already described; see p. ). on one hand, it is clearly stated that this second phase of thought's activity is in reality the _same_ as the first phase: since all objectification involves positing, since positing involves distinction of one matter from others, and since this involves placing it in a series or group in which each is measurably marked off, as to the degree and nature of its diversity, from every other. we are told that we are only considering "a really inseparable operation" of thought from two different sides: first, as to the effect which objectifying thought has upon the matter as set over against the feeling _subject_, secondly, the effect which this objectification has upon the matter in relation to _other matters_.[ ] afterward, however, these two operations are declared to be radically different in type and nature. the first is determinant and formative; it gives ideas "the shape without which the logical spirit could not accept them." in a way it dictates "its own laws to its object-matter."[ ] the second activity of thought is rather passive and receptive. it simply recognizes what is already there. "thought can make no difference where it finds none already in the matter of impressions."[ ] "the first universal, as we saw, can only be experienced in immediate sensation. it is no product of thought, but something that thought finds already in existence."[ ] the obviousness of this further contradiction is paralleled only by its inevitableness. thought is in the air, is arbitrary and wild in dealing with meanings, unless it gets its start and cue from actual experience. hence the necessity of insisting upon thought's activity as just recognizing the contents already given. but, on the other hand, prior to the work of thought there is to lotze no content or meaning. it requires a work of thought to detach anything from the flux of sense-irritations and invest it with a meaning of its own. this dilemma is inevitable to any writer who declines to consider as correlative the nature of thought-activity and thought-content from the standpoint of their generating conditions in the movement of experience. viewed from such a standpoint the principle of solution is clear enough. as we have already seen (p. ), the internal dissension of an experience leads to detaching certain values previously absorptively integrated into the concrete experience as part of its own qualitative coloring; and to relegating them, for the time being, (pending integration into further immediate values of a reconstituted experience) into a world of bare meanings, a sphere qualified as ideal throughout. these meanings then become the tools of thought in interpreting the data, just as the sense-qualities which define the presented situation are the immediate object to thought. the two _as mutually referred_ are content. that is, the datum and the thought-mode or idea as connected are the object of thought. to reach this unification is thought's objective or goal. exactly the same value is idea, as either tool or content, according as it is taken as instrumental or as accomplishment. every successive cross-section of the thought-situation presents what may be taken for granted as the outcome of previous thinking, and consequently as the determinant of further reflective procedure. taken as defining the point reached in the thought-function and serving as constituent unit of further thought, it is content. lotze's instinct is sure in identifying and setting over against each other the material given to thought and the content which is thought's own "building-stone." his contradictions arise simply from the fact that his absolute, non-historic method does not permit him to interpret this joint identity and distinction in a working, and hence relative, sense. ii. the question of how the possibility of meanings, or thought-contents, is to be understood merges imperceptibly into the question of the real objectivity or validity of such contents. the difficulty for lotze is the now familiar one: so far as his logic compels him to insist that these meanings are the possession and product of thought (since thought is an independent activity), the ideas are merely ideas; there is no test of objectivity beyond the thoroughly unsatisfactory and formal one of their own mutual consistency. in reaction from this lotze is thrown back upon the idea of these contents as the original matter given in the impressions themselves. here there seems to be an objective or external test by which the reality of thought's operations may be tried; a given idea is verified or found false according to its measure of correspondence with the matter of experience as such. but now we are no better off. the original independence and heterogeneity of impressions and of thought is so great that there is no way to compare the results of the latter with the former. we cannot compare or contrast distinctions of worth with bare differences of factual existence (vol. i, p. ). the standard or test of objectivity is so thoroughly external that by original definition it is wholly outside the realm of thought. how can thought compare its own contents with that which is wholly outside itself? or again, the given material of experience apart from thought is precisely the relatively chaotic and unorganized; it even reduces itself to a mere sequence of psychical events. what rational meaning is there in directing us to compare the highest results of scientific inquiry with the bare sequence of our own states of feeling; or even with the original data whose fragmentary and uncertain character was the exact motive for entering upon scientific inquiry? how can the former in any sense give a check or test of the value of the latter? this is professedly to test the validity of a system of meanings by comparison with that whose defects and errors call forth the construction of the system of meanings by which to rectify and replace themselves. our subsequent inquiry simply consists in tracing some of the phases of the characteristic seesaw from one to the other of the two horns of the now familiar dilemma: either thought is separate from the matter of experience, and then its validity is wholly its own private business; or else the objective results of thought are already in the antecedent material, and then thought is either unnecessary, or else has no way of checking its own performances. . lotze assumes, as we have seen, a certain independent validity in each meaning or qualified content, taken in and of itself. "blue" has a certain validity, or meaning, in and of itself; it is an object for consciousness as such. after the original sense-irritation through which it was mediated has entirely disappeared, it persists as a valid idea, as a meaning. moreover, it is an object or content of thought for others as well. thus it has a double mark of validity: in the comparison of one part of my own experience with another, and in the comparison of my experience as a whole with that of others. here we have a sort of validity which does not raise at all the question of _metaphysical_ reality (vol. i, pp. , ). lotze thus seems to have escaped from the necessity of employing as check or test for the validity of ideas any reference to a real outside the sphere of thought itself. such terms as "conjunction," "franchise," "constitution," "algebraic zero," etc., etc., claim to possess objective validity. yet none of these professes to refer to a reality beyond thought. generalizing this point of view, validity or objectivity of meaning means simply that which is "identical for all consciousness" (vol. i, p. ); "it is quite indifferent whether certain parts of the world of thought indicate something which has beside an independent reality outside of thinking minds, or whether all that it contains exists only in the thoughts of those who think it, but with equal validity for them all" (vol. i, p. ). so far it seems clear sailing. difficulties, however, show themselves, the moment we inquire what is meant by a self-identical content for all thought. is this to be taken in a static or in a dynamic way? that is to say: does it express the fact that a given content or meaning is _de facto_ presented to the consciousness of all alike? does this coequal presence guarantee an objectivity? or does validity attach to a given meaning or content in so far as it directs and controls the further exercise of thinking, and thus the formation of further _new_ contents of consciousness? the former interpretation is alone consistent with lotze's notion that the independent idea as such is invested with a certain validity or objectivity. it alone is consistent with his assertion that concepts precede judgments. it alone, that is to say, is consistent with the notion that reflective thinking has a sphere of ideas or meanings supplied to it at the outset. but it is impossible to entertain this belief. the stimulus which, according to lotze, goads thought on from ideas or concepts to judgments and inferences, is in truth simply the lack of validity, of objectivity in its original independent meanings or contents. a meaning as independent is precisely that which is not invested with validity, but which is a mere idea, a "notion," a fancy, at best a surmise which may turn out to be valid (and of course this indicates possible reference); a standpoint to have its value determined by its further active use. "blue" as a mere detached floating meaning, an idea at large, would not gain in validity simply by being entertained continuously in a given consciousness; or by being made at one and the same time the persistent object of attentive regard by all human consciousnesses. if this were all that were required, the chimera, the centaur, or any other subjective construction, could easily gain validity. "christian science" has made just this notion the basis of its philosophy. the simple fact is that in such illustrations as "blue," "franchise," "conjunction," lotze instinctively takes cases which are not mere independent and detached meanings, but which involve reference to a region of cosmic experience, or to a region of mutually determining social activities. the conception that reference to a _social_ activity does not involve the same sort of reference of thought beyond itself that is involved in physical matters, and hence may be taken quite innocent and free of the metaphysical problem of reference to reality beyond meaning, is one of the strangest that has ever found lodgment in human thinking. either both physical and social reference or neither, is metaphysical; if neither, then it is because the meaning functions, as it originates, in a specific situation which carries with it its own tests (see p. ). lotze's conception is made possible only by unconsciously substituting the idea of object as content of thought for a large number of persons (or a _de facto_ somewhat for every consciousness), for the genuine definition of object as a determinant in a scheme of experience. the former is consistent with lotze's conception of thought, but wholly indeterminate as to validity or intent. the latter is the test used experimentally in all concrete thinking, but involves a radical transformation of all lotze's assumptions. a given idea of the conjunction of the franchise, or of blue, is valid, not because everybody happens to entertain it, but because it expresses the factor of control or direction in a given movement of experience. the test of validity of idea[ ] is its functional or instrumental use in effecting the transition from a relatively conflicting experience to a relatively integrated one. if lotze's view were correct, "blue" valid once would be valid always--even when red or green were actually called for to fulfil specific conditions. this is to say validity always refers to rightfulness or adequacy of performance in an asserting of connection--not to the meaning as detached and contemplated. if we refer again to the fact that the genuine antecedent of thought is a situation which is tensional as regards its existing status, or disorganized in its structural elements, yet organized as emerging out of the unified experience of the past and as striving as a whole, or equally in all its phases, to reinstate an experience harmonized in make-up, we can easily understand how certain contents may be detached and held apart as meanings or references, actual or possible (according as they are viewed with reference to the past or to the future). we can understand how such detached contents may be of use in effecting a review of the entire experience, and as affording standpoints and methods of a reconstruction which will maintain the integrity of experience. we can understand how validity of meaning is measured by reference to something which is not mere meaning; by reference to something which lies beyond the idea as such--viz., the reconstitution of an experience into which thought enters as mediator. that paradox of ordinary experience and of scientific inquiry by which objectivity is given alike to matter of perception and to conceived relations--to facts and to laws--affords no peculiar difficulty, because we see that the test of objectivity is everywhere the same: anything is objective in so far as, through the medium of conflict, it controls the movement of experience in its reconstructive transition from one unified form to another. there is not first an object, whether of sense-perception or of conception, which afterward somehow exercises this controlling influence; but the objective is such in virtue of the exercise of function of control. it may only control the act of inquiry; it may only set on foot doubt, but this is direction of subsequent experience, and, in so far, is a token of objectivity. so much for the thought-content or meaning as having a validity of its own. it does not have it as isolated or given or static; it has it in its dynamic reference, its use in determining further movement of experience. in other words, the "meaning" or idea as such, having been selected and made-up with reference to performing a certain office in the evolution of a unified experience, can be tested in no other way than by discovering whether it does what it was intended to do and what it purports to do.[ ] . lotze has to wrestle with this question of validity in a further aspect: what constitutes the objectivity of thinking as a total attitude, activity, or function? according to his own statement, the meanings or valid ideas are after all only building-stones for logical thought. validity is thus not a question of them in their independent existences, but of their mutual reference to each other. thinking is the process of instituting these mutual references; of building up the various scattered and independent building-stones into the coherent system of thought. what is the validity of the various forms of thinking which find expression in the various types of judgment and in the various forms of inference? categorical, hypothetical, disjunctive judgment; inference by induction, by analogy, by mathematical equation; classification, theory of explanation--all these are processes of reflection by which mutual connection in an individualized whole is given to the fragmentary meanings or ideas with which thought as it sets out is supplied. what shall we say of the validity of such processes? on one point lotze is quite clear. these various logical acts do not really enter into the constitution of the valid world. the logical forms as such are maintained _only_ in the process of thinking. the world of valid truth does not undergo a series of contortions and evolutions, paralleling in any way the successive steps and missteps, the succession of tentative trials, withdrawals, and retracings, which mark the course of our own thinking.[ ] lotze is explicit upon the point that it is only the thought-content in which the process of thinking issues that has objective validity; the act of thinking is "purely and simply an inner movement of our own minds, made necessary to us by reason of the constitution of our nature and of our place in the world" (vol. ii, p. ). here the problem of validity presents itself as the problem of the relation of the act of thinking to its own product. in his solution lotze uses two metaphors: one derived from building operations, the other from traveling. the construction of a building requires of necessity certain tools and extraneous constructions, stagings, scaffoldings, etc., which are necessary to effect the final construction, but yet which do not enter into the building as such. the activity has an instrumental, though not a constitutive, value as regards its product. similarly, in order to get a view from the top of a mountain--this view being the objective--the traveler has to go through preliminary movements along devious courses. these again are antecedent prerequisites, but do not constitute a portion of the attained view. the problem of thought as activity, as distinct from thought as content, opens up altogether too large a question to receive complete consideration at this point. fortunately, however, the previous discussion enables us to narrow the point which is in issue just here. it is once more the question whether the activity of thought is to be regarded as an independent function supervening entirely from without upon antecedents, and directed from without upon data; or whether it marks merely a phase of the transformation which the course of experience (whether practical, or artistic, or socially affectional or whatever) undergoes in entering into a tensional status where the maintenance of its harmony of content is problematic and hence an aim. if it be the latter, a thoroughly intelligent sense can be given to the proposition that the activity of thinking is instrumental, and that its worth is found, not in its own successive states as such, but in the result in which it comes to conclusion. but the conception of thinking as an independent activity somehow occurring after an independent antecedent, playing upon an independent subject-matter, and finally effecting an independent result, presents us with just one miracle the more. i do not question the strictly instrumental character of thinking. the problem lies not here, but in the interpretation of the nature of the organ and instrument. the difficulty with lotze's position is that it forces us into the assumption of a means and an end which are simply and only external to each other, and yet necessarily dependent upon each other--a position which, whenever found, is so thoroughly self-contradictory as to necessitate critical reconsideration of the premises which lead to it. lotze vibrates between the notion of thought as a tool in the external sense, a mere scaffolding to a finished building in which it has no part nor lot, and the notion of thought as an immanent tool, as a scaffolding which is an integral part of the very operation of building, and set up for the sake of the building-activity which is carried on effectively only with and through a scaffolding. only in the former case can the scaffolding be considered as a _mere_ tool. in the latter case the external scaffolding is not itself the instrumentality; the actual tool is the _action_ of erecting the building, and this action involves the scaffolding as a constituent part of itself. the work of erecting is not set over against the completed building as mere means to an end; it _is_ the end taken in process or historically, longitudinally viewed. the scaffolding, moreover, is not an external means to the process of erecting, but an organic member of it. it is no mere accident of language that "building" has a double sense--meaning at once the process and the finished product. the outcome of thought is the thinking activity carried on to its own completion; the activity, on the other hand, _is_ the outcome taken anywhere short of its own realization, and thereby still going on. the only consideration which prevents easy and immediate acceptance of this view is the notion of thinking as something purely formal. it is strange that the empiricist does not see that his insistence upon a matter extraneously given to thought only strengthens the hands of the rationalist with his claim of thinking as an independent activity, separate from the actual make-up of the affairs of experience. thinking as a merely formal activity exercised upon certain sensations or images or objects sets forth an absolutely meaningless proposition. the psychological identification of thinking with the process of association is much nearer the truth. it is, indeed, on the way to the truth. we need only to recognize that association is of contents or matters or meanings, not of ideas as bare existences or events; and that the type of association we call thinking differs from the associations of casual fancy and revery in an element of control by reference to an end which determines the fitness and thus the selection of the associates, to apprehend how completely thinking is a reconstructive movement of actual contents of experience in relation to each other, and for the sake of a redintegration of a conflicting experience. there is no miracle in the fact that tool and material are adapted to each other in the process of reaching a valid conclusion. were they external in origin to each other and to the result, the whole affair would, indeed, present an insoluble problem--so insoluble that, if this were the true condition of affairs, we never should even know that there was a problem. but, in truth, both material and tool have been secured and determined with reference to economy and efficiency in effecting the end desired--the maintenance of a harmonious experience. the builder has discovered that his building means building tools, and also building material. each has been slowly evolved with reference to its fit employ in the entire function; and this evolution has been checked at every point by reference to its own correspondent. the carpenter has not thought at large on his building and then constructed tools at large, but has thought of his building in terms of the material which enters into it, and through that medium has come to the consideration of the tools which are helpful. life proposes to maintain at all hazards the unity of its own process. experience insists on being itself, on securing integrity even through and by means of conflict. this is not a formal question, but one of the placing and relations of the matters or values actually entering into experience. and this in turn determines the taking up of just those mental attitudes, and the employing of just those intellectual operations, which most effectively handle and organize the material. thinking is adaptation _to_ an end _through_ the adjustment of particular objective contents. the thinker, like the carpenter, is at once stimulated and checked in every stage of his procedure by the particular situation which confronts him. a person is at the stage of wanting a new house: well then, his materials are available resources, the price of labor, the cost of building, the state and needs of his family, profession, etc.; his tools are paper and pencil and compass, or possibly the bank as a credit instrumentality, etc. again, the work is beginning. the foundations are laid. this in turn determines its own specific materials and tools. again, the building is almost ready for occupancy. the concrete process is that of taking away the scaffolding, clearing up the grounds, furnishing and decorating rooms, etc. this specific operation again determines its own fit or relevant materials and tools. it defines the time and mode and manner of beginning and ceasing to use them. logical theory will get along as well as does reflective practice, when it sticks close by and observes the directions and checks inherent in each successive phase of the evolution of the cycle of experiencing. the problem in general of validity of the thinking process as distinct from the validity of this or that process arises only when thinking is isolated from its historic position and its material context. . but lotze is not yet done with the problem of validity, even from his own standpoint. the ground shifts again under his feet. it is no longer a question of the validity of the idea or meaning with which thought is supposed to set out; it is no longer a question of the validity of the process of thinking in reference to its own product; it is the question of the validity of the product. supposing, after all, that the final meaning, or logical idea, is thoroughly coherent and organized; supposing it is an object for all consciousness as such. once more arises the question: what is the validity of even the most coherent and complete idea?--a question which rises and will not down. we may reconstruct our notion of the chimera until it ceases to be an independent idea and becomes a part of the system of greek mythology. has it gained in validity in ceasing to be an independent myth, in becoming an element in systematized myth? myth it was and myth it remains. mythology does not get validity by growing bigger. how do we know the same is not the case with the ideas which are the product of our most deliberate and extended scientific inquiry? the reference again to the content as the self-identical object of all consciousness proves nothing; the matter of a hallucination does not gain worth in proportion to its social contagiousness. or the reference proves that we have not as yet reached any conclusion, but are entertaining a hypothesis--since social validity is not a matter of mere common content, but of securing participation in a commonly adjudged social experience through action directed thereto and directed by consensus of judgment. according to lotze, the final product is, after all, still thought. now, lotze is committed once for all to the notion that thought, in any form, is directed by and at an outside reality. the ghost haunts him to the last. how, after all, does even the ideally perfect valid thought apply or refer to reality? its genuine subject is still beyond itself. at the last lotze can dispose of this question only by regarding it as a metaphysical, not a logical, problem (vol. ii, pp. , ). in other words, _logically_ speaking, we are at the end just exactly where we were at the beginning--in the sphere of ideas, and of ideas only, plus a consciousness of the necessity of referring these ideas to a reality which is beyond them, which is utterly inaccessible to them, which is out of reach of any influence which they may exercise, and which transcends any possible comparison with their results. "it is vain," says lotze, "to shrink from acknowledging the circle here involved ... all we know of the external world depends upon the ideas of it which are within us" (vol. ii, p. ). "it is then this varied world of ideas within us which forms the sole material directly given to us" (vol. ii, p. ). as it is the only material given to us, so it is the only material with which thought can end. to talk about knowing the external world through ideas which are merely within us is to talk of an inherent self-contradiction. there is no common ground in which the external world and our ideas can meet. in other words, the original implication of a separation between an independent thought-material and an independent thought-function and purpose lands us inevitably in the metaphysics of subjective idealism, plus a belief in an unknown reality beyond, which unknowable is yet taken as the ultimate test of the value of our ideas as just subjective. the subjectivity of the psychical event infects at the last the meaning or ideal object. because it has been taken to be something "in itself," thought is also something "in itself," and at the end, after all our maneuvering we are where we began:--with two separate disparates, one of meaning, but no existence, the other of existence, but no meaning. the other aspect of lotze's contradiction which completes the circle is clear when we refer to his original propositions, and recall that at the outset he was compelled to regard the origination and conjunctions of the impressions, the elements of ideas, as themselves the effects exercised by a world of things already in existence (see p. ). he sets up an independent world of thought, and yet has to confess that both at its origin and termination it points with absolute necessity to a world beyond itself. only the stubborn refusal to take this initial and terminal reference of thought beyond itself as having a historic meaning, indicating a particular place of generation and a particular point of fulfilment in the drama of evolving experience, compels lotze to give such bifold objective reference a purely metaphysical turn. when lotze goes on to say (vol. ii, p. ) that the measure of truth of particular parts of experience is found in asking whether, when judged by thought, they are in harmony with other parts of experience; when he goes on to say that there is no sense in trying to compare the entire world of ideas with a reality which is non-existent, excepting as it itself should become an idea, lotze lands where he might better have frankly commenced.[ ] he saves himself from utter skepticism only by claiming that the explicit assumption of skepticism, the need of agreement of a ready-made idea as such, with an extraneous independent material as such, is meaningless. he defines correctly the work of thought as consisting in harmonizing the various portions of experience with each other: a definition which has meaning only in connection with the fact that experience is continually integrating itself into a wholeness of coherent meaning deepened in significance by passing through an inner distraction in which by means of conflict certain contents are rendered partial and hence objectively conscious. in this case the test of thought is the harmony or unity of experience actually effected. in that sense the test of reality is beyond thought, as thought, just as at the other limit thought originates out of a situation which is not reflectional in character. interpret this before and beyond in a historic sense, as an affair of the place occupied and rôle played by thinking as a function in experience in relation to other functions, and the intermediate and instrumental character of thought, its dependence upon unreflective antecedents for its existence, and upon a consequent experience for its test of final validity, becomes significant and necessary. taken at large, it plunges us in the depths of a hopelessly complicated and self-revolving metaphysic. v a critical study of bosanquet's theory of judgment[ ] bosanquet's theory of the judgment, in common with all such theories of the judgment, necessarily involves the metaphysical problem of the nature of reality and of the relation of thought to reality. that the judgment is the function by which knowledge is attained is a proposition which would meet with universal acceptance. but knowledge is itself a relation of some sort between thought and reality. the view which any logician adopts as to the nature of the knowledge-process is accordingly conditioned by his metaphysical presuppositions as to the nature of reality. it is equally true that the theory of the judgment developed from any metaphysical standpoint serves as a test of the validity of that standpoint. we shall attempt in the present paper to show how bosanquet's theory of the judgment develops from his view of the nature of reality, and to inquire whether the theory succeeds in giving such an account of the knowledge-process as to corroborate the presupposition underlying it. bosanquet defines judgment as "the intellectual function which defines reality by significant ideas and in so doing affirms the reality of those ideas" (p. ).[ ] the form of the definition suggests the nature of his fundamental problem. there is, on the one hand, a world of reality which must be regarded as having existence outside of and independently of the thoughts or ideas we are now applying to it; and there is, on the other hand, a world of ideas whose value is measured by the possibility of applying them to reality, of qualifying reality by them. the judgment is the function which makes the connection between these two worlds. if judgment merely brought one set of ideas into relation with another set, then it could never give us anything more than purely hypothetical knowledge whose application to the real world would remain forever problematic. it would mean that knowledge is impossible, a result which seems to be contradicted by the existence of knowledge. the logician must, therefore, as bosanquet tells us, regard it as an essential of the act of judgment that it always refers to a reality which goes beyond and is independent of the act itself (p. ). his central problem thus becomes that of understanding what the nature of reality is which permits of being defined by ideas, and what the nature of an idea is that it can ever be affirmed to be real. how does the real world get representation in experience, and what is the guarantee that the representation, when obtained, is correct? the defining of the problem suggests the view of the nature of reality out of which bosanquet's theory of the judgment grows. the real world is to him a world which has its existence quite independently of the process by which it is known. the real world is there to be known, and is in no wise modified by the knowledge which we obtain of it. the work of thought is to build up a world of ideas which shall represent, or correspond to, the world of reality. the more complete and perfect the correspondence, the greater our store of knowledge. translated into terms of the judgment, this representational view means that the subject of the judgment must always be reality, while the predicate is an idea. but when we examine the content of any universal judgment, or even of an ordinary judgment of perception, the subject which appears in the judgment is evidently not reality at all, if by reality we mean something which is in no sense constituted by the thought-process. when i say, "the tree is green," the subject, tree, cannot be regarded as a bit of reality which is given ready-made to the thought-process. the ability to perceive a tree, to distinguish it from other objects and single it out for the application of an idea, evidently implies a long series of previous judgments. the content "tree" is itself ideal. as bosanquet forcibly states it: "if a sensation or elementary perception is in consciousness (and if not we have nothing to do with it in logic), it already bears the form of thinking" (p. ). how, then, can it serve as the subject of a judgment? bosanquet's solution of the problem is to say that the real subject of a judgment is not the grammatical subject which appears in a proposition, but reality itself. in the more complex forms of judgment the reference to reality is disguised by the introduction of explicit ideas to designate the portion of reality to which reference is made (pp. , ). in the simplest type of judgment known, however, the qualitative judgment of perception, the reference to reality appears within the judgment itself. the relations of thought to reality and of the elements of the judgment to one another can, accordingly, most readily be seen in the consideration of this rudimentary form of judgment in which the various parts lie bare before us. bosanquet describes it as follows: if i say, pointing to a particular house, "that is my home," it is clear that in this act of judgment the reference conveyed by the demonstrative is indispensable. the significant idea "my home" is affirmed, not of any other general significant idea in my mind, but of something which is rendered unique by being present to me in perception. in making the judgment, "that is my home," i extend the present sense-perception of a house in a certain landscape by attaching to it the ideal content or meaning of "home;" and moreover, in doing this, i pronounce the ideal content to be, so to speak, of one and the same tissue with what i have before me in my actual perception. that is to say, i affirm the meaning of the idea, or the idea considered as a meaning, to be a real quality of that which i perceive in my perception. the same account holds good of every perceptive judgment; when i see a white substance on a plate and judge that "it is bread" i affirm the reference, or general meaning which constitutes the symbolic idea "bread" in my mind, to be a real quality of the spot or point in present perception which i attempt to designate by the demonstrative "this." the act defines the given but indefinite real by affirmation of a quality, and affirms reality of the definite quality by attaching it to the previously undefined real. reality is given for me _in_ present sensuous perception, and _in_ the immediate feeling of my own sentient existence that goes with it. (pp. , .) again, he says that the general features of the judgment of perception are as follows: there is a presence of a something in contact with our sensitive self, which, as being so in contact, has the character of reality; and there is the qualification of this reality by the reference to it of some meaning _such as can_ be symbolized by a name (p. ). our point of contact with reality, the place where reality gets into the thought-process, is, according to this view, to be found in the simplest, most indefinite type of judgment of perception. we meet with reality in the mere undefined "this" of primitive experience. but each such elementary judgment about an undefined "this" is an isolated bit of experience. each "this" could give us only a detached bit of reality at best, and the further problem now confronts us of how we ever succeed in piecing our detached bits of reality together to form a real world. bosanquet's explanation is, in his words, this: the real world, as a definite organized system, is _for me_ an extension of this present sensation and self-feeling by means of judgment, and it is the essence of judgment to effect and sustain such an extension (p. ). again he says: the subject in every judgment of perception is some given spot or point in sensuous contact with the percipient self. but, as all reality is continuous, the subject is not _merely_ this given spot or point. it is impossible to confine the real world within this or that presentation. every definition or qualification of a point in present perception is affirmed of the real world which is continuous with present perception. the ultimate subject of the perceptive judgment is the real world as a whole, and it is of this that, in judging, we affirm the qualities or characteristics. (p. .) the problem is the same as that with which bradley struggles in his treatment of the subject of the judgment, and the solution is also the same. bradley's treatment of the point is perhaps somewhat more explicit. like bosanquet, he starts with the proposition that the subject of the judgment must be reality itself and not an idea, because, if it were the latter, judgment could never give us anything but a union of ideas, and a union of ideas remains forever universal and hypothetical. it can never acquire the uniqueness, the singularity, which is necessary to make it refer to the real. uniqueness can be found only in our contact with the real. but just where does our contact with the real occur? bradley recognizes the fact that it cannot be the _content_--even in the case of a simple sensation--which gives us reality. the content of a sensation is a thing which is in my consciousness, and which has the form which it presents because it is in my consciousness. reality is precisely something which is not itself sensation, and cannot be in my consciousness. if i say, "this is white," the "this" has a content which is a sensation of whiteness. but the sensation of whiteness is not reality. the experience brings with it an assurance of reality, not because its content is the real, but because it is "my direct encounter in sensible presentation with the real world."[ ] to make the matter clearer, bradley draws a distinction between the _this_ and the _thisness_. in every experience, however simple, there is a content--a "thisness"--which is not itself unique. considered merely as content, it is applicable to an indefinite number of existences; in other words, it is an idea. but there is also in every experience a "this" which is unique, but which is not a content. it is a mere sign of existence which gives the experience uniqueness, but nothing else. the "thisness" falls on the side of the content, and the "this" on the side of existence. it is exactly the distinction which bosanquet has in mind in the passages quoted in which he tells us that "reality is given for me _in_ present sensuous perception, and _in_ the immediate feeling of my own sentient existence which goes with it;" and again when he says: "there is a presence of a something in contact with our sensitive self, which, as being so in contact, has the character of reality." the same point is made somewhat more explicitly in his introduction when he says that the individual's present perception is not, indeed, reality as such, but is his present point of contact with reality as such (p. ). but has this distinction between the content of an experience and its existence solved the problem of how we _know_ reality? when bosanquet talks of knowing reality, he means possessing ideas which are an accurate reproduction of reality. it is still far from clear how, according to his own account, we could ever have any assurance that our ideas do represent reality accurately, if we can nowhere find a point at which the content of an experience can be held to give us reality. the case is still worse when we go beyond the problem of how any particular bit of reality can be known, and ask ourselves how reality as a whole can be known. the explanation offered by both bradley and bosanquet is that by means of judgment we extend the bit of reality of whose existence we get a glimpse through a peep-hole in the curtain of sensuous perception, and thus build up the organized system of reality. in a passage previously quoted, bosanquet tells us that all reality is continuous, and therefore the real subject of a judgment cannot be the mere spot or point which is given in sensuous perception, but must be the real world as a whole. but how does he know that reality is continuous, and that the real world is an organized system? our only knowledge of reality comes through judgment, and judgment brings us into contact with reality only at isolated points. when he tells us that reality is a continuous whole, he does so on the basis of a metaphysical presupposition which is not justifiable by his theory of the judgment. the only statement about reality which could be maintained on the basis of his theory is that some sort of a reality exists, but the theory furnishes equal justification for the assurance that this reality is of such a nature that we can never know anything more about it than the bare fact of its existence. moreover, the bare fact of the existence of reality comes to us merely in the form of a feeling of our own sentient existence which goes with sense-perception. but the mere assurance that somewhere behind the curtain of sensuous perception reality exists (even if this could go unchallenged), accompanied by the certainty that we can never by any possibility know anything more about it, is practically equivalent to the denial of the possibility of knowledge.[ ] although the denial of the possibility of knowledge seems to be the logical outcome of the premises, it is not the conclusion reached by bosanquet. at the outset of his treatise, bosanquet propounds the fundamental question we have been considering in these words: "how does the analysis of knowledge as a systematic function, or system of functions, explain that relationship in which truth appears to consist, between the human intelligence on the one hand, and fact or reality on the other?" his answer is: "to this difficulty there is only one reply. if the object-matter of reality lay genuinely outside the system of thought, not only our analysis, but thought itself, would be unable to lay hold of reality." (pp. , .) the statement is an explicit recognition of the impossibility of bridging the chasm between a reality outside the content of knowledge and a known real world. it brings before us the dilemma contained in bosanquet's treatment of the subject of the judgment. on the one hand the subject of the judgment must be outside the realm of my thoughts. if it were not, judgment would merely establish a relation between my ideas and would give me no knowledge of the real world. on the other hand, the subject of the judgment must be within the realm of my thoughts. if it were not, i could never assert anything of it; could never judge, or know it. the stress he lays on the first horn of the dilemma has been shown. it remains to show his recognition of the second horn, and to find out whether or not he discovers any real reconciliation between the two. bosanquet sums up the section of the introduction on knowledge and its content, truth, with the following paragraph: the real world for every individual is thus emphatically _his_ world; an extension and determination of his present perception, which perception is to him not indeed reality as such, but his point of contact with reality as such. thus in the enquiry which will have to be undertaken as to the logical subject of the judgment, we shall find that the subject, however it may shift, contract, and expand, is always in the last resort some greater or smaller element of this determinate reality, which the individual has constructed by identifying significant ideas with that world of which he has assurance through his own perceptive experience. in analyzing common judgment it is ultimately one to say that _i judge_ and that _the real world for me, my real world, extends itself_, or maintains its organized extension. this is the ultimate connection by which the distinction of subject and predication is involved in the act of affirmation or enunciation which is the differentia of judgment. (pp. , ). here the subject of the judgment appears as an element of a reality _which the individual has constructed_ by identifying significant ideas with that world of which he has assurance through his own perceptive experience. but the very point with reference to the subject of the judgment previously emphasized is that it is not and cannot be something which the individual has constructed. the subject of the judgment must be reality, and reality does not consist of ideas, even if it be determined by them. it does not mend matters to explain that the individual has constructed his real world by identifying significant ideas with that world of which he has assurance through his own perceptive experiences, because, as we have seen, "the individual's perceptive experiences" either turn out to be merely similar mental constructions made at a prior time, so that nothing is gained by attaching to them, or else they mean once more the mere shock of contact which is supposed to give assurance that some sort of reality exists, but which gives no assurance of what it is. that and what, this and thisness still remain detached. when he talks of _the real world for any individual_ we are left entirely in the dark as to what the relation between _the real world as it is for any individual_ and _the real world as it is for itself_ may be, or how the individual is to gain any assurance that _the real world as it is for him_ represents _the real world as it is for itself_. another attempt at a reconciliation of these opposing views leaves us no better satisfied. the passage is as follows: the real world, as a definite organized system, is _for me_ an extension of this present sensation and self-feeling by means of judgment, and it is the essence of judgment to effect and sustain such an extension. it makes no essential difference whether the ideas whose content is pronounced to be an attribute of reality appear to fall within what is given in perception, or not. we shall find hereafter that it is vain to attempt to lay down boundaries between the given and its extension. the moment we try to do this we are on the wrong track. the given and its extension differ not absolutely but relatively; they are continuous with each other, and the metaphor by which we speak of an extension conceals from us that the so-called "given" is no less artificial than that by which it is extended. it is the character and quality of being directly in contact with sense-perception, not any fixed datum of content, that forms the constantly shifting center of the individual's real world, and spreads from that center over every extension which the system of reality receives from judgment. (p. .) in this passage by the "given" he evidently means the content of sensory experience, the thisness, the what. it is, as he says, of the same stuff as that by which it is extended. both the given and that by which it is extended are artificial in the sense of not being _real_ according to bosanquet's interpretation of reality; they are ideas. but if all this is admitted, what becomes of the possibility of knowledge? bosanquet undertakes to rescue it by assuring us again that it is the character and quality of being directly in contact with sense-perception, not any fixed datum of content, that forms the center of the individual's real world and gives the stamp of reality to his otherwise ideal extension of this center. here again we find ourselves with no evidence that the _content_ of our knowledge bears any relation to reality. we have merely the feeling of vividness attached to sensory experience which seems to bring us the certainty that there is some sort of a reality behind it, but this is not to give assurance that our ideal content even belongs rightfully to that against which we have bumped, much less of _how_ it belongs--and only this deserves the title "knowledge." in the chapter on "quality and comparison," in which he takes up the more detailed treatment of the simplest types of judgment of perception, he comes back to the same contradiction, and again attempts to explain how both horns of his dilemma must be true. the passage is this: the reality to which we ascribe the predicate is undoubtedly self-existent; it is not _merely_ in my mind or in my act of judgment; if it were, the judgment would only be a game with my ideas. it is well to make this clear in the case before us, for in the later forms of the judgment it will be much disguised. still the reality which attracts my concentrated attention is also within my act of judgment; it is not even the whole reality present to my perception; still less of course the whole self-existent reality which i dimly presuppose. the immediate subject of the judgment is a mere aspect, too indefinite to be described by explicit ideas except in as far as the qualitative predication imposes a first specification upon it. _this_ reality _is_ in my judgment; it is the point at which the actual world impinges upon my consciousness as real, and it is only by judging with reference to this point that i can refer the ideal content before my mind to the whole of reality which i at once believe to exist, and am attempting to construct. the subject is both in and out of the judgment, as reality is both in and out of my consciousness. (pp. , .) the conclusion he reaches is a mere restatement of the difficulty. the problem he is trying to solve is how the subject _can_ be both in and out of the judgment, and how the subject without is related to the subject within. the mere assertion that it is so does not help us to understand it. his procedure seems like taking advantage of two meanings of sense-perception, its conscious quality and its brute abrupt immediacy, and then utilizing this ambiguity to solve a problem which grows out of the conception of judgment as a reference of idea to reality. turning from his treatment of the world of fact to his discussion of the world of idea, from the subject to the predicate, as it appears in his theory of the judgment we find again a paradox which must be recognized and cannot be obviated. an idea is essentially a meaning. it is not a particular existence whose essence is uniqueness as is the case with the subject of the judgment, but is a meaning whose importance is that it may apply to an indefinite number of unique existences. its characteristic is universality. and yet an idea regarded as a psychical existence, an idea as a content in my mind, is just as particular and unique as any other existence. how, then, does it obtain its characteristic of universality? bosanquet's answer is that it must be universal by means of a reference to something other than itself. its meaning resides, not in its existence as a psychical image, but in its reference to something beyond itself. now, any idea that is affirmed is referred to reality, but do ideas exist which are not being affirmed? if so, their reference cannot be to reality. bosanquet discusses the question in the second section of his introduction as follows: it is not easy to deny that there is a world of ideas or of meanings, which simply consists in that identical reference of symbols by which mutual understanding between rational beings is made possible. a _mere_ suggestion, a _mere_ question, a _mere_ negation, seem all of them to imply that we sometimes _entertain_ ideas without affirming them of reality, and therefore without affirming their reference to be a reference to something real or their meaning to be fact. we may be puzzled indeed to say what an idea can mean, or to what it can refer, if it does not mean or refer to something real--to some element in the fabric continuously sustained by the judgment which is our consciousness. on the other hand, it would be shirking a difficulty to neglect the consideration that an idea, while denied of reality, may nevertheless, or even must, possess an identical and so intelligible reference--a symbolic value--for the rational beings who deny it. a reference, it may be argued, must be a reference to something. but it seems as if in this case the something were the fact of reference itself, the rational convention between intelligent beings, or rather the world which has existence, whether for one rational being or for many, merely as contained in and sustained by such intellectual reference. i only adduce these considerations in order to explain that transitional conception of an objective world or world of meanings, distinct from the real world or world of facts, with which it is impossible wholly to dispense in an account of thought starting from the individual subject. the paradox is that the real world or world of fact thus seems for us to fall within and be included in the objective world or world of meanings, as if all that is fact were meaning, but not every meaning were fact. this results in the contradiction that something is objective, which is not real. (pp. , .) in the seventh section of the introduction bosanquet explains his meaning further by what the reader is privileged to regard as a flight of the imagination--a mere simile--which he thinks may, nevertheless, make the matter clearer. we might try to think that the world, _as known to each of us_, is constructed and sustained by his individual consciousness; and that every other individual also frames for himself, and sustains by the action of his intelligence, the world in which he in particular lives and moves. of course such a construction is to be taken as a reconstruction, a construction by way of knowledge only; but for our present purpose this is indifferent. thus we might think of the ideas and objects of our private world rather as corresponding to than as from the beginning identical with those which our fellow-men are occupied in constructing each within his own sphere of consciousness. and the same would be true even of the objects and contents within our own world, in as far as an act or effort would be required to maintain them, of the same kind with that which was originally required to construct them.... thus the paradox of reference would become clearer. we should understand that we refer to a correspondence by means of a content. we should soften down the contradiction of saying that a name to meet which we have and can get nothing but an idea, nevertheless does not stand for that idea but for something else. we should be able to say that the name stands for those elements in the idea which correspond in all our separate worlds, and in our own world of yesterday and of today, considered as so corresponding. (pp. , .) according to this view, the idea obtains the universality which constitutes it an idea by a sort of process of elimination. it is like a composite photograph. it selects only the common elements in a large number of particular existences, and thus succeeds in representing, or referring to, all the particular existences which have gone to make it up. but when we come to consider the bearing which this view of universality, or generalized significance, has on our estimate of the knowledge-process, we feel that it has not solved the problem for us. in the first place, the idea _in its existence_ is just as particular when regarded as made up of the common elements of many ideas as is any of the ideas whose elements are taken. a composite photograph is just as much a single photograph as any one of the photographs which are taken to compose it. the chasm between the particularity of the psychical image and the universality of its meaning is not bridged by regarding the content of the image as made up by eliminating unlike elements in a number of images. the stuff with which thought has to work is still nothing more than a particular psychical image, and the problem of what gives it its logical value as a general significance is still unsolved. nor does it seem possible to find anything in the _existence_ of the image which could account for its reference to something outside of itself. the _fact_ of reference itself becomes an ultimate mystery.[ ] but even waiving this difficulty, the judgment must still appear truncated, if it really totally disregard a part of its content--_i. e._, the particular existence of the image as part of the judging consciousness. the theory holds that the particular existence of the image has no logical value. it is only its meaning, or general reference, which has logical value. but the image _qua_ image is just as real as that to which it is supposed to refer. if the judgment really does ignore its existence, then it ignores a portion of the reality it attempts to represent, and stands self-confessed as a failure.[ ] at still another point, ideas, as bosanquet represents them, prove to be unsatisfactory tools to use in the work of building up reality. in bosanquet's words: "the meaning tyrannizes over the psychical image in another respect. besides crushing out of sight its particular and exclusive existence, it also crushes out part of its content" (p. ). the idea, as we use it, is not, as to content, a complete or accurate representation of anything real. to take bosanquet's illustration: some one speaks to me of the Ægean sea, which i have never seen. he tells me that it is a deep blue sea under a cloudless sky, studded with rocky islands. the meanings of these words are a problem set to my thought. i have to meet him in the world of objective references, which as intelligent beings we have in common. how i do this is my own affair, and the precise images at my command will vary from day to day, and from minute to minute. it sounds simple to say that i combine my recollections of sea and sky at torbay with those of the island-studded waters of orkney or the hebrides. even so, there is much to adjust and to neglect; the red cliffs of torbay, and the cloudy skies of the north. but then again, my recollections are already themselves symbolic ideas; the reference to torbay or the hebrides is itself a problem set to thought, and puts me upon the selection of index-elements in fugitive images that are never twice the same. i have _first_ to symbolize the color of torbay, using for the purpose any blue that i can call to mind, and fixing, correcting, subtracting from, the color so recalled, till i reduce it to a mere index quality; and _then_ i have to deal in the same way with the meaning or significant idea so obtained, clipping and adjusting the qualities of torbay till it seems to serve as a symbol of the Ægean. (pp. , .) and by the time all this is performed what sort of a representation of reality is the idea? evidently a very poor and meager and fragmentary one. it is so poor and fragmentary, that it cannot itself be that which is affirmed of reality. it must be some other fuller existence to be found in the world of meanings which is affirmed. and yet how the meager content of the idea succeeds in referring to the world of meanings, and acting as the instrument for referring a meaning to reality, is not at all clear. it seems impossible to explain reference intelligibly by the concept of a _correspondence_ of contents. the fundamental difficulty in the interpretation of the predicate is the same one that we encountered in the interpretation of the subject. if the predicate is to be affirmed of reality (and if it be not, it has no logical value), then it must, when affirmed, be in some sense an accurate representation of reality. but the predicate is an idea, and, moreover, an idea which is, both in its existence and in its meaning palpably the outcome of transformations wrought upon given sensory contents by the individual consciousness. since the one point of contact with reality is in sensory experience, the more simple sensory experiences are reacted upon and worked over, the farther they recede from reality. the idea seems, therefore, in its very essence, a thing which never can be affirmed of reality. as image it is itself a reality, but not affirmed; as meaning it is that reality (the image) manipulated for individual ends. why suppose that by distorting reality we get it in shape to affirm _of_ reality? moreover, the farther an idea is removed from immediate sensory experience--in other words, the more abstract it becomes--the less is the possibility of affirming it of reality. the final outcome of this point of view, if we adhere rigorously to its logic is that the more thinking we do, the less we know about the real world. bosanquet avoids this conclusion by a pure act of faith. if knowledge is to be rescued, we must believe that the work done by consciousness upon the bits of reality given in sensory experience really does succeed in building up a knowledge of reality for us. as bosanquet puts it: "the presentation of reality, qualified by an ideal content, is one aspect of subject and predication; and my individual percipient consciousness determining itself by a symbolic idea is the other. that the latter is identified with the former follows from the claim of conscious thought that its nature is to know."[ ] (p. .) to sum up the situation, bosanquet starts out with the assumption that by knowledge we must mean knowledge of a world entirely independent of our ideas. if we fail to make this assumption, knowledge becomes merely a relation between ideas. but its whole importance seems to us to rest on the conviction that it does give us knowledge of a world which is what it is quite independently of our ideas about it, and cannot in any sense be modified by what we think about it. what knowledge does is to give us a copy or representation of the real world, whose value depends on the accuracy of the representation. and yet when we examine any individual knowing consciousness, the subject which appears within the judgment is never some portion of the world which exists outside of the knowing consciousness, but always some portion of the world which exists within the knowing consciousness, and which is constituted by the knowledge process. the predicate which is affirmed of reality is constantly found to derive its meaning, its generalized significance, not from its correspondence with, or reference to, the real world outside of the knowing consciousness, but from reference to a world of meanings, which consists in a sort of convention among rational beings--a world whose existence is distinctly within the knowing consciousness and not outside of it.[ ] between the real world, as bosanquet conceives it, and the world of knowledge, we find inserted on the side of the subject, the world _as known to each of us_, and on the side of the predicate, the _objective world of meanings_. neither of these is the real world. both of them are ideal, _i. e._, are constructions of the individual consciousness. we nowhere find any satisfactory explanation of how these ideal worlds are related to the real world. there is merely the assertion that we must believe that they represent the real world in order that we may believe that knowledge exists. but the fact remains that whenever we try to analyze and explain any particular judgment, what we find ourselves dealing with is always the world as it exists to us as subject, and the objective world of meanings as predicate. if we stop here, then knowledge turns out to be just what bosanquet asserted at the outset that it was _not, i. e._, a relation between ideas. when we demand a justification for going farther than this, we find none except the claim of conscious thought that its nature is to know--a claim whose justice we have no possible means of testing, and which would not, even if admitted, be of the slightest value in deciding which _particular_ judgment is true and which false. bosanquet's development of his subject has proved to be throughout the necessary logical outcome of the presuppositions with reference to reality from which he starts. the fundamental difficulty of erecting a theory of the knowledge-process upon such a basis is recognized by him at the start in a passage already quoted: "if the object-matter of reality lay genuinely outside the system of thought, not only our analysis, but thought itself, would be unable to lay hold of reality" (p. ). but, in spite of this assertion, his fundamental conception of reality remains that of a system which does lie outside the thought-process. his theory is an attempt to reconcile the essentially irreconcilable views that reality is outside of the thought-process, and that it is inside of the thought-process, and he succeeds only by calling upon our faith that so it is. if it be true, as it seems to him to be, that we are compelled to adhere to both of these views of reality, then surely there is no other outcome. it means, however, that we finally resign all hope of _knowing_ reality. we may _have faith_ in its existence, but we have no way of deciding what particular judgment has reality in it as it should have it, and what as it should not. all stand (and fall) on the same basis. but does not bosanquet himself point out a pathway which, if followed farther, would reach a more satisfactory view of the realm of knowledge? he has shown us that the only sort of reality _we know_, or can know, is the reality which appears within our judgment-process--the reality as known to us. would it not be possible to drop the presupposed reality outside of the judgment-process (with which judgment is endeavoring to make connections) and content ourselves with the sort of reality which appears within the judgment-process? in other words, may there not be a satisfactory view of reality which frankly recognizes its organic relation to the knowledge-process, without at the same time destroying its value as reality? is it possible to admit that reality is in a sense constituted in the judgment without making it at the same time the figment of the individual imagination--"a game with ideas"? let us assume for the moment that the real difficulty with mr. bosanquet's conception, the error that keeps him traveling in his hopeless circles, is the notion that truth is a matter of reference of ideas as such to reality as such, leading us to oscillate between the alternatives that either all ideas have such reference, and so are true, constitute knowledge; or else none have such reference, and so are false; or else are mere ideas to which neither truth nor falsity can be attributed. let us ask if truth is not rather some _specific_ relation within experience, something which characterizes one idea rather than another, so that our problem is not how an idea can refer to a reality beyond itself, but what are the marks by which we discriminate a true reference from a false one. then let us ask for the criterion used in daily life and in science by which to test reality. if we ask the philosophically unsophisticated individual why he believes that his house still exists when he is away from it and has no immediate evidence of the fact, he will tell you it is because he has found that he can go back to it time and again and see it and walk into it. it never fails him when he acts upon the assumption that it is there. he would never tell you that he believed in its existence when he was not experiencing it because his mental picture of his house stood for and represented accurately an object in the real world which was nevertheless of a different order of existence from his mental picture. when you ask the physicist why he believes that the laws of motion are true, he will tell you that it is because he finds that bodies always do behave according to them. he can predict just what a body will do under given circumstances. he is never disappointed however long he takes it for granted that the laws of motion are true and that bodies behave according to them. the only thing that could make him question their truth would be to find some body which did not prove to behave in accordance with them. the criterion is the same in both cases. it is the practical criterion of what as a matter of fact will work. that which can safely be taken for granted as a basis for further action is regarded as real and true. it remains real so long, and only so long, as it continues to fulfil this condition. as soon as it ceases to do so, it ceases to be regarded as real. when a man finds that he can no longer obtain the accustomed experience of seeing and entering his house, he ceases to regard it as real. it has burned down, or been pulled down. when a physicist finds that a body does not, as a matter of fact, behave as a given law leads him to expect it would behave, he ceases to regard the law as _true_. the contrast between the naïve view of the criterion of reality and the one we have just been discussing may be brought out by considering how we should have to interpret from each standpoint the constant succession of facts in the history of science which have ceased to be facts. for illustration take the former fact that the earth is flat. it ceased to be a fact, says the theory we have been reviewing, because further thought-constructions of the real world convinced us that there is no reality which the idea "flat-world" represents. the idea "round-world" alone reproduces reality. it ceased to be a fact, says the naïve view, because it ceased to be a safe guide for action. men found they could sail around the world. correspondence in one case is pictorial, and its existence or non-existence can, as we have seen, never be ascertained. in the other, correspondence is response, adjustment, the co-meeting of specific conditions in further constituting of experience. in actual life, therefore, the criterion of reality which we use is a practical one. the test of reality does not consist in ascertaining the relationship between an idea and an _x_ which is not idea, but in ascertaining what experience can be taken for granted as a safe basis for securing other experiences. the evident advantage of the latter view, leaving aside for the moment the question of its adequacy in other respects, is that it avoids the fundamental skepticism at once suggested by the former. how can we ever be sure that the fact which we have discovered will stand the test of further thought-constructions? perhaps it comes no nearer to reality than the discarded one. obviously we never _can_ be sure that any particular content of thought represents reality so accurately and perfectly that it will never be subject to revision. if, however, the test of reality is the _adequacy_ of a given content of consciousness as a stimulus to action, as a mode of control, we have an applicable standard. a given content of consciousness is real--is a fact--so long as the act resulting from it is adequate in adaptation to other contents. it ceases to be real as soon as the act it stimulates proves to be inadequate. the view which places the ultimate test of facts, not in any relationship of contents or existences, but in the practical outcome of thought, is the one which seems to follow necessarily from a thoroughgoing conception of the judgment as a function--an act. our fundamental biological conception of the activities of living organisms is that acts exist for the sake of their results. acts are always stimulated by some definite set of conditions, and their value is always tested by the adequacy with which they meet this set of conditions. the judgment is no exception to the rule. it is always an act stimulated by some set of conditions which needs readjusting. its outcome is a readjustment whose value is and can be tested only by its adequacy. it is accordingly entirely in line with our reigning biological conceptions to expect to find the ultimate criterion of truth and reality in the practical outcome of thought, and to seek for an understanding of the nature of the "real" and of the "ideal" within the total activity of judgment. one difficulty besets us at the outset of such an investigation--that of being sure that we have a genuine judgment under examination. a large portion of the so-called judgments considered by logicians, even by those who emphasize the truth that a judgment is an _act_, are really not judgments at all, but contents of thought which are the outcome of judgments--what might be called dead judgments, instead of live judgments. when we analyze a real act of judgment, as it occurs in a living process of thought, we find given elements which are always present. there is always a certain situation which demands a reaction. the situation is always in part determined and taken for granted, and in part questioned. it is determined in so far as it is a definite situation of some sort; it is undetermined in so far as it furnishes an inadequate basis for further action and therefore comes to consciousness as a problem. for example, take one of the judgments bosanquet uses. "this is bread." we have first to inquire when such a judgment actually occurs in the living process of thought. a man does not make such a judgment in the course of his thinking unless there is some instigation to do so. perhaps he is in doubt as to whether the white object he perceives is bread or cake. he wants some bread, but does not want cake. a closer inspection convinces him that it is bread, and the finished judgment is formulated in the proposition: "this is bread." what is the test of the reality of the bread, and the truth of the judgment? evidently the act based on it. he eats the bread. if it tastes like bread and affects him like bread, then the bread was real and the judgment true. if, on the other hand, it does not taste like bread, or if it makes him violently ill, then the "bread" was not real and the judgment was false. in either case, the "this"--the experience to be interpreted--is unquestioned. the man does not question the fact that he has a perception of a white object. so much is taken for granted and is unquestioned within that judgment. but there is another part of the experience which is questioned, and which remains tentative up to the conclusion of the act of judgment; that is the doubt as to whether the perceived white object is bread or something else. every live judgment, every judgment as it normally occurs in the vital process of thought, must have these phases. it is only when a judgment is taken out of its context and reduced to a mere memorandum of past judgments that it fails to reveal such parts. the man may, of course, go farther back. he may wonder whether this is really white or not. but he falls back then on something else which he takes unquestioningly--a "this" experience of some sort or other. so far we have considered the practical criterion of reality merely as the one which is actually operative in everyday life, and as the one suggested by our biological theory of the functions of living organisms. it also offers a suggestion for the modified view of the nature of reality for which we are in search. our previous discussion brought out incidentally a contradiction in the traditional theory of the nature of reality which it will be worth while to consider further. in dealing with the subject of the judgment, reality seemed to be made synonymous with fact. in this sense fact, or the real, was set off against the ideal. knowledge was viewed as the correspondence between real and ideal. when we came to deal with the ideal itself--with the predicate of the judgment--there appeared in it an element of fact or reality which proved a serious stumbling-block for the theory. as image in my mind, the idea is just as real as the so-called facts; but this sort of reality according to the theory in question is neither the reality about which we are judging nor a real quality of it. both bradley and bosanquet are forced to admit that the judgment ignores it, and is in so far by nature inadequate to its appointed task of knowing reality. the suggestion which the situation offers for a new theory is that the view of reality has been too narrow. reality must evidently be a broad enough term to cover both fact and idea. if so, the reality must be nothing more nor less than the total process of experience with its continual opposition of fact and idea, and their continual resolution through activity. that which previous theory has been calling the real is not the total reality, but merely one aspect of it. the problem of relation of fact and idea is thus the problem of the relation of one form of reality to another, and so a determinate soluble one, not a _merely_ metaphysical or general one. granting this, does it still remain true that reality in the narrower sense, reality as fact, can be regarded as a different order of existence from the ideal, and set over against the thought-process? evidently not. fact and idea become merely two aspects of a total reality. the way in which fact and idea are distinguished has already been suggested by the practical and biological criterion of fact, or reality in the narrower sense. from this point of view, fact is not a different order of existence from idea, but is merely a part of the total process of experience which functions in a given way. it is merely that part of experience which is taken as given, and which serves as a stimulus to action. thus the essential nature of fact, or reality in the popular sense, falls not at all on the side of its content, but on the side of its function. similarly the ideal is merely that part of the total experience which is taken as tentative. there is no problem as to how either of them is related to reality. in this relationship they _are_ reality. that which previous theories had been calling the whole of reality now appears as merely one aspect of it--the fact aspect--artificially isolated from the rest. when we translate this view of the nature of reality into terms of a theory of the judgment, we find that we can agree with bosanquet in his definition of a judgment. it is an act, and an act which refers an ideal content to reality. the judgment must be an act, because it is essentially an adaptation--a reaction toward a given situation. the subject of the judgment is that part of the content of experience which represents the situation to be reacted to. it is that which is taken for granted as given in each case. now this is, as we have seen, reality--in the narrower sense of that term. what bosanquet has been calling reality now appears merely as the subject of the judgment taken out of its normal function and considered as an isolated thing. it is an artificial abstraction. it is accordingly true, as bosanquet insists, that the subject of the judgment must always be reality--both in his sense of the term and in ours. this reality is not real, however, by virtue of its independence from the judgment, but by virtue of its function within the judgment. his fundamental problem with reference to the subject of the judgment is disposed of from this point of view. the subject is wholly within the judgment, not in any sense outside of it; but it is at the same time true that the subject of the judgment is reality. the fact that the subjects of all judgments--even those of the most elementary type--bear evident marks of the work done by thought upon them, ceases to be a problem. the subject is essentially a thing constituted by the doubt-inquiry process, and functioning within it. the necessity for an intermediate _real world as it is to me_ between the real world and the knowing process disappears, because the _real world as it is to me_ is the only real world of which the judgment can take account. there is no longer any divorce between the content of the subject and its existence. reality in his sense of the term--reality as fact--does not fall on the side of _existence_ in distinction from content, but on the side of _function_ in distinction from content. the predicate of the judgment is that part of the total experience which is taken as doubtful, or tentative. as we have seen, every act of adaptation involves a definite situation to be reacted to (subject) and an indefinite or tentative material with which to react (predicate). we have pointed out that a situation which demands a judgment never appears in consciousness as mere questioned or questionable situation.[ ] there is always present, as soon as the doubt arises, some sort of tentative solution. this is the predicate or idea. just as the fact, or real in the narrower sense, is that which is taken as given in the situation, so the ideal is that which is taken as tentative. its ideality does not consist in its reference to another order of existence, the objective world of meanings, but in its function within the judgment, the estimate of the whole situation as leading up to the adequate act. just as we no longer have any need for the mediation of the _real world as known to me_ between subject and reality, so we no longer need _the objective world of meanings_ to bridge the chasm between the predicate and reality. the difficulty of understanding how ideas can be used to build up facts disappears when we regard fact and idea, not as different orders of existence, but as contents marking different phases of a total function. ideas, as bosanquet represented them, proved to be extremely unsatisfactory tools to use in building up a knowledge of reality. in the first place, their value as instruments of thought depends upon their universality. we have already reviewed bosanquet's difficulties in attempting to explain the universality of ideas. the universality of an idea cannot reside in its mere existence as image. its existence is purely particular. its universality must reside in its reference to something outside of itself. but no explanation of how the particular existence--image--could refer to another and fuller content of a different order of existence could be discovered. the fact of reference remained an ultimate mystery. from the new point of view the image gains its universality through its organizing function. it represents an organized habit which may be brought to bear upon the present situation, and which serves, by directing action, to organize and unify experience as a whole. it is only as function that the concept of reference can be made intelligible. of course, considered as content, the idea is just as particular from this point of view as from any other. we still have to discuss the question as to whether or not the particularity of the idea has a logical value. the fact that it had none in bosanquet's theory sets a limit to the validity of thought. but if the real test of the validity of a judgment is the act in which it issues, then the existential aspect of the idea must have logical value. the existential aspect of the idea is the "my" side of it. it is as my personal experience that it exists. but it is only as my idea that it has any impulsive power, or can issue in action. far from being ignored, therefore, the existential aspect is essential to the logical, the determinative, value of an idea. ideas, according to the representational theory of knowledge, proved to be a poor medium for knowing reality in still another respect. they are in their very nature contents that have been reduced from the fulness of experience to mere index-signs. even though their reference to a fuller content in the objective world of meanings presented no problem, still this objective world of meanings is far removed from reality. and yet, in order to know, we must be able to affirm ideas of reality. on the functional theory of ideas, their value does not rest at all upon their representational nature. they are not taken either in their existence or in their meaning as representations of any other content. they are taken as contents which mark a given function, and their value is determined entirely by the adequacy of the function of which they are the conscious expression. their content may be as meager as you please. it may have been obtained by a long process of reducing and transforming sensory experience, but if it serve to enable its possessor to meet the situation which called it up with the appropriate act, then it has truth and value in the fullest sense. the reduction of the idea to a mere index-sign presents no problem when we realize that it is the tool of a given function, not the sign for a different and fuller content. the idea thus becomes a commendable economy in the thought-process, rather than a reprehensible departure from reality. we have already upon general considerations criticised the point of view which holds that ideality consists in reference to another content. in arguing that this reference cannot be primarily to reality itself, but rather to an intermediate world of meanings, bosanquet cites the question and the negative judgment. in the question ideas are not affirmed of reality, and in negation they are definitely denied of reality, hence their reference cannot be to reality. it must therefore be to an objective world of meanings. it may be worth while to point out in passing that, from the functional point of view, the part played by ideas in the question and in negative judgment is the same that it is in affirmation. we have brought out the fact that all judgment arises in a doubt. the earliest stage of judgment is accordingly a question. whether the process stops at that point, or is carried on to an affirmation or negation, depends upon the particular conditions. the ideas which appear in questions present no other problem than those of affirmation. they are ideas, not by virtue of their reference to another content in the world of meanings, but by virtue of their function, _i. e._, that of constituting that part of the total experience which is taken as doubtful, and hence as in process. in order to make this point clear with reference to negative judgments, it will be necessary to consider the relation of negative and positive judgments somewhat more in detail. all judgment is in its earliest stages a question, but a question is never _mere_ question. there are always present some suggestions of an answer, which make the process really a disjunctive judgment. a question might be defined as a disjunctive judgment in which one member of the disjunction is expressed and the others implied. if the process goes on to take the form of affirmation or negation, one of the suggested answers is selected. to follow out the illustration of the bread used above, the judgment arises in a doubt as to the nature of the white object perceived, but the doubt never takes the form of a blank question. it at once suggests certain possible solutions drawn from the mass of organized experience at the command of the person judging. at this stage the judgment is disjunctive. in the illustration it would probably take the form: "this is either bread or cake." the further course of the judgment rejects the cake alternative, and selects the bread, and the final outcome of the judgment is formulated in the proposition: "this is bread." but how did it happen that it did not take the form: "this is not cake"? that proposition is also involved in the outcome, and implied in the judgment made. the answer is that the form taken by the final outcome depends entirely on the direction of interest of the person making the judgment. if his interest happened to lie in obtaining bread, then the outcome would naturally take the form: "this is bread," and his act would consist in eating it. if he happened to want cake, the natural form would be, "this is not cake," and his act would consist in refraining from eating. in other words, the question as to whether a judgment turns out to be negative or positive is a question of whether the stress of interest happens to fall on the selected or on the rejected portions of the original disjunction. every determination of a subject through a predicate includes both. the selection of one or the other according to interest affects the final formulation of the process, but does not change the relations of its various phases. an idea in a negative judgment is just what it is in a positive judgment. in neither case is it constituted an idea by reference to some other content. so far we have outlined bosanquet's theory of the judgment; have noted the apparently insoluble problems inherent in his system, and have sketched a radically different theory which offered a possible solution for his difficulties. it now remains to develop the implications of the new theory further by comparing its application to some of the more important problems of logic with that of bosanquet. in closing we shall have to inquire to what extent the new theory of the judgment with its metaphysical implications has proved more satisfactory than that of bosanquet. the special problems to be considered are ( ) the relation of judgment to inference; ( ) the parts of the judgment and their relationship; ( ) the time element in the judgment; and ( ) the way in which one judgment can be separated from another. . the discussion of the relation between judgment and inference comes up incidentally in bosanquet's treatment of the distinction between a judgment and a proposition (p. ). the proposition, he says, is merely the enunciative sentence which represents the act of thought called judgment. with this distinction we should agree. in his discussion of the point, however, he criticises hegel's doctrine that a judgment is distinguished from a proposition in that a judgment maintains itself against a doubt, while a proposition is a mere temporal affirmation, not implying the presence of a doubt. the ground of his criticism is that judgment must be regarded as operative before the existence of a conscious doubt, and that, while it is true, as hegel suggests, that judgment and inference begin together, they both begin farther back than the point at which conscious doubt arises. doubt marks the point at which inference becomes conscious of its ground. now, it is undoubted that inferences in which the ground is implicit exist at an earlier stage of experience than those in which it is explicit. the former we usually call simple apprehension, and the latter judgment. what bosanquet wishes to do is to make the term "judgment" cover both the implicit and the explicit activities. the question at once arises whether such a use of terms is accurate. there is certainly a wide difference between an inference which is conscious of its ground, and one which is not. it is conceivably a distinction of philosophic importance. to slur the difference by applying one name to both accomplishes nothing. it will be remembered that the presence of a conscious doubt is the criterion of judgment adopted in the standpoint from which we have been criticising bosanquet's theory. we should accordingly make the term "inference" a wider one than the term "judgment." a judgment is an inference which is conscious of its ground. since fact and idea have been represented as constituted in and through judgment, the question which at once suggests itself is: what, from such a standpoint, is the criterion of fact and idea in the stage of experience previous to the appearance of judgment? the answer is that the question involves the psychological fallacy. there is no such distinction as fact and idea in experience previous to the appearance of judgment. the distinction between fact and idea arises only at the higher level of experience at which inference becomes conscious of its grounds. to ask what they were previous to that is to ask _what_ they were before they _were_--a question which, of course, cannot be answered. our reason for not adopting hegel's distinction between a judgment and a proposition would accordingly not be the same as bosanquet's. the question has already been touched upon in the distinction between dead and live judgments. what hegel calls a proposition is really nothing but a dead judgment. his illustration of a temporal affirmation is the sentence: "a carriage is passing the house." that sentence would be a judgment, he says, only in case there were some doubt as to whether or not a carriage was passing. but the question to be answered first is: when would such a "statement" occur in the course of our experience? it is impossible to conceive of any circumstances in which it would naturally occur, unless there were some doubt to be solved either of our own or of another. perhaps one is expecting a friend, and does not know at first whether it is a carriage or a cart which is passing. perhaps some one has been startled, and asks: "what is this noise?" what hegel wishes to call a proposition is, accordingly, nothing but a judgment taken out of its setting. . in dealing with the traditional three parts of the judgment--subject, predicate, and copula--bosanquet disposes of the copula at once, by dividing the judgment into subject and predication. but the two terms "subject" and "predication" are not co-ordinate. subject, as he uses it, is a static term indicating a _content_. predication is a dynamic term indicating the act of predicating. it implies something which is predicated of something else, _i. e._, two contents and the act of bringing them into relation. now, if what we understand by the copula is the _act_ of predicating abstracted from the content which is predicated of another content, then it does not dispose of the copula as a separate factor in judgment to include thing predicated and act of predicating under the single term "predication." the term "predication" might just as reasonably be made to absorb the subject as well, and would then appear--as it really is--synonymous with the term "judgment." but bosanquet's difficulties with the parts of the judgment are not disposed of even by the reduction to subject and predication. he goes on to say: it is plain that the judgment, however complex, is a single idea. the relations within it are not relations between ideas, but are themselves a part of the idea which is predicated. in other words, the subject must be outside the judgment in order that the content of the judgment may be predicated of it. if not, we fall back into "my idea of the earth goes round my idea of the sun," and this, as we have seen, is never the meaning of "the earth goes round the sun." what we want is, "the real world has in it as a fact what i mean by earth-going-round-sun." (p. .) we have already pointed out the difficulties into which bosanquet's presupposition as to the nature of reality plunges him. this is but another technical statement of the same problem. if the subject is really outside of judgment, then the entire _content_ of the judgment must fall on the side of predicate, or idea. in the paragraphs that follow, bosanquet brings out the point that the judgment must nevertheless contain the distinction of subject and predicate, since it is impossible to affirm without introducing a distinction into the _content_ of the affirmation. yet he considers this distinction to be _merely_ a difference within an identity. it serves to mark off the grammatical subject and predicate, but cannot be the essential distinction of subject and predicate. his solution of the puzzle is really the one for which we have been contending, _i. e._, that "the real world is primarily and emphatically my world," but he still cannot be satisfied with that kind of a real world as ultimate. behind the subject which presents my world he postulates a real world which is not my world, but which my world represents. it is the relation between this real world and the total content of a judgment which he considers the essential relation of judgment. this leaves him--as we have pointed out--as far as ever from a theory of the relation of thought to reality, and, moreover, with no criterion for the distinction of subject and predicate within the judgment. to say that it is a difference within an identity does not explain how, on a mere basis of content, such a difference is distinguished within an identity or how it assumes the importance it actually has. he vibrates between taking the whole intellectual content as predicate, the reality to be represented as subject (in which case the copula would be the "contact of sense-perception") and a distinction appearing without reasonable ground or bearing _within_ the intellectual content. when subject and predicate are regarded as the contents in which phases of a function appear, this difficulty no longer exists. . in discussing the time relations within judgment (p. ) bosanquet first disposes of the view which holds that the subject is prior to the predicate in time, and is distinguished from the predicate by its priority. he emphasizes the fact that no content of consciousness can have the significance of a subject, except with reference to something already referred to it as predicate. but while it cannot be true that the parts of the judgment fall outside of one another in time, it is yet evident that in one sense at least the judgment is in time. to make this clear, bosanquet draws a provisional distinction between the process of arriving at a judgment and the completed judgment. the process of arriving at a judgment is a process of passing from a subject with an indefinite provisional predicate--a sort of disjunctive judgment--to a subject with a defined predicate. this process is evidently in time, but it is as evidently not a transition from subject to predicate. it is, as he says, a modification, _pari passu_, of both subject and predicate. the same distinction, he thinks, must hold of the judgment when completed. but this throws us into a dilemma with reference to the time-factor in judgment. time either is or is not an essential factor in judgment. if it is not essential, then how explain the evident fact that the judgment as an intellectual process does have duration? if it is essential, then how explain the fact that its parts do not fall outside one another in time? bosanquet evidently regards the former problem as the easier of the two. his solution is that, while the judgment is an intellectual process in time, still this is a purely external aspect. the essential relation between subject and predicate is not in time, since they are coexistent; therefore time is not an essential element in judgment. the first point at which we take issue with this treatment of time in relation to judgment is in the distinction between the process of arriving at the judgment and the completed judgment. bosanquet himself defines judgment as an intellectual act by which an ideal content is referred to reality. now, at what point does this act begin? certainly at the point where an ideal content is first applying to reality, and this, as he points out, is at the beginning of the process which he describes as the process of arriving at a judgment. it is nothing to the point that at this stage the predicate is tentative, while later it becomes defined. his process of arriving at the judgment is exactly the process we have been describing as the early stages of any and every judgment. when he talks about the judgment as completed, he has apparently shifted from the dynamic view of judgment implied in his definition to a static view. all he could mean by a completed judgment--in distinction to the total activity of arriving at a judgment--is the new content of which we find ourselves possessed when the total process of predication is complete. but this content is not a judgment at all. it is a new construction of reality which may serve either as subject or as predicate in future judgments. now, if we regard the judgment as the total activity by which an ideal content is referred to reality, then must we not regard time as an essential element? bosanquet answers this question in the negative, because he believes that if time is an essential element, then the parts of the judgment must necessarily fall outside one another in time. but is this necessary? if the essence of judgment is the very modification, _pari passu_, of subject and predicate, then time must be an essential element in it, but it is not at all necessary that its elements should fall outside of one another in time. in other words, the dilemma which bosanquet points out on p. is not a genuine one. there is no difficulty involved in admitting that the judgment is a transition in time, and still holding that its _parts_ do not fall outside _one another_ in time. his own solution of the problem--_i. e._, that, although judgment is an intellectual process in time, still time is not an essential feature of it, because subject and predicate are coexistent and judgment is a relation between them--involves a desertion of his dynamic view of judgment. he defines judgment, not as a relation between subject and predicate, but as an intellectual _act_.[ ] . the discussion of the time-element in judgment leads up to the next puzzle--that as to the way in which one judgment can be marked off from another in the total activity of thought. bosanquet has pointed out that subject and predicate are both of them present at every stage of the judging process, and are undergoing progressive modification. if, therefore, we take a cross-section of the process at any point, we find both subject and predicate present; but a cross-section at one point would not reveal quite the same subject and predicate as the cross-section at another point. he comes to the conclusion that judgment breaks up into judgments as rhomboidal spar into rhomboids (p. ). it is, accordingly, quite arbitrary to mark out any limits for a single judgment. the illustration he gives of the point is as follows: take such an every-day judgment of mixed perception and inference as, "he is coming down stairs and going into the street." it is the merest chance whether i break up the process thus, into two judgments as united by a mere conjunction, or, knowing the man's habits, say, when i hear him half way down stairs, "he is going out." in the latter case i summarize a more various set of observations and inferences in a single judgment; but the judgment is as truly single as each of the two which were before separated by a conjunction; for each of them was also a summary of a set of perceptions, which might, had i chosen, have been subdivided into distinct propositions expressing separate judgments; _e. g._, "he has opened his door, and is going toward the staircase, and is half way down, and is in the passage," etc. if i simply say, "he is going out," i am not a whit the less conscious that i judge all these different relations, but i then include them all in a single systematic content "going out." (p. .) but is it a question of merest chance which of these various possibilities is actualized? is bosanquet really looking--as he thinks--at the actual life of thought, or is he considering, not what as a matter of fact does take place under a concrete set of circumstances, but what might take place under slightly differing sets of circumstances? if it is true that judgment is a crisis developing through adequate interaction of stimulus and response into a definite situation, beginning with doubt and ending with a solution of the doubt, then it is not true that its limits are purely arbitrary. it begins with the appearance of the problem and its tentative solutions, and ends with the solution of a final response. it does, of course, depend upon momentary interest, but this does not make its limits arbitrary, for the interest is inherent, not external. in the case of bosanquet's illustration, the question of whether one judgment or half a dozen is made is not a question of merest chance. it depends upon where the interest of the person making the judgment is centered--in other words, upon what is the particular doubt to be solved. if the real doubt is as to whether the man will stay in his room or go out, then when he is heard leaving his room the solution comes in the form: "he is going out." but if the doubt is as to whether he will stay in his room, go out, or go into some other room, then the succession of judgments occurs, each of which solves a problem. "he has opened his door"--then he is not going to stay in his room; "he is going toward the staircase"--then he is not going into a room in the opposite direction, etc. it is impossible to conceive of such a series of judgments as actually being made, unless each one represents a problematic situation and its determination. the only time that a man would, as a matter of fact, choose to break up the judgment, "he is going out," into such a series, would be the time when each member of the series had its own special interest as representing a specific uncertain aim or problem. nor is it altogether true that in making the judgment, "he is going out," one is not a whit the less conscious that he judges all these different relations. he judges only such relations as are necessary to the solution of the problem in hand. if hearing the man open his door is a sufficient basis for the solution, then that is the only one which consciously enters into the formation of the judgment. we have attempted to bring out in the preceding pages what seem to be the contradictions and insoluble problems involved in bosanquet's theory of the judgment, and to exhibit them as the logical outcome of his metaphysical presuppositions. we have also tried to develop another theory of the judgment involving a different view of the nature of reality, and to show that the new theory is able to avoid the difficulties inherent in bosanquet's system. the change in view-point briefly is this: instead of regarding the real world as self-existent, independently of the judgments we make about it, we viewed it as the totality of experience which is assured, _i. e._, determined as to certainty or specific availability, through the instrumentality of judgment. we thus avoided the essentially insoluble problem of how a real world whose content is self-existent quite outside of knowledge can ever be correctly represented by ideas. the difficulty in understanding the relation of the subject and the predicate of judgment to reality disappears when we cease to regard reality as self-existent outside of knowledge. subject and predicate become instrumentalities in the process of building up reality. thought no longer seems to carry us farther and farther from reality as ideas become abstract and recede from the immediate sensory experience in which contact with the real occurs. on the contrary, thought carries us constantly toward reality. finally, we avoid the fundamental skepticism about the possibility of knowledge which, from the other standpoint, is forced upon us by the long succession of facts which have faded into the realm of false opinions, and the lack of any guarantee that our present so-called knowledge of reality shall not meet the same fate. from that point of view, reality seems to be not only unknown, but unknowable. the criticism sure to be passed upon the alternative view developed is that the solution of bosanquet's problems which it affords is not a real solution, but rather the abandonment of an attempt at a solution. it represents reality as a thing which is itself in process of development. it would force us to admit that the reality of a hundred years ago, or even of yesterday, was not in content the reality of today. a growing, developing reality is, it will be said, an imperfect reality, while we must conceive of reality as complete and perfect in itself. the only answer which can be made is to insist again that we have no right to assume that reality is such an already completed existence, unless such an assumption enables us to understand experience and organize it into a consistent whole. the attempt of this paper has been to show that such a conception of reality really makes it inherently impossible to give an intelligible account of experience as a whole, while the view which regards reality as developing in and through judgment does enable us to build up a consistent and understandable view of the world. this suggests that the "perfect" may not after all be that which is finished and ended, but that whose reality is so abundant and vital as to issue in continuous self-modification. the reality that evolves and moves may be more perfect, less finite, than that which has exhausted itself. moreover, only the view that reality is developmental in quality, and that the instrument of its development is judgment involving the psychical in its determination of subject and predicate gives the psychical as such any significant place in knowledge or in reality. according to the view of knowledge as representation of an eternal content, the psychical is a mere logical surd. vi typical stages in the development of judgment logic aims at investigating the general function of knowing. but knowing, it is commonly asserted, is constituted as judgment. furthermore, there is reason to believe that judgment undergoes well-marked changes in its development. consequently, an understanding of the judgment-function and of its epochs in development is of prime importance. in carrying through the investigation we shall endeavor, first, to state and to defend a certain presupposition with reference to the character of the judgment-function; second, to exhibit the application of this presupposition in the typical stages of judgment. i judgment is essentially _instrumental_. this is the presupposition which we must explain and make good. and we shall accomplish this by way of an analysis of judgment as meaning. it cannot be denied that what we call knowledge is concerned with the discrimination of valid meaning. to know is to appreciate the _meaning_ of things and the meaning _of things_ is the same with valid meaning. judging determines knowledge, and in the same act develops meaning. to put it otherwise, knowledge is a matter of _content_; _content_ is _meaning_, and we have knowledge when we have meaning satisfactorily determined. it is evident, therefore, that if we would understand the judging-function, we must first make clear to ourselves the nature and rôle of _meaning_. meaning is universally embodied in _ideas_. to know, to understand the meaning, to get ideas, are the same. now, in ideas two factors may be distinguished. first, every idea has as its base an image or emphasized portion of experience. in some forms of ideation we are more immediately aware of the presence of images than in others, but no idea--even the most abstract--can exist apart from an ultimate base. second, every idea is equally a function of _reference_ and _control_. as _reference_, the idea projects in the mind's view an anticipation of experiences and of the conditions upon which these experiences depend for their realization; as _control_, ideas are agencies in turning anticipations into realizations.[ ] to be more specific on both points: since the days of galton it has been almost a commonplace in psychology that ideas are embodied in forms of imagery which vary for and in different individuals. it has been maintained, it is true, that in abstract forms of thought, imagery disappears. this objection is met in two ways. for one, words--the vehicle of many abstract ideas--involve imagery of a most pronounced type: for another, every idea, when examined closely, discloses an image, no matter how much for the time being this has been driven into obscurity by the characteristics of reference and control. furthermore, when we examine the anticipatory aspect of ideas, the presence of imagery both with reference to outcome and to conditions is so evident that its presence will scarcely be denied. the second point may be illustrated in several ways. in everyday life anticipation and realization are inseparable from the nature and use of ideas. "hat" means anticipation of protection to the head and the tendency toward setting in motion the conditions appropriate to the realization of this anticipation. the same factors are evident in the boy's definition of a knife as "something to whittle with." again it is maintained that intelligence is an essential factor in human self-consciousness. by this is meant that human beings are universally aware in some degree of what they are about. and this awareness consists in understanding the meaning of their actions, of forecasting the outcome of various kinds of activity, of apprehending beforehand the conditions connected with determinate results. within this sphere we speak of certain men as being pre-eminently intelligent, meaning that for such men outcomes are previewed and connected with their appropriate conditions far beyond the range of ordinary foresight. finally, scientific intelligence is essentially of this kind. it aims at understanding the varying types of process which operate in nature and thus at possessing itself of information with reference to results to be expected under determinate conditions. for example, the knowledge acquired in his researches by louis pasteur enabled him to predict the life or death of animals inoculated with charbon virus according as they had or had not been vaccinated previously. his information, in other words, became an instrument for the control and eradication of the disease. and what is true of this case is true of all science. to the scientist ideas are "working hypotheses" and have their value only as they enable him to predict, and to control. and while it is true that the scientist usually overlooks the so-called _practical_ value of his discoveries, it is none the less true that in due time the inventor follows the investigator. the investigator is content to construct and show the truth of his idea. the inventor assumes the truth of the investigator's work and carries his idea as a constructive principle into the complications of life. to both men "knowledge is power," although the "power" may be realized in connection with different interests. but if this be true, ideas can no longer be regarded as copies in individual experience of some pre-existing reality. they are rather instruments for transforming and directing experience, by way of constructing anticipations and the conditions appropriate to their realization. herein also consists their truth or falsity. the true idea is reliable, carrying us from anticipation to realization; the false idea is unreliable, and fails in bringing the promised result. now, in the development of instruments generally, we may distinguish a rule-of-thumb or more or less unreflective stage of construction, and one entirely reflective. as to use there is the distinction of inexpert and expert control. this leads us to expect that in the thought-function also certain typical stages of construction and of control may be found. to the investigation of this point we shall next direct attention. ii in its development from crude to expert forms judgment exhibits three typical stages--_the impersonal_, _the reflective_, and _the intuitive_. these we shall consider in order of development. but first it is to be noticed that these stages of judgment are not to be regarded as hard and fast distinctions of the kind that no indications of the higher are to be found in the lower types, but rather as working distinctions within a process of continuous development. . _the impersonal judgment._--ever since the days of the greek grammarians the impersonal judgment has been considered an anomaly in logic. and the reason is not far to seek. from the time of aristotle it has been customary to maintain that judgments, when analyzed, disclose a subject and a predicate. logically considered, these appear to be entirely correlative, for, as erdmann puts it,[ ] "an event without a substrate, a quality without a subject, is altogether unpresentable." but there is in all languages a class of judgments, such as, "it rains," "it snows," "fire!" in which no directly asserted subject is discoverable. to these the name impersonal and subjectless has been given. here then is the difficulty. if we admit that the impersonal expression involves predication, we must, in all consistency, search for a subject, while at the same time the subject refuses to disclose itself. in ancient days the orthodox logician confined his search to language and to the spoken or written proposition. the unorthodox critic maintained, in opposition to this, that a subject was provided only by warping and twisting the natural sense of the impersonal expression. and thus the matter stood until the development of modern comparative philology. it was then demonstrated beyond the possibility of doubt that the "it" (or its equivalent) of the impersonal is a purely contentless form word. language provides no subject whatsoever. so strong, however, is the hold of tradition that the search has been renewed. attention has been turned upon the mental processes involved, and this time with more apparent result. although there has been no general agreement with reference to the subject, a classification of the different views may still be made. (_a_) the subject is universal and undetermined; (_b_) it is individual and more or less determined; (_c_) between these extremes lies almost every intermediate degree conceivable. ueberweg maintains that the subject of the impersonal is the actual totality of present experience. when we ask, "what rains?" we must understand a reference to our general environment, in which no special element is singled out. sigwart, on the other hand, maintains that the subject can be construed only as the actual sense-impression. this diversity of opinion might seem to indicate that, were it not for the constraining power of theory, a subject would scarcely be thought of for the impersonal. still it must be admitted that when we examine the impersonal expression closely we can discover a sense-impression, whether definite or indefinite, combined with an idea. this would seem to give the case to the orthodox logician, for he will at once claim the sense-impression as the subject and the idea as the predicate of the judgment. but we must have a care. predication is usually held to consist in a _reference_ of predicate _to_ subject. the factors of the judgment are, as it were, held apart. in the impersonal no such thing as this can be discovered. the meaning is so close a unity that impression and idea are entirely fused. we may analyze the expression and find them there, but by so doing we destroy the immediacy which is an essential characteristic of the impersonal. in other words, the impersonal does not analyze itself. it is entirely unconscious of its make-up. and yet it is definite and applies itself with precision: if i am in a lecture-hall and hear the fire-alarm, the thought "fire!" which enters my mind leads to an immediate change in my conduct. i arise, move quietly out, and prepare for duty. if, on the other hand, i open the street door and the rain strikes my face, i ejaculate "raining!" turn, reach for my umbrella, and pass out protected. in both cases i act _knowingly_ and with _meaning_, but i do not analyze the movement either of thought or of action. a correlate to the unreflective impersonal judgment is found in early custom. custom embodies social ideas and is an instrument for the determination and control of action. individuals moved by custom know what they are about and act with precision according as custom may demand. but it is notorious that custom is direct and unreflective. it represents social instruments of control which have grown up without method and which represent the slow accretion of rule-of-thumb activities through many ages. so in the impersonal judgment we have a type of intellectual instrument which has been brought to a high degree of precision in use, but which still retains the simplicity and certainty of an unquestioned instrument of action. for this reason, whatever complexity of elements the impersonal may present to a reflective view, it does not contain to itself. consequently it may be best to say that to the impersonal there is neither subject, predicate, nor reference of the one to the other. these are distinctions which arise only when the instrument of action has been questioned and the mind turns back upon the meaning which it has unhesitatingly used, analyzing, investigating, constructing, laying bare the method and function of its tools. thus arises a new and distinctive type of judgment, viz., the reflective. . _the reflective judgment._--by the reflective judgment is to be understood that form of meaning whose structure and function have become a problem to itself. the days of naïve trust and spontaneous action have gone by. inquiry, criticism, aloofness, stay the tendency to immediate action. meaning has grown worldly wise and demands that each situation shall explain itself and that the general principles and concrete applications of its own instruments shall be made manifest. hence in the various forms of reflective thought we find the progressive steps in which meaning comes to full consciousness of its function in experience. the demonstrative judgment (the simplest of the reflective type) carries doubt, criticism, construction, and assertion written on the face of it. for example, in the expression, "that is hot," we do not find the directness and immediacy of response characteristic of the simpler impersonal "hot." instead, we note a clash of tendencies, a suspension of the proposed action, a demand for and a carrying out of a reconsideration of the course of action, the emergence of a new meaning, and the consequent redirection of activities. an iron lies upon the hearth; i stretch out my hand to return it to its place; i stop suddenly, having become conscious of signs of warmth; the thought arises in my mind, "that is hot;" i experiment and find my judgment correct; i search for a cloth, and thus protected carry out my first intention. again, a hunter notes a movement in the thicket, quickly raises his gun, and is about to fire. something in the movement of the object arrests him. he stops, thinking, "that is a man, perhaps." what has caught the eye has arrested his action, has become a demand, and not until the situation has become clear can the hunter determine what to do. in other words, he must reflectively assure himself what the object is before he can satisfy himself as to how he should act. subject and predicate have arisen and have consciously played their parts in the passage from doubt to decision. under the heading "individual judgments" are classed such expressions as, "that ship is a man-o'-war," "russia opposes the policy of the open door in china." in both these cases it is evident that an advance in definiteness of conception and of complexity of meaning has been made, while at the same time we recognize that the instrumental characteristics of the thought-movement remain the same. in considering the subject of the judgment we note that the stimulus presents itself partly as a determinate factor and partly as a problem--an insistent demand. the expression, "that ship is a man-o'-war," might be written, "that is a ship and of the kind man-o'-war," and it thus constitutes what sigwart calls a "double synthesis." as used in actual judgment, however, the two are held together and constitute the statement of a single stimulus of which a certain portion is evident and a certain portion is in doubt. the working out of the difficulty is given in the predicate "is a man-o'-war," in which we at once detect the instrumental characteristics fundamental to all judgment. to illustrate: at the close of the battle of santiago, in the spanish-american war, smoke appeared upon the horizon revealing the presence of a strange ship. instantly attention was directed to it, and it became a problem for action--a demand for instrumental information. soon it was identified as a man-o'-war, and the american ships were cleared for action. closer approach raised a further question with reference to its nationality. after some debate this also was resolved, and hostile demonstrations were abandoned. the universal judgment is sometimes said to exhibit two distinct forms. investigation, however, has proved this statement to be incorrect. instances taken in themselves and apart from their character are of no logical significance. advance is made by weighing instances and not by counting them. in short, the true universal is the hypothetical judgment, and the reason for this may be readily shown. the hypothetical judgment is essentially double-ended. on the one hand, it is a statement of the problem of action in terms of the conditions which will turn the problem into a solution. on the other hand, it is an assertion that once the conditions of action have been determined the result desired may be attained. here we note that the judgment has come to clear consciousness of itself and of the part which it plays in experience. it has now obtained an insight into the criterion of its legitimate employment, _i. e._, of its truth and falsity. and this insight makes the justification of its claim almost self-evident. for, inasmuch as the hypothetical judgment says, "if such and such conditions be realized, such and such a result will be obtained," the test of the claim is made by putting the conditions into effect and watching whether the promised experience is given. and further, since it has been found that the judgment formulated as a hypothesis actually accomplishes what it promises, we must admit that the hypothetical judgment is also categorical. these two factors cannot be separated from each other. it is true that the hypothetical judgment reduces every valid meaning to the form, "_if_ certain conditions be realized," but it as plainly and positively asserts, "such and such results _will_ be obtained." when we grasp the absolute correlativity of the hypothetical and categorical aspects of judgment, we realize at once the essentially instrumental character of judgment, when it comes to consciousness of its structure and function. it arises in the self-conscious realization of a problem. this it reflects upon and sizes up. when the difficulty has been apprehended, the judgment emerges as the consciousness of the conditions which will attain the desired end of action freed and unimpeded. this may be illustrated by reference to the work of pasteur cited above. his investigations began in a problem set for him by agricultural conditions in france. a certain disease had made the profitable rearing of sheep and cattle almost an impossibility. after long and careful examination he discovered the beneficial effects of vaccination. to him the conditions which governed the presence of the disease became apparent, and this knowledge furnished him with an instrument by means of which one difficulty was removed from the path of the stock-raiser. in this illustration we have an epitome of the work accomplished everywhere by the scientist. it is his task to develop and to reduce to exact terms instruments of control for the varied activities of life. in its parts and as a whole each instrument is intelligently constructed and tested so that its make-up and function are exactly known. because of this, reasoned belief now takes the place of unreflective trust as that was experienced in the impersonal stage of judgment. what at first hand might appear to be a loss was in reality a gain; the breakdown of the impersonal was the first step in the development of an instrument of action conscious of its reason for being, its methods and conditions of action. these latter constitute the distinctive subject and predicate of the reflective judgment. this brings us to the connection between the hypothetical character of this form of judgment and its universality. and this perhaps will now be quite apparent. the reflective judgment lays bare an objective connection between the conditions and outcomes of actions. it proves its point by actually constructing the event. such being the case, universality is no more than a statement of identical results being predictable wherever like conditions are realized. if it be true that "man is mortal," then it is an identical statement to insist that, "wherever we find men there we shall also find mortality." and this point brings us naturally to the treatment of the disjunctive judgment: "a is either b or c or d." in the disjunctive judgment the demand is not for the construction of a reliable instrument of action, but for the resolution of a doubt as to which instrument is precisely fitted to the circumstances. in fact, the disjunctive judgment involves the identification of the practical problem. when we say of a man, "he is either very simple or very deep," we have no doubt as to our proper course of action in either case. if he is simple, then we shall do so and so; if he is deep, then another course of action follows. we can lay out alternative courses beforehand, but the point of difficulty lies here: "but just which is he?" in short, the disjunctive judgment is the demand for and the attempt at a precise diagnosis of a concrete problem. to illustrate: a patient afflicted with aphasia is brought to a physician. the fact that the trouble is aphasia may be quite evident. but what precisely is the form and seat of the aphasia? to the mind of the educated physician the problem will take on the disjunctive form: "this is either subcortical or cortical aphasia. if subcortical, intelligence will not be impaired; if cortical, the sensor and motor tracts will be in good condition." appropriate tests are made and the subcortical possibilities are shut out. the disjunction disappears and the judgment emerges: "this is a case of cortical aphasia." but now a new disjunction arises. it is either the sensory or motor form of cortical aphasia, and, whichever one of these, it is again one of several possibilities. as the alternatives arise, the means for discriminating them arise also; determinate symptoms are observed, and in due time the physician arrives at the final conclusion: "this is sensory cortical aphasia of the visual type." having determined this, his method of action is assured, and he proceeds to the appropriate operation. thus, finally, we are brought to a form of judgment aware not only of its motive, method, and justification, but also to one aware of its specific application to individual cases. thus it would seem as though judgment had returned upon itself and had completed the determination of its sphere of action. and in one sense this is true. in the disjunctive judgment, as inclusive of the motives of the hypothetical and categorical forms, the reflective judgment would appear to have come to its limit of development. one thing, however, remains to be considered, viz., the development from crude to expert uses of intellectual instruments. . _the intuitive judgment._--as stated above, the intuitive type of judgment depends upon efficiency in the use of judgment. in this regard there is a great similarity between the impersonal and the intuitive judgments. both are immediate and precise. but there is a radical and essential difference. the impersonal judgment knows nothing of the strict analysis, insight, and constructive power of the reflective judgment. the intuitive judgment, on the other hand, includes the results of reflection and brings them to their highest power. paradoxically put, in the intuitive judgment there is so much reflection that there is no need for it at all. to the intuitive judgment there is no hesitation, no aloofness. action is direct, but entirely self-conscious. that such a type of judgment as the intuitive exists there can be no doubt. there is all the difference in the world between the quality of consciousness of a mere layman and that of an expert, no matter what the line. the layman must size up a situation. it is a process whose parts are successive, whether much or little difficulty be experienced. for the expert situations are taken in at a glance, parts and whole are simultaneous and immediate. yet the meaning is entirely exact. the expert judgment is self-conscious to the last degree. while other individuals are thinking out what to do, the expert has it, sees the advantage, adjusts, and moves. demand and solution jump together. how otherwise can we explain, for example, the action of an expert ball-player? witness his rapid reactions, his instantaneous adjustments. mistakes of opponents which would never be noticed by the average player are recognized and seized upon. on the instant the new opening is seen, the adjustment is evident, the movement made. illustrations to the same effect could be drawn from other modes of life, _e. g._, music, the military life, etc. that intuitive judgments are not more common is a proof in itself of their distinctive character and value. only in so far as we become experts in our special fields of experience and have reduced our instruments of action to precise control, can we expect the presence of intuitive judgments. they remain, therefore, as the final outcome of the judgment-function made perfect in its technique and use. in conclusion we shall make a brief summary of our investigation and a criticism of certain current theories of judgment. judgment is essentially instrumental. its function is to construct, justify, and refine experience into exact instruments for the direction and control of future experience through action. it exhibits itself first in the form of instruments developed unsystematically in response to the hard necessities of life. in a higher stage of development the instrumental process itself is taken into account, and systematically developed until in the methodical procedure of science the general principles of knowledge are laid bare and efficient instruments of action constructed. finally, constant, intelligent use results in complete control, so that within certain spheres doubt and hesitancy would seem to disappear as to the character of the tools used, and remain only as a moment in determining their wisest or most appropriate employ. the criticism indicated is based upon the instrumental character of judgment and is directed against all theories which contend that knowledge is a "copying" or "reproducing" of reality. in whatever form this "copy" theory be stated, the question inevitably arises how we can compare our ideas with reality and thus know their truth. on this theory, what we possess is ever the copy; the reality is beyond. in other words, such a theory logically carried out leads to the breakdown of knowledge. only a theory which contains and constructs its criterion within its own specific movement can verify its constructions. such a theory is the instrumental. judgment constructs a situation in consciousness. the values assigned in this situation have a determining influence upon values further appreciated. the construction arrived at concerns future weal and woe. thus gradually a sense of truth and falsity attaches to the construing of situations. one sees that he _must_ look beyond _this_ situation, because the way he estimates _this_ situation is fraught with meaning beyond itself. hence the critically reflective judgment in which hesitancy and doubt direct themselves at the attitude, elements, and tools involved in defining and identifying the situation, instead of at the situation itself _in toto_. instead of developing a complex of experience through assigning qualities and meanings to the _situation_ as such, some one of the quales is selected, to have _its_ significance determined. it becomes, _pro tempore_, the situation judged. or the same thing takes place as regards some "idea" or value hitherto immediately fastened upon and employed. in either case we get the reflective judgment, the judgment of pure relationship as distinct from the constructive judgment. but the judgment of relation, employing the copula to refer a specified predicate to a specified object, is after all only for the sake of controlling some immediate judgment of constructive experience. it realizes itself in forming the confident habit of prompt and precise mental adjustment to individualized situations. vii the nature of hypothesis in the various discussions of the hypothesis which have appeared in works on inductive logic and in writings on scientific method, its structure and function have received considerable attention, while its origin has been comparatively neglected. the hypothesis has generally been treated as that part of scientific procedure which marks the stage where a definite plan or method is proposed for dealing with new or unexplained facts. it is regarded as an invention for the purpose of explaining the given, as a definite conjecture which is to be tested by an appeal to experience to see whether deductions made in accordance with it will be found true in fact. the function of the hypothesis is to unify, to furnish a method of dealing with things, and its structure must be suitable to this end. it must be so formed that it will be likely to prove valid, and writers have formulated various rules to be followed in the formation of hypotheses. these rules state the main requirements of a good hypothesis, and are intended to aid in a general way by pointing out certain limits within which it must fall. in respect to the origin of the hypothesis, writers have usually contented themselves with pointing out the kind of situations in which hypotheses are likely to appear. but after this has been done, after favorable external conditions have been given, the rest must be left to "genius," for hypotheses arise as "happy guesses," for which no rule or law can be given. in fact, the genius differs from the ordinary plodding mortal in just this ability to form fruitful hypotheses in the midst of the same facts which to other less gifted individuals remain only so many disconnected experiences. this unequal stress which has been laid on the structure and function of the hypothesis in comparison with its origin may be attributed to three reasons: ( ) the facts, or data, which constitute the working material of hypotheses are regarded as given to all alike, and all alike are more or less interested in systematizing and unifying experience. the purpose of the hypothesis and the opportunity for forming it are thus practically the same for all, and hence certain definite rules can be laid down which will apply to all cases where hypotheses are to be employed. ( ) but beyond this there seems to be no clue that can be formulated. there is apparently a more or less open acceptance of the final answer of the boy zerah colburn, who, when pressed to give an explanation of his method of instantaneous calculation, exclaimed in despair: "god put it into my head, and i can't put it into yours."[ ] ( ) and, furthermore, there is very often a strong tendency to disregard investigation into the origin of that which is taken as given, for, since it is already present, its origin, whatever it may have been, can have nothing to do with what it is now. the facts, the data, are _here_, and must be dealt with as they _are_. their past, their history or development, is entirely irrelevant. so, even if we could trace the hypothesis farther back on the psychological side, the investigation would be useless, for the rules to which a good hypothesis must conform would remain the same. whether or not it can be shown that zerah colburn's ultimate explanation is needed in logic as little as laplace asserted a similar one to be required in his celestial mechanics, it may at least be possible to defer it to some extent by means of a further psychological inquiry. it will be found that psychological inquiry into the origin of the hypothesis is not irrelevant in respect to an understanding of its structure and function; for origin and function cannot be understood apart from each other, and, since structure must be adapted to function, it cannot be independent of origin. in fact, origin, structure, and function are organically connected, and each loses its meaning when absolutely separated from each other. it will be found, moreover, that the data which are commonly taken as the given material are not something to which the hypothesis is subsequently applied, but that, instead of this external relation between data and hypothesis, the hypothesis exercises a directive function in determining what are the data. in a word, the main object of this discussion will be to contend against making a merely convenient and special way of regarding the hypothesis a full and adequate one. though we speak of facts and of hypotheses that may be applied to them, it must not be forgotten that there are no facts which remain the same whatever hypothesis be applied to them; and that there are no hypotheses which are hypotheses at all except in reference to their function in dealing with our subject-matter in such a way as to facilitate its factual apprehension. data are selected in order to be determined, and hypotheses are the ways in which this determination is carried on. if, as we shall attempt to show, the relation between data and hypothesis is not external, but strictly correlative, it is evident that this fact must be taken into account in questions concerning deduction and induction, analytic and synthetic judgments, and the criterion of truth. its bearing must be recognized in the investigation of metaphysical problems as well, for reality cannot be independent of the knowing process. in a word, the purpose of this discussion of the hypothesis is to determine its nature a little more precisely through an investigation of its rather obscure origin, and to call attention to certain features of its function which have not generally been accorded their due significance. i _the hypothesis as predicate._--it is generally admitted that the function of the hypothesis is to provide a way of dealing with the data or subject-matter which we need to organize. in this use of the hypothesis it appears in the rôle of predicate in a judgment of which the data, or facts, to be construed constitute the subject. in his attempts to reduce the movements of the planets about the sun to some general formula, kepler finally hit upon the law since known as kepler's law, viz., that the squares of the periodic times of the several planets are proportional to the cubes of their mean distances from the sun. this law was first tentatively advanced as a hypothesis. kepler was not certain of its truth till it had proved its claim to acceptance. neither did newton have at first any great degree of assurance in regard to his law of gravitation, and was ready to give it up when he failed in his first attempt to test it by observation of the moon. and the same thing may be said about the caution of darwin and other investigators in regard to accepting hypotheses. the only reason for their extreme care in not accepting at once their tentative formulations or suggestions was the fear that some other explanation might be the correct one. this rejection of other possibilities is the negative side of the matter. we become confident that our hypothesis is the right one as we lose confidence in other possible explanations; and it might be added, without falling into a circle, that we lose confidence in the other possibilities as we become more convinced of our hypothesis. it appears that such may be the relation of the positive and negative sides in case of such elaborate hypotheses as those of kepler and newton; but is it true where our hypotheses are more simple? it is not easy to understand why the fact that the hypothesis is more simple, and the time required for its formulation and test a good deal shorter, should materially change the state of affairs. the question remains: why, if there is no opposition, should there be any uncertainty? in all instances, then, the hypothesis appears as one among other possible predicates which may be applied to our data taken as subject-matter of a judgment. _the predicate as hypothesis._--suppose, then, the hypothesis is a predicate; is the predicate necessarily a hypothesis? this is the next question we are called upon to answer, and, since the predicate cannot very well be taken aside from the judgment, our question involves the nature of the judgment. while it will not be necessary to give a very complete account of the various definitions of the judgment that might be adduced, still the mention of a few of the more prominent ones may serve to indicate that something further is needed. in definitions of the judgment sometimes the subjective side is emphasized, sometimes the objective side, and in other instances there are attempts to combine the two. for instance, lotze regards the judgment as the idea of a unity or relation between two concepts, with the further implication that this connection holds true of the object referred to. j. s. mill says that every proposition either affirms or denies existence, coexistence, sequence, causation, or resemblance. trendelenburg regards the judgment as a form of thought which corresponds to the real connection of things, while ueberweg states the case a little differently, and says that the essence of judgment consists in recognizing the objective validity of a subjective connection of ideas. royce points to a process of imitation and holds that in the judgment we try to portray by means of the ideas that enter into it. ideas are imitative in their nature. sigwart's view of the judgment is that in it we say something about something. with him the judgment is a synthetic process, while wundt considers its nature analytic and holds that, instead of uniting, or combining, concepts into a whole, it separates them out of a total idea or presentation. instead of blending parts into a whole, it separates the whole into its constituent parts. bradley and bosanquet both hold that in the judgment an ideal content comes into relation with reality. bradley says that in every judgment reality is qualified by an idea, which is symbolic. the ideal content is recognized as such, and is referred to a reality beyond the act. this is the essence of judgment. bosanquet seems to perceive a closer relation between idea and reality, for although he says that judgment is the "intellectual function which defines reality by significant ideas," he also tells us that "the subject is both in and out of the judgment, as reality is both in and out of my consciousness." in all these definitions of judgment the predicate appears as ideal. an ideal content is predicated of something, whether we regard this something as an idea or as reality beyond, or as reality partly within and partly without the act of judging; and it is ideal whether we consider it as one of the three parts into which judgments are usually divided, or whether we say, with bosanquet and bradley, that subject, predicate, and copula all taken together form a single ideal content, which is somehow applied to reality. moreover, we not only judge about reality, but it seems to be quite immaterial to reality whether we judge concerning it or not. many of our judgments prove false. not only do we err in our judgments, but we often hesitate in making them for fear of being wrong; we feel there are other possibilities, and our predication becomes tentative. here we have something very like the hypothesis, for our ideal content shows itself to be a tentative attempt in the presence of alternatives to qualify and systematize reality. it appears, then, on the basis of the views of the judgment that have been mentioned, that not only do we find the hypothesis taking its place as the predicate of a judgment, but the predicate is itself essentially of the nature of a hypothesis. in the views of the judgment so far brought out, reality, with which it is generally admitted that the judgment attempts to deal in some way, appears to lie outside the act of judging. now, everyone would say that we make some advance in judging, and that we have a better grasp of things after than before. but how is this possible if reality lies without or beyond our act of judging? is the reality we now have the same that we had to begin with? if so, then we have made no advance as far as the real itself is concerned. if merely our conception of it has changed, then it is not clear why we may not be even worse off than before. if reality does lie beyond our judgment, then how, in the nature of the case, can we ever know whether we have approached it or have gone still farther away? to make any claim of approximation implies that we do reach reality in some measure, at least, and, if so, it is difficult to understand how it lies beyond, and is independent of, the act of judging. _further analysis of judgment._--it remains to be seen whether a further investigation of the judgment will still show the predicate to be a hypothesis. it is evident that in some cases the judgment appears at the end of a more or less pronounced reflective process, during which other possible judgments have suggested themselves, but have been rejected. the history of scientific discovery is filled with cases which illustrate the nature of the process by which a new theory is developed. for instance, in darwin's _formation of vegetable mould through the action of earth worms_, we find the record of successive steps in the development of his hypothesis. darwin suspected from his observations that vegetable mold was due to some agency which was not yet determined. he reasoned that if vegetable mold is the result of the life-habits of earthworms, _i. e._, if earth is brought up by them from beneath the surface and afterward spread out by wind and rain, then small objects lying on the surface of the ground would tend to disappear gradually below the surface. facts seemed to support his theory, for layers of red sand, pieces of chalk, and stones were found to have disappeared below the surface in a greater or less degree. a common explanation had been that heavy objects tend to sink in soft soil through their own weight, but the earthworm hypothesis led to a more careful examination of the data. it was found that the weight of the object and the softness of the ground made no marked difference, for sand and light objects sank, and the ground was not always soft. in general, it was shown that where earthworms were found vegetable mold was also present, and _vice versa_. in this investigation of darwin's the conflicting explanations of sinking stones appear within the main question of the formation of vegetable mold by earthworms. the facts that disagreed with the old theory about sinking stones were approached through this new one. but the theories had something in common, viz., the disappearance of the stones or other objects: they differed in their further determination of this disappearance. in this case it may seem as if the facts which were opposed to the current theory of sinking stones were seen to be discrepant only after the earthworm hypothesis had been advanced; the conflict between the new facts and the old theory appears to have arisen through the influence of the new theory. there are cases, however, where the facts seem clearly to contradict the old theory and thus give rise to a new one. for example, we find in darwin's introduction to his _origin of species_ the following: "in considering the origin of species it is quite conceivable that a naturalist reflecting on the mental affinities of organic beings, on their embryological relations, their geographical distribution, geological succession, and other such facts, might come to the conclusion that species had not been independently created but had descended, like varieties, from other species." it would seem from this statement that certain data were found for which the older theory of independent creation did not offer an adequate explanation. and yet the naturalist would hardly "reflect" on all these topics in a comparative way unless some other mode of interpretation were already dawning upon him, which led him to review the accepted reflections or views. as a more simple illustration, we may cite the common experience of a person who is uncertain concerning the identity of an approaching object, say, another person. at first he may not be sure it is a person at all. he then sees that it is someone, and as the person approaches he is inclined to believe him to be an acquaintance. as the supposed acquaintance continues to approach, the observer may distinguish certain features that cause him to doubt, and then relinquish his supposition that it is an acquaintance. or, he may conclude at once that the approaching person is another individual he knows, and the transition may be so readily made from one to the other that it would be difficult to determine whether the discordant features are discordant before the new supposition arises, or whether they are not recognized as conflicting till this second person is in mind. or, again, the identification of the new individual and the discovery of the features that are in conflict with the first supposition may appear to go on together. now, marked lines of likeness appear between this relatively simple judgment and the far more involved ones of scientific research. in the more extended scientific process we find data contradicting an old theory and a new hypothesis arising to account for them. the hypothesis is tested, and along with its verification we have the rejection, or rather the modification, of the old theory. similarly, in case of the approaching stranger all these features are present, though in less pronounced degree. in scientific investigation there is an interval of testing by means of more careful consideration of the data and even actual experimentation. before an explanation is accepted subject to test, a number of others may have been suggested and rejected. they may not have received even explicit recognition. in case of the identification of the stranger this feature is also present. between two fairly definite attempts to identify the mind does not remain a mere blank or stationary, but other possible identifications may be suggested which do not have sufficient plausibility to command serious attention; they are only comparatively brief suggestions or tendencies. it is to be noted that in all these instances the first supposition was not _entirely_ abandoned, but was modified and more exactly determined. (why it could not be wholly false and the new one wholly new, will be considered later in connection with discussion of the persistence and re-formation of habit.) there was such a modification of the old theory as would meet the requirements of the new data, and the new explanations thus contained both old and new features. we have seen that the predicate of the scientific judgment is a hypothesis which is consciously applied to certain data. if the similarity between the scientific judgment and the more immediate and simple judgment is to be maintained, it is clear that the predicate of the simple judgment must be of like nature. the structure of the two varieties of judgment differs only in the degree of explicitness which the hypothesis acquires. that is, the predicate of a judgment, as such, is ideal; it is meaning, significant quality. if conditions are such as to make the one judging hesitant or doubtful the mind wavers; the predicate is not applied at once to the determination or qualification of data, and hence comes to more distinct consciousness on its own account. from being "ideal," it becomes _an_ idea. yet its sole purpose and value remains in its possible use to interpret data. let the idea remain detached, and let the query whether it be a true predicate (_i. e_., really fit to be employed in determining the present data) become more critical, and the idea becomes clearly a hypothesis.[ ] in other words, the hypothesis is just the predicate-function of judgment definitely apprehended and regarded with reference to its nature and adequacy. _psychological analysis of judgment._--this hypothetical nature of the predicate will be even more apparent after a further psychological analysis, which, while applying more directly to the simpler and more immediate judgments, may be extended to the more involved ones as well. in psychological terms, we may say, in explanation of the judging process, that some stimulus to action has failed to function properly as a stimulus, and that the activity which was going on has thus been interrupted. response in the accustomed way has failed. in such a case there arises a division in experience into sensation content as subject and ideal content as predicate. in other words, an activity has been going on in accordance with established habits, but upon failure of the accustomed stimulus to be longer an adequate stimulus this particular activity ceases, and is resumed in an integral form only when a new habit is set up to which the new or altered stimulus is adequate. it is in this process of reconstruction that subject and predicate appear. sensory quality marks the point of stress, or seeming arrest, while the ideal or imaged aspect defines the continuing activity as projected, and hence that with which start is to be made in coping with the obstacle. it serves as standpoint of regard and mode of indicated behavior. the sensation stands for the interrupted habit, while the image stands for the new habit, that is, the new way of dealing with the subject-matter.[ ] it appears, then, that the purpose of the judgment is to obtain an adequate stimulus in that, when stimulus and response are adjusted to each other, activity will be resumed. but if this reconstruction and response were to follow at once, would there be any clearly defined act of judging at all? in such a case there would be no judgment, properly speaking, and no occasion for it. there would be simply a ready transition from one line of activity to another; we should have changed our method of reaction easily and readily to meet the new requirements. on the one hand, our subject-matter would not have become a clearly recognized datum with which we must deal; on the other hand, there would be no ideal method of construing it.[ ] activity would have changed without interruption, and neither subject nor predicate would have arisen. in order that judgment may take place there must be interruption and suspense. under what conditions, then, is this suspense and uncertainty possible? our reply must be that we hesitate because of more or less sharply defined alternatives; we are not sure which predicate, which method of reaction, is the right one. the clearness with which these alternatives come to mind depends upon the degree of explicitness of the judgment, or, more exactly, the explicitness of the judgment depends upon the sharpness of these alternatives. alternatives may be carefully weighed one against the other, as in deliberative judgments; or they may be scarcely recognized as alternatives, as in the case in the greater portion of our more simple judgments of daily conduct. _the predicate is essentially hypothetical._--if we review in a brief résumé the types of judgment we have considered, we find in the explicit scientific judgment a fairly well-defined subject-matter which we seek further to determine. different suggestions present themselves with varying degrees of plausibility. some are passed by as soon as they arise. others gain a temporary recognition. some are explicitly tested with resulting acceptance or rejection. the acceptance of any one explanation involves the rejection of some other explanation. during the process of verification or test the newly advanced supposition is recognized to be more or less doubtful. besides the hypothesis which is tentatively applied there is recognized the possibility of others. in the disjunctive judgment these possible reactions are thought to be limited to certain clearly defined alternatives, while in the less explicit judgments they are not so clearly brought out. throughout the various forms of judgment, from the most complex and deliberate down to the most simple and immediate, we found that a process could be traced which was like in kind and varied only in degree. and, finally, in the most immediate judgments where some of these features seem to disappear, the same account not only appears to be the most reasonable one, but there is the additional consideration, from the psychological side, that were not the judgment of this doubtful, tentative character, it would be difficult to understand how there could be judgment as distinct from a reflex. it appears, then, that throughout, the predicate is essentially of the nature of a hypothesis for dealing with the subject-matter. and, however simple and immediate, or however involved and prolonged, the judgment may be, it is to be regarded as essentially a process of reconstruction which aims at the resumption of an interrupted experience; and when experience has become itself a consciously intellectual affair, at the restoration of a unified objective situation. ii _criticism of certain views concerning the hypothesis._--the explanation we have given of the hypothesis will enable us to criticise the treatment it has received from the empirical and the rationalistic schools. we shall endeavor to point out that these schools have, in spite of their opposed views, an assumption in common--something given in a fixed, or non-instrumental way; and that consequently the hypothesis is either impossible or else futile. bacon is commonly recognized as a leader in the reactionary inductive movement, which arose with the decline of scholasticism, and will serve as a good example of the extreme empirical position. in place of authority and the deductive method, bacon advocated a return to nature and induction from data given through observation. the new method which he advanced has both a positive and a negative side. before any positive steps can be taken, the mind must be cleared of the various false opinions and prejudices that have been acquired. this preliminary task of freeing the mind from "phantoms," or "eidola," which bacon likened to the cleansing of the threshing-floor, having been accomplished, nature should be carefully interrogated. there must be no hasty generalization, for the true method "collects axioms from sense and particulars, ascending continuously and by degrees, so that in the end it arrives at the most general axioms." these axioms of bacon's are generalizations based on observation, and are to be applied deductively, but the distinguishing feature of bacon's induction is its carefully graduated steps. others, too, had proceeded with caution (for instance galileo), but bacon laid more stress than they on the subordination of steps. it is evident that bacon left very little room for hypotheses, and this is in keeping with his aversion to anticipation of nature by means of "phantoms" of any sort; he even said explicitly that "our method of discovery in science is of such a nature that there is not much left to acuteness and strength of genius, but all degrees of genius and intellect are brought nearly to the same level."[ ] bacon gave no explanation of the function of the hypothesis; in his opinion it had no lawful place in scientific procedure and must be banished as a disturbing element. instead of the reciprocal relation between hypothesis and data, in which hypothesis is not only tested in experience, but at the same time controls in a measure the very experience which tests it, bacon would have a gradual extraction of general laws from nature through direct observation. he is so afraid of the distorting influence of conception that he will have nothing to do with conception upon any terms. so fearful is he of the influence of pre-judgment, of prejudice, that he will have no judging which depends upon ideas, since the idea involves anticipation of the fact. particulars are somehow to arrange and classify themselves, and to record or register, in a mind free from conception, certain generalizations. ideas are to be registered derivatives of the given particulars. this view is the essence of empiricism as a logical theory. if the views regarding the logic of thought before set forth are correct, it goes without saying that such empiricism is condemned to self-contradiction. it endeavors to construct judgment in terms of its subject alone; and the subject, as we have seen, is always a co-respondent to a predicate--an idea or mental attitude or tendency of intellectual determination. thus the subject of judgment can be determined only with reference to a corresponding determination of the predicate. subject and predicate, fact and idea, are contemporaneous, not serial in their relations (see pp. - ). less technically the failure of bacon's denial of the worth of hypothesis--which is in such exact accord with empiricism in logic--shows itself in his attitude toward experimentation and toward observation. bacon's neglect of experimentation is not an accidental oversight, but is bound up with his view regarding the worthlessness of conception or anticipation. to experiment means to set out from an idea as well as from facts, and to try to construe, or even to discover, facts in accordance with the idea. experimentation not only anticipates, but strives to make good an anticipation. of course, this struggle is checked at every point by success or failure, and thus the hypothesis is continuously undergoing in varying ratios both confirmation and transformation. but this is not to make the hypothesis secondary to the fact. it is simply to remain true to the proposition that the distinction and the relationship of the two is a thoroughly contemporaneous one. but it is impossible to draw any fixed line between experimentation and scientific observations. to insist upon the need of systematic observation and collection of particulars is to set up a principle which is as distinct from the casual accumulation of impressions as it is from nebulous speculation. if there is to be observation of a directed sort, it must be with reference to some problem, some doubt, and this, as we have seen, is a stimulus which throws the mind into a certain attitude of response. controlled observation is inquiry, it is search; consequently it must be search for something. nature cannot answer interrogations excepting as such interrogations are put; and the putting of a question involves anticipation. the observer does not inquire about anything or look for anything excepting as he is after something. this search implies at once the incompleteness of the particular given facts, and the possibility--that is ideal--of their completion. it was not long until the development of natural science compelled a better understanding of its actual procedure than bacon possessed. empiricism changed to experimentalism. with experimentalism inevitably came the recognition of hypotheses in observing, collecting, and comparing facts. it is clear, for instance, that newton's fruitful investigations are not conducted in accordance with the baconian notion. it is quite clear that his celebrated four rules for philosophizing[ ] are in truth statements of certain principles which are to be observed in forming hypotheses. they imply that scientific technique had advanced to a point where hypotheses were such regular and indispensable factors that certain uniform conditions might be laid down for their use. the fourth rule in particular is a statement of the relative validity of hypothesis as such until there is ground for entertaining a contrary hypothesis. the subsequent history of logical theory in england is conditioned upon its attempt to combine into one system the theories of empiristic logic with recognition of the procedure of experimental science. this attempt finds its culmination in the logic of john stuart mill. of his interest in and fidelity to the actual procedure of experimental science, as he saw it, there can be no doubt. of his good faith in concluding his _introduction_ with the words following there can be no doubt: "i can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing, or with any reference for its fitness in being employed in establishing, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided." yet mill was equally attached to the belief that ultimate reality, as it is for the human mind, is given in sensations, independent of ideas; and that all valid ideas are combinations and convenient ways of using such given material. mill's very sincerity made it impossible that this belief should not determine, at every point, his treatment of the thinking process and of its various instrumentalities. in book iii, chap. , mill discusses the logic of explanation, and in discussing this topic naturally finds it necessary to consider the matter of the proper use of scientific hypotheses. this is conducted from the standpoint of their use as that is reflected in the technique of scientific discovery. in book iv, chap. , he discusses "abstraction or the formation of conceptions"--a topic which obviously involves the forming of hypotheses. in this chapter, his consideration is conducted in terms, not of scientific procedure, but of general philosophical theory, and this point of view is emphasized by the fact that he is opposing a certain view of dr. whewell. the contradiction between the statements in the two chapters will serve to bring out the two points already made, viz., the correspondent character of datum and hypothesis, and the origin of the latter in a problematic situation and its consequent use as an instrument of unification and solution. mill first points out that hypotheses are invented to enable the deductive method to be applied earlier to phenomena; that it does this by suppressing the first of the three steps, induction, ratiocination, and verification. he states that: the process of tracing regularity in any complicated, and at first sight confused, set of appearances is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption.... _neither induction nor deduction would enable us to understand even the simplest phenomena_, if we did not often commence by anticipating the results; by making a provisional supposition, at first essentially conjectural, as to some of the very notions which constitute the final object of the inquiry.[ ] if in addition we recognize that, according to mill, our direct experience of nature always presents us with a complicated and confused set of appearances, we shall be in no doubt as to the importance of ideas as anticipations of a possible experience not yet had. thus he says: the order of nature, as perceived at a first glance, presents at every instant a chaos followed by another chaos. we must decompose each chaos into single facts. we must learn to see in the chaotic antecedent a multitude of distinct antecedents, in the chaotic consequent a multitude of distinct consequents.[ ] in the next section of the same chapter he goes on to state that, having discriminated the various antecedents and consequents, we then "are to inquire which is connected with which." this requires a still further resolution of the complex and of the confused. to effect this we must vary the circumstances; we must modify the experience as given with reference to accomplishing our purpose. to accomplish this purpose we have recourse either to observation or to experiment: "we may either _find_ an instance in nature _suited to our purposes_, or, by an artificial arrangement of circumstances, _make_ one" (the italics in "suited to our purpose" are mine; the others are mill's). he then goes on to say that there is no real logical distinction between observation and experimentation. the four methods of experimental inquiry are expressly discussed by mill in terms of their worth in singling out and connecting the antecedents and consequents which actually belong together, from the chaos and confusion of direct experience. we have only to take these statements in their logical connection with each other (and this connection runs through the entire treatment by mill of scientific inquiry), to recognize the absolute necessity of hypothesis to undertaking any directed inquiry or scientific operation. consequently we are not surprised at finding him saying that "the function of hypotheses is one which must be reckoned absolutely indispensable in science;" and again that "the hypothesis by suggesting observations and experiments puts us on the road to independent evidence."[ ] since mill's virtual retraction, from the theoretical point of view, of what is here said from the standpoint of scientific procedure, regarding the necessity of ideas is an accompaniment of his criticism of whewell, it will put the discussion in better perspective if we turn first to whewell's views.[ ] the latter began by stating a distinction which easily might have been developed into a theory of the relation of fact and idea which is in line with that advanced in this chapter, and indeed in this volume as a whole. he questions (chap. ) the fixity of the distinction between theory and practice. he points out that what we term facts are in effect simply accepted inferences; and that what we call theories are describable as facts, in proportion as they become thoroughly established. a true theory is a fact. "all the great theories which have successively been established in the world are now thought of as facts." "the most recondite theories when firmly established are accepted as facts; the simplest facts seem to involve something of the nature of theory." the conclusion is that the distinction is a historic one, depending upon the state of knowledge at the time, and upon the attitude of the individual. what is theory for one epoch, or for one inquirer in a given epoch, is fact for some other epoch, or even for some other more advanced inquirer in the same epoch. it is theory when the element of inference involved in judging any fact is consciously brought out; it is fact when the conditions are such that we have never been led to question the inference involved, or else, having questioned it, have so thoroughly examined into the inferential process that there is no need of holding it further before the mind, and it relapses into unconsciousness again. "if this greater or less consciousness of our own internal act be all that distinguishes fact from theory, we must allow that the distinction is still untenable" (untenable, that is to say, as a fixed separation). again, "fact and theory have no essential difference except in the degree of their _certainty and familiarity_. theory, when it becomes firmly established and steadily lodged in the mind becomes fact." (p. ; italics mine.) and, of course, it is equally true that as fast as facts are suspected or doubted, certain aspects of them are transferred into the class of theories and even of mere opinions. i say this conception might have been developed in a way entirely congruous with the position of this chapter. this would have happened if the final distinction between fact and idea had been formulated upon the basis simply of the points, "relative certainty and familiarity." from this point of view the distinction between fact and idea is one purely relative to the doubt-inquiry function. it has to do with the evolution of an experience as regards its conscious surety. it has its origin in problematic situations. whatever appears to us as a problem appears as contrasted with a possible solution. whatever objects of thought refer particularly to the problematic side are theories, ideas, hypotheses; whatever relates to the solution side is surety, unquestioned familiarity, fact. this point of view makes the distinctions entirely relative to the exigencies of the process of reflective transformation of experience. whewell, however, had no sooner started in this train of thought than he turns his back upon it. in chap. he transforms what he had proclaimed to be a relative, historic, and working distinction into a fixed and absolute one. he distinguishes between sensations and ideas, not upon a genetic basis with reference to establishing the conditions of further operation; but with reference to a fundamentally fixed line of demarkation between what is passively _given_ to the mind and the _activity_ put forth by the mind. thus he reinstates in its most generalized and fixed, and therefore most vicious, form the separation which he has just rejected. sensations are a brute unchangeable element of fact which exists and persists independent of ideas; an idea is a mode of mental operation which occurs and recurs in an independent individuality of its own. if he had carried out the line of thought with which he began, sensation as fact would have been that residuum of familiarity and certainty which cannot be eliminated, however much else of an experience is dissolved in the inner conflict. idea as hypothesis or theory would have been the corresponding element in experience which is necessary to redintegrate this residuum into a coherent and significant experience. but since whewell did not follow out his own line of thought, choosing rather to fall back on the kantian antithesis of sense and thought, he had no sooner separated his fact and idea, his given datum and his mental relation, than he is compelled to get them together again. the idea becomes "a general relation which is imposed upon perception by an act of the mind, and which is different from anything which our senses directly offer to us" (p. ). such conceptions are necessary to connect the facts which we learn from our senses into truths. "the ideal conception which the mind itself supplies is superinduced upon the facts as they are originally presented to observation. before the inductive truth is detected, the facts are there, but they are many and unconnected. the conception which the discoverer applies to them gives them connection and unity." (p. .) all induction, according to whewell, thus depends upon superinduction--imposition upon sensory data of certain ideas or general relations existing independently in the mind.[ ] we do not need to present again the objections already offered to this view: the impossibility of any orderly stimulation of ideas by facts, and the impossibility of any check in the imposition of idea upon fact. "facts" and conception are so thoroughly separate and independent that any sensory datum is indifferently and equally related to any conceivable idea. there is no basis for "superinducing" one idea or hypothesis, rather than any other, upon any particular set of data. in the chapter already referred to upon abstraction, or the formation of conceptions, mill seizes upon this difficulty. yet he and whewell have one point in common: they both agree in the existence of a certain subject-matter which is given for logical purposes quite outside of the logical process itself. mill agrees with whewell in postulating a raw material of pure sensational data. in criticising whewell's theory of superinduction of idea upon fact, he is therefore led to the opposite assertion of the complete dependence of ideas as such upon the given facts as such--in other words, he is led to a reiteration of the fundamental baconian empiricism; and thus to a virtual retraction of what he had asserted regarding the necessity of ideas to fruitful scientific inquiry, whether in the way of observation or experimentation. the following quotation gives a fair notion of the extent of mill's retraction: the conceptions then which we employ for the colligation and methodization of facts, do not develop themselves from within, _but are impressed upon the mind from without_; they are never obtained otherwise than by way of comparison and abstraction, and, in the most important and most numerous cases, are evolved by abstraction _from the very phenomena which it is their office to colligate_.[ ] even here mill's sense for the positive side of scientific inquiry suffices to reveal to him that the "facts" are somehow inadequate and defective, and are in need of assistance from ideas--and yet the ideas which are to help out the facts are to be the impress of the unsure facts! the contradiction comes out very clearly when mill says: "the really difficult cases are those in which the conception destined to create light and order out of darkness and confusion has to be sought for among the very phenomena which it afterward serves to arrange."[ ] of course, there is a sense in which mill's view is very much nearer the truth than is whewell's. mill at least sees that "idea" must be relevant to the facts or data which it is to arrange, which are to have "light and order" introduced into them by means of the idea. he sees clearly enough that this is impossible save as the idea develops _within_ the same experience in which the "dark and confused" facts are presented. he goes on to show correctly enough how conflicting data lead the mind to a "confused feeling of an analogy" between the data of the confused experience and of some other experience which is orderly (or already colligated and methodized); and how this vague feeling, through processes of further exploration and comparison of experiences, gets a clearer and more adequate form until we finally accept it. he shows how in this process we continually judge of the worth of the idea which is in process of formation, by reference to its appropriateness to _our purpose_. he goes so far as to say: "the question of appropriateness is relative to the _particular object we have in view_."[ ] he sums up his discussion by stating: "we cannot frame good general conceptions beforehand. that the conception we have obtained is the one we want can only be known when we have _done the work for the sake of which we wanted it_."[ ] this all describes the actual state of the case, but it is consistent only with a logical theory which makes the distinction between fact and hypothesis instrumental in the transformation of experience from a confused into an organized form; not with mill's notion that sensations are somehow finally and completely given as ultimate facts, and that ideas are mere re-registrations of such facts. it is perfectly just to say that the hypothesis is impressed upon the mind (in the sense that any notion which occurs to the mind is impressed) _in the course_ of an experience. it is well enough, if one define what he means, to say that the hypothesis is impressed (that is to say, occurs or is suggested) through the medium of given facts, or even of sensations. but it is equally true that the _facts_ are presented and that _sensations_ occur within the course of an experience which is larger than the bare facts, because involving the conflicts among them and the corresponding intention to treat them in some fashion which will secure a unified experience. facts get power to suggest ideas to the mind--to "impress"--only through their position in an entire experience which is in process of disintegration and of reconstruction--their "fringe" or feeling of tendency is quite as factual as they are. the fact that "the conception we have obtained is the one we want can be known only when we have done the work for the sake of which we wanted it," is enough to show that it is not bare facts, but facts in relation to want and purpose and purpose in relation to facts, which originate the hypothesis. it would be interesting to follow the history of discussion of the hypothesis since the time of whewell and of mill, particularly in the writings of jevons, venn, and bosanquet. this history would refine the terms of our discussion by introducing more complex distinctions and relations. but it would be found, i think, only to refine, not to introduce any fundamentally new principles. in each case, we find the writer struggling with the necessity of distinguishing between fact and idea; of giving the fact a certain primacy with respect to testing of idea and of giving the idea a primacy with respect to the significance and orderliness of the fact; and of holding throughout to a relationship of idea with fact so intimate that the idea develops only by being "compared" with facts (that is, used in construing them), and facts get to be known only as they are "connected" through the idea--and we find that what is a maze of paradoxes and inconsistencies from an absolute, from a non-historic standpoint, is a matter of course the moment it is looked at from the standpoint of experience engaged in self-transformation of meaning through conflict and reconstitution. but we can only note one or two points. jevons's "infinite ballot-box" of nature which is absolutely neutral as to any particular conception or idea, and which accordingly requires as its correlate the formation of every possible hypothesis (all standing in themselves upon the same level of probability) is an interesting example of the logical consequences of feeling the need of both fact and hypothesis for scientific procedure and yet regarding them as somehow arising independently of each other. it is an attempt to combine extreme empiricism and extreme rationalism. the process of forming hypotheses and of deducing their rational consequences goes on at random, because the disconnectedness of facts as given is so ultimate that the facts suggest one hypothesis no more readily than another. mathematics, in its two forms of measurements as applied to the facts, and of calculation as applied in deduction, furnishes jevons the bridge by which he finally covers the gulf which he has first himself created. venn's theory requires little or no restatement to bring it into line with the position taken in the text. he holds to the origin of hypothesis in the original practical needs of mankind, and to its gradual development into present scientific form.[ ] he states expressly: the _distinction between what is known and what is not known is essential to logic_, and peculiarly characteristic of it in a degree not to be found in any other science. inference is the process of passing from one to the other; from facts which we had accepted as premises, to those which we have not yet accepted, _but are in the act of doing so by the very process in question_. no scrutiny of the facts themselves, regarded as objective, can ever detect these characteristics of their greater or less familiarity to our minds. we must introduce also the subjective element if we wish to give any adequate explanation of them.[ ] venn, however, does not attempt a thoroughgoing statement of logical distinctions, relations, and operations, as parts "of the act of passing from the unknown to the known." he recognizes the relation of reflection to a historic process, which we have here termed "reconstruction," and the origin and worth of hypothesis as a tool in the movement, but does not carry his analysis to a systematic form. iii _origin of the hypothesis._--in our analysis of the process of judgment, we attempted to show that the predicate arises in case of failure of some line of activity going on in terms of an established habit. when the old habit is checked through failure to deal with new conditions (_i. e._, when the situation is such as to stimulate two habits with distinct aims) the problem is to find a new method of response--that is, to co-ordinate the conflicting tendencies by building up a single aim which will function the existing situation. as we saw that, in case of judgment, habit when checked became ideal, an idea, so the new habit is first formalized as an ideal type of reaction and is the hypothesis by which we attempt to construe new data. in our inquiry as to how this formulation is effected, _i. e._, how the hypothesis is developed, it will be convenient to take some of the currently accepted statements as to their origin, and show how these statements stand in reference to the analysis proposed. _enumerative induction and allied processes._--it is pointed out by welton[ ] that the various ways in which hypotheses are suggested may be reduced to three classes, viz., enumerative induction, conversion of propositions, and analogy. under the head of "enumeration" he reminds us that "every observed regularity of connection between phenomena suggests a question as to whether it is universal." there are numerous instances of this in mathematics. for example, it is noticed that + = ^ , + + = ^ , + + + = ^ , etc.; and one is led to ask whether there is any general principle involved, so that the sum of the first _n_ odd numbers will be _n_^ , where _n_ is any number, however great. in this early form of inductive inference there are two divergent tendencies. one is the tendency to complete enumeration. this _tendency_ is clearly ideal--it transcends the facts as given. to look for all the cases is thus itself an experimental inquiry, based upon a hypothesis which it endeavors to test. but in most cases enumeration can be only incomplete, and we are able to reach nothing better than probability. hence the other tendency in the direction of an analysis of content in search for a principle of connection in the elements in any _one_ case. for if a characteristic belonging to a number of individuals suggests a class where it belongs to all individuals, it must be that it is found in every individual as such. the hypothesis of complete class involves a hypothesis as to the character of each individual in the class. thus a hypothesis as to extension transforms itself into one as to intension. but it is analogy which welton considers "the chief source from which new hypotheses are drawn." in the second tendency mentioned under enumerative induction, that is, the tendency to analysis of content or intension, we are naturally led to analogy, for in our search for the characteristic feature which determines classification among the concrete particulars our first step will be an inference by analogy. in analogy attention is turned from the number of observed instances to their character, and, because particulars have some feature in common, they are supposed to be the same in still other respects. while the best we can reach in analogy is probability, the arguments may be such as to result in a high degree of certainty. the form of the argument is valuable in so far as we are able to distinguish between essential and nonessential characteristics on which to base our analogy. what is essential and what nonessential depends upon the particular end we have in view. in addition to enumerative induction, which welton has mentioned, it is to be noted that there are a number of other processes which are very similar to it in that a number of particulars appear to furnish a basis for a general principle or method. such instances are common in induction, in instruction, and in methods of proof. if one is to be instructed in some new kind of labor, he is supposed to acquire a grasp of the method after having been shown in a few instances how this particular work is to be done; and, if he performs the manipulations himself, so much the better. it is not asked why the experience of a few cases should be of any assistance, for it seems self-evident that an experienced man, a man who has acquired the skill, or knack, of doing things, should deal better with all other cases of similar nature. there is something very similar in inductive proofs, as they are called. the inductive proof is common in algebra. suppose we are concerned in proving the law of expansion of the binomial theorem. we show by actual calculation that, if the law holds good for the _n_th power, it is true for the _n_+first power. that is, if it holds for any power, it holds for the next also. but we can easily show that it does hold for, say, the second power. then it must be true for the third, and hence for the fourth, and so on. whether this law, though discovered by inductive processes, depends on deduction for the conclusiveness of its proof, as jevons holds;[ ] whether, as erdmann[ ] contends, the proof is thoroughly deductive; or whether wundt[ ] is right in maintaining that it is based on an exact analogy, while the fundamental axioms of mathematics are inductive, it is clear that in such proofs a few instances are employed to give the learner a start in the right direction. something suggests itself, and is found true in this case, in the next, and again in the next, and so on. it may be questioned whether there is usually a very clear notion of what is involved in the "so on." to many it appears to mark the point where, after having been taken a few steps, the learner is carried on by the acquired momentum somewhat after the fashion of one of newton's laws of motion. whether the few successive steps are an integral part of the proof or merely serve as illustration, they are very generally resorted to. in fact, they are often employed where there is no attempt to introduce a general term such as _n_, or _k_, or _l_, but the few individual instances are deemed quite sufficient. such, for instance, is the custom in arithmetical processes. we call attention to these facts in order to show that successive cases are utilized in the course of explanation as an aid in establishing the generality of a law. in geometry we find a class of proofs in which the successive steps seem to have great significance. a common proof of the area of the circle will serve as a fair example. a regular polygon is circumscribed about the circle. then as the number of its sides are increased its area will approach that of the circle, as its perimeter approaches the circumference of the circle. the area of the circle is thus inferred to be [pi]_r_^ , since the area of the polygon is always ( / )_r_× perimeter, and in case of the circle the circumference = [pi]_r_. here again we get under such headway by means of the polygon that we arrive at the circle with but little difficulty. had we attempted the transition at once, say, from a circumscribed square, we should doubtless have experienced some uncertainty and might have recoiled from what would seem a rash attempt; but as the number of the sides of our polygon approach infinity--that mysterious realm where many paradoxical things become possible--the transition becomes so easy that our polygon is often said to have truly become a circle. similarly, some statements of the infinitesimal calculus rest on the assumption that slight degrees of difference may be neglected. though the more modern theory of limits has largely displaced this attitude in calculus and has also changed the method of proof in such geometrical problems as the area of the circle, the underlying motive seems to have been to make transitions easy, and thus to make possible a continued application of some particular method or way of dealing with things. but granted that this is all true, what has it to do with the origin of the hypothesis? it seems likely that the hypothesis may be suggested by a few successive instances; but are these to be classed with the successive steps in proof to which we have referred? in the first place, we attempt to prove our hypothesis because we are not sure it is true; we are not satisfied that there are no other tenable hypotheses. but if we do test it, is not such test enough? it depends upon how thorough a grasp we have of the situation; but, in general, each test case adds to its probability. the value of tests lies in the fact that they strengthen and tend to confirm our hypothesis by checking the force of alternatives. one instance is not sufficient because there are other possible incipient hypotheses, or more properly tendencies, and the enumeration serves to bring one of these tendencies into prominence in that it diminishes other vague and perhaps subconscious tendencies and strengthens the one which suddenly appears as the mysterious product of genius. the question might arise why the mere repetition of conflicting tendencies would lead to a predominance of one of them. why would they not all remain in conflict and continue to check any positive result? it is probably because there never is any absolute equilibrium. the successive instances tend to intensify and bring into prominence some tendency which is already taking a lead, so to speak. and it may be said further in this connection that only as seen from the outside, only as a mechanical view is taken, does there appear to be an excluding of definitely made out alternatives. in explanation of the part played by analogy in the origin of hypotheses, welton points out that a mere number of instances do not take us very far, and that there must be some "_specification_ of the instances as well as numbering of them," and goes on to show that the argument by enumerative induction passes readily into one from analogy, as soon as attention is turned from the number of the observed instances to their character. it is not necessary, however, to pass to analogy through enumerative induction. "when the instances presented to observation offer immediately the characteristic marks on which we base the inference to the connection of s and p, we can proceed at once to an inference from analogy, without any preliminary enumeration of the instances."[ ] welton, and logicians generally, regard analogy as an inference on the basis of partial identity. because of certain common features we are led to infer a still greater likeness. both enumerative induction and analogy are explicable in terms of habit. we saw in our examination of enumerative induction that a form of reaction gains strength through a series of successful applications. analogy marks the presence of an identical element together with the tendency to extend this "partial identity" (as it is commonly called) still farther. in other words, in analogy it is suggested that a type of reaction which is the same in certain respects may be made similar in a greater degree. in enumerative induction we lay stress on the number of instances in which the habit is applied. in analogy we emphasize the content side and take note of the partial identity. in fact, the relation between enumerative induction and analogy is of the same sort as that existing between association by contiguity and association by similarity. in association by contiguity we think of the things associated as merely standing in certain temporal or spatial relations, and disregard the fact that they were elements in a larger experience. in case of association by similarity we regard the like feature in the things associated as a basis for further correction. in conversion of propositions we try to reverse the direction of the reaction, so to speak, and thereby to free the habit, to get a mode of response so generalized as to act with a minimum cue. for instance, we can deal with a in a way called b, or, in other words, in the same way that we did with other things called b. if we say, "man is an animal," then to a certain extent the term "animal" signifies the way in which we regard "man." but the question arises whether we can regard all animals as we do man. evidently not, for the reaction which is fitting in case of animals would be only partially applicable to man. with the animals that are also men we have the beginning of a habit which, if unchecked, would lead to a similar reaction toward all animals, _i. e._, we would say: "all animals are men." man may be said to be the richer concept, in that only a part of the reaction which determines an object to be a man is required to designate it as an animal. on the other hand, if we start with animal, then (except in case of the animals which are men) there is lacking the subject-matter which would permit the fuller concept to be applied. by supplying the conditions under which animal=man we get a reversible habit. the equation of technical science has just this character. it represents the maximum freeing or abstraction of a predicate _qua_ predicate, and thereby multiplies the possible applications of it to subjects of future judgments, and lessens the amount of shearing away of irrelevancies and of re-adaptation necessary when so used in any particular case. _formation and test of the hypothesis._--the formation of the hypothesis is commonly regarded as essentially different from the process of testing, which it subsequently undergoes. we are said to observe facts, invent hypotheses, and _then_ test them. the hypothesis is not required for our preliminary observations; and some writers, regarding the hypothesis as a formulation which requires a difficult and elaborate test, decline to admit as hypotheses those more simple suppositions, which are readily confirmed or rejected. a very good illustration of this point of view is met with in wundt's discussion of the hypothesis, by an examination of which we hope to show that such distinctions are rather artificial than real. the subject-matter of science, says wundt,[ ] is constituted by that which is actually given and that which is actually to be expected. the whole content is not limited to this, however, for these facts must be supplemented by certain presuppositions, which are not given in a factual sense. such presuppositions are called hypotheses and are justified by our fundamental demand for unity. however valuable the hypothesis may be when rightly used, there is constant danger of illegitimately extending it by additions that spring from mere inclinations of fancy. furthermore, the hypothesis in this proper scientific sense must be carefully distinguished from the various inaccurate uses, which are prevalent. for instance, hypotheses must not be confused with expectations of fact. as cases in point wundt mentions galileo's suppositions that small vibrations of the pendulum are isochronous, and that the space traversed by a falling body is proportional to the square of the time it has been falling. it is true that such anticipations play an important part in science, but so long as they relate to the facts themselves or to their connections, and can be confirmed or rejected any moment through observation, they should not be classed with those added presuppositions which are used to co-ordinate facts. hence not all suppositions are hypotheses. on the other hand, not every hypothesis can be actually experienced. for example, one employs in physics the hypothesis of electric fluid, but does not expect actually to meet with it. in many cases, however, the hypothesis becomes proved as an experienced fact. such was the course of the copernican theory, which was at first only a hypothesis, but was transformed into fact through the evidence afforded by subsequent astronomical observation. wundt defines a theory as a hypothesis taken together with the facts for whose elucidation it was invented. in thus establishing a connection between the facts which the hypothesis merely suggested, the theory furnishes at the same time partly the foundation (_begründung_) and partly the confirmation (_bestätigung_) of the hypothesis.[ ] these aspects, wundt insists, must be sharply distinguished. every hypothesis must have its _begründung_, but there can be _bestätigung_ only in so far as the hypothesis contains elements which are accessible to actual processes of verification. in most cases verification is attainable in only certain elements of the hypothesis. for example, newton was obliged to limit himself to one instance in the verification of his theory of gravitation, viz., the movements of the moon. the other heavenly bodies afforded nothing better than a foundation in that the supposition that gravity decreases as the square of the distance increases enabled him to deduce the movements of the planets. the main object of his theory, however, lay in the deduction of these movements and not in the proof of universal gravity. with the darwinian theory, on the contrary, the main interest is in seeking its verification through examination of actual cases of development. thus, while the newtonian and the greater part of the other physical theories lead to a deduction of the facts from the hypotheses, which can be verified only in individual instances, the darwinian theory is concerned in evolving as far as possible the hypothesis out of the facts. let us look more closely at wundt's position. we will ask, first, whether the distinction between hypotheses and expectations is as pronounced as he maintains; and, second, whether the relation between _begründung_ and _bestätigung_ may not be closer than wundt would have us believe. as examples of the hypothesis wundt mentions the copernican hypothesis, newton's hypothesis of gravitation, and the predictions of the astronomers which led to the discovery of neptune. as examples of mere expectations we are referred to galileo's experiments with falling bodies and pendulums. in case of newton's hypothesis there was the assumption of a general law, which was verified after much labor and delay. the heliocentric hypothesis of copernicus, which was invented for the purpose of bringing system and unity into the movements of the planets, has also been fairly well substantiated. in the discovery of neptune we have, apparently, not the proof of a general law or the discovery of further peculiarities of previously known data, but rather the discovery of a new object or agent by means of its observed effects. in each of these instances we admit that the hypothesis was not readily suggested or easily and directly tested. if we turn to galileo's pendulum and falling bodies, it is clear first of all that he did not have in mind the discovery of some object, as was the case in the discovery of neptune. did he, then, either contribute to the proof of a general law or discover further characteristics of things already known in a more general way? wundt tells us that galileo only determined a little more exactly what he already knew, and that he did this with but little labor or delay. what, then, is the real difference between hypothesis and expectation? if we compare galileo's determination of the law of falling bodies with newton's test of his hypothesis of gravitation, we see that both expectation and hypothesis were founded on observation and took the form of mathematical formulæ. each tended to confirm the general law expressed in its formula, though there was, of course, much difference in the time and labor required. if we compare the copernican hypothesis with galileo's supposition concerning the pendulum, we find again that they agree in regard to general purpose and method, and differ in the difficulty of verification. if the experiment with the pendulum only substituted exactness for inexactness, did the copernican theory do anything different in _kind_? it is true that the more exact statement of the swing of the pendulum was expressed in quantitative form, but quantitative statement is no criterion of either the presence or the absence of the hypothesis. again, we may compare the pendulum with kepler's laws. what was kepler's hypothesis, that the square of the periodic times of the several planets are proportional to the cubes of their mean distances from the sun, except a more exact formulation of facts which were already known in a more general way? wundt's position seems to be this: whenever a supposition or suggestion can be tested readily, it should not be classed as a hypothesis. this would make the distinction one of degree rather than kind, and it does not appear how much labor we must expend, or how long our supposition must evade our efforts to test it, before it can win the title of hypothesis. in the second place, we have seen that wundt draws a sharp line between _begründung_ and _bestätigung_. it is doubtless true that every hypothesis requires a certain justification, for unless other facts can be found which agree with deductions made in accordance with it, its only support would be the data from which it is drawn. such support as this would be obtained through a process too clearly circular to be seriously entertained. the distinction which wundt draws between _begründung_ and _bestätigung_ is evidently due to the presence of the experimental element in the latter. for descriptive purposes this distinction is useful, but is misleading if it is understood to mean that there is mere experience in one case and mere inference in the other. the difference is rather due to the relative parts played by inference and by accepted experience in each. in _begründung_ the inferential feature is the more prominent, while in _bestätigung_ the main emphasis is on the experiential aspect. it must not be supposed, however, that either of these aspects can be wholly absent. it is difficult to understand how any hypothesis can be entertained at all unless it meets in some measure the demand with reference to which it was invented, viz., a unification of conflicts in experience. and, _in so far_, it is confirmed. the motive which casts doubt upon its adequacy is the same that leads to its re-forming as a hypothesis, as a mental concept. the difficulties in wundt's position are thus due to a failure to take account of the reconstructive nature of the judgment. the predicate, supposition, or hypothesis, whatever we may choose to call it, is formed because of the check of a former habit. the judgment is an ideal application of a new habit, and its test is the attempt to act in accordance with this ideal reconstruction. it must not be thought, however, that our supposition is first fully developed and then tried and accepted or rejected without modification. on the contrary, its growth is the result of successive minor tests and corresponding minor modifications in its form. formation and test are merely convenient distinctions in a larger process in which forming, testing, and _re_-forming go on together. the activity of experimental verification is not only a testing, a confirming or weakening of the validity of a hypothesis, but it is equally well an evolution of the _meaning_ of the hypothesis through bringing it into closer relations with specific data not previously included in defining its import. _per contra_, a purely reflective and deductive consideration which develops the idea as hypothesis, _in so far_ as it introduces the determinateness of previously accepted facts within the scope, comprehension, or intension of the idea, is in so far forth, a verification. if the view which we have maintained is correct, the hypothesis is not to be limited to those elaborate formulations of the scientist which he seeks to confirm by crucial tests. the hypothesis of the investigator differs from the comparatively rough conjecture of the plain man only in its greater precision. indeed, as we have attempted to show, the hypothesis is not a method which we may employ or not as we choose; on the contrary, as predicate of the judgment it is present in a more or less explicit form if we judge at all. whether the time and labor required for its confirmation or rejection is a matter of a lifetime or a moment, its nature remains the same. its function is identical with that of the predicate. in short, the hypothesis is the predicate so brought to consciousness and defined that those features which are not noticed in the ordinary judgment are brought into prominence. we then recognize the hypothesis to be what in fact the predicate always is, viz., a method of organization and control. viii image and idea in logic the logic of sense-impressions and of ideas as copies of sense-impressions has had its day. it engaged in a conflict with dogmatism, and scored a decisive victory. it overthrew the dynasty of prescribed formulæ and innate ideas, of ideas derived ready-made from custom and social usage, ancient enough to be lost in the remote obscurity of divine sources; and enthroned in their place ideas derived from, and representative of, the sense-experiences of a very real and present world. it marked a reaction from dogma back to the original meaning of dogma, back to the seeming, the appearance, of things. so thoroughly did bacon and hobbes, locke and hume, to mention only these four, do their work, that many of the problems growing out of the conflict itself, to say nothing of the scholastic traditions that were combated, have come to have merely a historical rather than a logical interest. logic no longer concerns itself very eagerly with the content or sensuous qualities of ideas, with their derivation from sense-impressions, or with questions as to the relation of copy to original, of representative to that which is presented. it is concerned rather with the constructive operations of thought, with meaning, reference to reality, inference--with intellectual processes. perhaps in no respect is this shifting of logical standpoint indicated more clearly than in the unregretful way with which the old logical interest in the sense-qualities of ideas is now made over to psychology. states of consciousness as such, we are told, are the proper study of psychology; whereas logic concerns itself with the relation of thought to its object. true, these states of consciousness include thought-states, as well as sense-impressions; ideas and concepts, as well as feelings and fancies; and the business of psychology is to observe, compare and classify, describe and chronicle, these states and whatever else is carried along in the stream of consciousness. but logic is concerned, not with these states of consciousness _per se_, least of all with the flotsam and jetsam of the stream, but with its reference to reality; not with the true, but with truth; not even with what consciousness does, but with how consciousness is to outdo itself, transcend itself, in a rational and universal whole. even an empirical logic has to arrange somehow the way to get from one sense-impression to another. in drawing this distinction between logic and psychology--a distinction which virtually amounts to a separation--two things are overlooked: first, that the distinction itself is a logical distinction, and may properly constitute a problem falling under the province of logical inquiry and theory; and, second, that the rather arbitrary and official setting apart of psychology to look after the task of studying states of consciousness does not carry with it the guarantee that psychology will confine itself exclusively to that task. this last point in particular must be my excuse for discussing the question of image and idea from the psychological rather than from the logical standpoint. the logic of ideas derived from sense-impressions has had its day. but even the very leavings of the past may have been gathered up and reconstructed by psychology in such a way as to anticipate some of the newer developments of logical theory and meet some of its difficulties. one can hardly hope to justify in advance a discussion based on such a sheer possibility. let us begin, rather, by noting down from the standpoint of logic some of the distinctions between image and idea, and the estimate of the logical function and value of mental imagery, and see in what direction they take us and whether they suggest a resort to an analysis from the standpoint of psychology. proceeding from the standpoint of logic to inquire into the logical function of mental imagery and into the distinction between image and idea, we shall come upon two opposed but characteristic answers. if the inquiry be directed to a member of the empirical school of logic, he would be bound to answer in the affirmative, so far as the question regarding the function of mental imagery is concerned. he would be likely to say, if he were loyal to the traditions of his school, that mental imagery is the counterpart of sense-perception, and is thus the representative of the data with which empirical logic is concerned. mental imagery, he would continue, is a representative in a literal sense, a copy, a reflection, of what comes to us through the avenues of sensation. true, it is not the perfect twin of sense-experience; else we could not tell them apart; indeed, there are times when the copy becomes so much like the original that we are deceived by it, as in dreams or in hallucinations. ordinarily, however, we are able to distinguish one from the other. two criteria are usually present; ( ) imagery is fainter, more fleeting, than the corresponding sense-experience; and ( ), save in the case of accurate memory-images, it is subject to a more or less arbitrary rearrangement of its parts, as when, for example, we make over the images of scenes we have actually experienced, to furnish forth the setting of some remote historical event. barring, or controlling and rectifying, its tendencies toward both arbitrary and constructive variations from the original, mental imagery is on the same level as sense-experience, and serves the same logical purpose. that is to say, it contributes to the data which constitute the foundations of empirical logic. it furnishes materials for the operations of observing, comparing, abstracting and generalizing. mental imagery helps to piece out the fragments that may be presented to sense-experience. it supplies the entire anatomy when only a single bone, say, is actually given. yet, however useful as a servant of truth, it has to be carefully watched, lest its spontaneous tendency to vary the actual order and coexistence of data lead the investigator astray. the copy it presents is, after all, a temporary makeshift, until it can be shown to correspond point for point to the now absent reality. mental imagery furnishes one with an illustrated edition of the book of nature, but the illustrations await the confirmation of comparison with the originals. mental imagery functions logically when it extends the area of data beyond the range of the immediate sense-perceptions of any given time, and thus makes possible a more comprehensive application of the empirical methods of observation, comparison, abstraction, and generalization. it functions logically when it acts as a feeder of logical machinery, though it is not indispensable to this machinery and does not modify its principles. the logical mill could grind up in the same way the pure grain of sense-perceptions, unmixed with mental images, but it would have to grind more slowly for lack of material. in other words, empirical logic could carry on its operations of observing, comparing, abstracting, and generalizing, solely on the basis of objects or data present to the senses, and with no extension of this basis in terms of imagery, or copies of objects not immediately present; but it would take more time for it to apply and carry through its operations. the logical machinery is the same in each case. the materials fed and the product issuing are the same in each case. imagery simply fulfils the function of providing a more copious grist. the empiricist's answer to our question regarding the logical function of mental imagery leaves that function in an uncertain and parlous state. imagery lacks the security of sense-perception on the one hand, and it has no part in the operation of thought on the other. it is a sort of hod-carrier, whose function it is to convey the raw materials of sense-perception to a more exalted position where someone else does all the work. i suppose this could be called a functional interpretation of a logical element. the question, then, would be whether an element so functioning is in any sense logical. as an element lying outside of the thought-process it owes no responsibility to logic; it is not amenable to its regulations. thought simply finds it expedient to operate with an agent over which it has no intrinsic control. the case might be allowed to rest here. yet were this extra-logical element of imagery to abandon thought, all conscious thinking as opposed to sense-perception would cease. a false alarm, perhaps. imagery may be so constituted that it is inseparably subordinated to thought and can never abandon it. thought may simply exude imagery. but imagery somehow has to represent sense-perception, also. it can hardly be a secretion of thought and a copy of sense-perceptions at one and the same time, unless the empiricist is willing to turn absolute idealist! before taking such a desperate plunge as this, it might be desirable to see whether there is any other recourse. there is another and a very different answer to the question regarding the logical function of mental imagery. to distinguish this answer from that of the associationist or empiricist, i will call it the answer of the conceptualist. i am not at all positive that this label would stick even to those to whom it might be applied with considerable justification. the terms "rationalistic" and "transcendental" might be preferred in opposition to the term "empirical." and we have the term "apperceptionist" in opposition to the term "associationist." if the term "conceptualist" is admissible, it should be brought down to date, perhaps, by making it "neo-conceptualist." the present difficulties regarding terminology would be eased considerably if we only had a convenient set of derivatives made from the word "meaning." since we have not, i will use derivatives made from the word "concept" to denote views opposite to those held by the empirical school. the conceptualist could be depended upon to answer our question in the negative. logical functions begin where the image leaves off. they begin with the _idea_, with meaning. the conceptualist distinguishes sharply between the image as a psychical existence and the idea, or concept, as logical meaning. on the one hand, you have the "image," not only as a mere psychical existence, but a mocking existence at that, fleeting, inconstant, shifting, never perhaps twice alike; yet, mind you, an _existence_, a _fact_--that must be admitted. on the other hand, you have the "idea," with "a fixed content or logical meaning,"[ ] which is referred by an act of judgment to a reality beyond the act.[ ] the "idea," the logical meaning, begins where the "image" leaves off. does this mean that the "idea" is wholly independent of the "image"? yes and no. the "idea" is independent of that which is ordinarily regarded as the special characteristic of an "image," namely, its quality, its sense-content. that is to say, the "idea" is independent of any particular "image," any special embodiment of sense-content. any image will do. as mr. bosanquet remarks in comparing the psychical images that pass through our minds to a store of signal flags: not only is it indifferent whether your signal flag of today is the same bit of cloth that you hoisted yesterday, but also, no one knows or cares whether it is clean or dirty, thick or thin, frayed or smooth, as long as it is distinctly legible as an element of the signal code. part of its content, of its attributes and relations, is a fixed index which carries a distinct reference; all the rest is nothing to us, and, except in a moment of idle curiosity, we are unaware that it exists.[ ] on the other hand, the "idea" could not operate as an idea, could not be in consciousness, save as it involves some imagery, however old, dirty, thin, and frayed. take the statement, "the angles of a triangle are equal to two right angles." if the statement means anything to a given individual, if it conveys an idea, it must necessarily involve some form of imagery, some qualitative or conscious content. but so far as the _meaning_ is concerned, it is a matter of complete indifference as to _what_ qualities are involved. these qualities may be in terms of visual, auditory, tactual, kinæsthetic, or verbal imagery. the individual may visualize a blackboard drawing of a triangle with its sides produced, or he may imagine himself to be generating a triangle while revolving through an angle of °. any imagery anyone pleases may be employed, so long as there goes with it somehow the _idea_ of the relation of equality between the angles of a triangle and two right angles. but the conceptualist does not stop here. the act of judgment comes in to affirm that the "idea" is no mere idea, but is a quality of the real. "the act [of judgment] attaches the floating adjective [the idea, the logical meaning] to the nature of the world, and, at the same time, tells one it was there already."[ ] the "idea," the logical meaning, begins where the "image" leaves off. yet, somehow, the "idea" could not begin, unless there were an "image" to leave off. an "image" is not an "idea," says the conceptualist. an "idea" is not an "image." ( ) an "image" is not an "idea," because an "image" is a particular, individual fragment of consciousness. it is so bound up with its own existence that it cannot reach out to the existence of an "idea," or to anything beyond itself. chemically speaking, it is an _avalent_ atom of consciousness, if such a thing is thinkable. mr. bosanquet raises the question: are there at all ideas which are not symbolic?... the answer is that _(a)_ in judgment itself the idea can be distinguished _qua_ particular in time or psychical fact, and _so far_ is not symbolic; and _(b)_ in all those human experiences from which we draw our conjectures as to the animal intelligence, when in languor or in ignorance image succeeds image without conscious judgment, we feel what it is to have ideas as facts and not as symbols.[ ] ( ) an "idea" is not an "image," because an idea _is_ meaning, which consists in a part of the content of the image, cut off, and considered apart from the _existence_ of the content or sign itself.[ ] this meaning, this fragment of psychical existence, lays down all claim to existence on its own account, that it may refer through an act of judgment to a reality beyond itself and beyond the act also. an "image" is not an "idea" and an "idea" is not an "image," because an "image" exists only as a quality, a sense-content, whereas an "idea" exists only as a relation, a reference to reality beyond. "on the one hand," to recall bradley's antinomy, "no possible idea [as a psychical image] can be that which it means.... on the other hand, no idea [as logical signification] is anything but just what it means." there is a significant point of agreement between the conceptualist and the empiricist. both regard imagery as on the level with sense-perception. for the empiricist, as we have seen, the fact that imagery may be compelled to serve as a yoke-fellow of sense-experience constitutes its logical value. for the conceptualist, however, the association of imagery with sense-experience is of no logical consequence whatsoever, save as it may help to intensify the distinction between imagery and meaning. to quote again from bradley: for logical purposes the psychological distinction of idea and sensation may be said to be irrelevant, while the distinction of idea and fact is vital. the image, or psychological idea, is for logic nothing but a sensible reality. it is on a level with the mere sensations of the senses. for both are facts and neither are meanings. neither are cut from a mutilated presentation and fixed as a connection. neither are indifferent to their place in the stream of psychical events, their time and their relations to the presented congeries. neither are adjectives to be referred from their existence, to live on strange soils, under other skies, and through changing seasons. the lives of both are so entangled with their environment, so one with their setting of sensuous particulars, that their character is destroyed if but one thread is broken.[ ] this point of agreement between conceptualism and empiricism, this placing of imagery and sense-experience on a common level, serves to bring into relief fundamental differences between the two schools of thought; fundamental, because they have to do with the nature of reality itself. the conceptualist in his zealous endeavor to distinguish between imagery and logical meaning has come perilously near driving imagery into the arms of reality. it is the opportunity of empiricism to make them one. how can conceptualism prevent the union? has it not disarmed itself? the act of judgment, which includes within itself logical meaning as predicate, refers to a reality beyond the act. both imagery and reality, then, lie outside of the act of judgment! what alliance, or _mésalliance_, may they not form, one with the other? the difficulties we have noted thus far in the discussion are due to a large extent, i believe, to incomplete psychological analysis of logical machinery. the empiricist has not carried the psychology of logic as far as the conceptualist, although the latter might be the loudest to disclaim the honor. i will not try to prove this statement, but simply give it as a reason why, in the interest of brevity, i shall pass with little comment over the psychological shortcomings and contributions of empirical logic, and devote what space remains to the psychology implicitly worked out by conceptual logic, and to its possible development, with special reference, of course, to the problem of the logical function of imagery. the logical distinction, which practically amounts to a separation between imagery and meaning, is the counterpart of the psychological distinction between stimulus and response, between the two poles of sensori-motor activity, where the stimulus is defined in consciousness in the form of imagery, in the form of sense-qualities centrally excited, and where the response is directed and controlled _via_ this imagery, so as to function in bringing some end, project, purpose, or ideal, nearer to realization, some problem nearer to solution. psychologically, there is no break between image and response, between thought and action. the stimulus is a condition of action, in both senses of the ambiguity of the word "condition." ( ) it _is_ action; it is a state or condition of action. ( ) it is also an initiation of action. _if_ the appropriate stimulus, then the desired action. the response to an image is the meaning of the image. or, the response to any stimulus _via_ an image--mediated, controlled or directed by an image--is the meaning of that image. the less imagery involved in any response, the greater the presumption in favor of the belief that the response is either an instinctive impulse or else has become a habit of mind, an adequate idea. the reduction and loss of sense-content which an image may undergo--the wearing away of an image, it is sometimes called--is not a sign that this sense-content has no logical function; but rather that it has fulfilled a logical function so well that it has made part of itself useless. the husk, to recall one of mr. bradley's comparisons, that useless husk, tends to fall away, to lapse from consciousness, after it has served the purpose of helping to bring the kernel of truth to fruition. this raises again the original question as to whether the sense-content, the quality, the existential quality, of an image has a logical function. i will ask first whether it has a function from the standpoint of psychology. we will agree with the empiricist that the content of an image is representative, that it is a return, a revival, of a sense-content previously experienced through the activity of sense-organs stimulated from the periphery. what is the function, then, of the representative image? sensation, quality, as we have implied above, is the stimulus come to consciousness. to explain how a stimulus can "come" to consciousness is a problem i will not attempt to go into here. i assume as a fact that there are times when we know what we are about; when we are conscious of the stimuli, or conditions of action, which are tending in this direction or in that, and when through this consciousness we exercise a controlling influence over action by selecting and reinforcing certain stimuli and suppressing or inhibiting others. it is true that we do not always realize to how great an extent our actions are controlled by stimuli which do not come to consciousness, by reflexes, instincts, and habits which do not rise above the threshold of imagery. and when this vast complex of hidden machinery is partly revealed to us, it may either cause the beholder to take a materialistic, mechanical, or fatalistic view of existence, to say that we are the victims of our own machinery, or else it may induce the other extreme of more or less mystic pronouncements regarding the province of the subconscious, of the subliminal self; thus out of partial views, out of half-truths, metaphysical problems arise and arm for mutual conflict. nevertheless, there is a presumption, amounting in most minds to a conviction, that we do at times consciously control some of our actions. and it is only making this conviction a little more explicit to say that we consciously control our actions through becoming aware of the stimuli, or conditions of action, and through selecting and reinforcing them. is it begging the question to speak of consciousness as exercising a selective function with reference to stimuli? from the standpoint of psychology, i cannot see that it is. no characteristic of consciousness has been more clearly made out, both reflectively and experimentally, than its selective function, than its ability to pick out and intensify within certain limits the stimuli or conditions of action. the representational image is a stimulus come to consciousness in the same way that a sensation is a stimulus come to consciousness. it is both a direct and an indirect stimulus. the terms "direct" and "indirect" are used as relative solely to the demands of the particular situation out of which they arise. by direct stimulus i mean a stimulus which initiates with almost no appreciable delay the response or attitude appropriate to the demands of a given situation, bridging the difficulties, removing the obstacles, or solving the problem with the minimum of conscious reflection. as an image becomes more and more of a working symbol, an idea, it tends to become simply a direct stimulus. by an "indirect stimulus" is meant a stimulus initiating a response which, if not inhibited, would be irrelevant to the situation, yet which may represent stimuli which are not found in the immediate field of sense-perception, and which are essential to the carrying on of the activity. the situation is a problematic one. acquired habits or mental adjustments break down at some point or fail to operate smoothly, either owing to the absence of customary stimuli or to the presence of new and untried conditions of action. part of the stress of meeting such a situation as this falls on the side of discovering appropriate stimuli and part on the side of developing out of habits already acquired new methods of response. in such a situation as this, imagery may function on the side of _stimulus_ when, taking its cue from the stimuli which are actually present, and which grow out of the strain and friction, it represents the missing conditions of action sufficiently to direct a search for them. it projects a map, so to speak, in which the fragmentary conditions immediately present to sense-perception may find their bearings, or in which in some way the missing members may be discovered. a familiar instance of this would be the experience one sometimes has in trying to recall the forgotten name of an acquaintance. the images of scenes associated with the acquaintance, of various letters and sounds of words associated with his name, which may be called to mind, do not function so much as direct stimuli as they do as intermediate or indirect stimuli. it is a case of casting about for the image that will function as a direct stimulus in bringing an acquired but temporarily lost adjustment into play. image functions on the side of _response_, on the side of developing new habits, new forms of adjustment, in so far as the conditions of action which it represents, or projects, are not the actual conditions of action, either because they are so inaccessible as to demand development of new habits for purposes of attaining them, or else because, though actually present, they stimulate relatively uncontrolled æsthetic or emotional responses, whose very expression, however, may be translated into a demand for more adequate, intelligent, controlled habits or adjustments. the conscious projection of the unattained, even of the unattainable, not only marks a certain degree of attainment, but is the initiation of further development. here we see again that a stimulus is a condition of action in both senses of the ambiguity of the word "condition." it is both a state or condition of activity, and an initiation or condition of further activity. as an indirect stimulus growing out of a problematic situation imagery necessarily brings in more or less irrelevant material. if i may be permitted the paradox, imagery would not be relevant if it did not bring in the irrelevant. the novelty of the situation makes it impossible to say in advance what will be relevant. hence the demand for range and play of imagery. it is only the successful adjustment finally hit upon and worked out that is the test of the relevancy of the imagery which anticipated it. even this test may be unfair, since it is likely to discount the value of imagery which is now ruled out, but which may have been indispensable in turning up the proper cues in the course of the process of reflection and experiment. to restate the point in regard to the psychological function of imagery. imagery functions in representing control as ideal, not as fact. it represents a possible process of reconstructing adjustments and habits; it is not an actual and complete readjustment. it arises normally in a stress, in the presence of fresh demands and new problems. it looks forward in every possible direction, because it is important and difficult to foresee consequences. but suppose the new adjustment to be made with reasonable success--reasonable, note. suppose the ideal to be realized. with practice the adjustment becomes less problematic, more under control--that is, it comes to require less conscious attention to bring it about. the image loses some of its sensuous content. it becomes worn away, more remote, until at last it becomes respectably vague and abstract enough to be classed as a concept. imagery is the stimulus of the reconstructive process between habit and habit, concept and concept, idea and idea. we now return to the original question regarding the logical function of imagery. there is only one condition, i believe, on which we can accept the assumption of both empiricist and conceptualist that imagery is on the same level with sense-perception, and that is the assumption that meaning, logical meaning, is on the same level with habit, habit naming the more obvious, overt forms of response to stimuli, logical meaning naming the more internal forms of response or reference. psychical response and logical reference thus become equivalent terms. we have seen that imagery may exercise two functions with reference to habit, as direct and as indirect stimulus; so also with reference to logical meaning, imagery may be the stimulus to a direct reference of the idea to reality, or it may present, or mirror, conditions with regard to which some new meaning is to be worked out. the quality, the sense-content, of imagery may _per se_ suffice directly to arouse a habitual attitude, to call forth an immediate reference to reality. it may cause one to "tumble" to what is taking place, to "catch on," to apprehend (pardon these expressions for the sake of their description of the motor aspect of meaning), as when we say, for example: "it came over me like a flash what i was to do, and i did it." our more abstract and complicated forms of judgment and reasoning, in which the imagery involved is reduced to the minimum of conscious, qualitative content, are of the same order, though at the other extreme, so far as immediate overt expression is concerned. we are working along lines of habitual activity so familiar that we can work almost in the dark. we need no elaborate imagery. guided only by the waving of a signal flag or by the shifting gleam of a semaphore, we thread our way swiftly through the maze of tracks worn smooth by use and habit. but suppose a new line of habit is to be constructed. no signal flags or semaphores will suffice. a detailed survey of the proposed route must be had, and here is where imagery with a rich and varied yet flexible sensuous content, growing out of previous surveys, may function in projecting and anticipating the new set of conditions, and thus become the stimulus of a new line of habit, of a new and more far-reaching meaning. as this new line of habit, of meaning, gets into working order with the rest of the system, imagery tends normally to decline again to the rôle of signal flags and semaphores. the distinction in logical theory between "image" and "idea" which we have been considering is only a half-truth from the point of view of psychology. it virtually limits the "idea" to a fixed, unalterable reference of a fragment of a desiccated image to a reality beyond. it indifferently loses the play and richness of imagery to the floating remnants of sense-content, or to an external reality. it limits itself to an examination of a final stage in thinking, a stage in which the image acts as a direct stimulus, a stage in which the sense-content of the image has little or no function _per se_, because this content now initiates directly a habitual adjustment, a worked-out and established adaptation of means to end. it overlooks the process of conscious reflection which logically precedes every such adjustment not purely instinctive or accidental, a process in which imagery as representational functions indirectly in bringing the resources of past experience, the fund of acquired habits, to bear upon the fragmentary and problematic elements of sense-experience actually present, thus maintaining the flow and continuity of experience. it fails to recognize that in the inseparable association of meaning with quality, of "idea" with "image," there goes the possibility of working out and applying new meanings from old, of developing deeper meanings, of testing and affirming more inclusive and universal meaning. we are confronted with this alternative. either the image has a logical function in virtue of its sense-content, or else the image functions logically merely as a symbol, the sense-content of which is a matter of complete logical indifference. according to the empiricist, the former is the case, according to the conceptualist, the latter. the empiricist would say that he needs the image to piece out the data upon which logical processes operate. having met this need, the image is retired from active service. for the empiricist the processes of thought, observing, comparing, generalizing, etc., are as independent of the data they use as, for the conceptualist, logical meaning, reference, and "idea" are independent of the sense-content of the "image." in reality he agrees with the conceptualist in excluding the sense-content of the image from the processes of thought, and hence from the domain of logic. from the standpoint of psychological theory the conceptualist is an improvement over the empiricist. he has gone a step farther in the analysis of thought-processes by showing that they are bound up with some kind of imagery, however irrelevant, inconsequential, and worn down the sense-quality of that imagery may be. his statement of ideas as references to reality lends itself readily, as we have seen, to the unitary conception in psychology of ideo-motor, or sensori-motor, activity. but is this where logical theory is to stop, while psychology as a study of "states of consciousness" takes up the unfinished tale and carries it forward? it seems hardly possible, unless logic is willing to give over its task of thinking about thinking. reduce the image to a mere symbol. let its sense-quality be a matter of complete indifference. what have you, then, but an elementary and primitive type of reflex action? it is of no particular consequence even from what sense-organ it appears to proceed, or whether it appears to be peripherally or centrally excited. it is simply a case of feel and act; touch and go. is this thinking? it may be regarded as either the germ or the finality of thinking, but what most of us are inclined to believe is the true subject-matter of logic is not to be limited to a simple reflex, or even to a chain of reflexes. it is something more complex, even if nothing more than an intricate tangle of chains of reflexes. the complexity of the process called thinking does not reside alone in the instinctive or habitual reflexes involved. the more instinctive and habitual any adjustment may be, the less is it a matter of thought, as everyone knows, although its biological complexity is none the less patent to one who looks at it from the outside. the complexity of the thinking process resides in consciousness also; it resides in the imagery, the stimuli, the mere symbols, if you like, that have "come" to consciousness. as soon as the complexity begins to be _felt_, as soon as any discrimination whatsoever begins to be introduced or appreciated, at that instant the sense-content, the quale, of imagery begins to have a logical function. conscious discrimination, however vague and evanescent, and the logical function of the quale of imagery are born together, unless one chooses to regard the more obvious and deliberate forms of conscious discrimination as more characteristic of a logical process. it is only as the sense-contents of various images are discriminated and compared that anything like thinking can be conceived to go on. the particular sense-content of an image, instead of being a matter of logical indifference, is the condition, the possibility, of thinking. the conceptualist has contributed to the data of descriptive psychology by calling attention, by implication at least, to the remote and reduced character of the imagery which may characterize thinking. but it by no means follows that the more remote and reduced the sense-content of an image becomes, the less important is that sense-content for thinking, the less demand for discrimination. on the contrary, the sense-content that remains may be of supreme logical importance. it may be the quintessence of meaning. it may be the conscious factor which, when discriminated from another almost equally sublimated conscious factor, may determine a whole course of action. the delicacy and rapidity with which these reduced forms of imagery as they hover about the margin of consciousness or flit across its focus are discriminated and caught, are points in the technique of that long art of thinking, begun in early childhood. the fact that questionnaire investigations--like that of galton's, for example--have in many instances failed to discover in the minds of scientists and advanced thinkers a rich and varied furniture of imagery does not argue the poverty of imagery in such minds; it argues, rather, a highly developed technique, a species of virtuosity, with reference to the sense-content of the types of imagery actually in use. to push a step farther the alternative we have already stated in a preliminary way: either the "idea," or "logical meaning," lies outside of the process of thinking, as a mere impulse or reflex; or else, in virtue of the sense-content of its "image," it enters into that conscious process of discrimination, comparison, and selection, of light and shade, of doubt and inquiry, which constitutes the evolution of a judgment, which makes the life-history of a movement of thought. ix the logic of the pre-socratic philosophy[ ] it is not the purpose of this study to show that the pre-socratics possessed a system of logic which is now for the first time brought to the notice of the modern world. indeed, there is nothing to indicate that they had reflected on mental processes in such a way as to call for an organized body of canons regulating the forms of concepts and conclusions. aristotle attributed the discovery of the art of dialectic to zeno the eleatic, and we shall see in the sequel that there was much to justify the opinion. but logic, in the technical sense, is inconceivable without concepts, and from the days of aristotle it has been universally believed that proper definitions owe their origin to socrates. a few crude attempts at definition, if such they may be rightly called, are referred to empedocles and democritus. but in so far as they were conceived in the spirit of science, they essayed to define things materially by giving, so to speak, the chemical formula for their production. significant as this very fact is, it shows that even the rudiments of the canons of thought were not the subjects of reflection. in his _organon_ aristotle makes it evident that the demand for a regulative art of scientific discourse was created by the eristic logic-chopping of those who were most deeply influenced by the eleatic philosophy. indeed, the case is quite parallel to the rise of the art of rhetoric. aristotle regarded empedocles as the originator of that art, as he referred the beginnings of dialectic to zeno. but the formulation of both arts in well-rounded systems came much later. as men conducted lawsuits before the days of tisias and corax, so also were the essential principles of logic operative and effective in practice before aristotle gave them their abstract formulation. while it is true, therefore, that the pre-socratics had no formal logic, it is equally true, and far more significant, that they either received from their predecessors or themselves developed the conceptions and the presuppositions on which the aristotelian logic is founded. one of the objects of this study is to institute a search for some of these basic conceptions of greek thought, almost all of which existed before the days of socrates, and to consider their origin as well as their logical significance. the other aim here kept in view is to trace the course of thought in which the logical principles, latent in all attempts to construct and verify theories, came into play. it is impossible, no doubt, to discover a body of thought which does not ground itself upon presuppositions. they are the warp into which the woof of the system, itself too often consisting of frayed ends of other fabrics, is woven with the delight of a supposed creator. rarely is the thinker so conscious of his own mental processes that he is aware of what he takes for granted. ordinarily this retirement to an interior line takes place only when one has been driven back from the advanced position which could no longer be maintained. emerson has somewhere said: "the foregoing generations beheld god and nature face to face; we through their eyes. why should not we also enjoy an original relation to the universe? why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us and not the history of theirs?" the difficulty lies precisely in our faith in immediate insight and revelation, which are themselves only short-cuts of induction, psychological short circuits, conducted by media we have disregarded. only a fundamentally critical philosophy pushes its doubt to the limit of demanding the credentials of those conceptions which have come to be regarded as axiomatic. the need of going back of aristotle in our quest for the truth is well shown by his attitude toward the first principles of the several sciences. to him they are immediately given--[greek: amesoi protaseis]--and hence are ultimate _a priori_. the historical significance of this fact is already apparent. it means that in his day these first principles, which sum up the outcome of previous inductive movements of thought, were regarded as so conclusively established that the steps by which they had been inferred were allowed to lapse from memory. no account of the history of thought can hope to satisfy the demands of reason that does not _explain_ the origin of the convictions thus embodied in principles. the only acceptable explanation would be in terms of will and interest. to give such an account would, however, require the knowledge of secular pursuits and ambitions no longer obtainable. it might be fruitful of results if we could discover even the theoretical interests of the age before thales; but we know that in modern times the direction of interest characteristic of the purely practical pursuits manifests its reformative influences in speculation a century or more after it has begun to shape the course of common life. hence we might misinterpret the historical data if they were obtainable. but general considerations, which we need not now rehearse, as well as indications contained in the later history of thought, hereinafter sketched, point to the primacy of the practical as yielding the direction of interest that determines the course it shall take. it was said above that the principles of science are the result of an inductive movement, and that the inductive movement is directed by an interest. hence the principles are contained in, or rather are the express definition of, the interest that gave them birth. in other words, there is implied in all induction a process of deduction. every stream of thought embraces not only the main current, but also an eddy, which here and there re-enters it. and this is one way of explaining the phenomenon which has long engaged the thought of philosophers, namely, the fact of successful anticipations of the discoveries of science or, more generally still, the possibility of synthetic judgments _a priori_. the solution of the problem is ultimately contained in its statement.[ ] to arrive at a stage of mentality not based on assumptions one would have, no doubt, to go back to its beginnings. greek thought, even in the time of thales, was well furnished with them. we cannot pause to catalogue them, but it may further our project if we consider a few of the more important. the precondition of thought as of life is that nature be uniform, or ultimately that the world be rational. this is not even, as it becomes later, a conscious demand; it is the primary ethical postulate which expresses itself in the confidence that it is so. viewed from a certain angle it may be called the principle of sufficient reason. closely associated with it is the universal belief of the early philosophers of greece that everything that comes into being is bound up inseparably with that which has been before; more precisely, that there is no absolute, but only relative, becoming. corollaries of this axiom soon appeared in the postulates of the conservation of matter or mass, and the conservation of energy, or more properly for the ancients, of motion. logically these principles appear to signify that the subject, while under definition, shall remain just what it is; and that, in the system constituted of subject, predicate, and copula, the terms shall "stay put" while the adjustment of verification is in progress. it is a matter of course that the constants in the great problem should become permanent landmarks. other corollaries derive from this same principle of uniformity. seeing that all that comes to be in some sense already is, there appears the postulate of the unity of the world; and this unity manifests itself not only in the integrity and homogeneity of the world-ground, but also in the more ideal conception of a universal law to which all special modes of procedure in nature are ancillary. in these we recognize the insistent demand for the organization of predicate and copula. side by side with these formulæ stands the other, which requires an ordered process of becoming and a graduated scale of existences, such as can mediate between the extremes of polarity. such series meet us on every hand in early greek thought. the process of rarefaction and condensation in anaximenes, the [greek: hodos anô katô] of heraclitus, the regular succession of the four empedoclean elements in almost all later systems--these and other examples spontaneously occur to the mind. the significance of this conception, as the representative of an effective copula, will presently be seen. more subtle, perhaps, than any of these principles, though not allowed to go so long unchallenged, is the assumption of a [greek: physis], that is, the assumption that all nature is instinct with life. the logical interpretation of this postulate would seem to be that the concrete system of things--subject, predicate, copula--constitutes a totality complete in itself and needing no jog from without. in this survey of the preconceptions of the early greek philosophers i have employed the terms of the judgment without apology. the justification for this course must come ultimately, as for any assumption, from the success of its application to the facts. but if "logic" merely formulates in a schematic way that which in life is the manipulation of concrete experience, with a view to attaining practical ends, then its forms must apply here as well as anywhere. logical terminology may therefore be assumed to be welcome to this field where judgments are formed, induction is made from certain facts to defined conceptions, and deductions are derived from principles or premises assumed. speaking then in these terms we may say that the pre-socratics had three logical problems set for them: first, there was a demand for a predicate, or, in other words, for a theory of the world. secondly, there was the need of ascertaining just what should be regarded as the subject, or, otherwise stated, just what it was that required explanation. thirdly, there arose the necessity of discovering ways and means by which the theory could be predicated of the world and by which, in turn, the hypothesis erected could be made to account for the concrete experience of life: in terms of logic this problem is that of maintaining an efficient copula. it is not assumed that the sequence thus stated was historically observed without crossing and overlapping; but a survey of the history of the period will show that, in a general way, the logical requirements asserted themselves in this order. . greek philosophy began its career with induction. we have already stated that the preconceptions with which it approached its task were the result of previous inductions, and indeed the epic and theogonic poetry of the greeks abounds in thoughts indicative of the consciousness of all of these problems. thus homer is familiar with the notion that all things proceed from water,[ ] and that, when the human body decays, it resolves itself into earth and water.[ ] other opinions might be enumerated, but they would add nothing to the purpose. when men began, in the spirit of philosophy, to theorize about the world, they assumed that it--the subject--was sufficiently known. its existence was taken for granted, and that which engaged their attention was the problem of its meaning. what predicate--so we may formulate their question--should be given to the subject? it is noticeable that their induction was quite perfunctory. but such is always the case until there are rival theories competing for acceptance, and even then the impulse to gather up evidence derived from a wide field and assured by resort to experiment comes rather with the desire to test a hypothesis than to form it. it is the effort to _verify_ that brings out details and also the negative instances. hence we are not to blame thales for rashness in making his generalization that all is water. we do not know what indications led to this conclusion. aristotle ventured a guess, but the motives assumed for thales agree too well with those which weighed with hippo to admit of ready acceptance. anaximander, feeling the need of deduction as a sequel to induction, found his predicate in the infinite. we cannot now delay to inquire just what he meant by the term; but it is not unlikely that its very vagueness recommended it to a man of genius who caught enthusiastically at the skirts of knowledge. anaximenes, having pushed verification somewhat farther and eliciting some negative instances, rejected water and the infinite and inferred that all was air. his [greek: archê] must have the quality of infinity, but, a copula having been found in the process of rarefaction and condensation, it must occupy a determinate place in the series of typical forms of existence. the logical significance of this thought will engage our attention later. meanwhile it may be well to note that thus far only _one_ predicate has been offered by each philosopher. this is doubtless due to the preconception of the unity and homogeneity of the world, of which we have already made mention. although at the beginning its significance was little realized, the conception was destined to play a prominent part in greek thought. it may be regarded from different points of view not necessarily antagonistic. one may say, as indeed has oftentimes been said, that it was due to ignorance. men did not know the complexity of the world, and hence declared its substance to be simple. again, it may be affirmed that the assumption was merely the naïve reflex of the ethical postulate that we shall unify our experience and organize it for the realization of our ideals. while increased knowledge has multiplied the so-called chemical elements, physics knows nothing of their differences, and chemistry itself demands their reduction. the extension and enlarged scope of homogeneity came in two ways: first, it presented itself by way of abstraction from the particular predicates that may be given to things. this was due to the operation of the fundamental assumption that the world must be intelligible. thus, even in anaximander, the world-ground takes no account of the diversity of things except in the negative way of providing that the contrariety of experience shall arise from it. we are therefore referred for our predicate to a somewhat behind concrete experience. the pythagoreans fix upon a single aspect of things as the essential, and find the meaning of the world in mathematical relations. the eleatics press the conception of homogeneity until it is reduced to identity. identity means the absence of difference; hence, spatially considered, it requires the negation of a void and the indivisibility of the world; viewed temporally, it precludes the succession of different states and hence the possibility of change. we thus reach the acute stage of the problem of the one and the many. the one is here the predicate, the subject is the many. the solution of the difficulty is the task of the copula, and we shall recur to the theme in due time. it may be well, however, at this point to draw attention to the fact that the one is not always identical with the predicate, nor the many with the subject. in the rhythmic movement of erecting and verifying hypotheses the interest shifts and what was but now the predicate, by taking the place of the premises, comes to be regarded as the given from which the particular is to be derived or deduced. there is thus likewise a shift in the positions of existence and meaning. the subject, or the world, was first assumed as the given means with which to construct the predicate, its meaning; once the hypothesis has been erected, the direction of interest shifts back to the beginning, and in the process of verification or deduction the quondam predicate, now the premises, becomes the given, and the task set for thought is the derivation of fact. for the moment, or until the return to the world is accomplished, the one is the only real, the manifold remains mere appearance. the second form in which the sense of the homogeneity of the world embodies itself is not, like the first, static, but is altogether dynamic. that which makes the whole world kin is neither the presence nor the absence of a quality, but a principle. the law thus revealed is, therefore, not a matter of the predicate, but is the copula itself. hence we must defer a fuller consideration of it for the present. . as has already been said, the inductive movement implies the deductive, and not only as something preceding or accompanying it, but as its inner meaning and ultimate purpose. so too it was with the earliest greek thinkers. their object in setting up a predicate was the derivation of the subject from it. in other words their ambition was to discover the [greek: archê] from which the genesis of the world proceeds. but deduction is really a much more serious task than would at first appear to one who is familiar with the aristotelian machinery of premises and middle terms. the business of deduction is to reveal the subject, and ordinarily the subject quite vanishes from view. induction is rapid, but deduction lags far behind. it may require but a momentary flash of "insight" on the part of the physical philosopher to discover a principle; if it is really significant, inventors will be engaged for centuries in deducing from it applications to the needs of life by means of contrivances. thus after ages we come to know more of the subject, which is thereby enriched. the contrivances are the representatives of the copula in practical affairs; in quasi-theoretical spheres they are the apparatus for experimentation. it has just been remarked that by the application of the principles to life it is enriched; in other words, it receives new meaning, and new meaning signifies a new predicate. theory is at times painfully aware of the multitude of new predicates proposed; rarely does it realize that there has been created a new heaven and a new earth. without the latter, the former would be absurd. men take very much for granted and regard almost every achievement as a matter of course. hence they do not become aware of their changed position except as it reflects itself in new schemes and in a larger outlook. the subject receives only a summary glance to discover what new predicate shall be evolved. hence, while there is in greek philosophy a strongly marked deductive movement, the theoretical results to the subject are insignificant. thales seems, indeed, to have had no means to offer for the derivation of the world, but he evidently had no doubt that it was possible. with him and with others the assumption, however vaguely understood, seems to have been that the subject, like the predicate, was simple. thus the essential unity of the world, considered as existence no less than as meaning, is a foregone conclusion. the sense of a division in the subject seems to arise with empedocles when, reaping the harvest of the eleatic definition of substance, he parted the world, as subject and as predicate, into four elements. we may, perhaps, pause a moment to consider the significance of the assumption of four elements which plays so large a part in subsequent philosophies. there is no need of enlarging on the importance of the association of multiple elements with the postulate that nothing is absolutely created and nothing absolutely passes away. these are indeed the pillars that support chemical science, and they further imply the existence of qualities of different rank; but that implication, as we shall see, lay even in the process of rarefaction and condensation introduced by anaximenes. the four elements concern us here chiefly as testifying to the fact that certain practical interests had summed up the essential characteristics of nature in forms sufficiently significant to have maintained themselves even to our day. in regard to fire, air, and water this is not greatly to be wondered at; it is a somewhat different case with earth. if metallurgy and other pursuits which deal with that which is roughly classed as earth had been highly enough developed to have reacted upon the popular mind, this element could not possibly have been assumed to be so homogeneous. the conception clearly reflects the predominantly agricultural interest of the greeks in their relation to the earth. this further illustrates the slow progress which deduction makes in the reconstitution of the subject. it is different, however, with anaxagoras and the atomists. apparently the movement begun by empedocles soon ran its extreme course. instead of four elements there is now an infinite number of substances, each differentiated from the other. the meaning of this wide swing of the pendulum is not altogether clear; but it is evident from the system of anaxagoras that the metals, for example, possessed a significance which they can not have had for empedocles. the opposite swing of the pendulum is seen in the later course of the eleatics. given a predicate as fixed and unified as they assumed, the subject cannot possibly be conceived in terms of it and hence it is denied outright. in the dialectic of zeno and melissus, dealing with the problems of the one and the many, there is much that suggests the solution offered by the atomists; but it is probably impossible now to ascertain whether these passages criticise a doctrine already propounded or pointed the way for successors. while the eleatics asserted the sole reality of the one, anaxagoras and the atomists postulated a multiplicity without essential unity. but the human mind seems to be incapable of resting in that decision; it demands that the world shall have not meanings, but a meaning. this demand calls not only for a unified predicate, but also for an effective copula. . we have already remarked that the steps by which the predicate was inferred are for the most part unknown. certain suggestions are contained in the reports of aristotle, but it is safe to say that they are generally guesses well or ill founded. the summary inductive mediation has left few traces; and the process of verification, in the course of which hypotheses were rejected and modified, can be followed only here and there in the records. almost our only source of information is the dialectic of systems. fortunately for our present purpose we do not need to know the precise form which a question assumed to the minds of the several philosophers; the efforts which they made to meet the imperious demands of logic here speak for themselves. at first there was no scheme for the mediation of the predicate back to the subject. indeed there seems not to have existed in the mind of thales a sense of its need. anaximander raised the question, but the process of segregation or separation ([greek: ekkrinesthai]) which he propounded was so vaguely conceived that it has created more problems than it solved. anaximenes first proposed a scheme that has borne fruits. he said that things are produced from air by rarefaction and condensation. this process offers not only a principle of difference, but also a regulative conception, the evaluation of which engaged the thought of almost all the later pre-socratics. it implies that extension and mass constitute the essential characters of substance, and, fully apprehended, contains in germ the whole materialistic philosophy from parmenides at one extreme to democritus and anaxagoras at the other. the difficulties inherent in the view were unknown to anaximenes; for, having a unitary predicate, he assumed also a homogeneous subject. the logical position of heraclitus is similar to that of anaximenes. he likewise posits a simple predicate and further signalizes its functional character by naming it fire. without venturing upon debatable ground we may say that it was the restless activity of the element that caused him to single it out as best expressing the meaning of things. its rhythmic libration typified to him the principle of change in existence and of existence in change. it is the "ever-living" copula, devouring subject and predicate alike and re-creating them functionally as co-ordinate expressions of itself. that which alone _is_, the abiding, is not the physical composition of a thing, but the law of reciprocity by which it maintains a balance. this he calls variously by the names of harmony, logos, necessity, justice. in this system of functional co-ordinates nothing escapes the accounting on 'change;[ ] all things are in continuous flux, only the nodes of the rhythm remaining constant. it is not surprising therefore that heraclitus has been the subject of so much speculation and comment in modern times; for the functional character of all distinctions in his system marks the affinity of his doctrines for those of modern psychology and logic.[ ] the pythagoreans, having by abstraction obtained a predicate, acknowledged the existence of the subject, but did not feel the need of a copula in the theoretical sphere, except as it concerned the inner relation of the predicate. to them the world was number, but number itself was pluralistic, or let us rather say dualistic. the odd and the even, the generic constituents of number, had somehow to be brought together. the bond was found in unity, or, again, in harmony. when they inquired how numbers constituted the world, their answer was in general only a nugatory exercise of an unbridled fancy.[ ] such and such a number was justice, such another, man. it was only in the wholly practical sphere of experiment that they reached a conclusion worth recording. its significance they themselves did not perceive. here, by the application of mathematical measurements to sounds, they discovered how to produce tones of a given pitch, and thus successfully demonstrated the efficiency of their copula. the eleatics followed the same general course of abstraction; but with them the sense of the unity of the world effaced its rich diversity. xenophanes does not appear to have pressed the conception so far as to deny all change within the world. parmenides, however, bated no jot of the legitimate consequences of his logical position, interpreting, as he did, the predicate, originally conceived as meaning, in terms of existence. that which is simply _is_. thus there is left only a one-time predicate, now converted into a subject of which only itself, as a brute fact, can be predicated. stated logically, parmenides is capable only of uttering identical propositions: a=a. the fallacious character of the report of the senses and the impossibility of becoming followed as a matter of course. where the logical copula is a mere sign of equation there can be neither induction nor deduction. we are caught in a theoretical _cul-de-sac_. we are not now concerned to know in what light the demand for a treatise on the world of opinion may have appeared to parmenides himself. the avenues by which men reach conclusions which are capable of simplification and syllogistic statement are too various to admit of plausible conjecture in the absence of specific evidence. but it is clear that his resort to the expedient reflected a consciousness of the state of deadlock. in that part of his philosophical poem he dealt with many questions of detail in a rather more practical spirit. following the lead of heraclitus and the pythagoreans he was more successful here than in the field of metaphysics. thus we see once more that the wounds of theory are healed by practice. but, as usual, even though the metaphysician does receive the answer to his doubts by falling into a severely practical pit and extricating himself by steps which he fashions with his hands, his mental habit is not thereby reconstructed. the fixed predicate of the eleatics was bequeathed to the platonic-aristotelian formal logic, and induction and deduction remained for centuries in theory a race between the hedgehog and the hare.[ ] the true significance of the destructive criticism brought to bear by zeno and melissus on the concepts of unity, plurality, continuity, extension, time, and motion is simply this: that when by a shift of the attention a predicate becomes subject or meaning fossilizes as existence, the terms of the logical process lose their functional reference and grow to be unmeaning and self-contradictory. we have already remarked that empedocles, anaxagoras, and the atomists sought to solve the problem of the one and the many, of the subject and the predicate, by shattering the unitary predicate and thus leaving the field to plurality in both spheres. but obviously they were merely postponing the real question. thought, as well as action, demands a unity somewhere. hence the absorbing task of these philosophers is to disclose or contrive such a bond of unity. the form which their quest assumed was the search for a basis for physical interaction.[ ] empedocles clearly believed that he was solving the difficulty in one form when he instituted the rhythmic libration between unity under the sway of love and multiplicity under the domination of hate. but even he was not satisfied with that. while love brought all the elements together into a sphere and thus produced a unity, it was a unity constituted of a mixture of elements possessing inalienable characters not only different but actually antagonistic. on the other hand, hate did indeed separate the confused particles, but it effected a sort of unity in that, by segregating the particles of the several elements from the others, it brought like and like together. in so far aristotle was clearly right in attributing to love the power to separate as well as to unite. moreover, it would seem that there never was a moment in which both agencies were not conceived to be operative, to however small an extent. empedocles asserted, however, that a world could arise only in the intervals between the extremes of victory in the contest between love and hate, when, so to speak, the battle was drawn and there was a general _mêlée_ of the combatants. it may be questioned, perhaps, whether he distinctly stated that in our world everything possessed its portion of each of the elements; but so indispensable did he consider this _mixture_ that its function of providing a physical unity is unmistakable. a further evidence of his insistent demand for unity--the copula--is found in his doctrine that only like can act on like; and the scheme of pores and effluvia which he contrived bears eloquent testimony to the earnest consideration he gave to this matter. for he conceived that all interaction took place by means of them. empedocles, then, may be said to have annulled the decree of divorce he had issued for the elements at the beginning. but the solution here too is found, not in the theoretical, but in the practical, sphere; for he never retracts his assertion that the elements are distinct and antagonistic. but even so his problem is defined rather than solved; for after the elements have been brought within microscopic distance of each other in the mixture, since like can act only on like, the narrow space that separates them is still an impassable gulf.[ ] anaxagoras endowed his infinitely numerous substances with the same characters of fixity and contrariety that mark the four elements of empedocles. for him, therefore, the difficulty of securing unity and co-operation in an effective copula is, if that be possible, further aggravated. his grasp of the problem, if we may judge from the relatively small body of documentary evidence, was not so sure as that of empedocles, though he employed in general the same means for its solution. he too postulates a mixture of all substances, more consciously and definitely indeed than his predecessor. believing that only like can act on like,[ ] he is led to assume not only an infinite multiplicity of substances, but also their complete mixture, so that everything, however small, contains a portion of every other. food, for example, however seeming-simple, nourishes the most diverse tissues of the body. thus we discover in the universal mixture of substances the basis for co-operation and interaction. anaxagoras, therefore, like empedocles, feels the need of bridging the chasm which he has assumed to exist between his distinct substances. their failure is alike great, and is due to the presuppositions they inherited from the eleatic conception of a severe homogeneity which implies an absolute difference from everything else. the embarrassment of anaxagoras increases with the introduction of the [greek: nous]. this agency was conceived with a view to explaining the formation of the world; that is, with a view to mediating between the myriad substances in their essential aloofness and effecting the harmonious concord of concrete things. while, even on the basis of a universal mixture, the function of the [greek: nous] was foredoomed to failure, its task was made more difficult still by the definition given to its nature. according to anaxagoras it was the sole exception to the composite character of things; it is absolutely pure and simple in nature.[ ] by its definition, then, it is prevented from accomplishing the work it was contrived to do; and hence we cannot be surprised at the lamentations raised by plato and aristotle about the failure of anaxagoras to employ the agency he had introduced. to be sure, the [greek: nous] is no more a _deus ex machina_ than were the ideas of plato or the god of aristotle. they all labored under the same restrictions. the atomists followed with the same recognition of the many, in the infinitely various kinds of atoms; but it was tempered by the assumption of an essential homogeneity. one atom is distinguished from another by characteristics due to its spatial relations. mass and weight are proportional to size. aristotle reports that, though things and atoms have differences, it is not in virtue of their differences, but in virtue of their essential identity, that they interact.[ ] there is thus introduced a distinction which runs nearly, but not quite, parallel to that between primary and secondary qualities.[ ] primary qualities are those of size, shape, and perhaps[ ] position; all others are secondary. on the other hand, that which is common to all atoms is their corporeity, which does indeed define itself with reference to the primary (spatial) qualities, but not alike in all. the atoms of which the world is constituted are alike in essential nature, but they differ most widely in position. it is the void that breaks up the unity of the world--atomizes it, if we may use the expression. it is the basis of all discontinuity. atoms and void are thus polar extremes reciprocally exclusive. the atoms in their utter isolation in space are incapable of producing a world. in order to bridge the chasm between atom and atom, recourse is had to motion eternal, omnipresent, and necessary. this it is that annihilates distances. in the course of their motion atoms collide, and in their impact one upon the other the atomists find the precise mode of co-operation by which the world is formed.[ ] to this agency are due what lucretius happily called "generating motions." the problem, however, so insistently pursued the philosophers of this time that the atomists did not content themselves with this solution, satisfactory as modern science has pretended to consider it. they followed the lead of empedocles and anaxagoras in postulating a widespread, if not absolutely universal, _mixture_. having on principle excluded "essential" differences among the atoms, the impossibility of finally distinguishing essential and non-essential had its revenge. important as the device of mixture was to empedocles and anaxagoras, just so unmeaning ought it to have been in the atomic philosophy, provided that the hypothesis could accomplish what was claimed for it. it is not necessary to reassert that the assumption of "individua," utterly alienated one from the other by a void, rendered the problem of the copula insoluble for the atomists. diogenes of apollonia is commonly treated contemptuously as a mere reactionary who harked back to anaximenes and had no significance of his own. the best that can be said of such an attitude is that it regards philosophical theories as accidental utterances of individuals, naturally well or ill endowed, who happen to express conclusions with which men in after times agree or disagree. a philosophical tenet is an atom, set somewhere in a vacuum, utterly out of relation to everything else. but it is impossible to see how, on this theory, any system of thought should possess any significance for anybody, or how there should be any progress even, or retardation. viewed entirely from without, the doctrine of diogenes would seem to be substantially a recrudescence of that of anaximenes. air is once more the element or [greek: archê] out of which all proceeds and into which all returns. again the process of transformation is seen in rarefaction and condensation; and the attributes of substance are those which were common to the early hylozoists. but there is present a keen sense of a problem unknown to anaximenes. what the early philosopher asserted in the innocence of the youth of thought, the later physiologist reiterates with emphasis because he believes that the words are words of life. the motive for recurring to the earlier system is supplied by the imperious demand for a copula which had so much distressed empedocles, anaxagoras, and the atomists. and here we are not left to conjecture, but are able to refer to the _ipsissima verba_ of our philosopher. after a brief prologue, in which he stated that one's starting-point must be beyond dispute, he immediately[ ] turned to his theme in these words:[ ] "in my opinion, to put the whole matter in a nutshell, all things are derived by alteration from the same substance, and indeed all are one and the same. and this is altogether evident. for if the things that now exist in the world--earth and water and air and fire and whatsoever else appears to exist in this world--if, i say, any one of these were different from the other, different that is to say in its proper peculiar nature, and did not rather, being one and the same, change and alter in many ways, then in no-wise would things be able to mix with one another, nor would help or harm come to one from the other, nor would any plant spring from the earth, nor any other living thing come into being, if things were not so constituted as to be one and the same." these words contain a singularly interesting expression of the need of restoring the integrity of the process which had been lost in the effort to solve the problem of the one and the many without abandoning the point of view won by the eleatics. aristotle and theophrastus paraphrase and sum up the passage above quoted by saying[ ] that interaction is impossible except on the assumption that all the world is one and the same. hence it is manifest, as was said above, that the return of diogenes to the monistic system of anaximenes had for its conscious motive the avoidance of the dualism that had sprung up in the interval and had rendered futile the multiplied efforts to secure an effective copula. we should note, however, that in the attempt thus made to undo the work of several generations diogenes retained the principle which had wrought the mischief. we have before remarked that the germ of the atomic philosophy was contained in the process of rarefaction and condensation. hence, in accepting it along with the remainder of anaximenes's theory, the fatal assumption was reinstated. it is the story of human systems in epitome. the superstructure is overthrown, and with the débris a new edifice is built upon the old foundations. in the entire course of philosophical thought from thales onward the suggestion of an opposition between the subject and the predicate had appeared. it has often been said that it was expressed by the search for a [greek: physis], or a _true nature_, in contrast with the world as practically accepted. there is a certain truth in this view; for the effort to attain a predicate which does not merely repeat the subject does imply that there is an opposition. but the efforts made to return from the predicate to the subject, in a deductive movement, shows that the difference was not believed to be absolute. this is true, however, only of those fields of speculation that lie next to the highways of practical life, which lead equally in both directions, or, let us rather say, which unite while they mark separation. in the sphere of abstract ideas the sense of embarrassment was deep and constantly growing deeper. the reconstruction, accomplished on lower levels, did not attain unto those heights. men doubted conclusions, but did not think to demand the credentials of their common presuppositions. side by side with the later philosophers whom we have mentioned there walked men whom we are wont to call the sophists. they were the journalists and pamphleteers of those days, men who, without dealing profoundly with any special problem, familiarized themselves with the generalizations of workers in special fields and combined these ideas for the entertainment of the public. they were neither philosophers nor physicists, but, like some men whom we might cite from our own times, endeavored to popularize the teachings of both. naturally they seized upon the most sweeping generalizations and the preconceptions which disclosed themselves in manifold forms. just as naturally they had no eyes with which to detect the significance of the besetting problems at which, in matters more concrete, the masters were toiling. hence the contradictions, revealed in the analysis we have just given of the philosophy of the age, stood out in utter nakedness. the result was inevitable. the inability to discover a unitary predicate, more still, the failure to attain a working copula, led directly to the denial of the possibility of predication. there was no truth. granted that it existed, it could not be known. even if known, it could not be communicated. in these incisive words of gorgias the conclusion of the ineffectual effort to establish a logic of science is clearly stated. but the statement is happily only the half-truth, which is almost a complete falsehood. it takes no account of the indications, everywhere present, of a needed reconstruction. least of all does it catch the meaning of such a demand. the sophists did not, however, merely repeat in abstract from the teachings of the philosophers. it matters not whether they originated the movement or not; at all events they were pioneers in the field of moral philosophy. here it was that they chiefly drew the inferences from the distinction between [greek: physei] and [greek: nomô]. nothing could have been more effective in disengaging the firmly rooted moral pre-possessions and rendering them amenable to philosophy. just here, at last, we catch a hint of the significance of the logical process. in a striking passage in plato's _protagoras_,[ ] which one is fain to regard as an essentially true reproduction of a discourse by that great man, justice and reverence are accorded true validity. on inquiring to what characteristic this honorable distinction is due, we find that it does not reside in themselves; it is due to _the assumption that a state must exist_. here, then, in a word, is the upshot of the logical movement. logical predicates are essentially hypothetical, deriving their validity from the interest that moves men to affirm them. when they lose this hypothetical character, as terms within a volitional system, and set up as entities at large, they cease to function and forfeit their right to exist. x valuation as a logical process the purpose of this discussion is to supply the main outlines of a theory of value based upon analysis of the valuation-process from the logical point of view. the general principle which we shall seek to establish is that judgments of value, whether passed upon things or upon modes of conduct, are essentially objective in import, and that they are reached through a process of valuation which is essentially of the same logical character as the judgment-process whereby conclusions of physical fact are established--in a word, that the valuation-process, issuing in the finished judgment of value expressive of the judging person's definitive attitude toward the thing in question, is constructive of an order of reality in the same sense as, in current theories of knowledge, is the judgment of sense-perception and science. our method of procedure to this end will be that of assuming, and adhering to as consistently as possible, the standpoint of the individual in the process of deliberating upon an ethical or economic problem (for, as we shall hold, all values properly so called are either ethical or economic), and of ascertaining, as accurately as may be, the meaning of the deliberative or evaluating process and of the various factors in it as these are presented in the individual's apprehension. it is in this sense that our procedure will be logical rather than psychological. we shall be concerned to determine the _meaning_ of the object of valuation as object, of the standard of value as standard, and of the valued object as valued, in terms of the individual's own apprehension of these, rather than to ascertain the nature and conditions of his apprehensions of these considered as psychical events. our attention will throughout be directed to these factors or phases of the valuation-process in their functional aspect of determinants of the valuing agent's practical attitude, and never, excepting for purposes of incidental illustration and in a very general and tentative way, as events in consciousness mediated by more "elementary" psychical processes. the results which we shall gain by adhering to this method will enable us to see not merely that our judgments of value are in function and meaning objective, but also that our judgments of sense-perception and science are, as such, capable of satisfactory interpretation only as being incidental to the attainment and progressive reconstruction of judgments of value. the first three main divisions will be given over to establishing the objectivity of content and function of judgments of value. the fourth division will present a detailed analysis of the two types of judgment of value, the ethical and economic, defining them and relating them to each other, and correlating them in the manner just suggested with judgment of the physical type. after considering, in the fifth part, certain general objections to the positions thus stated, we shall proceed in the sixth and concluding division to define the function of the consciousness of value in the economy of life.[ ] i the system of judgments which defines what one calls the objective order of things is inevitably unique for each particular individual. no two men can view the world from the standpoint of the same theoretical and practical interests, nor can any two proceed in the work of gaining for themselves knowledge of the world with precisely equal degrees of skill and accuracy. each must be prompted and guided, in the construction of his knowledge of single things and of the system in which they have their being, by his own particular interests and aims; and even when one person in a measure shares in the interests and aims of another, the rate and manner of procedure will not be the same for both, nor will the knowledge gained be for both equally systematic in arrangement or in interrelation of its parts. each man lives in a world of his own--a world, indeed, identical in certain fundamental respects with the worlds which his fellow-men have constructed for themselves, but one nevertheless necessarily unique through and through because each man is a unique individual. there is, doubtless, a "social currency" of objects which implies a certain identity of meaning in objects as experienced by different individuals. the existence of society presupposes, and its evolution in turn develops and extends, a system of generally accepted objects and relations. nevertheless, the "socially current object" is, as such, an abstraction just as the uniform social individual is likewise an abstraction. the only concrete object ever actually known or in any wise experienced by any person is the object as constructed by that person in accordance with his own aims and purposes, and in which there is, therefore, a large and important share of meaning which is significant to no one else. it is needless in this discussion to dwell at length upon the general principle of recent "functional" psychology, that practical ends are the controlling factors in the acquisition of our knowledge of objective things. we shall take for granted the truth of the general proposition that cognition, in whatever sphere of science or of practical life, is essentially teleological in the sense of being incidental always, more or less directly, to the attainment of ends. cognition, as the apperceptive or attentive process, is essentially the process of scrutinizing a situation (whether theoretical or practical) with a view to determining the availability for one's intended purpose of such objects and conditions as the situation may present. the objects and conditions thus determined will be made use of or ignored, counted upon as advantageous or guarded against as unfavorable--in a word, responded to--in ways suggested by their character as ascertained through reference to the interest in question. in this sense, then, objective things as known by individual persons are essentially complex stimuli whose proper function and reason for being it is to elicit useful responses in the way of conduct--responses conducive to the realization of ends. from this point of view, then, the difference between one person's knowledge of a particular object and another's signifies ( ) a difference between these persons' original purposes in setting out to gain knowledge of the object, and ( ) consequently a difference between their present ways of acting with reference to the object. the bare object as socially current is, at best, for each individual simply a ground upon which subsequent construction may be made; and the subsequent construction which each individual is prompted by his circumstances and is able to work out in judgment first makes the object, for this individual, real and for his purposes complete. now, it is our primary intention to show that objects are, in cases of a certain important class, not yet ready to serve the person who knows them in their proper character of stimuli, when they have been, even exhaustively, defined in merely physical terms. it is very often not enough that the dimensions of an object and its physical properties, even the more recondite ones as well as those more commonly understood--it is often not enough for the purposes of an agent that these characters should make up the whole sum of his knowledge of the object in question. a measure of knowledge in terms of physical categories is often only a beginning--the result of a preliminary stage of the entire process of teleological determination, which must be carried through before the object of attention can be satisfactorily known. in the present study of the logic of valuation we shall be occupied exclusively with the discussion of cases of this kind. in our judgments of sense-perception and physical science we have presented to us material objects in their physical aspect. when these latter are inadequate to suggest or warrant overt conduct, our knowledge of them must be supplemented and reconstructed in ways presently to be specified. it is in the outcome of judgment-processes in which this work of supplementing and reconstructing is carried through that the consciousness of value, in the proper sense, arises, and these processes, then, are those which we shall here consider under the name of "processes of valuation." they will therefore best be approached through specification of the ways in which our physical judgments may be inadequate. let us, then, assume, as has been indicated, that the process of acquiring knowledge--that is to say, the process of judgment or attention--is in every case of its occurrence incidental to the attainment of an end. we must make this assumption without attempting formally to justify it--though in the course of our discussion it will be abundantly illustrated. let us, in accordance with this view, think of the typical judgment-process as proceeding, in the main, as follows: first of all must come a sense of need or deficiency, which may, on occasion, be preceded by a more or less violent and sudden shock to the senses, forcibly turning one's attention to the need of immediate action. by degrees this sense of need will grow more definite and come to express itself in a more or less "clear and distinct" image of an end, toward which end the agent is drawn by desire and to which he looks with much or little of emotion. the emergence of the end into consciousness immediately makes possible and occasions definite analysis of the situation in which the end must be worked out. salient features of the situation forthwith are noticed--whether useful things or favoring conditions, or, on the other hand, the absence of any such. thus predicates and then subjects for many subsidiary judgments in the comprehensive judgment-process emerge together in action and interaction upon each other. the predicates, developed out of the general end toward which the agent strives, afford successive points of view for fresh analyses of the situation. the logical subjects thus discovered--_objects_ of attention and knowledge--require, on the other hand, as they are scrutinized and judged, modification and re-examination of the end. the end grows clearer and fuller of detail as the predicates or implied ("constituent") ideas which are developed out of it are distinguished from each other and used in making one's inventory of the objective situation. conversely, the situation loses its first aspect of confusion and takes on more and more the aspect of an orderly assemblage of objects and conditions, useful, indifferent, and adverse, by means of which the end may in greater or less measure be attained or must, in however greatly modified a form, be defeated. now, in this development of the judgment-process, it must be observed, the end must be more or less clearly and consistently conceived throughout as an _activity_, if the objective means of action which have been determined in the process are not to be, at the last, separate and unrelated data still requiring co-ordination. if the end has been so conceived, the means will inevitably be known as members of a mechanical _system_, since the predicates by which they have been determined have at every point involved this factor of amenability to co-ordination. the judgment-process, if properly conducted and brought to a conclusion, must issue at the end in the functional unity of a finished plan of conduct with a perfected mechanical co-ordination of the available means. we have now to see that much more may be involved in such a process as this than has been explicitly stated in our brief analysis. for the end itself may be a matter of deliberation, just as must be the physical means of accomplishing it; and, again, the means may call for scrutiny and determination from other points of view than the physical and mechanical. the final action taken at the end may express the outcome of deliberate ethical and economic judgment as well as of judgments in the sphere of sense-perception and physical science. let us consider, for example, that one's end is the construction of a house upon a certain plot of ground. this end expresses the felt need of a more comfortable or more reputable abode, and has so much of general presumption in its favor. there may, however, be many reasons for hesitation. the cost in time or money or materials on hand may tax one's resources and injuriously curtail one's activities along other lines. and there may be ethical reasons why the plan should not be carried out. the house may shut off a pleasing prospect from the view of the entire neighborhood and serve no better end than the gratification of its owner's selfish vanity. it will cost a sum of money which might be used in paying just, though outlawed, debts. now, from the standpoint of such problems as these the fullest possible preliminary knowledge of the physical and mechanical fitness of our means must still be very abstract and general. it would be of use in any undertaking like the one we have supposed, but it is not sufficient in so far as the problem is one's own problem, concrete, particular, and so unique. one may, of course, proceed to the stage of physical judgment without having settled the ethical problems which may have presented themselves at the outset. the end may be entertained tentatively as a hypothesis until certain mechanical problems have been dealt with. but manifestly this is only postponement of the issue. the agent is still quite unprepared, even after the means have been so far determined, to take the first step in the execution of the plan; indeed, his uncertainty is probably only the more harassing than before. moreover, the economic problems in the case are now more sharply defined, and these for the time being still further darken counsel. manifestly the need for deliberation is at this point quite as urgent as the need for physical determination can ever be, and the need is evidenced in the same way by the actual arrest and postponement of overt conduct. the agent, despite his physical knowledge, is not yet free to embrace the end and, having done so, use thereto the means at his disposal. it is plainly impossible to use the physical means until one knows in terms of substance and attribute or cause and effect, or whatever other physical categories one may please, what manner of behavior may be expected of them. so likewise is it as truly impossible, for one intellectually and morally capable of appreciating problems of a more advanced and complex sort, to exploit the physical properties thus discovered until ethical determination of the end and economic determination of the means have been completed.[ ] there are, then, we conclude, cases in which physical determination of the means is by itself not a sufficient preparation for conduct--in which there are ethical and economic problems which delay the application of the physical means to the end to which they may be physically adapted. indeed, so much as this may well appear as sufficiently obvious without extended illustration. everyone knows that it is nearly always necessary, in undertaking any work in which material things are used as means, to count the cost; and everyone knows likewise that not every end that is in any way attractive and within one's reach may without more ado be taken as an object of settled desire and effort. it is indeed needless to elaborate these commonplaces in the sense in which they are commonly understood. however, such is not our present purpose. our purpose is the more specific one of showing that the meaning of objectivity must be widened so as to include ( ) the "universe" of ends in their ethical aspect and ( ) the economic aspect of the means of action, as well as ( ) the physical aspect to which the character of objectivity is commonly restricted. we shall maintain that these are parts or phases of a complete conception of reality, and that of them, consequently, objectivity must be predicated for every essential reason connoted by such characterization of the world of things "external" to the senses. it has been with this conclusion in mind, then, that we have sought to emphasize the frequent serious inadequacy, for practical purposes, of the merely physical determination of the means in one's environment. the principle thus suggested would imply that the ethical and economic stages in the one inclusive process of reflective attention should be regarded as involving, when they occur, the same logical function of judgment as is operative in the sphere of sense-perception and the sciences generally. ethical and economic factors must on occasion be present at the final choice and shaping of one's course of conduct, along with the physical determinations of environing means and conditions which one has made in sense-perception. there is, then, it would appear, at least a fair presumption, though not indeed an _a priori_ certainty, that these ethical and economic factors or conditions have, like the physical, taken form in a _judgment-process_ which will admit of profitable analysis in accordance with whatever general theory of judgment one may hold as valid elsewhere in the field of knowledge. this presumption we shall seek to verify. now, our interest in thus determining, first of all, the logical character of these processes will readily be understood from this, that, in the present view, these are the processes, and the only ones in our experience, which are properly to be regarded as processes of valuation. we shall hold that valuation, and so all consciousness of value, properly so called, must be either ethical or economic; that the only conscious processes in which values can come to definition are these processes of ethical and economic judgment. the present theory of value is, then, essentially a logical one, in the sense of holding that values are determined in and by a logical--that is, a judgmental--valuation-process and in its details is closely dependent upon the general conception of judgment of which the outlines have been sketched above. accordingly, the exposition must proceed in the following general order: assuming the conception of judgment which has been presented (which our discussion will in several ways further illustrate and so tend to confirm), we shall seek to show that the determinations made in ethical and economic judgment are in the proper sense objective. this will involve, first of all, a statement of the conditions under which the ethical and economic judgments respectively arise--which statement will serve to distinguish the two types of judgment from each other. we shall then proceed to the special analysis of the ethical and economic forms from the standpoint of our general theory of judgment, thereby establishing in detail the judgmental character of these parts of the reflective process. this analysis will serve to introduce our interpretation of the consciousness of value as a factor in the conduct and economy of life. ii let us then define the problem of the objective reference of the valuational judgments by stating, as distinctly as may be, the conditions by which ethical and economic deliberation, respectively, are prompted. a study of these conditions will make it easier to see in what way the judgments reached in dealing with them can be objective. when will an end, presenting itself in consciousness in the manner indicated in our brief analysis of the judgment-process, become the center of attention, thereby checking the advance, through investigation of the possible means, to final overt action? this is the general statement of the problem of the typical ethical situation. manifestly there will be no ethical deliberation if the imaged end at once turns the attention toward the environment of possible means, instead of first of all itself becoming the object instead of the director of attention; there will be no suspension of progress toward final action, excepting such as may later come through difficulty in the discovery and co-ordination of the means. however, there are cases in which the emergence of the end forthwith is followed by a check to the reflective process, and the agent shrinks from the end presented in imagination as being, let us say, one forbidden by authority or one repugnant to his own established standards. the end may in such a case disappear at once; very often it will insistently remain. on this latter supposition, the simplest possibility will be the development of a mere mechanical tension, a "pull and haul" between the end, or properly the impulses which it represents, and the agent's habit of suppressing impulses of the class to which the present one is, perhaps intuitively, recognized as belonging. the case is the common one of "temptation" on the one side and "principle" or "conscience" on the other, and so long as the two forces remain thus in hard-and-fast opposition to each other there can be no ethical deliberation or judgment in a proper sense. the standard or habit may gain the day by sheer mechanical excess of power, or the new impulse, the temptation, may prevail because its onset can break down the mechanical resistance. out of such a situation as this, however, genuine ethical deliberation may arise on condition that standard and "temptation" can lose something of their abstractness and their hard-and-fast opposition, and develop into terms of concrete meaning. the agent may come to see that the end is in some definite way of really vital interest and too important to be put aside without consideration. he may, of course, in this fall into gross self-sophistication, like the drunkard in the classical instance who takes another glass to test his self-control and thereby gain assurance, or he may act with wisdom and with full sincerity, like dorothea casaubon when she renounced the impossible task imposed by her departed husband. in the moral life one can ask or hope for complete exemption from the risk of self-deception with as little reason as in scientific research. but however this may be, our present interest is in the method, not in particular results of ethical reflection. whether properly so in a particular case or not, the imaged end may come to seem at least plausibly defensible on grounds of principle which serve to sanction certain other modes of conduct to which a place is given in the accepted scheme of life; or the end may simply press for a relatively independent recognition on the very general ground that its emergence represents an enlargement and new development of the personality.[ ] the end may thus cease to stand in the character of blind self-assertive impulse, and press its claim as a positive means of future moral growth, as bringing freedom from repressive and enfeebling restraints and as tending to the reinforcement of other already valued modes of conduct. on the other hand, the standard will cease to stand as mere resistance and negation, and may discover something of its hidden meaning as a product of long experience and slow growth, and as perhaps a vital part of the organization of one's present life, not to be touched without grave risk. now, on whichever side the development may first commence, a like development must soon follow on the other, and it is the action and reaction of standard and prospective or problematic end upon each other that constitutes the process of ethical deliberation or judgment. just as in the typical judgment-process, as sketched above, so also here predicate and subject _develop each other_, when once they have given over their first antagonism and come to the attitude of reasoning together. the predicate explains itself that the subject or new end may be searchingly and fairly tested; and under this scrutiny the subject develops its full meaning as a course of conduct, thereby prompting further analysis and reinterpretation of the standard. but this is not the place for detailed analysis of the process;[ ] here we are concerned only to define the type of situation, and this we may now do in the following terms: the indispensable condition of ethical judgment is the presence in the agent's mind of at least two rival interesting ends or systems of such ends. in the foregoing, the subject of the judgment is the new end that has arisen; the predicate or "standard" is the symbol for the old ends or values which in the tension of the judgment-process must be brought to more or less explicit enumeration--and, we must add, reconstruction also. indeed, it is important, even at this stage of our discussion, to observe that predicate and standard are not equivalent in meaning. the predicate, or predicative side, of judgment is the imagery of control in the process, which, as we have seen, develops with the subject side; while the term "standard" connotes the rigid fixity which belongs to the inhibiting concept or ideal in the stage before the judgment-process proper can begin. the ethical judgment-process is, in a word, just the process of reconstructing standards--as in its other and corresponding aspect it is the process of interpreting new ends. those who oppose measures of social reform or new modes of conduct or belief on alleged grounds of "immorality" instinctively feel in doing so that the change may make its way more easily against a resistance that will candidly explain itself; and, on the other side of the social judgment-process, the more fanatical know how to turn to good advantage for their propaganda the bitterness or contempt of those who represent the established order. on both sides there are those who trust more in mechanical "pull and haul" than in the intrinsic merits of their cause. thus it is by encountering some rival end or entire system of ends, as symbolized by an ideal, that a new end emerging out of impulse comes to stand for an agent, as the center of a problem of conduct, and so to occupy the center of attention. and it thereby becomes an object, as we shall hold, which must be more fully defined in order that it may be _valued_, and accordingly be held to warrant a determinate attitude toward itself on the agent's part. we have now to define in the same general terms the typical economic situation. in economic theory as in common thought it is not the contemplated act of applying certain means to the attainment of an end regarded as desirable that functions as the logical subject of valuation. the thing or object valued in the economic situation is one's present wealth, whether material or immaterial, one's services or labor--whatever one gives in exchange or otherwise sets apart for the attainment of a desired end or, proximately, to secure possession of the necessary and sufficient means to the attainment of a desired end. the object of attention in the valuing process is here not itself an end of action. in this respect the economic type of judgment is like the physical, for in both the object to be valued is a certain means which one is seeking to adapt to some more or less definitely imaged purpose; or a condition of which one wishes, likewise for some special purpose, to take advantage. the ultimate goal of all judgment is the determination of a course of conduct looking toward an end, and our present problem may accordingly be stated in the following terms: under what circumstances in the judgment-process does it become necessary to the definition and attainment of an end as yet vague and indeterminate that the requisite means, as in part already physically determined, should be further scrutinized in attention and determined from the economic point of view? or, in a word: what is the "jurisdiction" of the economic point of view? for ordinary judgements of sense-perception the presence in consciousness of a single unquestioned end is the adequate occasion, as our analysis (assuming its validity) has shown. for ethical judgment we have seen that the presence of conflicting ends is necessary; and we shall now hold that this condition is necessary, though not, without a certain qualification, adequate, for the economic type as well. if an imaged end can hold its place in consciousness without a rival, and the physical means of attaining it have been found and co-ordinated, then the use or consumption of the means must inevitably follow, without either ethical or economic judgement; for, to paraphrase the saying of professor james, nothing but an end can displace or inhibit effort toward another end. the economic situation differs, then, from the ethical in this, that the end or system of ends entering into competition with the one for the time being of chief and primary interest has been brought to consciousness through reference to those "physical" means which already have been determined as necessary to this latter end. the conflict of ends in the economic situation, that is to say, is not due to a direct and intrinsic incompatibility between them. where there manifestly is such incompatibility, judgment will be of the ethical type--as when building the house involves the foreclosure of a mortgage, and so, in working an injury to the holder of the site, may do violence to one's ideal of friendship or of more special obligation; or when an impulse to intemperate self-indulgence is met by one's ideal of social usefulness. in cases such as these one clearly sees, or can on reflection come to see, in what way an evil result to personal character will follow upon the imminent misdeed, and in what way suppression of the momentary impulse will conserve the entire approved and established way of life. very often, however, the conflicting ends are related in no such mutually exclusive way. each may be in itself permissible and compatible with the other, and, so far as any possible ethical discrimination can determine, there is no ground for choice between them. thus it is only through the fact that both ends are dependent upon a limited supply of means that one would, for example, ever bring together and deliberately oppose in judgment the purpose of making additions to his library and the necessity of providing a store of fuel for the winter. both ends in such a case are in themselves indeed permissible in a general way, but they may very well not both of them be economically possible, and hence, for the person in question and in the presence of the economic conditions which confront him, not, in the last analysis, both ethically possible. when there is a conflict between two ends that stand in close organic relation in the sense explained above, the problem is an ethical one; when the conflict is, in the sense explained, one of competition between ends ethically permissible--not at variance, either one, that is, with other ends _directly_--for the whole or for a share of one's supply of means, the problem is of the economic type.[ ] there are three typical cases in which economic judgment or valuation of the means is necessary, and the enumeration of these will make clear the relation between the ethical and the economic types of judgment: ( ) first may be mentioned the case in which ethical deliberation has apparently reached its end in the formation of a plan of action which, so far as one can see, on ethical grounds is unobjectionable. a definite "temptation" may have been overcome, or out of a more complex situation a satisfactory ethical compromise or readjustment may have been developed with much difficulty. now, there are very often cases in which such a course of action still may not be entered on without further hesitation; for, if the plan be one requiring for its working out the use of material means, the fact of an existing limitation of one's supply of means must bring hitherto unthought of ends into conflict with it. there are doubtless many situations in which one's moral choice may be carried into practice without consideration of ways and means, as when one forgives an injury or holds his instinctive nature under discipline in the effort to attain an ascetic or a genuinely social ideal of character. but more often than the moral rigorist cares to see, questions of an economic nature must be raised after the ethical "evidence is all in"--questions which are probably more trying to a sensitive moral nature than those more dramatic situations in which the real perils of self-sophistication are vastly less, and the simpler, sharper definition of the issue makes possible a less difficult, though a more decisive and edifying, victory. ( ) in the second place are those cases in which the end that has emerged is without conspicuous moral quality, because, although it may represent some worthy impulse, it has not been obliged to make its way to acceptance against the resistance of desires less worthy than itself. this is the ideal case of economic theory in which "moral distinctions are irrelevant," and the economic man is free, according to the myth, to perform his hedonistic calculations without thought of moral scruple. the end ethically acceptable in itself, like the enriching of one's library, must, when the means are limited, divert a portion of the means from other uses, and will thus, _through reference to the indispensable means_, engage in conflict with other ends quite remotely, if in the agent's knowledge at all, related with itself. ( ) finally we reach the limit of apparent freedom from ethical considerations in the operations of business institutions, and perhaps especially in those of large business corporations. apart from the routine operations of a business which involve no present exercise of the valuing judgment, there are constantly in such institutions new projects which must be considered, and which commonly must involve revaluation of the means. in this revaluation the principle of greatest revenue is supposed to be the sole criterion, regardless of other personal or social points of view from which confessedly the measure might be considered. but such a supposition, however true to the facts of current business practice it may be, we must hold to be an abstraction when viewed from the standpoint of the social life at large, and hence no real exception to our general principle. the economic and the ethical situations differ, as types, only in the closeness of relation between the ends that are in conflict and in the manner in which the ends are first brought into conflict--not in respect of the intrinsic nature of the ends which are involved in them.[ ] it is this difference which, as we shall see, explains why ethical valuation must be of ends, and economic valuation, on the other hand, of means. we have yet to see _in what way_ valuation of the means of action can serve to resolve a difficulty of the type which has thus been designated as economic. the question must be deferred until a more detailed analysis of the economic judgment-process can be undertaken. it is enough for our present purpose to note that the subject of valuation in this process _is_ the means, and to see that under the typical conditions which have been described some further determination of the means than the merely physical one of their factual availability for the competing ends is needed.[ ] physically and mechanically the means are available for each one of the ends or groups of ends in question; the pressing problem is to determine for which one of the ends, if any, or to what compromise or readjustment of certain of the ends or all of them, the means at hand are in an economic sense most properly available.[ ] from this preliminary discussion of the ethical and economic situations we must now pass to discuss the objectivity of the judgments by which the agent meets the difficulties which such situations as these present. we shall seek to show that these judgments are constructive of an objective order of reality. it will be necessary in the first place to determine the psychological conditions of the more commonly recognized experience of objectivity in the restricted sphere of sense-perception. there might otherwise remain a certain antecedent presumption against the thesis which we wish to establish even after the direct argument had been presented.[ ] iii common-sense and natural science certainly tend to identify the objectively real with the existent in space and time. the physical universe is held to be palpably real in a way in which nothing not presented in sensuous terms can be. to most minds doubtless it is difficult to understand why plato should have ascribed to the ideas a higher degree of reality than that possessed by the particular objects of sense-perception, and still more difficult to understand his ascription of real existence to such ideas as those of beauty, justice, and the good. there is a certain apparent stability in a universe presented in "immediate" sense-perception--a universe with which we are in constant bodily intercourse--that seems not to belong to a mere order of relations which, if known in any sense, is not known to us through the senses. moreover, knowledge of the physical world is felt to possess a higher degree of certainty than does any knowledge we can have of supposed economic or moral truth, or of economic or moral standards. of such knowledge one is disposed to say, as mr. spencer does of metaphysics, that at the best it presupposes a long and elaborate inferential process which, as long, is likely to be faulty; whereas physical truth is immediate or else, when inference is involved in it, easy to be tested by appeal to immediate facts. physical reality is a reality that can be seen and handled and felt as offering resistance, and this is evidence of objectivity of a sort not to be found in other spheres of knowledge for which the like claim is made. the force of these impressions (and it would not be difficult to find stronger statements in the history of scientific and ethical nominalism) diminishes if one tries to determine in what consists that objectivity which they uncritically assume as given in sense-perception. for one must recognize that not all our possible modes of sense-experience are equally concerned in the presentation of this perceived objective world. certain sensory "quales" are immediately referred to outward objects as belonging to them. certain others are, in a way, "inward," either not more definitely localized at all or merely localized in the sense-organ which mediates them. now, the reason for this difference cannot lie in the content of the various sense-qualities abstractly taken. a visual sensation, apart from the setting in which it occurs in common experience, can be no more objective in its reference--indeed, can have no more reference of any kind--than the least definite and instructive organic sensation. for the degree of distinctness with which one discriminates sense-qualities depends upon the number and importance of the interpretative associations which it is important from time to time to "connect" with them; or, conversely, the sense-qualities are not _self_-discriminating in virtue of an intrinsic objective reference or meaning which each possesses and which drives it apart from all the rest. indeed, an intrinsic meaning, if a sensation could possess one, would not only be superfluous in the development of knowledge, but, as likely to be mistaken for the acquired or functional meaning, even seriously confusing.[ ] now, it must be granted that, if the "simple idea of sensation" is without objective reference, no association with it of similarly abstract sensations can supply the lack. a "movement" sensation, or a tactual, having in itself no such meaning, cannot merely by being "associated" with a similarly meaningless visual sensation endow this latter with reference to an object. objective reference is, in fact, not a sensuous thing; it is not a conscious "element," nor does it arise from any combination or fusion of such. it is neither _in_ the association of ideas as a constituent member, nor does it belong to the association considered as a sequence of psychical states. instead, in our present view, it belongs to or arises out of the activity through which and with reference to which associations are first of all established. it is an aspect or kind of reference or category under which any sense-quality or datum is apperceived when it is held apart from the stream of consciousness in order that it may receive new meaning as a stimulus; and a sensation functioning in such a "state of consciousness"[ ] is a psychical phenomenon very different from the conscious element of "analytical" psychology. the extent to which it is true that the objective world of sense-perception is pre-eminently visual and tactual is then merely an evidence of the extent to which the exigencies of the life-process have required finer sense-discrimination for the sake of more refined reaction within these spheres as compared with others. our conclusion, then, must be that the consciousness of objectivity is not as such sensuous, even as given in our perception of the material world. the world, as viewed from the standpoint of a particular, practical emergency, is an objective world, not in virtue of its having a "sensuous" or a "material" aspect as something existent _per se_, but because it is a world of stimuli in course of definition for the guidance of activity.[ ] it will be well to give further positive exposition of the meaning of the view thus stated. to return once more to our fundamental psychological conception, knowledge is essentially relevant to the solution of particular problems of more or less urgency and of various kinds and figures in the solution of such problems as the assemblage of consciously recognized symbols or stimuli by which various actions are suggested. the object as known is therefore not the same as the object as apprehended in other possible modes of being conscious of it. the workman who is actually using his tool in shaping his material, or the warrior who is actually using his weapon in the thick of combat, is, if conscious of these objects at all (and doubtless he may be conscious of them at such times), not conscious of them _as objects_--as the one might be, for example, in adjusting the tool for a particular kind of use, and the other in giving a keen edge to his blade. under these latter circumstances the tool or weapon is an _object_, and its observed condition, viewed in the light of a purpose of using the object in a certain way, is regarded as properly suggesting certain changes or improvements. and likewise will the tool or the weapon have an objective character in the agent's apprehension in the moment of identifying and selecting it from among a number of others, or even in the act of reaching for it, especially if it is inconveniently placed. but in the act of freely using one's objective means the category of the objective plays no part in consciousness, because at such times there is no judgment respecting the means--because there is no sufficient occasion for the isolation of certain conscious elements from the rest of the stream of conscious experience to be defined as stimuli to certain needed responses. such isolation will not normally take place so long as the reactions suggested by the conscious contents involved in the experience are fully adequate to the situation. objects are not normally held apart as such from the stream of consciousness in which they are presented and recognized as possessing qualities warranting certain modes of conduct, excepting as it has become necessary to the attainment of the agent's purposes to modify or reconstruct his activity.[ ] are things, then, apprehended as objective in virtue of the agent's attitude toward them, or is the agent's attitude in a typical case grounded upon an antecedent determination of the objectivity of the things in question? we must answer, in the first place, that there can be no such antecedent determination. we may, it is true, speak of believing, on the evidence of sight or touch, that a certain object is really present before us. but neither sight nor touch possesses in itself, as a particular sense-quality, any objective meaning. if touch is _par excellence_ the sense of the objective and the appeal to touch the test of objectivity, this can only be because touch is the sense most closely and intimately connected in our experience with action. after any interval of hesitation and judgment, action begins with contact with and manipulation of the physical means which have been under investigation. not only is touch the proximate stimulus and guide to manipulation, but all relevant knowledge which has been gained in any judgment-process, through the other senses, and especially through sight, must ultimately be reducible to terms of touch or other contact sense. the alleged tactual evidence of objectivity is, then, rather a confirmation than a difficulty for our present view. in short, we must dismiss as impossible the hypothesis that there can be a consciousness of objectivity which is not dependent upon and an expression of primary antecedent tendencies toward motor response to the presented stimulus. it is our attitude toward the prospective stimulus that mediates the consciousness of an object standing over against us. so far, indeed, is it from being true that objectivity is a matter for special determination antecedently to action that by common testimony the conviction of objectivity comes to us quite irresistibly. the object forces itself upon us, as we say, and "whether we will or no" we must recognize its presence there before us and its independence of any choice of ours or of our knowledge. in the cautious manipulation of an instrument, in the laborious shaping of some refractory material, in the performance of any delicate or difficult task, one's sense of the objectivity of the thing with which one works is as obtrusive as remorse or grief, and as little to be shaken off. we shall revert to this suggested analogy at a later stage in our discussion. we are now in a position to define more precisely the nature of the conditions in which the sense of objectivity emerges, and this will bring us to the point at which the objective import of our economic and ethical judgments can profitably be discussed. we have said that the world of the physical is objective, not in virtue of the sensuous terms in which it is presented, but because it is a world of stimuli for the guidance of human conduct. under what circumstances, then, are we conscious of stimuli in their capacity of guides or incentives or grounds of conduct? and the answer must be that stimuli are interpreted as such, and so take on the character of objectivity, when their precise character as stimuli is still in doubt, and they must therefore receive further definition. for example, a man pursued by a wild beast must find some means of escape or defense, and, seeing a tree which he may climb or a stone which he may hurl, will inspect these as well as may be with reference to their fitness for the intended purpose. it is at just such moments as these, then, that physical things become things for knowledge and take on their stubbornly objective character--that is to say, when they are essentially problematic. now, in order that any physical thing may be thus problematic and so possess objective character for knowledge, it must ( ) be in part understood, and so prompt certain more or less indiscriminate responses; and ( ) be in part as yet not understood--in such wise that, while there are certain indefinite or unmeasured tendencies on the agent's part to respond to the object--climb the tree or hurl the stone--there is also a certain failure of complete unity in the co-ordination of these activities, a certain contradiction between different suggestions of conduct which different observed qualities of the tree or stone may give, and so hesitation and arrest of final action. the pursued man views the tree suspiciously before trusting himself to its doubtful strength, or weighs well the stone and tests its rough edges before pausing to throw it. thus, to state the matter negatively, there are two possible situations in which the sense of objectivity, if it emerge into consciousness at all, cannot long continue. an object---as, for example, some strange shrub or flower--which, in the case we are supposing, may attract the pursued wayfarer's notice, may awaken no responses relevant to the emergency in which the agent finds himself; and it will therefore forthwith lapse from consciousness. or, on the other hand, the object, as the tree or stone, may rightly or wrongly seem to the agent so completely satisfactory, or, rather, in effect may _be_ so, as instantly to prompt the action which otherwise would come, if at all, only after a period of more or less prolonged attention. in neither of these cases, then, is there a problematic object. in the one the thing in question is wholly apart from any present interest, and therefore lapses. in the other case the thing seen is comprehended on the instant with reference to its general use and merges immediately into the main stream of the agent's consciousness without having been an object of express attention. in neither case, therefore, is there hesitation with reference to the thing in question--any conflict between inconsiderate positive responses prompted by certain features of the object and inhibitions due to recognition of its shortcomings. in a word, in neither case is there any judgment or possibility of judgment, and hence no sense of objectivity. we can have consciousness of an object, in the strict sense of the term, only when some part or general aspect of the total situation confronting an agent excites or seems to warrant responses which must be held in check for further determination. in terms of consciousness, an object is always an object of attention--that is, an object which is under process of development and reconstruction with reference to an end. an inhibited impulse to react in a more or less definite way to a stimulus is, then, the adequate condition of the emergence in consciousness of the sense of objectivity. so long as an activity is proceeding without check or interruption, and no conflict develops between motor responses prompted by different parts or aspects of the situation, the agent's consciousness will not present the distinction of objective and subjective. the mode of being conscious which accompanies free and harmonious activity of this sort may be exemplified by such experiences as æsthetic appreciation, sensuous enjoyment, acquiescent absorption in pleasurable emotion, or even intellectual processes of the mechanical sort, such as easy computation or the solution of simple algebraic problems--processes in which no more serious difficulty is encountered than suffices to stimulate a moderate degree of interest. if, however, reverting to the illustration, our present need for a stone calls for some property which the stone we have seized appears to lack, consciousness must pass over into the reflective or attentive phase. the stone will now figure as an _object_ possessing certain qualities which render it in a general way relevant to the emergency before us. a needed quality is missing, and this defect must hold in check all the imminent responses until discovery of the missing quality can set them free. in a word, the stone as known to us has assumed the station of subject in a judgment-process, and our effort is, if possible, to assign to it a new predicate relevant to our present situation. psychologically speaking, the stone is an object, a stimulus to which we are endeavoring to find warrant for responding in some new or reconstructed way. in this process we must assume, then, first of all, an interest on the agent's part in the situation as a whole, which in the first place, in terms of the illustration, makes the pursued one note the tree or stone--which might otherwise have escaped his notice as completely as any passing cloud or falling leaf--and suggests what particular qualities or adaptabilities should be looked for in it. given this interest in "making something" out of the total situation as explaining the recognition of the stone and the impulse to seize and hurl it, we find the sense of the stone's objectivity emerging just in the arrest of the undiscriminating impulse. the stone must have a certain meaning as a stimulus first of all, but it must be a meaning not yet quite defined and certain of acceptance. the stone will be an _object_ only if, and so long as, the undiscriminating impulses suggested by these elements of meaning are held in check in order that they may be ordered, supplemented, or made more definite. it is, then, the essence of the present contention that physical things are _objective_ in our experience in virtue of their recognized inadequacy as means or incentives of action--an inadequacy which, in turn, is felt as such in so far as we are seeking to use them as means or grounds of conduct, or to avail ourselves of them as conditions, in coping with the general situation from which our attention has abstracted them. from this analysis of the conditions of the consciousness of objectivity we must now proceed to inquire whether in the typical ethical and economic situations, as they have been described, essentially these same conditions are present. in the ethical situation, according to our statement, the subject of the judgment (the object of attention) is the new end which has just been presented in imagination, and we have now to see that the agent's attitude toward this end is for our present purpose essentially the same as toward a physical object which is under scrutiny. for just as the physical object is such for consciousness because it is partly relevant (whether in the way of furthering or of hindering) to the agent's purpose, but as yet partly not understood from this point of view, so the imaged end may likewise be ambiguous. the agent's moral purpose may be the (very likely mythical) primitive one of which we read in "associational" discussions of the moral consciousness--that of avoiding punishment. it may be that of "imitative," sympathetic obedience to authority--a sentiment whose fundamental importance for ethical psychology has long remained without due recognition.[ ] it may be loyalty to an ideal of conscience, or yet again a purpose of enlargement and development of personality. but on either supposition the compatibility of the end with the prevailing standard or principle of decision may be a matter of doubt and so call for judgment. the problem will, of course, be a problem in the full logical sense as involving judgment of the type described in our discussion of the ethical situation only when the attitudes of obedience to authority and to fixed ideals have been outgrown; but, on the other hand, as might be shown, it is just the inevitable increasing use of judgment with reference to these formulations of the moral life which gradually undermines them and, by a kind of "internal dialectic" of the moral consciousness, brings the agent to recognition as well as to more perfect practice of a logical or deliberative method. the end, then, is, in the typical ethical situation, an _object_ which one must determine by analysis and reconstruction as a means or condition of moral "integrity" and progress. it is, accordingly, in the second place, an object upon whose determination a definite activity of the agent is regarded by him as depending. just as in the physical judgment-process the object is set off over against the self and regarded as a given thing which, when once completely defined, will prompt certain movements of the body, so here the contemplated act is an object which, when fully defined in all its relevant psychological and sociological bearings, will prompt a definite act of rejection or acceptance by the self. now, it might be shown, as we believe, that the complete psychological and sociological definition of the course of conduct _is_ in truth the full explanation of the choice; there is no _separate_ reaction of the moral self to which the course of conduct is, as defined, an external stimulus. so also in the sphere of physical judgment complete definition passes over into action--or the appreciative mode of consciousness which accompanies action--without breach of continuity. but within the judgment-process in all its forms there is in the agent's apprehension this characteristic feature of apparent separation between the subject as an objective thing presently to be known and used or responded to, and the predicate as a response yet to be perfected in details, but at the right time, when one has proper warrant, to be set free. it is not our purpose here to speak of metaphysical interpretations or misinterpretations of this functional distinction; but only to argue from the presence of the distinction in the ethical type of judgment as in the physical as genuine an objectivity for the ethical type as can be ascribed to the other. the ethical judgment is objective in the sense that in it an object--an imaged mode of conduct taken as such--is presented for development to a degree of adequacy at which one can accept it or reject it as a mode of conduct. the ethical predicates right and wrong, good and bad, each pair representing a particular standpoint, as we shall later see, signify this accepting or rejecting movement of the self, this "act of will," of which, as an act in due time to be performed, the agent is more or less acutely conscious in the course of moral judgment. in the economic situation also, as above described, there is present the requisite condition of the consciousness of objectivity. here, as in the ethical situation, an object is presented which one must redetermine, and toward which one must presently act in a way likewise to be determined in detail in judgment. we shall defer until a later stage discussion of the reason why this subject of the economic judgment is the _means_ in the activity that is in progress. we are not yet ready to show that the means _must_ be the center of attention under the conditions which have been specified. here we need only note the fact of common experience that economic judgment does center upon the means, and show that in this fact is given the objective status of the means in the judgment-process; for the economic problem is essentially that of withdrawing a portion, a "marginal increment," of the means from some use or set of uses to which they are at present set apart, and applying it to the new end that has come to seem, on ethical grounds at least, desirable; and we may regard this diversion as the essentially economic act which, in the agent's apprehension during judgment, is contingent upon the determination of the means. the object as economic is accordingly the means, or a marginal portion of the means, which is to be thus diverted (or, so to speak, exposed to the likelihood of such diversion), and its determination must be of such a nature as to show the economic urgency, or at least the permissibility, of this diversion. into this determination, manifestly, the results of much auxiliary inquiry into physical properties of the means must enter--such properties, for example, as have to do with its technological fitness for its present use as compared with possible substitutes, and its adaptability for the new use proposed. taking the word in the broad sense of _object of thought_, it is always an object in space and time to which the economic judgment assigns an economic value; and it is true here (just the same is true, _mutatis mutandis_, of the psychological and sociological determinations necessary to the fixation of ethical value) that the _economically motivated_ physical determination of the objective means from the standpoint of the emergency in hand is the full "causal" explanation of the economic act. it must, however, be carefully observed that this physical determination is in the typical case altogether incidental, from the agent's standpoint, to the assignment of an economic character or value to the means--a value which will at the close of the judgment come to conscious recognition. as we shall see, the process is directed throughout by reference to economic principles and standards, and what shall be an adequate determination in the case depends upon the precision with which these are formulated and the strenuousness with which they are applied. in a word, the economic judgment assigns to the physical object, as known at the outset, a new non-physical character. throughout the judgment-process this character is gaining in distinctness, and at the end it is accepted as the value of the means, as warrant for the diversion of them to the new use which has been decided on.[ ] we have now to consider whether in the actual ethical and economic experience of men there is any direct evidence confirming the conclusions which our logical analysis of the respective situations would appear to require. can any phases of the total experience of working out a satisfactory course of conduct in these typical emergencies be appealed to as actually showing at least some tacit recognition that these types of judgment present each one an order of reality or an aspect of the one reality? in the first place, then, one must recognize that in the agent's own apprehension a judgment of value has something more than a purely subjective meaning. it is never offered, by one who has taken the trouble to work it out more or less laboriously and then to express it in terms which are certainly objective, as a mere announcement of _de facto_ determination or a registration of arbitrary whim and caprice. one no more means to announce a groundless choice or a choice based upon pleasure felt in contemplation of the imaged end than in his judgments concerning the physical universe he means to affirm coexistences and sequences, agreements and disagreements, of "ideas" as psychical happenings. that there is an ethical or economic truth to which one can appeal in doubtful cases is, indeed, the tacit assumption in all criticism of another's deliberate conduct; the contrary assumption, that criticism is merely the opposition of one's own private prejudice or desire to the equally private prejudice or desire of another, would render all criticism and mutual discussion of ethical problems meaningless and futile in the plain man's apprehension as in the philosopher's. for the plain man has a spontaneous confidence in his knowledge of the material world which makes him look askance at any alleged analysis of his sense-perceptions and scientific judgments into "associations of ideas," and the same confidence, or something very like it, attaches to judgments of these other types. it may perhaps be easier (though the concession is a very doubtful one) to destroy a naïve confidence in the objectivity of moral truth than a like confidence in scientific knowledge, but it must be remembered that the plain man's sense of the urgency, at least of ethical problems, if not of economic, is commonly less acute than for the physical. in the plain man's experience serious moral problems are infrequent--problems of the true type, that is, which cannot be disposed of as mere cases of temptation; one must have attained a considerable capacity for sympathy and a considerable knowledge of social relations before either the recognition of such problems or proper understanding of their significance is possible. moral and economic crises are not vividly presented in sensuous imagery excepting in minds of developed intelligence, experience, and imaginative power; and the judgments reached in coping with them do not, as a rule, obviously call for nicely measured, calculated, and adjusted bodily movements. the immediate act of executing an important economic judgment may be a very commonplace performance, like the dictation of a letter, and an ethical decision may, however great its importance for future overt conduct, be expressed by no immediate visible movements of the body. but this possible difference of impressiveness between physical and other types of judgments is from our present standpoint unessential; and indeed, after all, it cannot be denied that there are persons whose sense of moral obligation is quite as distinct and influential, and even sensuously vivid, as their conviction of the real existence of an external world. to the average man it certainly is clear that, as dr. martineau declares, "it is an inversion of moral truth to say ... that honour is higher than appetite _because_ we feel it so; we feel it so because it _is_ so. this '_is_' we know to be not contingent on our apprehension, not to arise from our constitution of faculty, but to be a reality irrespective of us in adaptation to which our nature is constituted, and for the recognition of which the faculty is given."[ ] and the impressiveness, to most minds, of likening the sublimity of the moral law to the visible splendor of the starry heavens would seem to suggest that the apprehension of moral truth is a mode of consciousness, in form at least, so far akin to sense-perception as to be capable of illustration and even reinforcement from that type of experience. at this point we must revert to a suggestion which presented itself above in another connection, but which at the time could not be further developed. this was, in a word, that there is often a feeling of _obtrusiveness_ in our appreciation of the objectivity of the things before us in ordinary sense-perception (or physical judgment) which is not unlike the felt insistence of remorse and grief.[ ] this feeling is so conspicuous a feature of the state of consciousness in physical judgment as frequently to serve the plain man as his last and irrefragable evidence of the metaphysical independence of the material world, and it is indeed a feature whose explanation does throw much light upon the meaning of the consciousness of objectivity as a factor within experience. now, there is another common feeling--or, as we do not scruple to call it, another emotion--which is perhaps quite as often appealed to in this way; though, as we believe, never in quite the same connection in any argument in which the two experiences are called upon to do service to the same end. material objects, we are told, are _reliable_ and _stable_ as distinguished from the fleeting illusive images of a dream--they have a "solidity" in virtue of which one can "depend upon them," are "hard and fast" remaining faithfully where one deposits them for future use or, if they change and disappear, doing so in accordance with fixed laws which make the changes calculable in advance. the material realm is the realm of "solid fact" in which one can work with assurance that causes will infallibly produce their right and proper effects, and to which one willingly returns from the dream-world in which his adversary, the "idealist," would hold him spellbound. we propose now briefly to consider these two modes of apprehension of external physical reality in the light of the general analysis of judgment given above--from which it will appear that they are, psychologically, emotional expressions of what have been set forth as the essential features of the judgment-situation, whether in its physical, ethical, or economic forms. from this we shall argue that there should actually be in the ethical and economic spheres similar, or essentially identical, "emotions of reality," and we shall then proceed to verify the hypothesis by pointing to those ethical and economic experiences which answer the description. we have seen that the center of attention or subject in the judgment-process is as such problematic--in the sense that there are certain of its observed and recognized attributes which make it in some sense relevant and useful to the purpose in hand, while yet other of its attributes (or absences of certain attributes) suggest conflicting activities. the object which one sees is certainly a stone and of convenient size for hurling at the pursuing animal. the situation has been analyzed and found to demand a missile, and this demand has led to search for and recognition of a stone. the stone, however, may be of a color suggesting a soft and crumbling texture, or its form may appear from a distance to be such as to make it practically certain to miss the mark, however carefully it may be aimed and thrown. until these points of difficulty have been ascertained, the stone is wanting still in certain essential determinations. so far as it has been certainly determined, it prompts to the response directly suggested by one's general end of defense and escape, but there are these other indications which hold this response in check and which, if verified, will cause the stone to be let lie unused. now, we have, in this situation of conflict or tension between opposed incitements given by the various discriminated characters of the object, the explanation of the aspect of obtrusiveness, of arbitrary resistance to and independence of one's will, which for the time being seems the unmistakable mark or coefficient of the thing's objectivity. for it is not the object as a whole that is obtrusive; indeed, clearly, there could be no obtrusiveness on the part of an "object as a whole," and in such a case there could also be no judgment. the obtrusion in the case before us is not a sense of the energy of a recalcitrant metaphysical object put forth upon a coerced and helpless human will, but simply a conscious interpretation of the inhibition of certain of the agent's motor tendencies by certain others prompted by the object's "suspicious" and as yet undetermined appearances or possible attributes. the object as amenable to use--those of its qualities which taken by themselves are unquestionable and clearly conducive to the agent's purpose--needs no attention for the moment, let us say. the attention is rather upon the dubious and to all appearance unfavorable qualities, and these for the time being make up the sum and content of the agent's knowledge of the object. on the other hand, the agent as an active self is identified with the end and with those modes of response to the object which promise to contribute directly to its realization. it is in this direction that his interest is set and he strains with all his powers of mind to move, and it is upon the self as identified with, and for the time being expressed in, the "effort of the agent's will" that the object as resistant, refusing to be misconstrued, obtrudes. one _must_ see the object and _must_ acknowledge its apparent, or in the end its ascertained, unfitness. one is "coerced." the situation is one of conflict, and it is out of the conflict that the essentially emotional experience of "resistance" emerges.[ ] the more special emotions of impatience, anger, or discouragement may in a given case not be present or may be suppressed, but the emotion of objectivity will still remain.[ ] on the same general principles the other of our two coefficients of reality may be explained. let us assume that the stone in our illustration has at last been cleared of all ambiguity in its suggestion, having been taken as a missile, and that the man in flight now holds it ready awaiting the most favorable moment for hurling it at his pursuer. it will hardly be maintained that under these conditions the coefficient of the stone's reality as an object consists in its obtrusiveness, in its resistance to or coercion of the self. the stone is now regarded as a fixed and determinate feature of the situation--a condition which can be counted on, whatever else may fail. over against other still uncertain aspects of the situation (which are now in _their_ turn real because resistant, coercive, and obtrusive) stands the stone as a reassuring fact upon and about which the agent can build up the whole plan of conduct which may, if all goes well, bring him safely out of his predicament. the stone has, so to speak, passed over to the "end" side of the situation, and although it may have to be rejected for some other means of defense, as the definition of the situation proceeds and the plan of action accordingly changes (as in some degree it probably must), nevertheless for the time being the imaged activities as stimulus to which the stone is now accepted are a fixed part of the plan and guide in further judgment of the means still undefined. the agent can hardly recur to the stone, when, after attending for a time to the bewildering perplexities of the situation, he pauses once more to take an inventory of his certain resources, without something of an emotional thrill of assurance and encouragement. in this emotional appreciation of the "solidity" and "dependability" of the object the second of our coefficients of reality consists. this might be termed the recognition, the other the perception, coefficient. classifying them as emotions, because both are phenomena of tension in activity, we should group the perception coefficient with emotions of the contraction type, like grief and anger, and the recognition coefficient with the expansion emotions, like joy and triumph. now, in the foregoing interpretation no reference has been made to any conditions peculiar to the physical type of judgment-situation. the ground of explanation has been the feature of arrest of activity for the sake of reconstruction, and this, if our analyses have been correct, is the essence of the ethical and economic situations as well as of the physical. can there then be found in these two spheres experiences of the same nature and emerging under the same general conditions as our perception and recognition coefficients of reality? if so, then our case for the objective significance and value of ethical and economic judgment is in so far strengthened. ( ) in the first place, then, the object in its economic character is problematic, assuming a desire on the agent's part to apply it, as means, to some new or freshly interesting end, because it has already been, and accordingly now is, set apart for other uses and cannot thoughtlessly be withdrawn from them. extended illustration is not needed to remind one that these established and hitherto unquestioned uses will haunt the economic conscience as obtrusively and inhibit the desired course of economic conduct with as much energy of resistance as in the other case will any of the contrary promptings of a physical object. moreover, the recognition coefficient may as easily be identified in this connection. if one's scruples gain the day, in such a case one has at least a sense of comforting assurance in the conservatism of his choice and its accordance with the facts, however unreconciled in another way one may be to the deprivation that has thus seemed to be necessary. if, however, the new end in a measure makes good its case and the modes of expenditure which the "scruples" represented have been readjusted in accordance with it, then the means, no less than before the new interpretation had been placed upon them, will enjoy the status of reality in the economic sense. they will be real now, however, not in the obtrusive way, as presenting aspects which inhibit the leading tendency in the judgment-process, but, instead, as means having a fixed and certain character in one's economic life, which, after the hesitation and doubt just now superseded, one may safely count upon and will do well to keep in view henceforth. ( ) in the second place, mere mention of the corresponding ethical experiences must suffice, since only extended illustration from literature and life would be fully adequate: on the one hand, the "still small voice" of conscience or the authoritativeness of duty, "stern daughter of the voice of god;" and, on the other, the restful assurance with which, from the vantage-ground of a satisfying decision, one may look back in wonder at the possibility of so serious a temptation or in rejoicing over the new-won freedom from a burdensome and repressive prejudice. this must for the present serve as positive exposition of our view as to the objective significance of the valuational types of judgment. there are certain essential points which have as yet not been touched upon, and there are certain objections to the general view the consideration of which will serve further to explain it; but the discussion of these various matters will more conveniently follow the special analysis of the valuational judgments, to which we shall now proceed. iv in the last analysis the ultimate motive of all reflective thought is the progressive determination of the ends of conduct. physical judgment, or, in psychological terms, reflective attention to objects in the physical world, is at every turn directed and controlled by reference to a gradually developing purpose, so that the process may also be described as one of bringing to fulness of definition an at first vaguely conceived purpose through ascertainment and determination of the means at hand. the problematic situation in which reflection takes its rise inevitably develops in this two-sided way into consciousness of a definite end on the one side, and of the means or conditions of attaining it on the other. it has been shown that there _may_ be involved in any finally satisfactory determination of a situation an explicit reflection upon and definition of the controlling end which is present and gives point and direction to the physical determination. but very often such is not the case. when a child sees a bright object at a distance and makes toward it, availing himself more or less skilfully of such assistance as intervening articles of furniture may afford, there is of course no consciousness on his part of any definite purpose as such, and this is to say that the child does not subject his conduct to criticism from the standpoint of the value or its ends. there is simply strong desire for the distant red ball, controlling all the child's movements for the time being and prompting a more or less critical inspection of the intervening territory with reference to the easiest way of crossing it. the purpose is implicitly accepted, not explicitly determined, as a preliminary to physical determination of the situation. if one may speak of a development of the purpose in such a case as this, one must say that the development into details comes through judgment of the environing conditions. to change the illustration in order not to commit ourselves to the ascription of too developed a faculty of judgment to the child, this is true likewise of any process of reflective attention in the mind of an adult in which a general purpose is accepted at the outset and is carried through to execution without reflection upon its ethical or economic character as a purpose. the specific purpose as executed is certainly not the same as the general purpose with which the reflective process took its rise. it is filled out with details, or may perhaps even be quite different in its general outlines. there has necessarily been development and perhaps even transformation, but our contention is that all this has been effected in and through a process of judgment in which the conditions of action, and not the purpose itself, have been the immediate objects of determination. upon these the attention has been centered, though of course the attention was directed to them by the purpose. to state the case in logical terms, it has been only through selection and determination of the means and conditions of action from the standpoint of predicates suggested by the general purpose accepted at the outset that this purpose itself had been rendered definite and practical and possible of execution. probably such cases are seldom to be found in the adult experience. as a rule, the course of physical or technological judgment will almost always bring to light implications involved in the accepted purpose which must inevitably raise ethical and economic questions; and the resolution of these latter will in turn afford new points of view for further physical determination of the situation. in such processes the logical points of the problem of ethical and economic valuation come clearly into view. in our earlier account of the matter it was more convenient to use language which implied that ethical and economic judgment must be preceded by implicit or explicit acceptance of a definite situation presented in sense-perception, and that these evaluating judgments could be carried through to their goal only upon the basis of such an inventory of fixed conditions. thus the ultimate ethical quality of the general purpose of building a house would seem to depend upon the precise form which this purpose comes to assume after the actual presence and the quality of the means of building have been ascertained and the economic bearings of the proposed expenditure have been considered. surely it is a waste of effort to debate with oneself upon the ethical rightness of a project which is physically impossible or else out of the question from the economic point of view. we are, however, now in a position to see that this way of looking at the matter is both inaccurate and self-contradictory. in the actual development of our purposes there is no such orderly and inflexible arrangement of stages; and if it is a waste of effort to deliberate upon a purpose that is physically impossible, it may, with still greater force, be argued that we cannot find, and judge the fitness of, the necessary physical means until we know what, precisely, it is that we wish to do. the truth is that there is constant interplay and interaction between the various phases of the inclusive judgment-process, or rather, more than this, that there is a complete and thoroughgoing mutual implication. it is indeed true that our ethical purposes cannot take form in a vacuum apart from consideration of their physical and economic possibility, but it is also true that our physical and economic problems are ultimately meaningless and impossible, whether of statement or of solution, except as they are interpreted as arising in the course of ethical conflict. we have, then, to do, in the present division, with situations in which, whether at the outset or from time to time during the course of the reflective process, there is explicit conflict between ends of conduct. these situations are the special province of the judgment of valuation. our line of argument may be briefly indicated in advance as follows: . the judgment of valuation, whether expressed in terms of the individual experience or in terms of social evolution, is essentially the process of the explicit and deliberate resolution of conflict between ends. as an incidental, though nearly always indispensable, step to the final resolution of such conflict, physical judgment, or, in general, the judgment of fact or existence, plays its part, this part being to define the situation in terms of the means necessary for the execution of the end that is gradually taking form. the two modes of judgment mutually incite and control each other, and neither could continue to any useful purpose without this incitement and control of the other. both modes of judgment are objective in content and significance. at the end of the reflective process and immediately upon the verge of execution of the end or purpose which has taken form the result may be stated or apprehended in either of two ways: ( ) directly, in terms of the end, and ( ) indirectly, in terms of the ordered system of existent means which have been discovered, determined, and arranged. if such final survey of the result be taken by way of preparation for action, or for whatever reason, the end will be apprehended as possessing ethical value and the means, under conditions later to be specified, as possessing economic value. . what then is the nature and source of this apprehension of end or means as valuable? the consciousness of end or means as valuable is an emotional consciousness expressive of the agent's practical attitude as determined in the just completed judgment of ethical or economic valuation and arising in consequence of the inhibition placed upon the activities which constitute the attitude by the effort of apprehending or imaging the valued object. ethical and economic value are thus strictly correlative; psychologically they are emotional incidents of apprehending in the two respective ways just indicated the same total result of the inclusive complex judgment-process. finally, as the moment of action comes on, the consciousness of the ethically valued end lapses first; then the consciousness of economic value is lost in a purely "physical," _i. e._, technological, consciousness of the means and their properties and interrelations in the ordered system which has been arranged; and this finally merges into the immediate and undifferentiated consciousness of activity as use of the means becomes sure and unhesitating. when we say that the ends which oppose each other in an ethical situation (that is, a situation for the time being seen in an ethical aspect) are related, and the ends in an economic situation are not, we by no means wish to imply that in the one case we have in this fact of relatedness a satisfactory solution at hand which is wanting in the other. to feel, for example, that there is a direct and inherent relationship between a cherished purpose of self-culture and an ideal of social service which seems now to require the abandonment of the purpose does not mean that one yet knows just _how_ the two ends should be related in his life henceforth; and again, to say that one can see no inherent relation between a desire for books and pictures and the need of food, excepting in so far as both ends depend for their realization upon a limited supply of means, is not to say that the issue of the conflict is not of ethical significance. such a view as we here reject would amount to a denial of the possibility of genuinely problematic ethical situations[ ] and would accord with the opinion that economic judgment as such lies apart from the sphere of ethics and is at most subject only to occasional revision and control in the light of ethical considerations. by the relatedness of the ends in a situation we mean the fact, more or less explicitly recognized by the agent, that the new, and as yet undefined, purpose which has arisen belongs in the same system with the end, or group of ends, which the standard inhibiting immediate action represents. the standard inhibits action in obedience to the impulse that has come to consciousness, and the image of the new end is, on its part, definite and impressive enough to inhibit action in obedience to the standard. the relatedness of the two factors is shown in a practical way by the fact that, in the first instance at least, they are tacitly expected to work out their own adjustment. by the process already described in outline, subject and predicate begin to develop and thereby to approach each other, and a provisional or partial solution of the problem may thus be reached without resort to any other method than that of direct comparison and adjustment of the ends involved on either side. the standard which has been called in question has enough of congruence with the new imaged purpose to admit of at least some progress toward a solution through this method. we can best come to an understanding of this recognition of the relatedness of the ends in ethical valuation by pausing to examine somewhat carefully into the conditions involved in the acceptance or reflective acknowledgment of a defined end of conduct as being one's own. any new end in coming to consciousness encounters some more or less firmly established habit represented in consciousness by a sign or symbolic image of some sort, the habit being itself the outcome of past judgment-process. our present problem is the significance of the agent's recognition of a relatedness between his new impulsive end and the end which represents the habit, and we shall best approach its solution by considering the various factors and conditions involved in the agent's conscious recognition of the established end as being such. in any determinate end there is inevitably implied a number of groups of factual judgments in which are presented the objective conditions under which execution of the end or purpose must take place. there is in the first place a general view of environing conditions, physical and social, presented in a group of judgments ( ) descriptive of the means at hand, of the topography of the region in which the purpose is to be carried out, of climatic conditions, and the like, and ( ) descriptive of the habits of thought and feeling of the people with whom one is to deal, their prejudices, their tastes, and their institutions. the project decided on may, let us say, be an individual or a national enterprise, whether philanthropic or commercial, which is to be launched in a distant country peopled by partly civilized races. in addition to these groups of judgments upon the physical and sociological conditions under which the work must proceed, there will also be a more or less adequate and impartial knowledge of one's own physical and mental fitness for the enterprise, since the work as projected may promise to tax one's physical powers severely and to require, for its successful conduct, large measure of industry, devotion, patience, and wisdom. indeed any determinate purpose whatever inevitably implies a more or less varied and comprehensive inventory of conditions. further illustration is not necessary for our present purpose. we may say that in a general way the conditions relevant to a practical purpose will group themselves naturally under four heads of classification, as physical, sociological, physiological, and psychological. all four classes are objective, though the last two embrace conditions peculiar to the agent as an individual over against the environment to which for purposes of his present activity he stands in a sense opposed. now our present interest is not so much in the enumeration and classification of possible relevant conditions in a typical situation as in the significance of these relevant conditions in the agent's apprehension of them. perhaps this significance cannot better be described than by saying that essentially and impressively the conditions are apprehended as, taken together, _warranting_ the purpose that has been determined. we appeal, in support of this account of the matter, to an impartial introspection of the way in which the means and conditions of action stand related to the formed purpose in the moment of survey of a situation. the various details presented in the survey of a situation are apprehended, not as bare facts such as one might find set down in a scientist's notebook, but as warranting--as closely, uniquely, and vitally relevant to--the action that is about to be taken. this, as we believe, is a fair account of the situation in even the commoner and simpler emergencies that confront the ordinary man. quite conspicuously is it true of cases in which the purpose is a purely technological one that has been worked out with considerable difficulty and is therefore not executed until after a somewhat careful survey of conditions has been taken. it is often true likewise in cases of express ethical judgment; if the ethical phases of the reflective process have not been excessively long and difficult, our definite sense of the ethical value of the act we are about to do lapses quite easily, and the factual aspects and features of the situation as given in one or more of the four classes which we have distinguished take on an access of significance in their character of warranting, confirming, or even compelling the act determined upon. of our ordinary sense-perception in the moments of its actual functioning no less than of conscience in its aspect of a moral perceptive faculty are the words of bishop butler sensibly true that "to preside and govern, from the very economy and constitution of man, belongs to it."[ ] i even in cases of more serious moral difficulty this sanctioning aspect of the means and conditions of action is not overshadowed. if the situation is one in which by reason of their complexity these play a conspicuous rôle and must be surveyed, by way of preparation on the agents' part, for performance of the act, they inevitably assume, for the agent, their proper functional character. in general, the conditions presented in the system of factual judgments have a certain "rightful authority" which they seem to lend to the purpose or end with reference to which they were worked out to their present degree of factual detail. the conditions can thus seem to sanction the end because conditions and end have been worked out together. gradual development on the one side prompts analytical inquiry upon the other and is in turn directed and advanced by the results of this inquiry. in the end the result may be read off either in terms of end or in terms of conditions and means.[ ] the two readings must be in accord and the agent's apprehension of the conditions as warrant for the end is expression in consciousness of this "agreement."[ ] now in this mode of apprehension of factual conditions there is a highly important logical implication--an implication which inevitably comes more and more clearly into view with the continued exercise of judgment, even though the agent's habit of interest in the scrutiny of perplexing situations may still remain, by reason of the want of trained capacity for a broader view, limited in its range quite strictly to the physical sphere. this implication is, we shall declare at once, that of an endeavoring, striving, active principle or self which can be helped or hindered in its unfolding by particular purposes and sets of corresponding conditions--can lose or gain, through devotion to particular purposes, in the breadth, fulness, and energy of its life. the agent's apprehension of and reference to this active principle of course varies in all degrees of explicitness, according to circumstances, from the vague awareness that is present in a simple case of physical judgment to the clear recognition and endeavor at definition that are characteristic of serious ethical crises. that the situation should develop and bring to light this factor is what should be expected on general grounds of logic--for to say that a set of conditions warrants or sanctions or confirms a given purpose implies that our purposes can stand in need of warrant, and this would seem to be impossible apart from reference to a process whose maintenance and development in and through our purposes are assumed as being as a matter of course desirable. it is of the essence of our contention that the apprehension of the conditions of action as _warranting the end_ is a primordial and necessary feature of the situation--indeed, its constitutive feature. if our concern were with the psychological development of self-consciousness as a phase of reflective experience, we should endeavor to show that this development is mediated in the first instance by the "subjective" phenomena of feeling, emotion, and desire which find their place _in the course_ of the judgment-process. we should then hold that, with the _conclusion_ of the judgment-process and the accompanying sense of the known conditions as reassuring and confirmatory of the end, comes the earliest possibility of a discriminative recognition of the self as having been all along a necessary factor in the process. we should hold that outside of the _process_ of reflective attention there can be no psychical or "elementary" _beginnings_ of self-consciousness, and then that, except as a development out of the experience to which we have referred as marking the _conclusion_ of the attentive process, there can be no recognized specific and in any degree definable consciousness of self. all this, however, lies rather beside our present purpose. we wish simply to insist that it is out of the apprehension of conditions as reassuring and confirmatory, out of this "primordial germ," that the agent's definite recognition of himself as a center of development and expenditure of energy takes its rise. here are the beginnings of the possibility of self-conscious ethical and economic valuation. this apprehension of the means as _warranting_ is, we have held, a fact even when the means surveyed are wholly of the physical sort, and we have thereby implied that consciousness of the self as "energetic" may take its rise in situations of this type or during the physical stage in the development of a more complex total situation. it would be an interesting speculation to consider to what extent and in what way the development of the sciences of sociology and physiology may have been essentially facilitated by the emergence of this form of self-consciousness. but however the case may stand with these sciences or with the rise of real interest in them in the mind of a given individual, interest in the objective psychological conditions of a contemplated act is certainly very closely dependent upon interest in that subjective self which one has learned to know through the past exercise of judgment in definition and contemplation of conditions of the three other kinds. the more diversified and complex the array of physical and social conditions with reference to which one is to act, the more important becomes not simply a clearly articulated knowledge of these, but also a knowledge of oneself. the self that is warranted in its purpose by the surveyed conditions must hold itself in a steady and consistent attitude during the performance on pain of "falling short of its opportunity" and thereby rendering nugatory the reflective process in which the purpose was worked out. experience abundantly shows how easily the assurance that comes with the survey of conditions may come to grief, though there may have been on the side of the conditions, so far as defined, no visible change; and in so far as self-consciousness has already emerged as a distinguishable factor in such situations, failures of the sort we here refer to are the more easily identified and interpreted. some sudden impulse may have broken in upon the execution of the chosen purpose; there may have been an unexpected shift of interest away from that general phase of life which the purpose represented; or in any one of a number of other ways may have come about a wavering and a slackening in the resolution which marked the commencement of action. the "energetic" self forthwith (if we may so express it) recognizes that the sanction which the conditions so far as then known gave to its purpose was a misleading because an incomplete one, and it proceeds to develop within itself a new range of objective fact in which may be worked out the explanation, and thereby a method of control, of these new disturbing phenomena. the qualities of patience under disappointment, courage in encountering resistance, steadiness and self-control in sustained and difficult effort--these qualities and others of like nature come to be discriminated from each other by introspective analysis and may be as accurately measured, and in general as objectively studied, as any of the conditions to a saving knowledge and respect of which one may already have attained, and these newly determined psychological conditions will henceforth play the same part in affording sanction to one's purposes as do the rest. an ordered system of psychological categories or points of view comes to be developed, and an accurate statement of conditions of personal disposition and capacity relevant to each emergency as it arises will hereafter be worked out--over against and in tension with one's gradually forming purposes in like manner as are statements of all the other relevant objective aspects of the situation.[ ] in the "energetic" self, we shall now seek to show, we have the common and essential principle of both ethical and economic valuation which marks these off from other and subordinate types of judgment. let us determine as definitely as possible the nature and function of this principle. the recognition of the chosen purpose as one favorable or otherwise to the self, and so the recognition of the self as capable of furtherance or retardation by its chosen purposes, is not always a feature of the state of mind which may ensue upon completed judgment. in the commoner situations of the everyday life of normal persons, as practically always in the lives of persons of relatively undeveloped reflective powers, it is quite wanting as a separate distinguished phase of the experience. in such cases it is present, if present at all, merely as the vaguely felt implicit meaning of the recognition that the known conditions sanction and confirm the purpose. such situations yield easily to attack and threaten none of those dangers, none of those possible occasions for regret or remorse, of which complex situations make the person of developed reflective capacity and long experience so keenly apprehensive. they are disposed of with comparatively little of conscious reconstruction on either the subject or the predicate side, and when a conclusion has been reached the agent's recognition of the conditions carries with it the comfortable though too often delusive assurance of the complete and perfect eligibility of the purpose. if the question of eligibility is raised at all, the answer is given on the tacit principle that "whatever purpose is, is right." to the "plain man," and to all of us on certain sides of our lives, every purpose for which the requisite means and factual conditions are found to be at hand is, just as our purpose, therefore right. the same experience of failure and disappointment which proves our purpose to have been, from the standpoint of enlargement and enrichment of the self, a mistaken one brings a clearer consciousness of the logic implicit in our first confident belief in the purpose, and at the same time emphasizes the need of making this logic explicit. the purpose, as warranted to us by the conditions and assembled means that lay before us, was our own, and _as our own_ was implicitly a purpose of furtherance of the self. the disappointment that has come brings this implication more clearly into view, and likewise the need of methodical procedure, not as before in the determination of _conditions_, but in the determination of purposes as such; for the essence of the situation is that the _execution_ of the purpose has brought to light some unforeseen consequence now recognized as having been all the while in the nature of things involved in the purpose. this consequence or group of consequences consists (in general terms) in the abatement or arrest of desirable modes of activity which find their motivation elsewhere in the agent's system of accepted ends, and it is registered in consciousness in that sense of restriction or repression from without which is a notable phase of all emotional experience, particularly in its early stages. the consequences are as undesirable as they are unexpected, and the reaction against them, at first emotional, presently passes over into the form of a reflective interpretation of the situation to the effect that the self has suffered a loss by reason of its thoughtless haste in identifying itself with so unsafe a purpose.[ ] it is the essential logical function of the consciousness of self to stimulate the valuation processes which take their rise in the stage of reflective thought thus attained. the consciousness of self is a peculiarly baffling theme for discussion from whatever point of view, because one finds its meaning shifting constantly between the two extremes of a subjectivity to which "all objects of all thought" are external and an objective thing or system of energies which is known just as other things are--known in a sense by itself, to be sure, but _known_ nevertheless, and thought of as an object standing in possible relations to other objects. now, it is of the subjective self that we are speaking when we say that its essential function is the stimulation or incitement of the valuation processes, but manifestly in order to serve thus it must nevertheless be presented in some sort of sensuous imagery. the subjective self may, in fact, be thought of in many ways--presented in many different sorts of imagery--but in all its forms it must be distinguished carefully from that objective self which, as described in psychology, is the assemblage of conditions under which the subjective or "energetic" self works out its purposes. it may be the pale, attenuated double of the body, or a personal being standing in need of deliverance from sin, or an atom of soul-substance, or, in our present terminology, a center of developing and unfolding energy. the significant fact is that, however different in content and in motive these various presentations of the subjective self may be, they are, one and all, as presentations and as in so far objective, stimuli to some definite response. the savage warrior deposits his double in a tree or stone for safety while he goes into battle; the self that is to be saved from sin is a self that prompts certain acceptable acts in satisfaction of the quasi-legal obligations that the fact of sin has laid upon the agent. the presented self, whatever the form it may assume as presentation, has its function, and this function is in general that of stimulus to the conservation and increase, in some sense, of the self that is not presented, but for whom the presentation is. now our own present description of the self as "energetic," as a center or source of developing and unfolding energy is in its way a presentation. it consists of sensuous imagery and suggests a mechanical process, or the growth of a plant perhaps, which if properly safeguarded will go on satisfactorily--a process which one must not allow to be perturbed or hindered by external resistance or internal friction or to run down. to many persons doubtless such an account would seem arbitrary and fantastic in the extreme, but no great importance need be attached to its details. the kind and number and sensuous vividness of the details in which this essential content of presentation may be clothed must of course depend, for each person, upon his psychical idiosyncrasy. indeed, as the habit of reflection upon purposes comes to be more firmly fixed, and the procedure of valuation to be consciously methodical and orderly, the sensuous content of the presented self must grow constantly more and more attenuated until it has declined into a mere unexpressed principle or maxim or tacit presumption, prescribing the free and impartial application of the method of valuation to particular practical emergencies as these arise. for a self, consisting of presented content of whatever sort, which one seeks to further through attentive deliberation upon concrete purposes, must, just in so far as it has _content_, determine the outcome of ethical judgment in definite ways. thus the soul that must be saved from sin (if this be the content of the presented self) is one that has transgressed the law in certain ways and the right relations that should subsist between creature and creator, and has thereby incurred a more or less technically definable guilt. this guilt can only be removed and the self rehabilitated in its normal relations to the law by an appropriate response to the situation--by a choice on the agent's part, first, of a certain technical procedure of repentance, and then of a settled purpose of living as the law prescribes.[ ] so also our own image of the self as "energetic" after the manner of a growing organism may well seem, if taken too seriously as to its presentational details, to foster a bias in favor of over-conservative adherence to the established and the accredited as such.[ ] the argument of the last few paragraphs may be restated in the following way in terms of the evolution of the individual's moral attitude or technique of self-control: . in the stage of moral evolution in which custom and authority are the controlling principles of conduct, moral judgment in the proper sense of self-conscious, critical, and reconstructive valuation of purposes is wanting. such judgment as finds here a place is at best of the merely casuistical type, looking to a determination of particular cases as falling within the scope of fixed and definite concepts. there is no self-consciousness except such as may be mediated by the sentiment of willing obedience. it is, at this stage, not the _particular sort_ of conduct which the law prescribes that in the agent's apprehension enlarges and develops the self; so far as any thought of enlargement and development of the self plays a part in influencing conduct, these effects are such as, in the agent's trusting faith, will come from an entire and willing acceptance of the law as such. "if any man will do his will, he shall know of the doctrine." moreover, the stage of custom and authority goes along with, in social evolution, either very simple social conditions or else conditions which, though very complex, are stable, so that in either case the conditions of conduct are in general in harmony with the conduct which custom and authority prescribe. the law, therefore, can be absolute and takes no account of possible inability to obey. the divine justice punishes infraction of the law simply as objective infraction; not as sin, in proportion to the sinner's responsibility. . but inevitably custom and authority come to be inadequate. as social conditions change, custom becomes antiquated and authority blunders, wavers, contradicts itself in the endeavor to prescribe suitable modes of individual conduct. obedience no longer is the way to light. the self becomes self-conscious through feeling more and more the repression and the misdirection of its energies that obedience now involves. this is the stage of subjective morality or conscience; and the rise of conscience, the attitude of appeal to conscience, means the beginning of endeavor at _methodical solution_ of those new problematic situations in the attempt to deal with which authority as such has palpably collapsed. we say, however, that conscience is the _beginning_ of this endeavor; for conscience is, in fact, an ambiguous and essentially transitional phenomenon. on the one hand conscience is the inner nature of a man speaking within him, and so the self furthers its own growth in listening to this expression of itself. in this aspect conscience is methodological. but on the other hand conscience _speaks_, and, speaking, must say something determinate, however general this something may be. in this aspect conscience is a _résumé_ of the _generic_ values realized under the system of custom and authority, but to the present continued attainment of which the _particular prescriptions_ of custom and authority are no longer adequate guides. conscience is thus at once an inward prompting to the application of logical method to the case in hand and a body of general or specific rules under some one of which the case can be subsumed. in ethical theory we accordingly find no unanimity as to the nature of conscience. at the one extreme it is the voice of god speaking in us or through us, in detailed and specific terms--and so, virtually, custom and authority in disguise. at the other it is an empty abstract intuition that the right is binding upon us--and, so, simply the hypostasis of demand for a logical procedure. the history of ethics presents us with all possible intermediate conceptions in which these extreme motives are more or less skilfully interwoven or combined in varying proportions. the truth is that conscience is essentially a transitional conception, and so necessarily looks before and after. in one of its aspects it is a self which has come to miss (and therefore to image for itself) the values and, it may be, a certain dawning sense of vitality and growth which obedience to authority once afforded.[ ] in its other aspect it is a self that is looking forward in a self-reliant way to the determination on its own account of its purposes and values. and finally, as for the environing world of means and conditions, clearly this is not necessarily harmonious with and amenable to conscience; indeed, in the nature of things it can be only partially so. the morality of conscience is, therefore, either mystical, a morality that seeks to escape the world in the very moment of its affirmation that the world is unreal (because worthless), or else it takes refuge in a virtual distinction between "absolute" and "relative" morality (to borrow a terminology from a system in which properly it should have no place), perhaps setting up as an intermediary between heaven and earth a machinery of special dispensation.[ ] . conscience professes in general, that is, to be autonomous, and the profession is, strictly speaking, a contradiction in terms. moreover, apart from considerations of the logic of the situation, theories of conscience have, as a matter of fact, always lent themselves kindly to theological purposes just as the theory of self-realization in its classic modern statement rests upon a metaphysical doctrine of the absolute.[ ] inevitably the movement concealed within this essentially unstable conception must have its legitimate outcome ( ) in a clearing of the presented self of its fixed elements of content, thus setting it free in its character of a non-presentational principle of valuation, and ( ) a setting apart of these elements of content from the principle of valuation as standards for reference and consultation rather than as law to be obeyed. we have thus correlated our account of the logic whereby the "energetic" self comes to explicit recognition as stimulus to the valuation-process with the three main stages in the moral evolution of the individual and the race. we were brought to this first-mentioned part of our discussion by our endeavor to find out the factors involved in the first acceptance of a conscious purpose (or, indifferently, the subsequent recognition of it as a standard)--an endeavor prompted by the need of distinguishing, with a view to their special analysis, the two types of valuation-process. we now return to this problem. the following illustration will serve our present undertaking: a lawyer or man of business is struck by the great need of honest men in public office, or has had his attention in some impressive way called to the fact of great inequality in the present distribution of wealth, and to the diverse evils resulting therefrom. these facts hold his attention, perhaps against his will, and at last suggest the thought of his making some personal endeavor toward improvement of conditions, political or social, as the case may be. on the other hand, however, the man has before him the promise of a successful or even brilliant career in his chosen occupation, and is already in the enjoyment of a substantial income, which is rapidly increasing. moreover, he has a family growing up about him, and he is not simply strongly interested in the early training and development of his children, and desirous of having himself some share in conducting it, but he sees that the suitable higher education of his children will in a few years make heavy demands upon his pecuniary means. here, then, we have a situation the analysis of which will enable us to distinguish and define the provinces of ethical and economic judgment. it is easy to see that we have here a conflict between ends. on the one side is the thought of public service in some important office or, let us say, the thought of bettering society in a more fundamental way by joining the propaganda of some proposed social reform. this end rests upon certain social impulses in the man's nature and appeals to him as strongly, we may fairly assume, as would any purpose of immediate self-interest or self-indulgence, so that it stands before him and urges him with an insistent pertinacity that at first even puts him on his guard against it as a temptation. over against this concrete end or subject of moral valuation stand other ends comprehended or symbolized in the ideals of regular and steady industry, of material provision for family, of paternal duty toward children, of scholarly achievement as lawyer or judge, and the like--ideals which are indeed practical and personal, but which, as they now function, are general or universal in character, are lacking in the concreteness and emotional quality which belong to the new purpose which has just come to imagination and has brought these ideals into action on the predicate side. will this life of social agitation really be quite "respectable," and befitting the character of a sober and industrious man? will it enable me to support and educate my family? will it permit me to devote sufficient attention to their present care and training? and will it not so warp my nature, so narrow and concentrate my interests, as in a measure to disqualify me for the right exercise of paternal authority over them in years to come? moreover, will not a life of agitation, of constant intercourse with minds and natures in many ways inferior to my own and those of my present professional associates, lower my intellectual and moral standards, and so make of me in the end a less useful member of society than i am at present? these and other questions like them present the issue in its earlier aspect. presently, however, the tentative purpose puts in its defense, appealing to yet other recognized ideals or standards of self-sacrifice, benevolence, or social justice as witnesses in its favor. the conflict thus takes on the subject-predicate form, as has already been explained. on the one hand we have the undefined but strongly insistent concrete purpose; on the other hand we have a number of symbolic concepts or universals standing for accepted and accredited habitual modes of conduct. the problem is that of working the two sides of the situation together into a unified and harmonious plan of conduct which shall be at once concrete and particular, as a plan chosen by way of solution of a given present emergency, and universal, as having due regard for past modes of conduct, and as itself worthy of consideration in coping with future emergencies. now, how shall we discriminate the ethical and the economic aspects of the situation which we have described? we shall most satisfactorily do this through a consideration of the various sorts of conditions and means of which account must be taken in working the situation through to a solution, or (to express it more accurately) the various sorts of conditions and means which need to be defined over against the purpose as the purpose gradually develops into detailed form. we may say, first of all, that there are _psychological_ conditions which must be taken into consideration in the case before us. our thesis is that in so far as a situation gives rise to the determination of psychological conditions and is advanced along the way toward final solution through determination of these, the situation is an ethical one. in other words, we hold that the ends at issue in the situation are "related" in so far as they depend upon the same set of psychological conditions. in so far as these statements are not true of the situation there must be a resort to economic judgment. by the general questions suggested above as presenting themselves to the agent we have indicated in what way the course of action taken must have regard to certain psychological considerations. entering upon the new way of life will inevitably lessen the agent's interest in his present professional pursuits and so make difficult, and in the end even irksome, any attempt at continuing in them either as a partial means of livelihood or as a recreation. the new work will be absorbing--as indeed it must be if it is to be worth while. in the same way the man must recognize that his nature is not one of the rare ones so richly endowed in capacity for sympathy that constant familiarity with general conditions of misery and suffering does not dull their fineness of sensibility to the special concerns and interests of particular individuals. if he takes his suffering fellow-men at large for his children, his own children will probably suffer just in so far the loss of a father's special sympathy and understanding care. and likewise he must be drawn away and isolated from his friends, for it will be hard for him, he must foresee, to hold free and intimate converse with men whose ways of thinking lie apart from his own controlling interest and for whose insensibility to the things that move him so profoundly he must come more and more to feel a certain impatience if not contempt. not to enlarge upon these possibilities and others of like nature, we must see that reflection upon the situation must presently bring to consciousness these various consequences of the kind of action which is proposed and a recognition that the ground of relation between them and the action proposed lies in certain qualities and limitations of his own nature. these latter are for him the general psychological conditions of action, his "empirical self," the general nature of which he has doubtless already come to be familiar with in many former situations perhaps wholly different in superficial aspect from from the present one. now, just in so far as there is this relation of mutual exclusiveness between the end proposed and certain of the standard ends or modes of conduct which are involved, judgment will be by the direct or ethical method of adjustment presently to be described. let us assume accordingly that a tentative solution of the problem has been reached to the effect that a portion of the lawyer's time shall be given to his profession and to his family life, and that the remainder shall be given to a moderate participation in the social propaganda. over against this tentative ethical solution, as its warrant in the sense explained above, will stand in the survey of the situation that may now be taken a certain fairly definite disposition or _anlage_ of the capacities and functions of the empirical self.[ ] now on the basis of the ethical solution thus reached there will be further study of the situation, perhaps as a result of failure in the attempt to carry the solution into practice, but more probably as a further preparation for overt action. forthwith it develops that the compromise proposed will be impossible. participation in the social agitation will excite hostility on the part of the classes from which possible clients would come and will cause distrust and a suspicion of inattention to details of business among the lawyer's present clientage. there are, in a word, a whole assemblage of "external" sociological conditions (and we need not stop to speak of physical conditions which co-operate with these and contribute to their effect) which effectually veto the plan proposed. in general these external conditions are such as to deprive the agent of the means of living in the manner which the ethical determination of the end proposes. in the present case, unless some other more feasible compromise can be devised, either the one extreme or the other must be chosen--either continuance in the profession and the corresponding general scheme of life or the social propaganda and reliance upon such scant and precarious income as it may incidentally afford. we can now define the economic aspect of a situation in terms of our present illustration. the end which the lawyer had in view in a vague and tentative way was, as we saw, defined with reference to his ethical standards--that is to say, a certain measure of participation in the new work was determined as satisfactory at once to his ideals of devotion to the cause of social justice and to his sense of obligation to himself and to his family. in this sense, logically speaking, a subject was defined to which a system of predicates, comprehended perhaps under the general predicate of right or good, applies. now, however, it appears, from the inspection of the material and social environment, that the execution of this purpose, perfectly in accord though it may be with the spiritual capacities and powers of the agent, is possible only on pain of certain other consequences, certain other sacrifices, which have not hitherto been considered. that a half-hearted interest in his profession would still not prevent his earning a moderate income from it was never questioned in the ethical "first approximation" to a final decision, but now the issue is fairly presented, and, as we must see, in a very difficult and distressing way; for the essence of the situation is that the ends now in conflict, that of earning a living and caring for his family and that of laboring for the social good, are not intrinsically (that is, from the standpoint of the empirical self) incompatible. on the contrary, these two ends are psychologically quite compatible, as the outcome of the ethical judgment shows; only the "external" conditions oppose them to each other. the difficulty of the case lies, then, just in the fact that the conflicting ends, both standing, as they do, for strong personal interests of the self, nevertheless cannot be brought to an adjustment by the direct method of an apportionment between them of the "spiritual resources" or "energies" of the self. instead, the case is one calling for an apportionment of the external means, and so, proximately, not for immediate determination of the final end, but for economic determination of the means. we come now to the task of describing, so far as this may be possible, the judgment or valuation-processes which correspond to the types of situation thus distinguished. we are able now to see that these must be constructive processes, in the sense that in and through them courses of conduct adapted to unique situations are shaped by the concourse of established standards with a new end which has arisen and put in its claim for recognition. we can see, moreover, that these valuation-processes effect a construction of a different order from that given in factual judgment. factual judgment determines external objects as means or conditions of action from standpoints suggested by the analysis and development of ends. judgments of valuation determine concrete purposes from standpoints given in recognized general purposes of the self--purposes which are general in virtue of their having been taken by abstraction from concrete cases, in which they have received particular formulation as purposes, and set apart as typical modes of conduct in general serviceable to the "energetic" self.[ ] logically factual judgment is at all times subordinate to valuational; when valuational judgment has become consciously deliberate, this logical subordination becomes explicit and factual judgment appears in its true character. its essential function is that of presenting the conditions which sanction and stimulate our ethically and economically determined purposes.[ ] finally, in the construction of purposes and reconstruction of standards in valuation the ideal of the expansion and development of the "energetic" self controls--not as a "presented" or contentual self prescribing particular modes of conduct, but as a principle prescribing the greatest possible openness to suggestion and an impartial application of the method of valuation to the case in hand. as we have said, in whatever sensuous image we figure the "energetic" self, its essential character lies in its function of stimulating methodical valuation. in place of the two-faced and ambiguous "presented" self, which is characteristic of the stage of conscience, we now have in the stage of valuation the "energetic" self on the one hand and standards on the other.[ ] we have now to consider the actual procedure of valuation, and first the ethical form as above defined. bearing in mind that we are not concerned with cases of obedience to authority or deference to conscience, let us take a case of genuine moral conflict such as we were considering some time since. suppose that one has the impulse to indulge in some form of amusement which he has been in the habit of considering frivolous or absolutely wrong. the end, as soon as imaged, or rather as the condition of its being imaged, encounters past habits of conduct symbolized by standards--standards which may be presented under a variety of forms, a maxim learned in early childhood, the ideal of a stoic sage or christian saint, the example of some friend, or a precept put in abstract terms, but which, however presented, are essentially symbolic of established habits of thought or action.[ ] solution of such a problem proceeds, in general, along two closely interwoven lines: ( ) collation and comparison of cases recognized as conforming to the standard, with a view to determining the standard type of conduct in a less ambiguous way, and ( ) definition of the relations between this type of conduct and other recognized types in the catalogue of virtues. now, these two movements are in fact inseparable, for, without reference to the entire system of virtues of which the one now asserting itself is a member, the comparison of cases with a view to definition of the virtue would be blind and hopeless of any outcome. the agent in the case before us desires to be temperate in amusement and to make profitable use of leisure time, but after all he may wonder whether these ideals really require the austerities of certain mediæval saints or the stoic _ataraxy_. the saint's feats of spiritual athletics may have served a useful purpose, in ruder times, as evidence of human power to lead a virtuous and thoughtful life, but can such self-denial now be required of the moral man? it is apparent, in short, that the superficially conceived ideal must be analyzed. we must consider the "spirit" of our saint or hero, not the letter of his conduct, as we say, and in interpreting it make due allowance for the conditions of the time in which he lived and the grade of general intelligence of those he sought to edify. whether our standard is a person or a parable or an abstractly formulated precept, the logic of the situation is the same in every case of judgment. the analysis of a standard cannot proceed without the "synthesis" or co-ordination of the type of conduct thereby defined with other distinguishable recognized types of conduct into a comprehensive ideal of life as a whole. in the last resort the implicit relations of all the virtues will be made explicit in the process of defining accurately any one of them. in the last resort, then, the predicate of the ethical judgment is the whole system of the recognized habits of the agent, and each judgment-process is in its outcome a readjustment of the system to accommodate the new habit that has been seeking admission. both the old habits and the new impulse have been modified in the process just as the intension of a class term and the particular "subsumed" under the class are reciprocally modified in the ordinary judgment of sense-perception. we are once more able to see that the process of ethical judgment or valuation is not a process of subsumption or classification, of _ascertaining_ the value of particular modes of conduct, but on the contrary a process of determining or _assigning_ value. each judgment process means a new and more or less thoroughgoing redetermination of the self and hence a fixation of the ethical value of the conduct whose emergence as a purpose gave rise to the process. the moral experience is not essentially and in its typical emergencies a _recognition_ of values with a view to shaping one's course accordingly, but rather a determining or a _fixation_ of values which shall serve for the time being, but be subject at all times to re-appraisal. if the present discussion were primarily intended as a contribution to general ethical theory, it would be a part of our purpose to show in detail that any formulation of an ethical ideal in contentual "material" terms must always be inadequate for practical purposes and hence theoretically indefensible. this, as we believe, could be shown true of the popularly current ideal of self-realization as well as of hedonism in its various forms and the older systems of conscience or the moral sense. these all are essentially fixed ideals admitting of more or less complete specification in point of content and regarded as tests or canons by appeal to which the moral quality of any concrete act can be deductively ascertained. they are the ethical analogues of such metaphysical principles as the cartesian god or the substance of spinoza, and the logic implied in regarding them as adequate standards for the valuation of conduct is the logic whereby the rationalist sought to deduce from concepts the world of particular things. the present desideratum in ethical theory would appear to be, not further attempts at definition of a moral ideal of any sort, but the development of a logical method for the valuation of ideals and ends in which the results of more modern researches in the theory of knowledge should be made use of--in which the concept of self should play the part, not of the concept of substance in a rationalistic metaphysics,[ ] but of such a principle as that of the conservation of energy, for example, in scientific inference.[ ] we have, then, in each readjustment of the activities of the self a reconstruction in knowledge of ethical reality--a reconstruction which at the same time involves the assignment of a definite value to the new mode of conduct which has been worked out in the readjustment. we conclude, then, that the ethical experience is one of continuous construction and reconstruction of an order of objective reality, within which the world of sense-perception is comprised as the world of more or less refractory means to the attainment of ethical purposes. in this process of construction of ethical reality current moral standards play the same part as concepts already defined--that is to say, the agent's present habits--do in the typical judgment of sense-perception. they play the part of symbols suggestive of recognized and heretofore habitual modes of action with reference to conduct of the type of the particular instance that is under consideration, serving thus to bring to bear upon the subject of the judgment sooner or later the entire moral self. the outcome is a new self, and so for the future a new standard, in which the past self as represented by the former standard and the new impulse have been brought to mutual adjustment. our position is that this adjustment is essentially experimental and that in it the _general principle_ of the unity and expansion of the self must be presupposed, as in inductive inference general principles of teleology, of the conservation of energy, and of organic interconnection of parts in living things are presupposed. the unity and increase of the self is not a test or canon, but a principle of moral experimentation.[ ] finally, we must note one further parallel between ethical judgment and the judgment of sense-perception and science. however the man of science may, as a nominalist, regard the laws of nature as mere observed uniformities of fact and particulars as the true realities, these same laws will nevertheless on occasion have a distinctly objective character in his actual apprehension of them. the stubbornness with which a certain material may refuse to lend itself to a desired purpose will commonly be reinforced, as a matter of apprehension, by one's recognition of the "scientific necessity" of the phenomenon. as offering resistance the thing itself, as we have seen, becomes objective; so also does the law of which this case may be recognized as only a particular example--and the other type of objectivity experience we need not here do more than mention as likewise possible in one's apprehension of the law as well as of the "facts" of nature. both types of objectivity attach to the moral law as well. the standard that restrains is one "above" us or "beyond" us. even kant, as the similitude of the starry heavens would suggest, was not incapable of a faint "emotion of the heteronomous," and authority in one form or another is a moral force whose objective validity as moral, both in its inhibiting and in its sanctioning aspects, human nature is prone to acknowledge. the apprehension of objectivity is everywhere, as we have held, emotional. one type of situation in which the moral law takes on this character is found in the interposition of the law to check a forward tendency; the other is found in the instant of transition from doubt to the new adjustment that has been reached. in the one case the law is "inexorable" in its demands. in the other case there are two possibilities: if the adjustment has been essentially a rejection of the new "temptation," the law which one obeys is one no longer inexorable, but sustaining, as a rock of salvation. if the adjustment is a distinctly new attitude, the sense of the objectivity of the principle embodied in it will commonly be less strong, if not for the time being almost wholly wanting; but in the moment of overt action it will in some degree wear the character of a firm truth upon which one has taken his stand. this general view of the logical constitution of the moral experience may suggest a comparison with the fundamental doctrine of the british intellectualist school. the intellectualist writers were very largely guided in their expositions by the desire of refuting on the one hand hobbes and on the other shaftesbury and hutcheson. against hobbes they wished to establish the obligatory character of the moral law entirely apart from sanction or enactment by political authority. against the sentimentalists they wished to vindicate its objectivity and permanence. this twofold purpose they accomplished by holding that the morality of conduct lies in its conformity to the "objective nature of things," the knowledge of which, in its moral aspects, is logically deducible from certain moral axioms, self-evident like those of mathematics. now this mathematical analogy is the key to the whole position of the intellectualist writers. by so conceiving the nature of knowledge these men seriously weakened their strong general position. mathematics is just that species of knowledge which is most remote from and apparently independent of any reference to conduct, and the intellectualists, by choosing it as their ideal, were thereby rendered incapable of explaining the obligatoriness of the moral law. an adequate psychology of knowledge would have obviated this difficulty in their system. the occasion for economic judgment is given, as we have seen, in a conflict between ends not incompatible, in view of any ascertainable conditions of the agent's nature as an empirical self, but inhibitory of each other in view of what we have described as conditions external to the agent. thus the lawyer in our illustration found his plan of compromise thwarted by the existence of such sociological conditions as would make the practice of his profession, in the manner intended, impossible, and so cut off his income. similarly the peasant in a european country finds that (for reasons which, more probably, he does not understand) he can no longer earn a living in the accustomed way, and emigrates to a country in which his capital and his physical energies may be more profitably employed. so also in the everyday lives of all of us ends and interests quite disparate, so far as any relation to each other through our psychical capacities is concerned, stand very frequently in opposition, nevertheless, and calling for adjustment. we must make a choice between amusement or intellectual pursuits or the means of æsthetic culture, on the one hand, and the common necessaries of life on the other, and the difficulty of the situation lies just in absence of any sort of "spiritual affinity" between these ends. there is no necessary ratio between the satisfaction of the common needs of life and the cultivation of the higher faculties--no ratio for which the individual can ever find a sanction in the constitution of his empirical self through the direct method of ethical valuation. the common needs must have their measure of recognition, but no attempted ethical valuation of them can ever come to a result convincingly warranted to the "energetic" self by psychological conditions. the economic situation as such is in this sense (that is, from the standpoint of any recognized ethical standards) unintelligible. it is this ethical unintelligibility that often lends a genuine element of tragedy to situations which press urgently and in which the ends at issue are of great ethical moment. it is no small matter to the emigrant, for example, that he must cut the very roots by which he has grown to the sort of man he finds himself to be. his whole nature protests against this violence, and questions its necessity, though the necessity is unmistakable and it would be quite impossible for him not to act accordingly. nevertheless, tragic as such a conflict may well be, it does not differ in any logically essential way, does not differ in its degree of strictly logical difficulty, from the ethically much less serious economic problems of our everyday life. now, we have already defined the economic act for which economic judgment is preparatory as being, in general terms, the diversion of certain means from a present use to which they have been devoted to a new use which has come to seem in a general way desirable.[ ] thus, in the cases just mentioned, the lawyer contemplates the virtual purchase of his new career by the income which his profession might in years to come afford him, the emigrant seeks a better market for his labor, and the pleasure-seeker and the ambitious student and the buyer of a commodity in the market propose to themselves, each one, the diversion from some hitherto intended use of a sum of money. manifestly it is immaterial from our logical point of view whether the means in question which one proposes to apply in some new way are in the nature of physical and mental strength, or materials and implements of manufacture ready to be used, or means of purchase of some sort wherewith the desired service or commodity may be obtained at once. the economic problem, to state it technically, is the problem of the _reapplicability of the means_, interpreting the category of means quite broadly. in a word, then, the method of procedure adapted to the economic type of situation is that of valuation of the means, not that of direct valuation of the ends. this method is one of valuation since, like the ethical method, it is determinative of a purpose, but it accomplishes this result in its own distinctive way. the problem of our present analysis will accordingly be how this method of valuation of the means is able to help toward an adjustment of disparate or unrelated ends which the ethical method is inadequate to effect. let us assume that a vague purpose of foreign travel, for example, has presented itself in imagination, and that the preliminary stage of ethical judgment has been passed through, with the result that the purpose, in a more definite form than it could have at first, is now ready for economic consideration. in the first place the cost of the journey must be determined, and this step, in terms of our present point of view, is simply a methodological device whereby certain ends which the standards involved in the stage of ethical judgment could not suggest or could not effectually take into co-operation with themselves in their determination of the end are brought into play. ascertaining the means suggests these disparate ends, these established modes of use of the means, with the result that the agent's "forward tendency" is checked. shall the necessary sums be spent in foreign travel or shall they be spent in the present ways--in providing various physical necessities and comforts, or for various forms of amusement, or in increasing investments in business enterprises? these modes of use do not admit of ethical comparison with the plan of foreign travel, and the agent's interest must therefore now be centered on the means. it is in this check to the agent's forward tendency that the logical status of the means is evinced. as merely so much money the means could only serve to further the execution of the purpose that is forming, since under the circumstances it could only prompt immediate expenditure. like the subject in factual judgment, the means in economic judgment have their problematic aspect which as effectually hinders the desired use of them as could any palpable physical defect. this problematic aspect consists in the fact of the present established mode of use which the now-forming purpose threatens to disturb, and it is the agent's interest in this mode of use that turns his attention to the valuation of the means. it need hardly be pointed out that in the economic life we find situations exactly corresponding to those of "conscience and temptation" and mechanical "pull and haul" which were discriminated in the ethical sphere and marked off from judgment properly so called. indeed it seems reasonable to think, on general grounds of introspection, that these methods of decision (if they deserve the name) are, relatively speaking, more frequently relied upon in the economic than in the moral life. the economic method of true judgment is roundabout and more complex and more difficult than ethical, and involves a more express recourse to those abstract conceptions which for the most part are only implicitly involved in valuation of the other type. the economic type of valuation, in fact, differs from the ethical, not in an absolute or essential way, but rather in the explicitness with which it brings to light and lays bare the vital elements in valuation as such. in general, then, the economic process would seem necessarily to embrace three stages, which will first of all be enumerated and then very briefly explained and discussed. these are: ( ) a preliminary consideration of the means necessary to attain the end--which must be vague and tentative, of course, for the reason that the end as imagined is so, as compared with the fulness of detail which must belong to it before it can be finally accepted; ( ) a consideration of the means, as thus provisionally taken, in the light of their present devotion to other purposes, this present devotion of them being the outcome, in some degree at least, of past valuation; ( ) final definition of the means with reference to the proposed use through an adjustment effected between this and the factors involved in the past valuation. . in the first stage as throughout, it must be carefully noted, the means are under consideration not primarily in their physical aspect, but simply as _subject to a possible redisposition_. thus it is not money as lawful currency receivable at the steamship office for an ocean passage, nor tools and materials and labor-power technically suitable for the production of a desired object, that is the subject of the economic judgment. the problem of redisposition would of course not be raised were the means not technically adaptable to the purpose, nor on the other hand can the means in the course of economic judgment, as a rule, escape some measure of further (factual) inquiry into their technical properties; but the standpoints are nevertheless distinct. again, it must be noted that the means in this first stage will be only roughly measured. the length of one's stay abroad, the size of the house one wishes to build, the purpose whatever it may be, is still undefined--these are in fact the very matters which the process must determine--and in the first instance it is "money in general" or "a large sum of money" with reference to which we raise the economic problem. the category of quantity is in fact essentially an economic one; it is essentially a standpoint for determining the means of action in such a way as to facilitate their economic valuation. the reader familiar with the writings of the austrian school of economists will easily recall how uniformly in their discussions of the principle of marginal utility these writers assume outright in the first place the division of the stock of goods into definite units, and then raise the question of how the value of a unit is measured. the stock contains already a hundred bushels of wheat or ten loaves of bread--apparently as a matter of metaphysical necessity--whereas in fact the essential economic problem is this very one of how "wheat at large" comes to be put in sacks of a certain size and "bread in general" to be baked in twelve-ounce loaves. the subdivision of the stock and the valuation of the unit are not successive stages, but inseparably correlative phases of the valuation-process as a whole. the outcome may be stated either way, in accordance with one's interest in the situation. . but the unmeasured means as redisposable in an as yet undetermined way bring to consciousness established measured uses to which the means have been heretofore assigned in definite amounts. in this way the process of determining a definite quantum as redisposable (which is to say, of attaining to a definite acceptable plan of conduct) can begin. how, then, does this fact of past assignment to uses still recognized as desirable figure in the situation? in the first place the past assignment may have been ( ) an outcome of past economic valuation, ( ) an unhesitating or non-economic act executive of an ethical decision, or ( ) an act of more or less conscious obedience to "conscience" or "authority." in either case it now stands as a course of conduct which at the time was, in the way explained above, _sanctioned_ to the agent, to the "energetic" self, by the means and conditions recognized as bearing upon it. in this sense, then, we have, in this recognition of the past adjustment and of the economic character which the means now have in virtue of it, what we may term a judgment of "energy-equivalence" between the means and their established uses. for to the agent it was the essential meaning of the sense of sanction felt when the means were assigned to these uses that the "energetic" self would on the whole be furthered thereby--and this in view of all the sacrifices that this use would entail, or in view of the sacrifices required for the production of the means, if the case were one in which the means were not at hand and could only be secured by a more or less extended production process. in the illustration we have been considering, it will be observed, there is an extensive schedule of present uses which the new project calls in question and from which the means must be diverted. this is in fact the commoner case. a new use of money will affect, as a rule, not simply a single present mode of expenditure, but will very probably involve a readjustment throughout the whole schedule of expenditure which our separate past valuations of money have in effect co-operated in establishing. so likewise if we wish to use part of a store of building materials or of food, or of any other subdivisible commodity, we encounter an ordered system of consumption rather than a single predetermined use which we have not yet enjoyed. where this is the case the whole process of valuation is greatly facilitated, but this is not essential. the means in cases of true economic valuation may be capable of but a single use, like a railroad ticket or a perishable piece of fruit, or of a virtually endless series of uses, like a painting or a literary masterpiece. whether the means figure as representing but a single use or stand for the conservation of an extensive system, their economic significance is the same. they are the "energy-equivalent" of this use or system of uses considered as an act or system of acts of consumption in furtherance of the self. their past assignment meant then and means now simply this, that the "energetic" self would thereby gain more than it would lose through the inevitable sacrifices. this is the economic significance of the means in virtue of which they are now problematic to the extent of checking, for a time at least, forward tendency toward the desired end.[ ] . the judgment of energy-equivalence, then, defines the inhibiting economic aspect of the means, and moreover defines it for the means as subdivided and set apart for a schedule of uses if this was the form of the past adjustments to which reference is made. the problem of the third stage of the process is that of "bringing subject and predicate together," as we have elsewhere expressed it--that is, of determining, in the light of the economic character of the means as just ascertained, what measure of satisfaction, if any, may be accorded to the new and as yet undefined desire. the new disposition of the means, if one is to be made, must bring to the "energetic" self a degree of furtherance and development which shall be sensibly as great as would come from the established method of consumption. the means, as economic, are means to the conservation of the old adjustment, and any new disposal of them or of any portion of them for a full or partial execution of the new purpose must make out at least as good a case. it must appear that the new disposition is not only physically possible, but also economically necessary in the light of the same principle of expansion of the self as sanctioned the disposition now in force. it must make the self in some way more efficient--whether more strong and symmetrical in body, more skilled in work, more clear of brain, or more efficient in whatever other concrete way may be desired. psychologically the sanction of any course of action which is taken as evidence of conformity to the general rule thus inadequately stated is the more or less strong sense of "relaxation" of attentive strain which comes with the shift of attention, in the final survey, from means to end. we may accordingly, for the sake of greater definiteness, restate in the following terms the process which has just been sketched: the ends in conflict at the outset are ends which do not sensibly bear upon each other through their dependence upon a common fund of psychical capacities or energies. they are related in the agent's experience solely through their dependence upon a common stock of physical means, and they do not therefore admit of adjustment through the ethical type of process. the economic process consists essentially of a revival in imagination of the experiences accompanying the former disposition of the means and a re-enforcement by these of the means in their adherence to that former and still recognized disposition. if an adapted form of the new end can be imagined which will mediate a like experience of relaxation when the attention shifts from the means, thus emotionally re-enforced in their economic status, to the end as thus conceived, the means will be recognized as economically redisposable. thus the method of valuation of the means makes possible, through appeal to the sensibly invariable experience of relaxation or assurance in the outcome of judgment, a co-ordination of disparate ends which the ethical method of direct adjustment could not effect.[ ] the economic process thus presents on analysis the same factors as does the ethical. on the subject side we have the means--which as economic are problematic as to their reapplicability. on the predicate side we have the suggested mode of reapplication in tension against conservative ideals of application to established purposes. just as it may be held that the general ethical predicate is that of right or good--that is, deserving of adoption into the system of one's ends--so the economic predicate applied to the means as these come in the end to be defined is the general concept reappliable. and in general the distinction of the types is not an ultimate one, for the more deliberately and rigorously the method of economic valuation is pursued--in such a case, for example, as that of the prospective emigrant--the stronger will be the agent's sense of a genuinely ethical sanction as belonging to the decision which is in the end worked out. the more certain and sincere, therefore, will be the agent's judgment that the means must be reapplied, for on the sense of sanction of which we speak rests the explicit judgment that the purpose formed is expansive of the self. from the analysis thus presented it must appear, therefore, that the economic type of judgment is in our sense a constructive process. its function is to determine a particular commodity or portion of a stock of some commodity in its economic character as _disposable_, and in performing this function it presents a definite reality in the economic order. moreover, in thus defining the particular, recourse is had to more or less distinctively namable economic standards which are in the last resort symbols representing established habits of consumption in the light of which the means, _prima facie_, seem not to be available for any other purposes. these economic standards, like ethical standards and the class concepts of science and our ordinary perceptual experience, are, with all due respect to nominalism, constitutive of a real world--a world which is real because it lends form and significance to our knowledge of particulars as stimuli to conduct. we have now before us sufficient reason for our thesis that the valuation-process in both its forms is constructive of an order of reality, and we have sufficiently explained the relation which the economic order bears to the inclusive and logically prior order of ethical objects and relations. we are now in a position to see that in being thus constructive of reality (taking the conception in its proper functional meaning) they are at the same time constructive of the self, since the reality which they construct is in its functional aspect the assemblage of means and conditions, of stimuli, in short, for the development and expansion of the self. we shall bring this main division of our study to a close with a series of remarks in explanation and illustration of this view. let us consider once more the factors present in the agent's final survey of the situation after the completion of the judgment-process and on the verge of action. these factors are, as we have seen, ( ) recognition of conditions sanctioning the purpose formed, ( ) recognition of the purpose as, in view of this sanction, warranted to the "energetic" self as an eligible method of expansion and development, and ( ) recognition of the "energetic" self, conversely, as in possession, in virtue of the favorable conditions given in factual judgment, of this new method of furtherance. these three factors are manifestly not so much factors co-operating in the situation as inseparable aspects of it distinguishable from each other and admitting of discriminative emphasis in accordance with the degree of reflective power which the individual may possess or choose to exercise. strictly speaking these three aspects are present in every conscious recognition of a purpose as one's own and as presently to be carried into effect, but they are not always present in equal conspicuousness, and never with equal logical importance for the individual. in fact this enumeration of aspects coincides with our enumeration of the three stages in the evolution of the individual's conscious moral attitude toward new purposes given in impulse--in the third of which the last named of these aspects comes to the fore with the others in logical or functional subordination to it. now it will be apparent on grounds of logic, as on the evidence of simple introspection, that in this third type of attitude--in the attitude of true valuation, that is to say--the energetic self cannot be identified with the chosen purpose. the purpose is a determinate specified act to be performed subject to recognized conditions, and with the use of the co-ordinated means; the self, on the other hand, is a process to which this particular purpose is, indeed, from the standpoint of the self's conservation and increase, indispensable, but which is nevertheless apart from the purpose in the sense that without the purpose it would still be a self, though perhaps a narrower and less developed one. our standpoint here as elsewhere, the reader must remember, is the logical. it is the standpoint of the agent's own interpretation of his experience of judgment during the judgment-process and at its close, and not the standpoint of the psychological mediation of this experience as a series of occurrences. thus we are here far from wishing to deny the general proposition that a man's purposes are an expression of his nature, as the psychologist might describe it, or the proposition that a man's conduct and his character are one and the same thing viewed from different points of view. we wish merely to insist upon the fact that these psychological propositions are not a true account of the agent's own experience of himself and of his purposes _while these latter are in the making or are on the verge of execution_. there is indeed no conflict between this "inside view" of the judgment-process and of the final survey and the psychological propositions just mentioned. the identity of conduct and character means not simply that as the man is so does he act, but quite as much, and in a more important way, that as he acts so is he and so does he become. it is, then, the essence of the agent's own view of the situation that his character is in the making and that the purpose is the method to be taken. to the agent the self is not, indeed, independent of the purpose, for plainly it is recognized that upon just this purpose the self is, in the sense explained, in a vital way dependent. nevertheless the self is in the agent's apprehension essentially beyond the purpose, and larger than the purpose, and even, we may say, metaphysically apart from it. now the conclusion which we wish to draw from this examination of the agent's attitude in judgment is that no formulation of an ideal self can ever be adequate to his purposes, not simply because any such formulation must, as green allows, inevitably be incomplete and inconsistent, but because the self as a process is in the agent's own apprehension of it inherently incapable of formulation. any formulation that might be attempted must be in terms of particular purposes (since in a modern ethical theory the self must be a "concrete" and not an abstract universal), and it is easy to see that any such would be, to the agent in the attitude of true ethical judgment, worse than useless. it could as contentual and concrete only be a composite of existing standards, more or less coherently put together, offered to the agent as a substitute for the new standard which he is trying to work out. if there were not need of a new standard there would be no judgment-process; the agent must be, to say the least, embarrassed, even if the unwitting imposture does not deceive him, when such a composite, useful and indeed indispensable in its proper place as a standard of reference and a source of suggestion, is urged upon him as suitable for a purpose which in the very nature of the case it is logically incapable of serving.[ ] to the agent, then, the "energetic" self can never be represented as an ideal--can never be expressed in terms of purpose--since it is in its very nature logically incongruous with any possible particular purpose or generalization of such purposes. it is commonly imaged by the agent in some manner of sensuous terms, but it is imaged, in so far as the case is one of judgment in a proper sense, for use as a stimulus to the methodical process of valuation--not as a standard, which if really adequate would make valuation unnecessary. the agent's consciousness of himself as "energetic" cannot be an ideal; it comes to consciousness only through the endeavor, first to follow, and then, in a later stage of moral development, to use ideals, and has for its function, as a presentation, the incitement of the process of methodical use of standards in the control of the agent's impulsive ends. it is not an anticipatory vision of the final goal of life, but the agent's coming to consciousness of the general impulse and movement of the life that is. it is an inevitable consequence of acceptance of a contentual view of the "energetic" self as one's ideal that reflective morality should tend to degenerate into an introspective conscientiousness constantly in unstable equilibrium between a pharisaical selfishness on the one hand and a morally scarcely more dangerous hypocrisy on the other. there is certainly much justice in the stinging characterization of "neo-hegelian egoism" which mr. taylor somewhere in his unsearchable book applies to the currently prevailing conventionalized type of idealistic ethics. if the self of the valuation-process is an ultimate goal of effort, then there must certainly be an irreconcilable contrast to the disadvantage of the latter between the plain man's objective desire for right conduct, as such, and for the welfare of his fellow-beings, and the moralist's anxious questionings of the rectitude of the motives by which his conformity to the fixed moral standard are prompted.[ ] into the value and significance of the attitude of conscientious examination of one's moral motives we are not here concerned to inquire, but need only insist, in accordance with our present view, that its value must be distinctly subordinate and incidental to the general course and outcome of the valuation-process. in the valuation-process, consciousness of self is not an object of solicitude, but simply, we repeat, a pure presentation of stimulus, having for its office the incitement, and if need be the reincitement, of the attitude of deference to the suggestions of old standards and openness to the petitions of new impulse, and of methodically bringing these to bear upon each other. the outcome of such a process, of course, cannot be predicted--and for the same reasons as make unpredictable the scientist's factual hypothesis. just as the scientist's data are incomplete and ill-assorted and unorganized, for the reason that they have, of necessity, been collected, and must at the outset be interpreted, in the light of present concepts, whose inadequacy the very existence of the problem at issue demonstrates, so the final moral purpose that shall be developed is not to be deduced from any possible inventory of the situation as it stands. the process in both cases is one of reconstruction, and the test of the validity of the reconstruction must in both cases be of the same essentially practical character. in both cases the process is constructive of reality, in the functional signification of the term. in both, the judgment process is constructive also of the self, in the sense that upon the determination of the agent's future attitude the cumulative outcome of his past attitudes is methodically brought to bear.[ ] v judgments of value are, then, objective in their import in the same sense as are the factual judgments in which the conditions of action are presented. the ideal problematic situation is, in the last resort, ethical, in the sense of requiring for its solution determination of the new end that has arisen with reference to existing standards. in structure and in function the judgment in which the outcome of this process is presented is knowledge, and objective in the only valid acceptation of the term. but, after all, it may be urged, is it not the essential mark of the objective that it should be accessible to all men, and not in the nature of the case valid for only a single individual? at best the objectivity of content which has been made out for the judgment of value is purely functional, and not such as can be verified by appeal to the consensus of other persons. the agent's _assurance_ of the reality of the economic or ethical subject-matter which he is endeavoring to determine, and his sense of the objectivity of the results which he reaches, need not be denied. these may well enough be illusions of personal prejudice or passion, or even normal illusions of the reflective faculty, like that of interpreting the secondary qualities of bodies as objective in the same sense as are the "bulk, figure, extension, number, and motion of their solid parts."[ ] any man can see the physical object to which i point, and verify with his own eyes the qualities which i ascribe to it, but no man can either understand or verify my judgment that the purpose i have formed is in accord with rational ideals of industry and self-denial, or that this portion of my winter's fuel may be given to a neighbor who has none. but this line of objection proves too much, for, made consistent with itself, it really amounts to a denial that the very judgment of sense-perception, to which it appeals so confidently as a criterion, has objective import. the first division of this study was intended to show that every object in the experience of each individual is for the individual a unique construction of his own, determined in form and in details by individual interests and purposes, and therefore different from that object in the experience of any other individual which in social intercourse passes current as the same. the real object is for me the object which functions in my experience, presenting problematic aspects for solution, and lending itself more or less serviceably to my purposes; and this object is, we hold, not the object as socially current, but the complete object which, as complete in its determination with reference to my unique purposes, cannot possibly have social currency. the objection as stated cuts away the very ground on which it rests, since the shortcoming which it finds in the judgment of ethical or economic value is present in the particular judgment of sense-perception also. the object about which i can assure myself by an immediate appeal to other persons is the object in its bare "conceptual" aspects--the object as a dictionary might define it, the commodity as it might be described in a trade catalogue, or the ethical act as defined by the criminal code or in the treatise of a moral philosopher. it is an object consisting of a central core or fixed deposit of meaning, which renders it significant in a certain general way to a number of persons, or even to all men, but which is not yet adequately known by me from the standpoint of my present forming purpose. in virtue of these conceptual characters it is adaptable to my purpose, which is as yet general and indeterminate; but in the nature of the case it cannot yet be known to me as applicable to my prospective concrete purpose, as this shall come to be through judgment. thus, if the test of objectivity of import is to be that the judgment shall present an object or a fact which, as presented, is socially current among men and not shut away in the individual intelligence apart from the possibility of social verification, then the apparent nominalism of the objection we are considering turns out to be the uttermost extreme of realism. such a test amounts to a virtual affirmation that the sole objective reality is the conceptual, and that the "accidents" of one's particular object of sense-perception are the arbitrary play of private preference or fancy. at this point, however, the objection may shift its ground and take refuge in some such position as the following: the real object is indeed the object which the individual knows in relation to his particular purpose, and it is indeed impossible that the individual's judgment should be limited in its content to coincidence with the conceptual elements of meaning which are socially current. the building-stone which one has judged precisely fit for a special purpose, the specimen which the mineralogist or the botanist examines under his microscope, the tool whose peculiarity of working one has learned to make allowance for in use--these all are, of course, highly individual objects, possessing for the person in question an indefinite number of objective aspects of which no other person can possibly be conscious at the time. and, more than this, even though the individual may, in his scrutiny of the object, have discovered no conspicuous new qualities in it which were not present in the socially current meaning, the object will still possess an individuality making it genuinely unique merely through its co-ordination with other objects in the mechanical process of working out the purpose in hand. it is at least an object standing here at just this time, a tool cutting this particular piece of stone and striking at this instant with this particular ringing sound, and these perhaps wholly nonessential facts will nevertheless serve to individualize the object (if one chances to think of them) in the sense of making it such a one as no other person knows. all this may be granted, the objection may allow, and yet the vital point remains; for this is not what it was intended, even in the first place, to deny. the vital point at issue is not whether the object which i know _is_ known as i know it by any other person, but whether, in the nature of things, it is one that _can_ be so known. herein, then, lies the difference between judgments of fact and judgments of value. the mineralogist can train his pupil to see precisely what he himself sees; and so likewise in any case of sense-perception, the object, however recondite may be the qualities or features which one may see in it, _can_ nevertheless be seen by any other person in precisely the same way on the single, more often not insuperably difficult, condition that the discoverer shall point these out or otherwise prepare the other for seeing them. but with the ton of coal which one may judge economically disposable for a charitable purpose the case stands differently, since it is not in its visible or other physical aspects that the ton of coal is here the subject of the judgment. it is as having been set apart _by oneself exclusively_ for other uses that the ton of coal now functions as an object and now possesses the character which the economic judgment has given it; and the case stands similarly with a contemplated act, of telling the truth in a trying situation. the valuation placed upon the commodity or upon the moral act depends essentially upon psychological conditions of temperament, disposition, mood, or whim into which it would be impossible for another person to enter, and these depend upon conditions of past training and native endowment which can never occur or be combined in future in precisely the same way for any other individual. in short, the physical object is _describable_ and _can_ be made socially current, though doubtless with more or less of difficulty, if other persons will attend to it and learn to see it as i see it; but the value of an economic object or a moral act depends upon my desires and feelings, and therefore must remain a matter of my private appreciation. in answering this amended form of the objection it is entirely unnecessary to discuss the issue of fact which it has raised as to whether or not complete description of a physical object or event is a practical or theoretical possibility. it need only be pointed out that at best such complete description can only be successful in its purpose on condition that the individual upon whom the experiment is tried be willing to attend and have the requisite "apperceptive background." the accuracy with which another person's knowledge shall copy the knowledge which i endeavor to impart to him must manifestly depend upon these two leading conditions, not to mention also the measure of my own pedagogical and literary skill. any consideration of such a purely psychological problem as is here suggested would be entirely out of place in a discussion the purpose of which is not that of analyzing the process of judgment, but that of interpreting its meaning aspects. let us grant the entire psychological possibility of making socially current in the manner here suggested the most highly individual and concrete cognition of an object one may please, and let us grant, moreover, that this possibility has been actually realized. this concurrent testimony of the witness will doubtless confirm one's impression of the accuracy of the process of observation and inference whereby the knowledge which has been imparted was first gained, but we must deny that it can do more than this. for indeed, apart from some independent self-reliant conviction of the objective validity of the knowledge in question, how should another's assent be taken as _confirmation_ and not rather as evidence of one's own mere skill in suggestion and of the other's susceptibility thereto? we must deny that even in the improved form the criterion of social currency is a valid one. in a word, the social currency of knowledge to the extent to which it can exist requires as its condition, and is evidence of, the equal social currency of certain interests, purposes, or points of view for predication; and if it be possible to make socially current an item of concrete knowledge, with all its concrete fulness of detail, then _a fortiori_ it must be possible to make socially current the concrete individual purpose with reference to which this item of knowledge first of all took form. whether such a thing be psychologically possible at all the reader may decide; but if it be possible in the sphere of knowledge of fact, then it must be possible in the sphere of valuation. in short, judgment in either field, in definition of a certain object or commodity or moral act as, for the agent, an objective fact possessing certain characters, involves the tacit assumption of social verifiability as a matter of course; but it does not rest upon this assumption, nor is this assumption the essence of its meaning. to say that my judgment is socially verifiable, that my concrete object of perception or of valuation would be seen as i see it by any person in precisely my place, is merely a tautological way of formally announcing that _i have made the judgment_ and have now a definite object which to me has a certain definite functional meaning. thus, instead of drawing a distinction between the realms of fact and value, as between what is or can be common to all intelligent beings and what must be unique for each individual one, we must hold that the two realms are coextensive. the socially current object answers to a certain general type of conscious purpose or interest active in the individual and so to a general habit of valuation, and the concrete object to a special determination of this type of purpose with reference to others in the recognized working system of life. the agent's final attitude, on the conclusion of the judgment-process, may be expressed in either sort of judgment--in a judgment of the value of commodity or moral purpose, or in a judgment of concrete fact setting forth the "external" conditions which warrant the purpose to the "energetic" self. throughout the judgment-process there is a correlation between the movement whereby the socially current object develops into the adapted means and that whereby the socially current type of conduct develops into the defined and valued purpose.[ ] at this point, however, a second general objection presents itself. however individual the content of my knowledge of physical fact may be, and however irrelevant, from the logical point of view, to my confidence in its objective validity may be the possibility of sharing it with other persons, nevertheless it refers to an object which is in some sense permanent, and therein differs from my valuations. in economic valuation i reach a definition of a certain commodity and am confirmed in it by all the conditions that enter into my final survey of the situation. but my desire for the new sort of consumption may fail, and so expose my valuation to easy attack from any new desire that may arise; or my supply of the commodity in question may be suddenly increased or diminished, and my valuation of the unit quantity thereby changed. likewise my ethical valuation may have to be reversed (as mr. taylor has insisted) by reason of a change of disposition or particular desire which makes impossible, except in obedience to some other and inclusive valuation, further adherence to it. and these changes take place without any accompanying sense of their doing violence to objective fact or, on the other hand, any judgment of their being in the nature of corrections of previous errors in valuation, and so more closely in accordance with the truth. moreover, a new valuation, taking the place of an old, does not supplement its predecessor as one set of judgments about a physical object may supplement another, made from a different point of view, but does literally take its place, and this without necessarily condemning it as having been erroneous. this general objection rests upon a number of fairly obvious misconceptions, and its strength is apparent only. in the first place, the question of the objectivity of any type of judgment must in the end, as we have seen, reduce itself to a question of the judgment's import to the agent. however the agent's valuations may shift from time to time, each several one will be sanctioned to the agent by the changed conditions exhibited in the inventory which the agent takes at the close of judgment which has formed it. the conditions have changed, and the valuation of the earlier purpose has likewise changed; but the new purpose is sanctioned by the new conditions, and the test of the presumed validity of the new valuation can only be in the manner already discussed[ ] the test of actual execution of the purpose. in the change, as the agent interprets the situation, there is no violation of the former purpose nor a nearer approach to truth. each valuation is true for the situation to which it corresponds. we are obviously not here considering the case of error. an error in valuation is evidenced to the agent, not by the need of a new valuation answering to changed conditions, but by the failure of a given valuation to make good its promise, although to all appearance conditions have remained unchanged. if the conditions have changed, then the purpose and the conditions _must_ be redetermined, if the expansion of the "energetic" self is to continue; but the former valuation does not thereby become untrue. these brief remarks should suffice by way of answer, but it will serve advantageously to illustrate our general position if we pursue the objection somewhat farther. the physical object is, nevertheless, _permanent_, it will be said, and this surely distinguishes it from the object (now freely acknowledged as such) of the value-judgment. to one man gold may be soluble in _aqua regia_ and to another worth so many pence an ounce, but different and individual as are these judgments and the standpoints they respectively imply, the gold is _one_, impartially admitting at the same time of both characterizations. on the other hand, one cannot judge an act good and bad at once. the purpose of deception that may be good is one controlled and shaped by ideals quite different from those which permit deception of the evil sort--is, in truth, taken as a total act, altogether different from the purpose of deception which one condemns, and not, like the "parcel of matter" in the two judgments about gold, the subject of both valuations. a brief consideration of the meaning of this "parcel of matter" will easily expose the weakness of the plea. in the last analysis the "parcel of matter" must for the agent reduce itself, let us say, to certain controllable energies centering about certain closely contiguous points in space and capable, in their exercise, of setting free or checking other energies in the system of nature. thus, put in _aqua regia_ the gold will dissolve, but in the atmosphere it retains its brilliant color, and in the photographer's solution its energies have still a different mode of manifestation. and thus it would appear that the various predicates which are applied to "gold" imply, each one, a unique set of conditions. gold is soluble in _aqua regia_, but not if it is to retain its yellow luster; which predicate is to be true of it depends upon the conditions under which the energies "resident in the gold" are to be set free, just as the moral character of an act depends upon the social conditions obtaining at the time of its performance--that is, upon the ideals with reference to which it has been shaped in judgment. how can one maintain that in a literal and concrete physical sense gold in process of solution is the "same" as gold entering into chemical combination? surely the energy conditions which constitute the "gold" in the two processes are not the same--and can one nowadays hope to find sameness in unchangeable atoms?[ ] in a word, the permanent substance or "real essence" that admits of various mutually supplementary determinations corresponding to diverse points of view is, strictly speaking, a convenient abstraction, and not an existent fact in time--and we shall maintain that the same species of abstraction has its proper place, and in fact occurs, in the sphere of moral judgment. the type of moral conduct that in every actual case of its occurrence in the moral order is determined in some unique and special way by relation to other standards is precisely analogous to the "substance" that is now dissolved in _aqua regia_ and now made to pass in the form of current coin, but cannot be treated in both ways at once. both are abstractions. the "gold" is a name for the general possibility of attaining any one of a certain set of particular ends by appropriately co-ordinating certain energies, resident elsewhere in the physical system, with those at present stored in this particular "parcel of matter;" the result to be attained depends not alone upon the "parcel of matter," but also upon the particular energies brought to bear upon it from without. now let us take a type of conduct which is sometimes judged good and sometimes bad. deception, for example, is such a type--and as a type it simply stands for the general possibility of furtherance or detriment to the "energetic" self according as it is determined in the concrete instance by ideals of social well-being or by considerations of immediate personal advantage. for the type-form of conduct--when considered, not as a type of mere physical performance, but as conduct in the technical sense of a possible purpose of the self--is, in the sense we have explained, a symbol for the general possibility of access or dissipation of spiritual energy--energy which must be set free by the bringing to bear of other energies upon it, and which furthers or works counter to the enlargement and development of the self according to the mode of its co-ordination with other energies which the self has already turned to its purposes.[ ] but actual conduct is concrete always and never typical; and so likewise, we have sought to show, actual "substance," the objective thing referred to in the factual judgment, is always concrete and never an essence. it is not a fixed thing admitting of a simultaneous variety of conflicting determinations and practical uses, but absolutely unique and already determined to its unique character by the whole assemblage of physical conditions which affect it at the time and which it in turn reacts upon. in the moral as in the physical sphere the fundamental category would, on our present account, appear to be that of energy. the particular physical object given in judgment is a concrete realization, in the form of a particular means or instrument, of that general possibility of attaining ends which the concept of a fixed fund of energy, interpreted as a logical postulate or principle of inference, expresses. the particular moral or economic act is a particular way in which the energy of the self may be increased or diminished. in both spheres the reality presented in the finished judgment is objective as being a stimulus to the setting free of the energies for which it stands. once more, then, our answer to the objection we have been considering must be that the object as the permanent substrate is merely an abstract symbol standing for the indeterminate means in general set over against the self. corresponding to it we have, on the other side, the concept of the "energetic" self--the self that is purposive in general, expansive somehow or other. the function of completed factual judgment in the development of experience is, we have held, that of warranting to the agent the completed purpose which his judgment of value expresses. this view calls for some further comment and illustration in closing the present division. in the first place the statement implies that the conditions which factual judgment presents in the "final survey" as sanctioning the purpose have not _determined_ the purpose, since prior to the determination of the purpose the conditions were not, and could not be, so presented. the question, therefore, naturally arises whether our meaning is that in the formation of our purposes in valuation the recognition of existing conditions plays no part. our answer can be indicated only in the barest outline as follows: the agent must, of course, in an economic judgment-process, recognize and take account of such facts as the technical adaptability of the means he is proposing to use to the new purpose that is forming, as also of environing conditions which may affect the success which he may meet with in applying them. he must consider also his own physical strength and qualities of mind with a view to this same technical problem. and similarly in ethical valuation, as we have seen, the psychology of the "empirical ego" must play its part. but the conditions thus recognized are, as we might seek to show more in detail, explainable as the outcome of past factual judgment-processes, and on the occasion of their original definition in the form in which they now are known played the sanctioning part of which we have so often spoken. they therefore correspond to the agent's accepted practical ideals, so that the control which his past experience exercises over his present conduct may be stated equally well in either sort of terms--in terms of his prevailing recognized standards, or in terms of his present knowledge of the conditions which his new purpose must respect. thus, in general, the concept of a physical order conditioning the conduct of all men and presented in a definite body of socially current knowledge is the logical correlate of the moral law conceived as a categorical imperative prescribing certain types of conduct. thus the error of regarding the agent's conduct in a present emergency as an outcome of existing determining conditions is logically identical with the corresponding error of the ethical theory of self-realization. the latter holds the logical possibility of a determinate descriptive ideal (already realized in the unchanging absolute self) which is adequate to the solution of all possible ethical problems. the former holds that all conduct must be subject to the determining force of external conditions which, if not at present completely known, are at least in theory knowable. the physical universe in its original nebulous state contained the "promise and potency" of all that has been in the way of human conduct and of all that is to be. into the fixed mechanical system no new energy can enter and from it none of the original fund of energy can be lost. this mechanical theory of conduct is the essential basis of the hedonistic theory of ethics; and it would not be difficult to show that green's criticism of this latter and his own affirmative theory of the moral ideal (as also the current conventional criticism of hedonism in the same tenor by the school of green) are in a logical sense identical with it. for the assumption that conduct is determined by existing objective conditions is precisely the logical correlate of the concept of a contentual and "realizable" ideal moral self.[ ] we may now interpret, in the light of our general view of the function of factual judgment, the concept of the "empirical self" referred to in our discussion of the various types of sanctioning condition which may enter into the "final survey." the "empirical self" of psychological science is a construction gradually put together by psychologist or introspective layman as an interpretation of the way in which accepted concrete modes of conduct, in the determination of which standards have been operative, have worked out in practice to the furtherance or impoverishment of the "energetic" self. we have seen that the ambiguous presented self which functions in the moral attitude of obedience to authority or to conscience gives place in the attitude of conscious valuation to apprehension of the "energetic" self, on the one hand, and descriptive concepts of particular types of conduct, on the other. the "empirical self" at the same time makes its appearance as a constantly expanding inventory of the "spiritual resources" which the "energetic" self has at its disposal. these are the functions of the soul which a functional psychology shows us in operation--powers of attention, strength of memory, fertility in associative recall, and the like--and these are the resources wherewith the "energetic" self may execute, and so exploit to its own furtherance, the purposes which, in particular emergencies, new end and recognized standards may work out in co-operation.[ ] vi in the foregoing pages we have consistently used the expressions "ethical and economic judgment" and "judgment of valuation" as synonymous. this may have seemed to the reader something very like a begging of the question from the outset, as taking for granted that very judgmental character of our valuational experience which it was the professed object of our discussion to establish. we are thus called upon very briefly to consider, first of all, the relations which subsist between the consciousness of value and the process which we have described as that of valuation. this will enable us, in the second place, to determine the logical function which belongs to the consciousness of value in the general economy of life. the consciousness of value is a perfectly definite and distinctive psychical fact mediated by a doubtless highly complex set of psychical or ultimately physiological conditions. as such it admits of descriptive analysis, and in a complete theory of value such descriptive analysis should certainly find a place. it would doubtless throw much light upon the origin of valuation as a process, and of valuing as an attitude, and admirably illustrate the view of the function of the consciousness of value to which a logical study of valuation as a process seems to lead us. this problem in analysis belongs, however, to psychology, and therefore lies apart from our present purpose; nor is it necessary to the establishment of our present view to undertake it. it is necessary for our purpose only to suggest, for purposes of identification, a brief description of the value-consciousness, and to indicate its place in the process of reflective thought. the consciousness of value may best be described, by way of first approximation, in the language of the austrian economists as a sense of the "importance" to oneself of a commodity or defined moral purpose. it belongs to the agent's attitude of survey or recapitulation which ensues upon the completion of the judgment-process and is mediated by attention to the ethical or economic object in its newly defined character of specific conduciveness to the well-being of the self. the commodity, in virtue of its ascertained physical properties, is adapted to certain modes of use or consumption which, through valuation of the commodity, have come to be accepted as desirable. the moral act likewise has been approved by virtue of its having certain definite sociological tendencies, or being conducive to the welfare and happiness of a friend. thus commodity or moral act, as the case may be, has a determinate complexity of meaning which has been judged as, in one sense, expansive of the self, and the value-consciousness we may identify as that sense of the valued object's importance which is mediated by recognition of it as the bearer of this complexity of concrete meaning. the meaning is, as we may say, "condensed" or "compacted" into the object as given in sense-perception, and because the meaning stands for expansion of the self, the object in taking it up into itself receives the character of importance as a valued object. the sense of importance thus is expressive of an attitude upon the agent's part. the concrete meanings which make up the content of the object's importance would inevitably, if left to themselves, prompt overt action. the commodity would forthwith be applied to its new use or the moral act would be performed. the self would, as we may express it, possess itself of the spiritual energies resident in the chosen purpose. the attitude of survey, however, inhibits this action of the self and the sense of importance is the resulting emotional apprehension of the value of the object hereby brought to recognition. now, it should be carefully observed that the particular concrete emotions appropriate to the details of the valued purpose are not what we here intend. the purpose may spring from some impulse of self-interest, hatred, patriotism, or love, and the psychical material of its presentation during the agent's survey will be the varied complex of qualitative emotion that comes from inhibition of the detailed activities which make up the purpose as a whole. so also the apprehension of the physical object of economic valuation is largely, if not altogether, emotional in its psychical constitution. psychologically these emotions are the purpose--they are the "stuff" of which the purpose as a psychical fact occurring in time is made. but we must bear in mind that it is not the purpose as a psychical fact that is the object of the agent's valuing--any more than is the tool with which one cuts perceived as a molecular mass or as an aggregation of centers of ether-stress. as a cognized object of value the purpose is, in our schematic terminology, a source of energy for the increase of the self, and thus the consciousness of value is the perfectly specific emotion arising from restraint put upon the self in its movement of appropriation of this energy. in contrast with the concrete emotions which are the substance of the purpose as presented, the consciousness of value may be called a "formal" emotion or the emotion of a typical reflective attitude. the valuing attitude we may then describe as that of "resolution" on the part of the self to adhere to the finished purpose which it now surveys, with a view to exploitation of the purpose. the connection between the valuation-process and the consciousness of value may be stated thus: the valuation-process works out (and necessarily in cognitive, objective terms) the purpose which is valued in the agent's survey. but this development of the purpose is at the same time determination of the "energetic" self to acceptance of the purpose that shall be worked out. thus the valuation-process is the source of the consciousness of value in the twofold way ( ) of defining the object valued, and ( ) of determining the self to the attitude of resolution to adhere to it and exploit it.[ ] the consciousness of value is the apprehension of an object in its complete functional character as a factor in experience. the function of the consciousness of value must now be very briefly considered. the phenomenon is a striking one, and apparently, as the economists especially have insisted, of much practical importance in the conduct of life.[ ] and yet on our account of the phenomenon, as it may appear, the problem of assigning to it a function must be, to say the least, difficult. for the consciousness of value is, we have held, emotional, and, on the conception of emotion in general which we have taken for granted throughout our present discussion, this mode of being conscious is merely a reflex of a state of tension in activity. as such it merely reports in consciousness a process of motor co-ordination already going on and in the nature of the case can contribute nothing to the outcome. now if it were in a direct way as immediately felt emotion that the consciousness of value must be functional if functional at all, then the problem might well be given up; but it would be a serious blunder to conceive the problem in this strictly psychological way. a logical statement of the problem would raise a different issue--not the question of whether emotion as emotion can in any sense be functional in experience, but whether the consciousness of value and emotion in general may not receive reflective interpretation and thereby, becoming objective, play a part as a factor in subsequent valuation-processes. indeed, the psychological statement of the problem misses the entire point at issue and leads directly to the wholly irrelevant general problem of whether any mode of consciousness whatever can, _as consciousness_, put forth energy and be a factor in controlling conduct. the present problem is properly a logical one. what is the agent's apprehension of the matter? in his subsequent reflective processes of valuation does the consciousness of value, which was a feature of the survey on a past occasion, receive recognition in any way and so play a part? this is simply a question of fact and clearly, as a question relating to the logical content of the agent's reflective process, has no connection with or interest in the problem of a possible dynamic efficacy of consciousness as such. the question properly is logical, not psychological or metaphysical. thus stated, then, the problem seems to admit of answer--and along the line already suggested in our account of economic valuation.[ ] recognition of the fact that the consciousness of value was experienced in the survey of a certain purpose on an earlier occasion confirms this purpose, holding the means, in an economic situation, to their appointed use and strengthening adherence to the standard in the ethical case. this recognition serves as stimulus to a reproduction, in memory, of the cognitive details of the earlier survey, and so in the ideal case to a more or less complete and recognizably adequate reinstatement of the earlier valuing attitude, and so to a reinstatement of the consciousness of value itself. the result is a strengthening of the established valuation, a more efficacious control of the new end claiming recognition, and an assured measure of continuity of ethical development from the old valuation to the new. the function thus assigned to the consciousness of value finds abundant illustration elsewhere in the field of emotion. the stated festivals of antiquity commemorative of regularly recurrent phases of agricultural and pastoral life, as also the festivals in observance of signal events in the private and political life of the individual, would appear to find, more or less distinctly, here their explanation. these festivals must have been prompted by a more or less conscious recognition of the social value inherent in the important functions making up the life of the community, and of the individual citizen as a member of the community and as an individual. they secured the end of a sustained and enhanced interest in these normal functions by effecting, through a symbolic reproduction of these, an intensified and glorified experience of the emotional meaning normally and inherently belonging to them.[ ] in the same way the rites of the religious cults of greece, not to mention kindred phenomena so abundantly to be found in lower civilizations as well as in our own, served to fortify the individual in a certain consistent and salutary course of institutional and private life.[ ] it has been taken for granted throughout that there are but two forms of valuation-process, the ethical and the economic. the reason for this limitation may already be sufficiently apparent, but it will further illustrate our general conception of the valuation-process briefly to indicate it in detail. what shall be said, for example, of the common use of the term "value" in such expressions as the "value of life," the "emotional value" of an object or a moral act, the "natural value" of a type of impulsive activity? in these uses of the word the reference is apparently to one's own incommunicable inner experience of living, of perception of the object, or of the impulse, which cannot be suggested to any other person who has not himself had the experience. my pleasure, my color-sensation in its affective aspect, my emotion, are inner and subjective, and i distinguish them by such expressions as the above from the visible, tangible object to which i ascribe them as constituting its immediate or natural value to me. this broader use of the term "value" has not found recognition in the foregoing pages, and it requires here a word of comment. so long as these phases of the experience of the object are not recognized as separable in thought from the object viewed as an external condition or means, they would apparently be better characterized in some other way. if, however, they are so recognized, and are thereby taken as determinative of the agent's practical attitude toward the thing, we have merely our typical situation of ethical valuation of some implied purpose as conducive to the self and economic valuation of the means as requisites for execution of the purpose. our general criterion for the propriety of terming any mode of consciousness the _value_ of an object must be that it shall perform a logical function and not simply be referred to in its aspect of psychical fact. the feeling or emotion, or whatever the mode of consciousness in question may be, must play the recognized part, in the agent's survey of the situation, of prompting and supporting a definite practical attitude with reference to the object. if, in short, the experience in question enters in any way into a conscious purpose of the agent, it may properly be termed a value.[ ] Æsthetic value also has not been recognized, and for the opposite reason. the sense of beauty would appear to be a correlate of relatively perfect attained adjustment between the agent and his natural environment or the conditions suggested more or less impressively by the work of art. there must, indeed, be present in the æsthetic experience an element of unsatisfied curiosity sufficient to stimulate an interest in the changing or diverse aspects of the beautiful object, but this must not be sufficient to prompt reflective judgment of the details presented. on the whole, the æsthetic experience would appear to be essentially post-judgmental and appreciative. it comes on the particular occasion, not as the result of a judgment-process of the valuational type, but as an immediate appreciation. as an immediate appreciation it has no logical function and on our principles must be denied the name of value. our standpoint must be that of the experiencing individual. the æsthetic experience as a type may well be a development out of the artistic and so find its ultimate explanation in the psychology of man's primitive technological occupations in the ordinary course of life. it is, as we have said, of the post-judgmental type, and so may very probably be but the cumulative outcome of closer and closer approximations along certain lines to a perfected adjustment with the conditions of life. it may thus have its origin in past processes of the reflective valuational type. nevertheless, viewed in the light of its actual present character and status in experience, the æsthetic must be excluded from the sphere of values. thus the realms of fact and value are both real, but that of value is logically prior and so the "more real." the realm of fact is that of conditions warranting the purposes of the self; as a separate order, complete and absolute in itself, it is an abstraction that has forgotten the reason for which it was made. reality in the logical sense is that which furthers the development of the self. the purpose that falls short of its promise in this regard is unreal--not, indeed, in the psychological sense that it never existed in imagination, but in the logical sense that it is no longer valued. within the inclusive realm of reality the realm of fact is that of the means which serve the concrete purposes which the self accepts. the completed purpose, however, is not _means_, since still behind and beyond it there can be no other concrete valued purpose which it can serve. nor is it an ultimate _end_, since in its character of accepted and valued end the self adheres _to_ it, and it therefore cannot express the _whole_ purpose of the self to whose unspecifiable fulness and increase of activity it is but a temporary probational contributor. it is rather in the nature of a formula or method of behavior to which the self ascribes reality by recognizing and accepting it as its own. xi some logical aspects of purpose introductory whenever and wherever it was discovered that the content of experience as given in immediate perception could be reconstructed through ideas, then and there began to emerge such questions as these: what is the significance of this reconstructive power? what is the relation between it and the immediate experience? what is the relative value of each in experience as a whole? what is their relation to truth and error? if thinking leads to truth, and thought must yet get its material from perception, how then shall the product of thought escape infection from the material? on the other hand, if truth is to be found in the immediate experience, can it here be preserved from the blighting effects of thought? for so insistent and pervasive is this activity of thought that it appears to penetrate into the sanctum of perception itself. turning to a third possibility, if it should be found that truth and error are concerned with both--that they are products of the combined activity of perception and reflection--then just what does each do? and what in their operations marks the difference between truth and error? or still again, if truth and error cannot be found in the operations of perception and reflection as such, then they must be located in the relation of these processes to something else. if so, what is this something else? out of such questions as these is logic born. there may be those who will object to some of these questions as "logical" problems--those who would limit logic to a description of the forms and processes of reconstruction, relegating the question of the criterion of truth and error to "epistemology." this objection we must here dismiss summarily by saying that, by whatever name it is called, a treatment of the forms and processes of thought must deal with the criterion of truth and error, since these different "forms" are just those which thought assumes in attempting to reach truth under different conditions. certainly in the beginning the greeks regarded their newly discovered power of thought as anything but formal. indeed, it soon became so "substantial" that it was regarded as simply a new world of fact, of existence alongside of, or rather above, the world of perception. but socrates hailed ideas as deliverers from the contradictions and paradoxes into which experience interpreted in terms of immediate sense-perception had fallen. in the concept socrates found a solution for the then pressing problems of social life. the socratic universal is not a mere empty form which thought imposes upon the world. it is something which thought creates in order that a life of social interaction and reciprocity may go on. this need not mean that the greeks were reflectively conscious of this, but that this was the way the concept was actually used and developed by socrates. in attempting to formulate the relation between this new world of ideas and immediate sense-experience, plato constructed his scheme of substantiation and participation. the platonic doctrine of substantiation and participation is an expression of the conviction that anything so valuable as socrates had shown ideas to be could not be merely formal or unreal. up to the discovery of these ideas reality lay in the "substances" of perception. hence in order to have that reality to which their worth, their value in life, entitled them, the ideas must be substantiated. this introduction of the newly discovered ideas into the world of substances and reality wrought, of course, a change in the conception of the latter--a change which has well-nigh dominated the entire philosophic development ever since. let us recall that the aim of socrates was to find something that would prevent society from going to pieces under the influence of the disintegrating conception of experience as a mere flux of given immediate content. now, in the concepts socrates discovered the basis for just this much-needed wholeness and stability. moreover, the fact that unity and stability were the actual social needs of the hour led not only to the concepts which furnished them being conceived as substantial and real, but to their being regarded as a higher type of reality, as "more real" than the given, immediate experiences of perception. they were higher and more real because, just then, they answered the pressing social need. the ideas supplied this unity because they furnished ends, purposes, to the given material of perception. the given is now given for something; for something more, too, than mere contemplation. socrates also showed, by the most acute analysis, that the content of these ends, these purposes, was social through and through. from the ethical standpoint this teleological character of the idea is clearly recognized. but as "real," the ideas must be stated in the metaphysical terms of substance and attribute. here the social need is abstracted from and lost to sight. the fundamental attributes of the ideas are now a metaphysical unity and stability. hence unity and stability, wholeness and completeness, are the very essence of reality, while multiplicity and change constitute the nature of appearance. thus does plato's reality become, as windelband says, "an immaterial eleaticism which seeks true being in the ideas without troubling itself about the world of generation and occurrence which it leaves to perception and opinion."[ ] now it is the momentum of this conception of reality as a stable and complete system of absolute ideas, the development of which we have just roughly sketched, that is so important historically. why this conception of reality, which apparently grew out of a particular historical situation, should have dominated philosophic theory for over two thousand years appears at first somewhat puzzling. those who still hold and defend it will of course say that this survival is evidence of its validity. but, after all, our human world may be yet very young. it may be that "a thousand years are but as yesterday." at any rate philosophy has never been in a hurry to reconstruct conceptions which served their day and generation with such distinction as did the platonic conception of reality. and this is true to the evolutionary instinct that experience has only its own products as material for further construction. on the other hand, the principle of evolution with equal force demands that only as _material_, not as final forms of experience, shall these products continue. it may be that philosophy has not yet taken the conception of evolution quite seriously. at all events it is certain that long after it has been found that, instead of being eternal and complete, the concept undergoes change, that it has simply the stability and wholeness demanded by a particular and concrete situation; after it has been discovered, in other words, that the stability and wholeness, instead of attaching to the content of an idea, are simply the functions of any content used as a purpose--after all this has been accepted in psychology, the conception of truth and reality which arose under an entirely different conception of the nature of thought still survives. this change in the conception of the character of the ideas, with no corresponding change in the conception of reality, marks the divorce of thought and reality and the rise of the epistemological problem. let us recall that in plato the relation between the higher and ultimate reality, as constituted by the complete and "eternal ideas," and the lower reality of perception, is that of archetype and ectype. perceptions attempt to imitate and copy the ideas. now, when the ideas are found to be changing, and when further the interpenetration of perception and conception is discovered, reality as fixed and complete must be located elsewhere. and just as in the old system it was the business of perception to imitate the "eternal ideas," so here it is still assumed that thought is to imitate the reality wherever now it is to be located. and as regards the matter of location, the old conception is not abandoned. the elder plato is mighty yet. reality must still be a completed system of fixed and eternal "things in themselves," "relations," or "noumena" of some sort which _our_ ideas, now constituted by both perception and conceptional processes, are still to "imitate," "copy," "reflect," "represent," or at least "symbolize" in some fashion. from this point on, then, thought has two functions: one, to help experience meet and reorganize into itself the results of its own past activity; the other, to reflect or represent in some sense the absolute system of reality. for a very long time the latter has continued to constitute the logical problem, the former being relegated to the realm of psychology. but this discovery of the reconstructive function of the idea and its assignment to the jurisdiction of psychology did not leave logic where it was before, nor did it lighten its task. logic could not shut its eyes to this "psychological" character of the idea.[ ] indeed, logic had to take the idea as psychology described it, then do the best it could with it for its purpose. the embarrassment of logic by this reconstructive character of the idea even aristotle discovered to some extent in the relation of the platonic perceptions to the eternal ideas. he found great difficulty in getting a flowing stream of consciousness to imitate or even symbolize an eternally fixed and completed reality. and since we have discovered, in addition, that the idea is so palpably a reconstructive activity, the difficulties have not diminished. in such a situation it could only be a question of time until solutions of the problem should be sought by attempting to bring together these two functions of the idea. perhaps after all the representation of objects in an absolute system is involved in the reconstruction of our experience. or perhaps what appears as reconstructions of our experience--as desiring, struggling, deliberating, choosing, willing, as sorrows and joys, failures and triumphs--are but the machinery by which the absolute system is represented. at any rate, these two functions surely cannot be regarded as belonging to the idea as color and form belong to a stone. we should never be satisfied with such a brute dualism as this. without any further historical sketch of attempts at this synthesis, i desire to pass at once to a consideration of what i am sure everyone will agree must stand as one of the most brilliant and in every way notable efforts in this direction--mr. royce's aberdeen lectures on "the world and the individual." it is the purpose here to examine that part of these lectures, and it is the heart of the whole matter, in which the key to the solution of the problem of the relation between ideas and reality is sought precisely in the purposive character of the idea. this will be found especially in the "introduction" and in the chapter on "internal and external meaning of ideas."[ ] i. the purposive character of ideas with his unerring sense for fundamentals, mr. royce begins by telling us that the first thing called for by the problem of the relation of ideas to reality is a discussion of the nature of ideas. here mr. royce says he shall "be guided by certain psychological analyses of the mere contents of our consciousness, which have become prominent in recent discussion."[ ] your intelligent ideas of things never consist of mere imagery of the thing, but always involve a consciousness of how you propose to act toward the thing of which you have ideas.... complex scientific ideas viewed as to their conscious significance are, as professor stout has well said, plans of action, ways of constructing the object of your scientific consciousness.... by the word idea, then, as we shall use it, when, after having criticised opposing theory, we come to state in these lectures our own thesis, i shall mean in the end any state of consciousness, whether simple or complex, which when present is then and there viewed as at least a partial expression, or embodiment of a single conscious purpose.... in brief, an idea in my present definition may, and in fact always does, if you please, appear to be representative of a fact existent beyond itself. but the _primary_ character which makes it an idea is _not its representative character_, is not its vicarious assumption of the responsibility of standing for a being beyond itself, but is its inner character as _relatively fulfilling the purpose_, that is as presenting the partial fulfilment of the purpose which is in the consciousness of the moment wherein the idea takes place.[ ]... now this purpose, just in so far as it gets a present conscious embodiment in the contents, and in the form of the complex state called the idea, constitutes what i shall hereafter call the internal meaning of the idea.[ ]... but ideas often seem to have a meaning; yes, as one must add, finite ideas always undertake or appear to have a meaning that is not exhausted by this conscious internal meaning presented and relatively fulfilled at the moment when the idea is there for our finite view. the melody sung, the artists' idea, the thought of your absent friend, a thought on which you love to dwell, all these not merely have their obvious internal meaning as meeting a conscious purpose by their very presence, but also they at least appear to have that other sort of meaning, that reference beyond themselves to objects, that cognitive relation to outer facts, that attempted correspondence with outer facts, which many accounts of our ideas regard as their primary inexplicable and ultimate character. i call this second, and for me still problematic, and derived aspect of the nature of ideas, their apparently external meaning.[ ] from all this it is quite evident that mr. royce accepts and welcomes the results of the work of modern psychology on the nature of the idea. the difficulty will come in making the connection between these accepted results and the platonic conception of ultimate reality as stated in the following: to be means simply to express, to embody the complete internal meaning of _a certain absolute system of ideas_. a system, moreover, which is genuinely implied in the true internal meaning or purpose of every finite idea, however fragmentary.[ ] it may be well to note here in passing that, notwithstanding the avowed subordination here of the representative to the reconstructive character of the ideas, the former becomes very important in the chapter on the relation of internal to external meaning, where the problem of truth and error is considered. in this account of the two meanings of the idea, which i have tried to state as nearly as possible in the author's own words, there appear some conceptions of idea, of purpose, and of their relation to each other, that play an important part in the further treatment and in determining the final outcome. in the description of the internal meaning there appear to be two quite different conceptions of the relation of idea to purpose. one regards the idea as itself constituting the purpose or plan of action; the other describes the idea as "the partial fulfilment" of the purpose. ( ) "complex scientific ideas, viewed as to their conscious significance, are, as professor stout has well said, _plans of action_." ( ) "you sing to yourself a melody; you are then and there conscious that the melody, as you hear yourself singing it, _partially fulfils_ and embodies a purpose."[ ] when we come to the problem of the relation between the internal and external meaning, we shall find that the idea as internal meaning comes into a third relation to purpose, viz., that of _having_ the further purpose to agree or correspond to the external meaning. "is the correspondence reached between idea and object the precise correspondence that the idea itself intended? if it is, the idea is true.... thus it is not mere agreement, but intended agreement, that constitutes truth."[ ] thus the idea is ( ) the purpose, ( ) the partial fulfilment of the purpose, and ( ) has a further purpose--to correspond to an object in the "absolute system of ideas." the first statement of the internal meaning as constituting the plan or purpose is, i take it, the conception of the internal meaning as an ideal construction which gives a working form, a definition to the "indefinite sort of restlessness" and blind feeling of dissatisfaction out of which the need of and demand for thought arises.[ ] this accords with the scientific conception of the idea as a working hypothesis. if this interpretation of idea were steadily followed throughout, it is difficult to see how it could fail to lead to a conception of reality quite different from that described as "a certain absolute system of ideas." the second definition of internal meaning is the one in which it is stated as the "partial expression," "embodiment," and "fulfilment" of a single conscious purpose, and in which subsequently and consequently the idea is identified with "any conscious act," for example, singing. the first part of the statement appears to say that the idea of a melody is in "partial fulfilment" of the idea regarded as the purpose to sing the melody. but, as the first statement of internal meaning implies, how can one have a purpose to sing the melody except in and through the idea? it is precisely the construction of an idea that transforms the vague "indefinite restlessness" and dissatisfaction into a purpose. the idea is the defining, the sharpening of the blind activity of mere sensation, mere want, into a plan of action. however, mr. royce meets this difficulty at once by the statement that the term "idea" here not only covers the activity involved in forming the idea, _e. g._, the idea of singing, but includes the action of singing, which fulfils this purpose. "in the same sense _any conscious act_ at the moment when you perform it not merely expresses, but is, in my present sense, an idea."[ ] but this sort of an adjustment between the idea as the purpose and as the fulfilment of the purpose raises a new question. what here becomes of the distinction between immediate and mediating experience? surely there is a pretty discernible difference between experience as a purposive idea and the experience which fulfils this purpose. to call them both "ideas" is at least confusing, and indeed it appears that it is just this confusion that obscures the fundamental difficulty in dealing, later on, with the problem of truth and error. to be sure, the very formation of the idea as the purpose, the "plan of action," is the beginning of the relief from the "indefinite restlessness." on the other hand, it defines and sharpens the dissatisfaction. when this vague unrest takes the form of a purpose to attain food or shelter, or to sing in tune, it is of course the first step toward solution. but this very definition of the dissatisfaction intensifies it. the idea as purpose, then, instead of being the fulfilment, appears to be the plan, the method of fulfilment. the fulfilling experience is the further experience to which the idea points and leads. to follow a little farther this relation between the purposive and fulfilling aspects of experience, it is of course apparent that the idea as the purpose, the "plan of action," must as a function go over into the fulfilling experience. my purpose to sing the melody must remain, in so far as the action is a conscious one, until the melody is sung. i say "as a function," for the specific content of this purpose is continuously changing. the purpose is certainly not the same in content after half the melody has been sung as it is at the beginning. this means that the purpose is being progressively fulfilled; and as part of the purpose is fulfilled each moment, so a part of the original content of the idea drops out; and when the fulfilling process of this particular purpose is complete, or is suspended--for, in mr. royce's view, it never is complete in human experience--that purpose then gives way to some other, perhaps one growing out of it, but still one regarded as another. a purpose realized, fulfilled, cannot persist as a purpose. we may desire to repeat the experience in memory; _i. e._, instead of singing aloud, simply, as mr. royce says, "silently recall and listen to its imagined presence." but here we must remember that the memory experience, as such, is not an idea in the logical sense at all. it is an immediate experience that is fulfilling the idea of the song which constitutes the purpose to recall it, just as truly as the singing aloud fulfils the idea of singing aloud. shouting, whistling, or "listening in memory to the silent notes" may all be equally immediate, fulfilling experiences. doubtless the idea as purpose involves memory, as mr. royce says.[ ] but it is a memory used as a purpose, and it is just this use of the memory material as a purpose that makes it a logical idea. in its content the purposive idea is just as immediate and as mechanical as any other part of experience. "psychology explains the presence and the partial present efficacy of this purpose by the laws of motor processes, of habit, or of what is often called association."[ ] here "idea," however, simply means, as mr. royce takes it in his second statement, conscious content of any sort. but this is not the meaning of "idea" in the logical sense. the logical idea is a conscious content used as an organizer, as "a plan of action," to get other contents. if, for example, in the course of writing a paper one wishes to recall an abstract distinction, as the distinction dawns in consciousness, it is not an idea in the logical sense. it is just as truly an immediate fulfilling experience as is a good golf stroke. so in the mathematician's most abstruse processes, which mr. royce so admirably portrays, the results for which he watches "as empirically as the astronomer alone with his star" are not ideas in the logical sense; they are immediate, fulfilling experiences.[ ] the distinction between the idea as the mediating experience--that is, the logical idea--and the immediate fulfilling experience is therefore not one of content, but of use. there is a sense, however, in which the idea as a purpose can be taken as the partial fulfilment of another purpose; in the sense that any purpose is the outgrowth of activity involving previous purposes. this becomes evident when we inquire into the "indefinite restlessness" and dissatisfaction out of which the idea as purpose springs. dissatisfaction presupposes some activity already going on in attempted fulfilment of some previous purpose. if one is dissatisfied with his singing, or with not singing, it is because one has already purposed to participate in the performance of a company of people which now he finds singing a certain melody, or one has rashly contracted to entertain a strenuous infant who is vociferously demanding his favorite ditty. this is only saying that any given dissatisfaction and the purpose to which it gives rise grow out of activity involving previous purposing. but this does not do away with the distinction between the idea as a purpose and the immediate fulfilling experience. if the discussion appears at this point to be growing somewhat captious, let us pass to a consideration of the relation between internal and external meanings, where the problem of truth and error appears, and where the vital import of these distinctions becomes more obvious. ii. purpose and the judgment mr. royce begins with the traditional definition of truth, which he then proceeds to reinterpret: truth is very frequently defined in terms of external meaning as _that about which we judge_.... in the second place, truth has been defined as the _correspondence between our ideas and their objects_[ ].... when we undertake to express the objective validity of any truth, we use judgment. these judgments, if subjectively regarded, that is, if viewed merely as processes of our own present thinking, whose objects are external to themselves, involve in all their more complex forms, combinations of ideas, devices whereby we weave already present ideas into more manifold structure, thereby enriching our internal meaning; but the act of judgment has always its other, its objective aspect. the ideas when we judge are also to possess external meaning.... it is true, as mr. bradley has well said, that the intended subject of every judgment is reality itself. the ideas that we combine when we judge about external meanings are to have value for us as truth only in so far as they not only possess internal meaning, but also imitate, by their structure, what is at once other than themselves, and, in significance, something above themselves. that, at least, is the natural view of our consciousness, just in so far as, in judging, we conceive our thought as essentially other than its external object, and as destined merely to correspond thereto. now we have by this time come to feel how hard it is to define the reality to which our ideas are thus to conform, and about which our judgments are said to be made, so long as we thus sunder external and internal meanings.[ ] _the universal judgment._--the problem is, then, to discover just the nature and ground of this relation between the internal and external meaning, between the idea and its object. this relation is established in the act of judgment. taking first _the universal judgment_, we find here that the internal meaning has at best only a negative relation to the external meaning. to say that all a is b is in fact merely to assert that the real world contains no objects that are a, but that fail to be of the class b. to say that no a is b is to assert that the real world contains no objects that are at once a and b.[ ] the universal judgments then "tell us indirectly what is in the realm of external meaning; but only by first telling us what is not."[ ] however, these universal judgments have after all a positive value in the realm of internal meaning; that is, as mere thought. this negative character of the universal judgments holds true of them, as we have just said, just in so far as you sunder the external and internal meaning, and just in so far as you view the real as the beyond, and as the merely beyond. if you turn your attention once more to the realm of ideas, viewed as internal meaning, you see, indeed, that they are constantly becoming enriched in their inner life by all this process. to know by inner demonstration that + = and that this is necessarily so, is not yet to know that the external world, taken merely as the beyond, contains any true or finally valid variety of objects at all, any two or four objects that can be counted.... on the other hand, so far as your internal meaning goes, to have experienced within that which makes you call this judgment necessary, is indeed to have observed a character about your own ideas which rightly seems to you very positive.[ ] this passage deserves especial attention. in the light of kant, and in view of mr. royce's general definition of the judgment as the reference of internal to external meanings, one is puzzled to find that for the mathematician the positive value of the judgment "two and two are four" is confined to the realm of internal meaning. to be sure, mr. royce says that this limitation of the positive value of the universal judgment to the world of internal meaning occurs only when the external and internal meaning are sundered. but the point is: does the mathematician or anyone else ever so sunder as to regard the judgment "two and two are four" as of positive value only as internal meaning? indeed, in another connection mr. royce himself shows most clearly that mathematical results are as objective and as empirical as the astronomer's star.[ ] nor would it appear competent for anyone to say here: "of course, they are not internal meanings _after_ we come to see, through the kind offices of the epistemologist, that the internal meanings are valid of the external world." we are insisting that they are never taken by the mathematician and scientists at first as merely internal meaning whose external meaning is then to be established. surely the mathematical judgment, or any other, does not require an epistemological midwife to effect the passage from internal to external meaning. the external meaning is there all the while in the form of the diagrams and motor tensions and images with which the mathematician works. the difficulty here again seems to be that the distinction above discussed between the idea in the logical sense, as purpose, and the immediate fulfilling experience is lost sight of. the relation between two and four is not first discovered as a merely internal meaning. it is discovered in the process of fulfilling some purpose involving the working out of this relation. so the sum of the angles of a triangle is not discovered as a mere internal meaning whose external meaning is then to be found. it is found _in working with_ the triangle. it is discovered _in_ the triangle. and, once more, it matters not if the triangle here is a mere memory image. in relation to the purpose, to the logical idea, it is as truly external and objective as pine sticks or chalk marks. the streams of motor, etc., images that flow spontaneously under the stimulus of the purpose are just as immediate fulfilling experiences as the manipulation of sticks or chalk lines. the difficulty in keeping the universal judgment, as a judgment, in terms of merely internal meaning may be seen from the following: as to these two types of judgments, the universal and the particular, they both, as we have seen, make use of experience. the universal judgments arise in the realm where experience and idea have already fused into one whole; and this is precisely the realm of internal meanings. here one constructs and observes the consequences of one's construction. but the construction is at once an experience _of fact and an idea_.... upon the basis of such ideal constructions one makes universal judgments. these in a fashion still to us, at this stage, mysterious, undertake to be valid of that other world--the world of external meaning.[ ] one is somewhat puzzled to know just what is meant by the fusion "of experience and idea." we must infer that it means the fusion of some aspect of experience which can be set over against idea, and this has always meant the external meaning, and this interpretation seems further warranted by the statement immediately following which describes the fusion as one "of _fact_ and idea." the situation then seems to be this: an internal and an external meaning, a fact and an idea, "fuse into one whole" and thus constitute that which is yet "precisely the realm of internal meanings," which aims to be valid of still another world of external meanings. and this waives the question of how experience fused into one whole can be an internal meaning, since as such it must be in opposition and reference to an external meaning; or conversely, how experience can be at once fact _and_ idea and still be "fused into one whole." nor does the difficulty disappear when we turn to the aspects of universality and necessity. what is the significance and basis of universality and necessity as confined merely to the realm of internal meaning? so far as your internal meaning goes, _to have experienced within that which makes you call this judgment necessary_ is, indeed, to have observed a character about your own ideas which rightly seems to you very positive.[ ] but what is it that we "experience within" which makes us call this judgment necessary? in the discussion of the relation of the universal judgment to the disjunctive judgment, through which the former is shown to get even its negative force, there is an interesting statement: one who inquires into a matter upon which he believes himself able to decide in universal terms, _e. g._, in mathematics, has present to his mind, at the outset, questions such as admit of alternative answers. "a," he declares, "in case it exists at all, is either b or c." further research shows universally, perhaps, that no a is b. the last sentence is the statement referred to. what is meant by "further research shows universally, perhaps, that no a is b"? what kind of "research," internal or external, can show this? in short, there appears to be as much difficulty with universality and necessity in the realm of internal meaning as in the reference of internal to external meaning.[ ] instead, however, of discussing this point, mr. royce pursues the problem of the relation of the external and internal meaning, and finds that regarded as sundered there is no basis so far for even the negative universality and necessity in the reference of the internal meaning to the external. for at this point arises the ancient question, how can you know at all that your judgment is universally valid, even in this ideal and negative way, about that external realm of validity, in so far as it is external, and is merely your other,--the beyond? must you not just dogmatically say that that world must agree with your negations? this judgment is indeed positive. but how do you prove it? the only answer has to be in terms which already suggest how vain is the very sundering in question. if you can predetermine, even if but thus negatively, what cannot exist in the object, the object then cannot be merely foreign to you. it must be somewhat predetermined by your meaning.[ ] but in the universal judgment this determination, as referred to the external meaning, is only negative. _the particular judgment._--it is then through the particular judgment that the universal judgment is to get any positive value in its reference to the external meaning. as has been repeatedly pointed out in the discussions on recent logic, the particular judgments--whose form is some a is b, or some a is not b--are the typical judgments that positively assert being in the object viewed as external. this fact constitutes their essential contrast with the universal judgments. they undertake to cross the chasm that is said to sunder internal and external meanings; and the means by which they do so is always what is called "external experience." it is now high time to ask why the internal meaning seeks this external meaning. why does it seek an object? why does it want to cross the chasm? in other words, what is the significance of the demand for the particular judgment? in the introduction we have been told, as a matter of description, that the internal meanings do seek the external meaning, but why do they? we have also been told that universal judgments "develop and enrich the realm of internal meaning." why, then, should there be a demand for the external meaning, for a further object? the answer is: we have our internal meanings. we develop them in inner experience. there they get presented as something of universal value, _but always in fragments_. they, therefore, so far dissatisfy. we conceive of the other wherein these meanings shall get some sort of final fulfilment.[ ] it is, then, the incomplete and fragmentary character of the internal meaning that demands the particular judgment. the particular judgment is to further complete and determine the incomplete and indeterminate internal meaning. and yet no sooner is this particular judgment made than we are told that "it is a form at once positive, and very unsatisfactorily indeterminate." again:[ ] the judgments of experience, the particular judgments, express a positive but still imperfect determination of internal meaning through external experience. the limit or goal of this process would be an individual judgment wherein the will expressed its own final determination.[ ] apparently, then, the particular judgment to which the internal meaning appeals for completion and determination only succeeds in increasing the fragmentary and indeterminate character. this brings us to another "previous question." just what are we to understand by this "fragmentary" and "indeterminate" character of the internal meaning? in what sense, with reference to what, is it incomplete and fragmentary? later we shall be told that it is with reference to "its own final and completely individual expression." this is to be reached in the individual judgment. and if we ask what is meant by this final, complete, and individual expression--which, by the way, no human being can experience--we read, wondering all the while how it can be known, that it is simply "the expression that seeks no other," that "is satisfied," that "is conclusive of the search for perfection."[ ] waiving for the present questions concerning the basis of this satisfaction and perfection, all this leaves unanswered our query concerning the other end of the matter, viz., the meaning and criterion of the fragmentary and indeterminate character of these internal meanings. if we here return to the first definition of internal meaning of the idea as a purpose in the sense of "a plan of action," such as "singing in tune," or getting the properties of a geometrical figure, it does not seem difficult to find a basis and meaning for this fragmentary and indeterminate character. first we may note in a general way that it is of the very essence of a plan or purpose to lead on to a fulfilling experience such as singing in tune, or reaching a mathematical equation. but here this fulfilling experience to which the plan points is not a mere working out of detail inside the plan itself, although, indeed, this does take place. if this were all the fulfilling experience meant, it is difficult to see how we should escape subjective idealism.[ ] we start with a relatively indeterminate idea and end with a more determinate _idea_, though, indeed, there is yet no criterion for this increased determination. to be sure, the idea as a plan of action, as has already been stated, does undergo change and does become, if you please, more definite and complete as a plan; but this does not constitute its fulfilment. its fulfilment surely is to be found in the immediate experiences of singing, etc., to which the idea points and leads. the fragmentary and incomplete character of the internal meaning as a plan of action does not, then, after all, so much describe the plan itself as it does the general condition of experience out of which the idea arises. experience takes on the form of a plan, of an idea, precisely because it has fallen apart, has become "fragmentary." it is just the business of the internal meaning, as mr. royce so well shows, to form a plan, an ideal, an hypothetical synthesis that shall stimulate an activity, which shall satisfactorily heal the breach. "fragmentary" is a quality, then, that belongs, not to the idea in itself considered, but to the general condition of experience, of which the idea as a plan is an expression. if, now, the fragmentary character of the internal meaning is determined simply with relation to the fulfilling experiences, such as singing in tune, adjustments of geometrical figures, etc., to which it points and leads, it seems as if the completion of the internal meaning must be defined in the same terms. and this would appear to open a pretty straight path to the redefinition of truth and error. iii. the criterion of truth and error at the outset, truth was defined as the "correspondence" or "agreement" of an idea with its object. but we have seen that correspondence or agreement with an object means the completion and determination of the idea itself, and since the idea is here a specific "plan of action," it would seem that the "true" idea would be the one that can complete itself by stimulating a satisfying activity. the false idea would be one that cannot complete itself in a satisfying activity, such as singing in tune, constructing a mathematical equation, etc., and just this solution is very clearly expounded by our author. in the case of mathematical inquiry, in just so far as we _pause satisfied_ we observe that there "is no other" mathematical fact to be sought _in the direction of the particular inquiry in hand_. satisfaction of purpose by means of _presented fact_ and such determinate satisfaction as sends us to no other experience for further light and fulfillment, precisely this outcome is itself the other that is sought when we begin our inquiry.[ ] so "when other facts of experience are sought," if i watch for stars or for a chemical precipitate, or for a turn in the stock market, or in the sickness of a friend, my ideas are true when they are satisfied with "the presented facts." again, it follows that the finally determinate form of the object of any finite idea is that form which the idea itself would assume whenever it became individuated, or in other words, became a completely determined idea, an idea or will fulfilled by a wholly adequate empirical content, for which no other content need be substituted or from the point of view of the satisfied idea, could be substituted.[ ] in such passages as these it seems clear that the test of the truth of an idea is its power to bring us to the point where we "pause satisfied," where "no other content need be substituted," etc. nor in such passages does there seem to be any doubt of reaching satisfaction in particular cases. here, it appears, we _may_ sing in tune, we _may_ get the desired precipitate, and possibly even interpret the stock market correctly. of course, the discord, the hunger, the loss, will come again; but so will new ideas, new truths. "man thinks in order to get control of his world and thereby of himself."[ ] then the control actually gained must measure the value, the truth of his thought. do you wish to sing in tune, "then your musical ideas are false if they lead you to strike what are then called false notes."[ ] it should also be noticed that here this desired determination does not consist in a further determination of the mere idea as such. it is found in "the presented fact," in the immediate activity of singing, of getting precipitates, etc. as has already been pointed out, it is only by using the term "idea" for both the purpose and the fulfilling act of singing that this "pause of satisfaction" can be ascribed to the further determination of the idea. as such, as also before remarked, the sort of determination that the idea here gets means its termination, its disappearance in the immediate experiences of singing, etc., to which it leads. the "indefinite restlessness" of hunger and cold would scarcely be satisfied by getting more determinate and specific _ideas_ only of food and shelter. the satisfaction comes when the ideas are "realized," when the "plans" are swallowed up in fulfilment. but in all this nothing has been said about "the certain absolute system of ideas," nor does there appear to be here any demand for it. to be sure, in the passages just considered, experience has been found to become "fragmentary," but it has also been found capable of healing, of wholing itself, not of course into any "final whole," but into the unity of "satisfaction" as regards "the particular inquiry in hand." there is of course failure as well, but this also is not final. it means simply that we must look farther for the "pause of satisfaction," that we must construct another idea, another "plan of action." but, after having shown that the idea as a plan of action may lead to satisfaction in the particular case, and that its success or failure so to do is one measure of its truth or falsity, we are now suddenly aroused to the fact that after all thought does not lead us to the completed "absolute system of ideas," to a final stage of eternal unbroken satisfaction. but never in our human process of experience do we reach that determination. it is for us the object of love and of hope, of desire and of will, of faith and of work, but never of present finding.[ ] if at this point one asks: whence this absolute system of ideas? why have we to reckon with it at all? there appears to be little that is satisfying. indeed, it seems difficult to get rid of the impression that this "certain absolute system of ideas" is on our hands as a philosophical heirloom from the time of plato, so hallowed by time and so established by centuries of acceptance that we have ceased to ask for its credentials. to ground it in the "essentially fragmentary character of human experience" appears to be a _petitio_, for experience does not appear "essentially fragmentary" in this sense until after the absolute system has been posited. and this brings to notice that at this point both the fragmentary and unitary characters of experience take on new meaning. so far this fragmentary character has been defined with reference to "the particular inquiry in hand." now, since the distinction between absolute and human experience has emerged, the fragmentary character becomes an absolute quality of the latter in contrast with the former. so, _mutatis mutandis_, of unity. up to this point unity, wholeness, has been possible within human experience in the case of particular problems, such as singing in tune, etc. but with the appearance of the absolute system of ideas, wholeness is now the exclusive quality of the latter, as incompleteness is of human experience, though of course the _working_ unity, the unity resulting in "pauses of satisfaction," must still remain in the latter. the problem now is to somehow work the absolute system of ideas into connection with the conception of the idea as a purpose, as a concrete plan of action. here is where the third conception of the relation between idea and purpose, described at the beginning, comes into play--the conception in which the idea, instead of being the purpose, or the fulfilment of a purpose, _has_ the purpose to correspond with, or represent "its own final and completely individual expression," contained in the absolute system. from the previous standpoint the idea's "own final and completely individual expression" has been found in the fulfilling experiences of singing in tune, getting mathematical equations, chemical precipitates, etc. here this complete individual experience can never be found in finite, human experience, but must be sought in the absolute system--and this can be only "the object of love and hope, of desire and will, never of present finding." notwithstanding the many previous protestations that the purposive function of the idea is its "primary" and "most essential" character, we are here forced to fall back upon correspondence--representation as the primary, the essential, and indeed, it appears at times, as the sole function. for in the attempt to bring these two functions together the purposive function is swallowed up in the representative. the idea still is, or has a purpose, a "plan of action," but this purpose, this plan, is now nothing but to represent and correspond with its own final and completed form in the absolute system. by this simple _coup_ is the purposive function of the idea reduced at once to the representative. nor is it pertinent to urge at this point that every purpose involves representation, that the plan must be some sort of an image or scheme which symbolizes and stimulates the thing to be done. this no one would question, but now the sole "thing to be done" apparently is to perfect this representation of the complete and individual form in the absolute system.[ ] once more, an array of passages could be marshaled from almost every page refuting any such interpretation as this, but they would be passages expounding the part played by the idea in such concrete experiences as singing, measuring, etc., not in representing an absolute system of ideas. even as regards the latter one might urge that, by insisting on the active character of the idea, we could after all regard this absolute system as a life of will after the fashion of our own, were it not at once described as "the complete embodiment," "the final fulfilment," of finite ideas. a life consisting of mere fulfilment seems a baffling paradox. and its timeless character only adds to the difficulty. moreover, if we regard the system as constituted by such concrete activities as measuring and singing, etc., while we have saved will, we shall now have to fallback upon our first conception of truth as found in the idea which unifies the fragmentary condition of experience as related to specific problems, not fragmentary as related to an absolute system. this brings us to the final and crucial point of the discussion, the part which purpose plays in the determination of _truth_ and _error_ from the standpoint of "the absolute system of ideas." when is this purpose of the idea to correspond with its absolute, final, and completed form fulfilled, or partially fulfilled? and here at the very outset is a difficulty. we have read repeatedly that the idea is itself "the partial fulfilment of a purpose." it is now to seek an object which shall increase this degree of fulfilment, but still this fulfilment shall be incomplete. and when we come to consider error, it too will be found to consist in a partial fulfilment. so it appears that there are three stages of "partial fulfilment" to be discriminated, one belonging to the idea itself, another to finite truth, and still another to error. returning to the problem, from this point on we find the two standpoints, that of the specific situation and that of the absolute system, so closely interwoven and entangled that they are followed with great difficulty. we have already seen that the idea seeks correspondence with its object, because it is "fragmentary," "incomplete," "indetermined." and there we found that this indeterminate and fragmentary character belonged to the idea as a purpose, a plan of seeking relief from some sort of "restlessness" and "dissatisfaction," such as singing out of tune, etc. here it is the incompleteness of an imperfect representation of its object in the absolute system that is the _motif_, and how it is to effect an improvement in its imperfect condition is now the problem. here again the appeal is to purpose. whatever may constitute the absolute system, one thing is assured: nothing in it can be an object except as the finite idea "intends it," purposes it, to be its object. again must we ask: on what basis is this object in the absolute system selected at all? in general the answer is: on the basis of a need of "further determination;" but when we further analyze this, we find it means on the basis of a specific want or need, such as food, shelter, measuring, singing, etc. the basis of the selection, then, is entirely on the side of the concrete, finite situation. here, too, we might ask: whence the confidence that there will be found something in the absolute system that will fulfil the purpose generated on the side of the finite? must we not here fall back on something like a pre-established harmony? to this our author would say: "yea, verily. the fact that the absolute system responds to the finite needs does precisely show that the finite and the absolute cannot be sundered." but when we try to state _how_ the purpose generated on the side of the finite can be met by the absolute system, the account again seems to run so much in terms of the finite experience that to call it a system of "final," "completed," and "fulfilled" ideas does not seem accurate. we must note here, too, the shifting in the sense of "purpose." the idea selects its object on the basis of the material needed to relieve the unrest and dissatisfaction of singing out of tune, etc. but now it is to be satisfied by increasing the extent of its representation of its object in the absolute system. and now, finally, what shall mark the attainment of this purpose of the idea to correspond and represent "its own completed form"? when is the correspondence and representation true? simply at the point where "we pause satisfied," where "no other content need be substituted, or from the point of view of the satisfied idea could be substituted." that is all; there is no other answer. there are other statements, but they all come to the same thing. for instance: it is true--this instant's idea--if, in its own measure, and on its own plan, it corresponds, even in its vagueness, to its own final and completely individual expression.[ ] but the moment we ask what this "final and individual expression" is, and what is meant by "in its own measure," and "on its own plan," we are thrown back at once upon the preceding statement. the next sentence following the passage just quoted does indeed define this "individual expression." "its expression would be the very life of fulfilment of purpose which this present idea already fragmentarily begins, as it were, to express." but how can we know that the expression is "fragmentary" unless we have some experience of wholeness? and here perhaps is the place to say, what has been implied all along, that this absolutely "fragmentary" character of human experience is an abstraction of the relatively disintegrated condition into which experience temporarily falls, which abstraction is then reinstated as a fixed quality, overlooking the fact that experience becomes fragmentary only that it may again become whole. the absolute system, the final fulfilment, is in the same case. it too is but the hypostatized abstraction of the function of becoming whole, of wholing and fulfilling, which manifests itself in the "pauses of satisfaction." "but," mr. royce would say, "the wholeness of the particular instance is after all not a true and perfect wholeness, because we can always think of the fulfilling experience as possibly different, as having a possibly different embodiment." but this implies also a different purpose. moreover, it abstracts the purpose from the specific conditions under which the purpose develops. thus in singing in tune one doubtless could easily imagine himself singing another tune, on another occasion, in another key, in a clear tenor instead of a cracked bass, etc. but if on _this_ occasion, in _this_ song, and with _this_ cracked bass voice one, accepting all these conditions, does, with malice aforethought, purpose to strike the tune, and happily succeeds, why, for that purpose formed under the known and accepted conditions, is not the accomplishment final and absolute? nor is the case any different, so far as i can see, in mathematical experience. to quote again: you think of numbers, and accordingly count one, two, three. your idea of these numbers is abstract, a mere generality. why? because there could be other cases of counting, and other numbers counted than the present counting process shows you, and why so? because your purpose in counting is not wholly fulfilled by the numbers now counted.[ ] i confess i cannot see here in what respect the purpose is not fulfilled. doubtless there could be "other cases of counting," and "other numbers," but these may not be included in my present purpose, which is simply to count here and now. in this passage the purpose is not very fully defined. one's counting is usually for something, if for nothing more than merely to illustrate the process. in this latter case one's purpose would be completely fulfilled by just the numbers used when he should "pause satisfied" with the illustration. or, if i wish to show the properties of numbers, then the discovery that there can always be more of them fulfils my purpose, since this endless progression is one of the properties. or yet again, if one should suddenly become enamored of the process of counting, and forthwith should purpose to devote the rest of his days to it, it would still be fortunate that there were always other numbers to be counted. in other words, the idea as a purpose is formed with reference to, and out of, specific conditions. in the last analysis the problem always is: what is to be done here and now with the actual material at hand, under the present conditions? as the purpose is determined by these specific conditions, so is the fulfilment. to say that the fulfilment might be different is virtually to say that the purpose might have been different, or indeed that the universe might have been different. this necessity of falling back upon the character of the idea as a purpose in the sense of the specific "plan of action" comes into still bolder relief in the consideration of error from the standpoint of "the absolute system of ideas." as already mentioned, the initial and persistent problem here is to distinguish at all between truth and error in our experience from this standpoint. all our efforts at representing the absolute system must fall short. what can we mean, then, by calling some of our ideas true and others false? the definition of error is as follows: an error is an error about a specific object, only in case the purpose, imperfectly defined by the vague idea at the instant when the error is made, is better defined, is in fact, better fulfilled by an object whose determinate character in some wise, although never absolutely, opposes the fragmentary efforts first made to define them.[ ] but in relation to the absolute system the later part of this statement holds of all our ideas. there always is the absolute object which would "better define" and "better fulfil" our purposes. hence it is only in reference to the "specific" instances of singing, measuring, etc., that a basis for the distinction can be found. here our plan is not true so long as its mission of relieving the specific unrest and dissatisfaction, the specific discord or hunger, is unfulfilled. the only criterion, then, which we have been able to find for the fulfilment of the purpose, for the truth of the idea as representing an object in the absolute system, is the sense of wholeness, the "pause of satisfaction," which we experience in realizing such specific purposes as "singing in tune." and if it be said again: "precisely so; this only shows how intimate is the relation between our experience and the absolute system of ideas;" then must it also be said once more, either that the absolute system can be nothing more than an abstraction of the element of wholeness or wholing in our experience, or that thus far the relation appears to rest upon sheer assumption. again, it may be insisted, as suggested at the outset of this discussion, that the idea can well have two purposes: one to help constitute and solve the specific problems of daily life; the other to represent the absolute system. very well, we must then make out a case for the latter. if the purposes are to be different, the purpose to represent the absolute should have a criterion of its own. this we have not been able to find. on the contrary, whenever pushed to the point of stating a criterion for the representation of the absolute system, we have had to appeal, in every case, to the fulfilment of a specific finite purpose. and even if this purpose to represent the absolute system had some apparent standard of its own, we should not be content to leave the matter so. we should scarcely be satisfied to observe as a mere matter of fact that the idea has a reconstructive function, and _also_ a representative function. such a brute dualism would be intolerable. iv. summary and conclusions in the end, the outcome of the endeavor to establish a connection between the relation of the idea to human experience and its relation to the absolute system does not appear satisfying. the idea is left either with two independent purposes--one to reconstruct finite experience, the other to represent and symbolize the absolute system--or one of these purposes is merged in the other. when the attempt is made from the standpoint of the absolute system, the reconstructive purpose is swallowed up in the representative. when, on the other hand, the need for a basis of distinction between truth and error "here on this bank and shoal of time" is felt, the representative disappears in the reconstructive function. nowhere are we able to discover a true unification. to be sure, we have been told again and again that the representation of the absolute object, if only we could accomplish it, would be "the final fulfilment," "completion," and "realization" of the human, finite purpose. but besides a confessed impotency at the very start, this involves, as we have seen, either a sudden transformation of the specific purpose of singing in tune, etc., into that of representing the absolute system, or a sheer assumption that the representation of the absolute object does somehow help in the realization of the specific finite purpose. nowhere is there any account of _how_ this help would be given. and this suggests that if the analysis of the idea as purpose, given at the outset of mr. royce's lecture, had been developed further, if the conditions and origin of purpose had been examined, it is difficult to see how this discrepancy could have escaped disclosure. mr. royce starts his account by simply accepting from psychology a general description of the purposive character of the idea. even in the more detailed passages on purpose we have nothing but descriptions of purpose after it is formed. nothing is said of the origin of this purposiveness. the purposive character of experience is of course very manifest, but what is the significance of this purposing in experience as a whole? what is the source and the material of the purposes? it is this uncritical acceptance of the purposive quality of the idea that obscures the irrelevancy of its relation to the absolute system. if the idea must merely be or have a purpose, then it may as well be that of representing the absolute system as any other. of course, there are troublesome questions as to how our finite ideas ever got such a purpose; but, after all, if it is simply a matter of having any sort of a purpose, representing the absolute system may answer as well as anything. but when now we come to deal with the problem of fulfilment, with the question of truth and error, we have to reckon with this neglect of the source of this purposiveness. it is this unanalyzed ground of the purpose that makes the matter of fulfilment so ambiguous. such an analysis, we believe, would have shown that the conditions out of which the idea as a purpose arises determine also the sort of fulfilment possible. there are, indeed, one or two very general, but very significant, statements in this direction, if they were only followed up. for instance: in doing what we often call "making up our minds" we pass from a vague to a definite state of will and of resolution. in such cases we begin with perhaps a very indefinite sort of restlessness which arouses the question: "what is it that i want, what do i desire, what is my real purpose?" in other words, what does this restlessness mean? what is the matter? what is to be done? purpose is born, then, out of restlessness and dissatisfaction. but whence comes this restlessness and dissatisfaction? surely we cannot at this point charge it to a discrepancy between our finite idea and the absolute object, since it is just this restlessness that is giving birth to the purposive idea. one thing, at any rate, appears pretty certain: this "indefinite restlessness" presupposes some sort of activity already going on. the restlessness is not generated in a vacuum. but why should this activity get into a condition to be described as "indefinite restlessness" and dissatisfaction? repugnant as it will be to many to have psycho-physical, to say nothing of biological, doctrines introduced into a logical discussion, i confess that, at this point facing the issue squarely, i see no other way. and it appears to me that just at this point it is the fear of phenomenalistic giants that has kept logic wandering so many years in the wilderness. what, then, in this action already going on is responsible for this restlessness? first let us note that "indefinite restlessness" and "dissatisfaction" are terms descriptive of what mr. james calls "the first thing in the way of consciousness." this assumes consciousness as a factor in activity. so that our question now becomes: what is the significance of this factor of restless, dissatisfied consciousness in activity? now, there appears no way of getting at the part which consciousness plays different from that of discovering the function of anything else. and this way is simply that of observing, as best we may, the conditions under which consciousness operates, and what it does. here the biologist and psychologist with one voice inform us that this indefinite restlessness which marks the point of the operation of consciousness arises where, in a co-ordinated system of activities, there develop out of the continuation of the activity itself new conditions calling for a readjustment and reconstruction of the activity, if it is to go on. consciousness then appears to be the function which makes possible the reorganization of the results of a process back into the process itself, thus constituting and preserving the continuity of activity. so interpreted, consciousness appears to be an essential element in the conception of a self-sustaining activity. this "indefinite restlessness," in which consciousness begins, marks, then, the operation of the function of reconstruction without which activity would utterly break down. precisely because, then, the idea "as a plan" is projected and constructed in response to this restlessness must its fulfilment be relevant to it. it is when the idea as a purpose, a plan, born out of this matrix of restlessness, begins to aspire to the absolute system, and attempts to ignore or repudiate its lowly antecedents, that the difficulties concerning fulfilment begin. they are the difficulties that beset every ambition which aspires to things foreign to its inherited powers and equipment. a detailed account at this point of the construction and fulfilment of the idea as "a plan of action" would contain a consecutive reinterpretation of mr. royce's principal rubrics. such an account the limits of this paper forbid. we shall have to be content with pointing out in a general way a few instances by way of illustration. in the first place, it is in this matrix of indefinite restlessness out of which the idea is born that the "fragmentary character of experience," of which mr. royce is so keenly conscious, appears. but, once more, this fragmentary character is discernible only by contrast with the wholeness on both sides of the fragments; the wholeness that precedes the restlessness, and the new "pause of satisfaction" toward which it points. nor must we forget that the habit matrix, out of the disintegration of which the restlessness is immediately born, does not exist as some metaphysical ultimate out of which thought as such has evolved. back of it is some previous purpose in whose service habit was enlisted. on the other hand, this disintegration means that the old purpose, the old plan, must be reconstructed; that it, along with the disintegrated habit, becomes the material for a new plan, a new wholing of experience. in the next place, the construction of this new plan of action does involve "re-presentation." the first step in the transition from the condition of "indefinite restlessness" toward a "plan" is the diagnosis, the definition of the restlessness. this involves the re-presentation in consciousness of the activities, out of which the restlessness has arisen. this re-presentation is also the beginning of the reconstruction. the diagnosis of the singing activity as being "out of tune" is the negative side of beginning to sing in tune. it is now a commonplace of psychology that all representation is reconstruction. and this is where mr. royce's emphasis of the symbolic, the algebraic, as against the copy type of representation, has its application. all we want here is some sort of an image--visual, auditory, motor, it matters not--that shall serve to focus attention upon the singing activities until they are reconstructed sufficiently to bring us to the "pause of satisfaction."[ ] but nowhere in all this is there any reference to the idea's object in the absolute system. nor does there appear to be any call or place for such reference. the representation here is a part of the very process of forming the plan of further reconstruction out of the materials of the specific situation. representation is not the plan's own end and aim. this is to stimulate a new set of activities that shall lead out of the present state of unrest and dissatisfaction. it is also true, as already mentioned, that in the process of fulfilling the plan, of realizing the idea, further determination and specification is produced in the plan itself. the idea as a plan is certainly not formed all at once. nor does it reach and maintain a fixed content. no purpose is ever realized in its original content. but this does not mean that its realization is, therefore, "partial," "incomplete," or "fragmentary." it is a part of its business to change. the purpose is not there for its own sake. the purpose is there as a _means_ to the reorganization and reconstruction of experience. it exists, as mr. royce says, as an instrument, "as a tool" for "introducing control into experience." and as, in the process of use, a tool always undergoes modification, so here, as an instrument for reconstructing habit, the plan, too, undergoes reconstruction. indeed, as regards its content, it is itself, as mr. royce says, as much a habit, as much "the product of association," as any part of experience. the purposing function, the purposing activity, remains; its content is constantly shifting. here, too, is where "the submission of the idea to the object" takes place. only, here, it is not a submission to an object already constituted as it is in mr. royce's conception of the absolute system. the idea as an hypothetical plan of action, as a trial construction, must be tested by the activities it is attempting to reconstruct. that is to say, at this point the question is: does the plan apply to the activities actually involved in the unrest? has it diagnosed the case properly, and is it therefore one in and through which these activities can operate and come to unity again? the "submission" here is the submission of the purpose, the end, to the material out of which it is formed, and with which it must work. but again this material to which the idea submits itself is anything but finally fixed and "complete" in form. on the contrary, as we have seen, it is just the fragmentary and incomplete condition of this material that calls for the idea. yet the idea as a plan must be true to its mission, and to this material, and in this sense must submit itself to whatever modifications and reconstruction the material "dictates" as necessary in order that it may function in and through the plan.[ ] on the other hand--and this is the point to which mr. royce gives most emphasis--it is equally apparent that "the idea must determine its object." on this all philosophy, from plato down, which approaches reality "from the side of ideas" is at stake. and this does not appear impossible if, again, the object is not already and eternally fixed and complete. if the object is one constructed out of the very mass of habit material which the idea is reconstructing, and if "determination" means not copying, but construction, then, indeed, must the idea "determine its object." just for that does it have its being. that is its sole mission. here the determination of the object by the idea is not a mere abstract postulate; it is not based upon a general consideration of the disastrous consequences to our logical and ethical assumptions, if it were not so determined. here not only the general necessity for it, but the _modus operandi_ of this determination, is apparent. but, at the risk of tedious iteration, must it again be said that for the determination of the completed and perfected object in the absolute system not only is there nowhere any _modus_ to be found, but, even if there were, it is difficult to see what it would have to do with the kind of determination demanded by such a specific sort of unrest as "singing out of tune," etc. the process of submission is thus a reciprocal one. neither in the object nor in the idea is there a fixed scheme or order _to_ which the other must submit and conform. and this is simply the logical commonplace that submission cannot be a one-sided affair, that determination must be reciprocal. this brings us to what might as well have been our introductory as our concluding observation. it has just been said that the determination of the object by the idea is a vital matter in any philosophy which approaches reality "from the side of ideas." such a way of approach must assert "the primacy of the world of ideas over the world as a fact."[ ] mr. royce thus further states the case: i am one of those who hold that when you ask what is an idea, and how can ideas stand in any true relation to reality, you attack the world knot in the way that promises most for the untying of its meshes. this way is of course very ancient. it is the way of plato.... it is in a different sense the way of kant. if you view philosophy in this fashion, you subordinate the study of the world as fact to a reflection upon the world as idea. begin by accepting upon faith and tradition the mere brute reality of the world as fact, and there you are sunk deep in an ocean of mystery.... the world of fact surprises you with all sorts of strange contrasts.... it baffles you with caprices like a charming and yet hopelessly wayward child, or like a bad fairy. the world of fact daily announces itself to you as a defiant mystery.[ ] here we have concisely stated at the outset of the lectures the position which we have seen to be fraught with so many difficulties: the position, namely, which accepts to start with the opposition of the world as idea and the world as fact, as something given, instead of something to be accounted for; and which assumes that this opposition stands in the way of reaching reality, whereas it possibly may be of the very essence of reality. to be sure, the above statement of this opposition between the world as fact and as idea is but the expository starting-point. and it is true that the rest of the argument is occupied in the attempt to close this breach. but, as we have seen, except where the idea is expounded as a specific purpose, arising out of a specific experience of unrest, such as singing out of tune, etc.--except in this case, the breach is taken as found and the attempt to heal it is made by working forward from the opposition as given instead of back to its source. this opposition, of course, has its forward goal, but the difficulty is to find it without an exploration of its source. it is back in that matrix out of which the opposition has arisen that the line of direction to the goal is to be found. moreover, in starting from this opposition of fact and idea as given, the only method of quelling it seems to be either that of reducing one side to terms of the other, or of appealing to some new, and therefore external unifying, agency. but if the factors in the opposition are found, not one in submission _to_ the other, nor having the "primacy" _over_ the other, but as co-ordinate and mutually determining functions, developed from a common matrix and co-operating in the work of reconstructing experience, some of the difficulties involved in the alternative methods just mentioned appear to drop out.[ ] the point may be clearer if we recur to the passage and ask just what is meant by "the defiantly mysterious," "baffling," and "capricious" character of the world as fact--as "brute reality." first, if by the world as "fact;" as "brute reality," we mean experience so brute that it is not yet "lighted up with ideas," it is difficult to see how it could be mysterious or capricious, since mystery and caprice appear only when experience ceases to be taken merely as it comes and an inquiry for connections and meanings has begun. that is to say, there can be neither mystery nor caprice except in relation to some sort of order. and order is always a matter of ideas. but it is sufficient to submit mr. royce's own statement on this point: we all of us from moment to moment have experience. this experience comes to us in part as brute fact; light and shade, sound and silence, pain and grief and joy.... these given facts flow by; and were they all, our world would be too much of a blind problem for us even to be puzzled by its meaningless presence.[ ] if next we take the world of fact as in contrast and co-ordinate with the world of ideas, mystery and caprice here, certainly, are not all on the side of the fact. here, again, must they be functions of the relation between fact and idea. we have seen that without thought there is neither mystery nor caprice. the idea then cannot take part in the production of mystery and caprice, and forthwith deny its parenthood. of course, mystery and caprice are not the final fruits of this co-ordinate opposition of fact and idea. they are but the _first_ fruits--the relatively unorganized embryonic mass which through the further activities of the parent functions shall develop into the symmetry of truth and law. there appears then no ultimate "primacy" of either idea or fact over the other. nor does either appear as a better way of approach _to_ reality than the other. it is only when we say: "lo! here in the idea," _or_ "lo! there in the fact is reality," that we find it "imperfect," "incomplete," and "fragmentary," and must straightway "look for another." but surely not in "a certain absolute system of ideas," which is "the object of love and hope, of desire and will, of faith and work, but never of present finding," shall we seek it. rather precisely in the loving and hoping, desiring and willing, believing and working, shall we find that reality in which and for which both the "world as fact" and the "world as idea" have their being. index absolute: as constituting reality, ; as related to truth and error, ff.; as a hypostatized abstraction, . absolute self, . accessory: thought as, ff. activity: as social, ; thought as, ; interrupted, and judgment, ; and hypothesis, ; as sensori-motor, , ; (see function, reconstruction). Æsthetic experience: appreciative rather than reflective, ; not a form of valuation, , . alternatives: in judgment, ; (see disjunction). analogy, , , ; in relation to habit, . anaxagoras: in relation to the one and the many, ; his [greek: nous], , . anaximander: and the infinite, ; his process of segregation, , . anaximenes: his [greek: archê], ; his scheme of rarefaction and condensation, , , , . angell, j. r., note, note. animism, note. antecedents of thought (see stimulus). applied logic: lotze's definition, . appreciation: distinguished from reflection, , ; not to be identified with valuation, - , . [greek: archê]: meaning of search for, ff. association of ideas: refers to meanings, , ; connection with thought, ; doctrine of: analogous to subjectivism in ethics, ; presupposes a mechanical metaphysics, , note. atomists: treatment of the one and the many, . austrian economists, , . authority and custom: logic of attitude of obedience to, ; social conditions compatible with dominance of, ; failure of, as moral control, . bacon: extreme empirical position, ff.; view of induction, , . "bad": practical significance of, as moral predicate, ; relation to "wrong," . baldwin, j. m., note, note. becoming: as relative, . "begrÜndung" and "bestÄtigung": wundt's distinction of, ; criticised, , . biology: view of sensation, ; use of, in logic, , . bosanquet, b., note, , , , , ; (see study v). bradley, f. h., note, note, ff., , , , , , , note , note, note, . brentano, note. butler, j., . certain, the: relation to tension, , ; as datum, . coefficients of reality, perception, and recognition: defined, - ; present in economic and ethical experience, - . coexistence, coincidence, and coherence, , , - , , , . conceptions: lotze's view of, ; bacon's attitude toward, ; relation to fact, ; function in greek philosophy, ; (see idea, image, hypothesis). conceptual logic: as related to idea and image, - . conscience: evolution of, , ; ambiguous and transitional character of, ; metaphysical implications of, as moral standard, ; not autonomous, . conscientiousness: dangers of, consequent upon ideal of self-realization, ; green's defense of, referred to, note. conservation: of energy and mass, ; (see energy). content of knowledge: and logical object, originates in tension, ; thought's own, ; and datum, ; as truth, ff.; as static and dynamic, , ff., ff.; (see study iv; objectivity, validity). continuity, , , . control: idea and, , . conversion of propositions, ; in relation to habit, . copernicus: his theory, ; compared with galileo's supposition, - . copula, ff.; scheme of mediation between subject and predicate, , ff. correspondence: of datum and idea, ; of thought-content and thought-activity, ; as criterion of truth, ff., ff. darwin, charles, , , . datum of thought, , , ; as fact, , , ; lotze's theory of, stated, ; criticised, ff.; relation to induction, ; and content, , ; (see study iii; content, fact, stimulus). deduction, , . definition: invented by socrates, . democritus: attempts at definition, . demonstrative judgment, . determination: as criterion of truth, ff.; impossibility of complete, in finite experience, . dewey, john, note, note, note , note, note. dialectic: zeno as originator of, . diogenes of apollonia, ff. disjunction: in judgment, , . dynamic: ideas as, and as static, , ; reality as, . earth: as an element, . economic judgment: involves same type of process as physical, ; a process of valuation, ; type of situation evoking, - , - , , ; distinguished from ethical, note, note, , , ; relation to physical, note ; subject of, the means of action, , ; analysis of process of, - ; distinguished from "pull and haul," , ; psychological account of, , ; a reconstructive process, , . "egoism, neo-hegelian," . ehrenfels, c. von, note. eidola: bacon's view of, . eleatics: their logical position, ff. elements: as four, ; as infinite, ff. emerson, r. w., , note. empedocles: attempts at definition, ; treatment of the one and the many, ff. empiricism, , , , , ff.; and rationalism, ; criticised, ; jevons, ; treatment of imagery, - . ends: controlling factors in acquisition of knowledge, ; may themselves be objects of attention and judgment, ; judgment of, inseparable from factual judgment, ; conflict of, related, the occasion for ethical judgment, - ; indirect conflict of unrelated, the occasion for economic judgment, - ; the subject-matter of ethical judgment, , ; definition of, the goal of all judgment, , ; not always explicit in judgment-process, , ; nature of relation between, in ethical judgment, , , , ; types of factual condition implied in acceptance of, , ; warranted by factual judgment, ; nature of, unrelatedness of, in economic judgment, - , , ; (see purpose). energy: principle of conservation of, , , ; not valid in sphere of valuation, . "energy-equivalence": principle of, in economic judgment, , ; meaning of, note. epistemology, - , , , , , , , , ; origin of problem of, , . erdmann, benno: concerning induction, . error: criterion of, . ethical judgment: involves same type of process as physical, ; a process of valuation, , ; type of situation evoking, - , - ; distinguished from mechanical "pull and haul" between ends, , ; distinguished from economic judgment, note, note, , , ; subject of, an end of action, ; analysis of process of, - ; a reconstructive process, , . existence: _versus_ meaning, , . experience: duality of, ; logic of, - ; how organized, ; relation of thought to organization of, - ; as disorganized, ; (see absolute, functions). experiment: as form of deduction, . fact: as equivalent to datum, , ff.; criteria for determining, ff.; as reality, ; in relation to both idea and reality, ff.; and theory, conflict between, , ; mutual dependence of, ; whewell's view of, ; (see datum, idea, reality, truth). factual judgment: inadequate to complete mediation of conduct, - ; controlled by ends, ; incidental to judgments of valuation, , ; types of, implied in acceptance of an end, , ; presents warrant for acceptance of ends, . fite, w., note. fragmentary, ; as quality of internal meaning, , ; as an attribute of finite experience, , ; (see stimulus, tension). functions: of experience, ; logic of, , ; distinguished from status, ; of thought, , , , ; total, as stimulus to thought, - , ; different, and logical distinctions, ; different, confused by lotze, ; sensations as, . genetic: method, significance of, , , ; distinctions, importance of, , , , , ; effect of ignoring, , , ; (see psychology). "good": practical significance of, as moral predicate, ; relation to "right," . gore, w. c., note. gorgias, . greek view of thought and reality, ff. green, t. h., note, note , note, note, , . habit: relation of judgment to, interruption and resumption of, ; and hypothesis, ; and analogy, ; and simple enumeration, ; and conversion, ; and logical meaning, ; logical function of, , . heraclitus: his position, ff. hippo, . hobbes, thomas, . homogeneity: of the world-ground, ; of the world, , . hutcheson, f., . hypothesis: nature of, vii, - ; unequal stress commonly laid on its origin, structure, and function, - ; relation of data and hypothesis strictly correlative, , , ; as predicate, , ; negative and positive sides of, , ; came to be recognized with rise of experimentalism, ; and test, , , ff.; origin of, , ff.; supposition and, ; interdependence of formation and test of, . idea: continuous with fact, , , ; distinction from fact, , ; lotze's confusion regarding, , , , ; association of, ; contrast with datum, - ; functional conception of, , ff.; objective validity of, - ; as entire content of judgment, ; existential aspect of, , ff., ; in relation to reference, ff., , ; representational theory of, ff., ff., , ff., ff.; universality of, ff., ff.; as not referred to reality, ff.; as forms of control, ; function in judgment, , ; distinguished from image, - ; distinction criticised, - ; problems accompanying discovery of, ; in greek thought, ; instrumental and representative functions of, ff., ff.; purposive character of, ff.; external and internal meaning of, ff.; royce's absolute system of, ; triple relation to purpose in royce's account, ff.; logical _versus_ memorial, ; in relation to fact and reality, ff.; (see hypothesis, image, predicate). ideas: platonic, . image: as merely fanciful, ; in relation to meaning, ; place of, in judgment, ; distinction from idea, - ; distinction criticised, - ; as direct and indirect stimulus, - . imagery: empirical criteria of, ; function of, ; as representative, - , ; psychological function of, - ; logical function of, , . immediate: as related to mediation, , ff. impression: lotze's definition of, , , , ; objective determination of, , ; objective quality of, , ; as psychic, ; as transformed by thought into meanings or ideas, ff.; (see idea, meaning, sensation). indeterminate: as quality of finite experience, . induction: bacon's view of, ; by enumeration and allied processes, ; and habit, ; _versus_ deduction, , . inference: lotze's view of, ; in relation to judgment, . instrumental: as character of thought, - , , , ff., ff.; (see purpose). interaction: physical, ff. interest: direction of, . invention: form of deduction, . james, william, note, note, . jevons, w. stanley, , . jones, henry, note, note, . judgment: lotze's definition of, and note; relation of, to ideas, ; structure of, note; bosanquet's theory of, ff.; as a function, ff.; dead and live, ; definition of, , ; relation to inference, ff.; limits of single, ff.; negative, ff.; of perception, ff., ; parts of, ff., , ; time relations of, ff.; as individual, ; as instrumental, , ; as categorical and hypothetical, ; as impersonal, ; as intuitive, ; various definitions of, ff.; analysis of, ff.; disjunctive, ; psychology of, ; purpose of, ; and interrupted activity, ; unique system of, - ; general analysis of, - ; purposive character of, ff.; universal, ; particular, ; individual, , ; mathematical, ff., ; (see economic, ethical, factual judgments, copula, predicate, reflection, subject). kant, i., , , note, , , . kepler, , . knowledge: in relation to reality, ff.; meaning and, ; "copy" and "instrumental" theories of, , , ; (see judgment, truth). kÜlpe, o., note. logic: origin of, ; types of, - ; as generic and specific, , ; relations to psychology, , , , , , , ff.; effect of modern psychology upon, ; relation to genetic method, - ; problems illustrated, , ; social significance of, ; eristic the source of formal, ; pre-socratic, ; and epistemology, , ; (see epistemology, psychology). lotze: criticised, studies ii, iii, iv; applied logic, ; thought as accessory, ; view of judgment, ; similarity between him and whewell, note; quoted, , , , , , , , note, , , , , , , , , , , , . many: the, and the one, ff., ff. marginal utility: principle of, , note. martineau, j., . mathematics: certain forms of proof in, ff.; judgments of, ff., . mcgilvary, e. b., note. mead, g. h., note, note. meaning: and logical idea, , , , , , ; as content of thought, ff.; three types of, ; as property of independent idea, - ; and association of ideas, , ; and reference, ; world of, , , ; and knowledge, , , ; equivalent to response, ; _versus_ existence, - ; inner and outer, ff.; (see content, idea, reference). means: as external and constitutive, ; reapplication of, the problem of economic valuation, , , , , , , ; objective in so far as not known adequately for one's purpose, ; definition of, incidental to all judgment, ; factual determination of, sometimes determinative of ends also, . mediation: in relation to the immediate, ff. melissus: his dialectic, . metaphysics, , , , , ; and logic of experience, ; as natural history, - ; worth, - ; logical and, , ; (see epistemology, logic). mill, j. stuart, , ff., , . mixture: logical meaning of idea of, , , . monism, . moore, a. w., note, note. motion: conservation of, . negation, , ff. neo-hegelian, , . newton, i., , , ; his notes for philosophizing, note. [greek: nomô] _versus_ [greek: physei], . normative and genetic, ; (see end, purpose, validity, value). obedience: a factor in genesis of morality, (see also authority and custom). object: how defined, , , , ; socially current, ; real, individual in significance, ; nature of the ethical, , ; of the economic, , , ; (see substance). objectivity: lotze's view of, (see study iv); types of, ; lotze's distinction of logical and ontological, , ; distinction denied, , ; scope of conception of, ; commonly denied to other than factual judgments, , ; not a property of sense-elements as such, , ; a category of "apperception," ; a mark of the problematic as such, , , ; not ascertainable by any specific method, ; "obtrusiveness" as evidence of, ; "reliability" as evidence of, ; conditions of experience of, - ; conditions of, present in the ethical and economic situations, - ; a real characteristic of ethical and economic judgment, - ; not dependent on social currency, - ; nor on possibility of social currency, - ; nor on permanence, - ; (see reality, validity). one: the, and the many, ff., ff. parmenides: his logical position, ff.; influence on platonic-aristotelian logic, . participation: significance of, in plato, ff. particularity: of an idea, , ; of a judgment, . perception: judgments of, ff., . perfect, the, . physical judgment (see factual judgment). [greek: physei] _versus_ [greek: nomô], . [greek: physis], , . plato, note; on ideas and reality, ff., , . pluralism, note. positing: thought as, . predicate: how constituted, note; in relation to reality, , ; as hypothesis, , , , , , ; develops out of imaged end, ; interaction with subject, ; in ethical judgment, , - ; in economic, , , - ; (see copula, judgment, hypothesis, idea, image). predication, ff. pre-established harmony: in royce's philosophy, . presuppositions, , . problematic (see tension). proof: inductive, , ; of hypothesis, , ; relation of, to origin of hypothesis, - ; wundt's view of, , . proposition: and judgment, . protagoras, . prudence: ethical status of, as a virtue, . pythagoreans, the: their logical position, ; use of experiment, . psychical: distinguished from physical, ; lotze's view of impression as barely, , , ; view criticised, - , , ; two meanings of, note; psychical mechanism, ; idea as, ; problem of logical and, and note, ; activity of thought also made, by lotze, and note; subjective result, ; (see impression). psychology: and logic, - , , , , , , , , ff., , ; principle of, functional, , ; genesis of, , ; logical value of functional, . psychologists' fallacy, . purpose: logical importance of, , , , , , , , , , , ; logical aspects of, study xi; in an idea, ff.; in judgment, ff.; in criterion of truth and error, ff.; origin of, as idea, ff.; as method, ; (see end, reconstruction). quales: of sensation, , , note. qualities: primary and secondary, . question: and judgment, , ff. rationalism: criticised, ff., ff., ff. rationality: of world, . reality: as constructed by thought, ff., ; as developing, ; as including fact and idea, , , , ; as independent of thought, , ff., ; as subject of subject, ff.; popular criterion of, ff.; possibility of knowledge of, ff., ff., ; for the individual, ff., , , ff.; as relative to judging, ; as given in sensation, ; "perception" and "recognition" coefficients of, - , ; these present in ethical and economical experience, - ; apprehension of, emotional, ; scope of complete conception of, , ; degrees of, ; platonic conception of, ff.; royce's conception of, ; as related to fact and idea, ff.; (see fact, truth, validity). reason, sufficient: principle of, . reconstruction: the function of thinking, , , , , , ; effect of denying this, , , ; data and, ff.; in judgment, , , , , , , , ; (see habit, stimulus, tension). reference: as social, ; problem of reference of ideas, ff.; as meaning, ff.; functional conception of, ; paradox of, ; idea as, . reflection: as derived, - ; naïve, , ; subject-matter of, , ; logic and, , , ; _versus_ constitutive thought, - ; distinguished, ; general nature of, ; end not always explicit in, ; outcome of, statable in terms of end or means, ; (see judgment, thought). reflective judgment, . representation: as one of the two functions of an idea, , ff., ; significance of, in ideal reconstruction, . response: failure of, and origin of judgment, . restlessness: as source of reflection and purpose, ff.; (see tension). rhetoric: origin of, , . "right" (see "good"). royce, josiah: referred to, note, ; theory of ideas discussed, - ; quoted, , , , , , , , , , , , , , , note, , , , , , , . satisfaction: pause of, as marking attainment of truth, ff. schiller, f. c. s., note, note. science: relation to naïve experience, , ; its historic stages, , ; distinction of logical procedure from epistemology, ; same history as philosophy, , . self, empirical: genesis and content of concept of, , , , note . self, "energetic": implied in experience of "warrant," , ; stimulus to development of concept of empirical self, - ; essential principle in all valuation, - ; evolution of moral attitude of reference to, - ; logical function of, in valuation, ; important place in economic valuation, , ; not capable of being described in terms of purpose or ideal, - ; bradley's misinterpretation of, note. self-realization (see also green, t. h.): theory of, as moral ideal futile, ; logically congruous with determinism and hedonism, , . sensations: logical import of, ; as functions of experience, ; as point of contact with reality, ; place in judgment, ; and ideas, ff.; (see impressions, psychical). sensori-motor activity, , . shaftesbury, . sigwart, c.: view of judgment, . skepticism, note, . "social currency": implies an identity of aspect of an object to different persons, ; object having, an abstraction like social individual, ; not a test of objectivity, - . socrates: function of concept, . sophists, the, . spencer, h., , note , note. standard (see also predicate): identified with predicate in ethical judgment, - ; function of, in ethical judgment, , , ; morphology and mode of reconstruction of, , ; an ultimate ethical, impossible, ; objectivity of, , . stimulus: of thought, , , , , - , , ; lotze's view of, , , ; view criticised, - ; confusion of datum with, ; defined, ; and judgment, - ; as condition of thinking, ff.; as direct and indirect, - ; of ethical judgment, - , ; of economic, judgment, - , ; (see content, datum). stout, g. f.: referred to, . stratton, g. m., note. structure, , , , , , ; (see function). subject: of judgment, how constituted, note; as constructed by thought, ff., ; as a part of judgment, ff.; as reality, ff.; as inside and outside of judgment, , ; functional theory of, , ; as that requiring explanation, , ff.; as modified by deduction, ; given by analysis of situation, ; interacts with predicate in judgment, ; of ethical judgment, , - ; of economic judgment, , , , - ; (see copula, datum, judgment, predicate). subjective: distinguished from objective, ; lotze's view of impressions as purely, , ; view criticised, ; definition of, ; developed only within reflection, , ; (see psychical). subjectivism: in lotze, , ; in royce, . subject-matter of thought: distinguished as stimulus, datum, and content, , , ; confusion of these (genetic) distinctions, , ; as antecedent, study ii; as datum, study iii; as content, study iv. substance: ethical theories based on logic involved in rationalistic conception of, , ; meaning of concept of, , ; type-form of conduct analogous to concept of a particular kind of, , . substantiation: significance of plato's, of ideas, ff. supposition and hypothesis, - . sweet, henry: quoted, note. synthetic (see reconstruction). taylor, a. e., note , note, , . teleology (see end, purpose). temptation: ethical, , ; economic, . tension: as stimulus to thought, , , , , , , ; in relation to constitution of sensory datum, , , , ; constitution of meaning as distinct from fact, , , , - , , , , - , ff.; (see purpose, reconstruction). thales: his [greek: archê], water, ; in relation to deduction, , . thought: forms of, ff.; as modes of organizing data, ; three kinds according to lotze, , ; as positing and distinguishing, ; validity of its function, - ; of its products, - ; instrumental character, - ; as discriminating sensory qualities, - ; (see judgment, reflection). time: as involved in judgment, ff. transcendentalism, , - . trendelenburg, a.: view of judgment, . truth: criterion of, ; bosanquet's conception of, ; popular criterion of, ff.; and purpose, study xi; representational _versus_ teleological view of, ff.; criterion of, ff.; (see objectivity, validity). ueberweg: view of judgment, . uniformity: of nature, . unity: of the world, . universal: first and second according to lotze, , , ; ideas as, ff., ; judgment as, ; mr. royce's treatment of, ff.; necessity and, . validity: of thought, , ; relation to genesis, , ; test, , ; defines content of thought, ; problem of, study iv; lotze's dilemma regarding, - ; of bare object of thought, - ; of activity of thought, - ; of product of thought, - ; (see objectivity, reality, truth). value: lotze's distinction of, from existence, , ; view criticised, , , ; organized, of experience, - ; determined in and by a logical process, ; nature of consciousness of, , - ; function of consciousness of, - ; properly mediate and functional in character, - . valuation (see also ethical judgment, economic judgment): includes only ethical and economic types of judgment, , , - ; general account of process of, , ; reconstructive of self as well as of reality, . venn, john: origin of hypothesis, . "warrant": consciousness of, accompanies purely factual as well as valuational judgment processes, , ; the constitutive feature of survey of factual conditions, , . welton, j.: origin of hypothesis, . whewell, william, ; view of sensations and ideas, , ; of induction, ; a certain agreement between him and mill, . wieser, f. von, note . will: as related to thought, note; (see activity, end, purpose). wundt, w.: view of judgment, ; view of mathematical induction, ; formation and proof of hypothesis, ff.; distinction between supposition and hypothesis, ff. "wrong" (see "bad"). xenophanes: his logical position, . zeno: his dialectic, . footnotes [ ] _logic_ (translation, oxford, ), vol. i, pp. , . italics mine. [ ] see angell, "the relations of structural and functional psychology to philosophy," _the decennial publications of the university of chicago_, vol. iii ( ), part ii, pp. - , - . [ ] see _philosophical review_, vol. xi, pp. - . [ ] see statements regarding the psychological and the logical in _the child and the curriculum_, pp. , . [ ] lotze, _logic_ (translation, oxford, ), vol. i, p. . for the preceding exposition see vol. i, pp. , , , , , ; also _microkosmus_, book v, chap. . [ ] lotze, _logic_, vol. i, pp. , . [ ] lotze, _logic_ (translation, oxford, ), vol. i, p. . [ ] _ibid._, vol. i, p. . [ ] _ibid._ [ ] _microkosmus_, book v, chap. . [ ] _logic_, vol. ii, p. ; see the whole discussion, §§ through . [ ] the emphasis here is upon the term "existences," and in its plural form. doubtless the distinction of some experiences as belonging to me, as mine in a peculiarly intimate way, from others as chiefly concerning other persons, or as having to do with things, is an early one. but this is a distinction of _concern_, of value. the distinction referred to above is that of making an _object_, or presentation, out of this felt type of value, and thereby breaking it up into distinct "events," etc., with their own laws of inner connection. this is the work of psychological analysis. upon the whole matter of the psychical i am glad to refer to professor george h. mead's article entitled "the definition of the psychical," vol. iii, part ii, of _the decennial publications of the university of chicago_. [ ] we have a most acute and valuable criticism of lotze from this point of view in professor henry jones, _philosophy of lotze_, . my specific criticisms agree in the main with his, and i am glad to acknowledge my indebtedness. but i cannot agree in the belief that the business of thought is to qualify reality as such; its occupation appears to me to be determining the reconstruction of some aspect or portion of reality, and to fall within the course of reality itself; being, indeed, the characteristic medium of its activity. and i cannot agree that reality as such, with increasing fulness of knowledge, presents itself as a thought-system, though, as just indicated, i have no doubt that reality appears as thought-specifications or values, just as it does as affectional and æsthetic and the rest of them. [ ] bradley's criticisms of rationalistic idealism should have made the force of this point reasonably familiar. [ ] the common statement that primitive man projects his own volitions, emotions, etc., into objects is but a back-handed way of expressing the truth that "objects," etc., have only gradually emerged from their life-matrix. looking back, it is almost impossible to avoid the fallacy of supposing that somehow such objects were there first and were afterward emotionally appreciated. [ ] of course, this very element may be the precarious, the ideal, and possibly fanciful of some other situation. but it is to change the historic into the absolute to conclude that therefore everything is uncertain, all at once, or as such. this gives metaphysical skepticism as distinct from the working skepticism which is an inherent factor in all reflection and scientific inquiry. [ ] but this is a slow progress within reflection. plato, who was influential in bringing this general distinction to consciousness, still thought and wrote as if "image" were itself a queer sort of objective existence; it was only gradually that it was disposed of as psychical, or a phase of immediate experience. [ ] of course, this means that what is excluded and so left behind in the problem of determination of _this_ objective content is regarded as psychical. with reference to other problems and aims this same psychic existence is initial, not survival. released from its prior absorption in some unanalyzed experience it gains standing and momentum on its own account; _e. g._, the "personal equation" represents what is eliminated from a given astronomic time-determination as being purely subjective, or "source-of-error." but it is initiatory in reference to new modes of technique, re-readings of previous data--new considerations in psychology, even new socio-ethical judgments. moreover, it remains a fact, and even a worthful fact, as a part of one's own "inner" experience, as an immediate _psychical reality_. that is to say, there is a region of _personal_ experience (mainly emotive or affectional) already recognized as a sphere of value. the "source of error" is disposed of by making it a _fact_ of this region. the recognition of falsity does not _originate_ the psychic (p. , note). [ ] of course, this is a further reflective distinction. the plain man and the student do not determine the extraneous, irrelevant, and misleading matter as image in a _psychological_ sense, but only as _fanciful_ or fantastic. only to the psychologist and for _his_ purpose does it break up into image and meaning. [ ] bradley, more than any other writer, has seized upon this double antithesis, and used it first to condemn the logical as such, and then turned it around as the impartial condemnation of the psychical also. see _appearance and reality_. in chap. he metes out condemnation to "thought" because it can never take in the psychical existence or reality which is present; in chap. , he passes similar judgment upon the "psychical" because it is brutally fragmentary. other epistemological logicians have wrestled--or writhed--with this problem, but i believe bradley's position is impregnable--from the standpoint of ready-made differences. when the antithesis is treated as part and lot of the process of defining the truth of a particular subject-matter, and thus as historic and relative, the case is quite otherwise. [ ] vol. i, pp. - . [ ] it is interesting to see how explicitly lotze is compelled finally to differentiate two aspects in the antecedents of thoughts, one of which is necessary in order that there may be anything to call out thought (a lack, or problem); the other in order that when thought is evoked it may find data at hand--that is, material in shape to receive and respond to its exercise. "the manifold matter of ideas is brought before us, not only in the _systematic order of its qualitative relationships_, but in the rich _variety of local and temporal combinations_.... the _combinations of heterogeneous ideas_ ... forms the _problems_, in connection with which the efforts of thought to reduce coexistence to coherence will _subsequently_ be made. the _homogeneous or similar_ ideas, on the other hand, give occasion to separate, to connect, and to count their repetitions." (vol. i, pp. , ; italics mine.) without the heterogeneous variety of the local and temporal juxtapositions there would be nothing to excite thought. without the systematic arrangement of quality there would be nothing to meet thought and reward it for its efforts. the homogeneity of qualitative relationships, _in the pre-thought material_, gives the tools or instruments by which thought is enabled successfully to tackle the heterogeneity of collocations and conjunctions also found in the same material! one would suppose that when lotze reached this point he might have been led to suspect that in this remarkable adjustment of thought-stimuli, thought-material, and thought-tools to one another, he must after all be dealing, not with something prior to the thought-function, but with the necessary elements in and of the thought-situation. [ ] _supra_, p. . [ ] for the identity of sensory experience with the point of greatest strain and stress in conflicting or tensional experience, see "the reflex arc concept in psychology," _psychological review_, vol. iii, p. . [ ] for the "accessory" character of thought, see lotze, vol. i, pp. , - , , etc. [ ] bosanquet, _logic_ (vol. i, pp. - ), and jones (_philosophy of lotze_, , chap. ) have called attention to a curious inconsistency in lotzes's treatment of judgment. on one hand, the statement is as given above. judgment grows out of conception in making explicit the determining relation of universal to its own particular, implied in conception. but, on the other hand, judgment grows not out of conception at all, but out of the question of determining connection in change. lotze's nominal reason for this latter view is that the conceptual world is purely static; since the actual world is one of change, we need to pass upon what really goes together (is causal) in the change as distinct from such as are merely coincident. but, as jones clearly shows, it is also connected with the fact that, while lotze nominally asserts that judgment grows out of conception, he treats conception as the result of judgment since the first view makes judgment a mere explication of the content of an idea, and hence merely expository or analytic (in the kantian sense) and so of more than doubtful applicability to reality. the affair is too large to discuss here, and i will content myself with referring to the oscillation between conflicting contents, and gradation of sensory qualities already discussed (p. , note). it is judgment which grows out of the former, because judgment is the whole situation as such; conception is referable to the latter because it _is_ one abstraction within the whole (the solution of possible meanings of the data) just as the datum is another. in truth, since the sensory datum is not absolute, but comes in a historical context, the qualities apprehended as constituting the datum simply define the locus of conflict in the entire situation. they are attributives of the contents-in-tension of the colliding things, not calm untroubled ultimates. on pp. and of vol. i, lotze recognizes (as we have just seen) that, as matter of fact, it is both sensory qualities in their systematic grading, or quantitative determinations (see vol. i, p. , for the recognition of the necessary place of the quantitative in the true concept), _and_ the "rich variety of local and temporal combinations," that provoke thought and supply it with material. but, as usual, he treats this simply as a historical accident, not as furnishing the key to the whole matter. in fine, while the heterogeneous collocations and successions constitute the problematic element that stimulates thought, quantitative determination of the sensory quality furnishes one of the two chief means through which thought deals with the problem. it is a reduction of the original colliding contents to a form in which the effort at redintegration gets maximum efficiency. the concept, as ideal meaning, is of course the other partner to the transaction. it is getting the various possible meanings-of-the-data into such shape as to make them most useful in construing the data. the bearing of this upon the subject and predicate of judgment cannot be discussed here. [ ] see vol. i, pp. , , , , , , for lotze's treatment of these distinctions. [ ] vol. i, p. ; see also vol. ii, pp. , . [ ] vol. ii, p. ; the same is reiterated in vol. ii, p. , where the question of origin is referred to as a corruption in logic. certain psychical acts are necessary as "conditions and occasions" of logical operations, but the "deep gulf between psychical mechanism and thought remains unfilled." [ ] _philosophy of lotze_, chap. , "thought and the preliminary process of experience." [ ] vol. i, p. . [ ] vol. i, p. ; last italics mine. [ ] vol. i, p. ; italics mine. [ ] see vol. i, pp. - . on p. this work is declared to be not only the first, but the most indispensable of all thought's operations. [ ] vol. i, p. . [ ] vol. i, p. . [ ] vol. i, p. ; see the strong statements already quoted, p. . what if this canon were applied in the first act of thought referred to above: the original objectification which transforms the mere state into an abiding quality or meaning? suppose, that is, it were said that the first objectifying act cannot make a substantial (or attached) quale out of a mere state of feeling; it must _find_ the distinction it makes there already! it is clear we should at once get a _regressus ad infinitum_. we here find lotze face to face with this fundamental dilemma: thought either arbitrarily forces in its own distinctions, or else just repeats what is already there--is either falsifying or futile. this same contradiction, so far as it affects the impression, has already been discussed. see p. . [ ] vol. i, p. . [ ] as we have already seen, the concept, the meaning as such, is always a factor or status in a reflective situation; it is always a predicate of judgment, in use in interpreting and developing the logical subject, or datum of perception. see study vii, on the hypothesis. [ ] royce, in his _world and individual_, vol. i, chaps. and , has criticised the conception of meaning as valid, but in a way which implies that there is a difference between validity and reality, in the sense that the meaning or content of the valid idea becomes real only when it is experienced in direct feeling. the above implies, of course, a difference between validity and reality, but finds the test of validity in exercise of the function of direction or control to which the idea makes pretension or claim. the same point of view would profoundly modify royce's interpretation of what he terms "inner" and "outer" meaning. see moore, _the university of chicago decennial publications_, vol. iii, on "existence, meaning, and reality." [ ] vol. ii, pp. , and in general book iii, chap. . it is significant that thought itself, appearing as an act of thinking over against its own content, is here treated as psychical. even this explicit placing of thinking in the psychical sphere, along with sensations and the associative mechanism, does not, however, lead lotze to reconsider his statement that the psychological problem is totally irrelevant and even corrupting as regards the logical. consequently, as we see in the text, it only gives him one more difficulty to wrestle with: how a process which is _ex officio_ purely psychical and subjective can yet yield results which are valid, in a logical, to say nothing of an ontological, sense. [ ] professor james's satisfaction in the contemplation of bare pluralism, of disconnection, of radical having-nothing-to-do-with-one-another, is a case in point. the satisfaction points to an æsthetic attitude in which the brute diversity becomes itself one interesting object; and thus unity asserts itself in its own denial. when discords are hard and stubborn, and intellectual and practical unification are far to seek, nothing is commoner than the device of securing the needed unity by recourse to an emotion which feeds on the very brute variety. religion and art and romantic affection are full of examples. [ ] lotze even goes so far in this connection as to say that the antithesis between our ideas and the objects to which they are directed is itself a part of the world of ideas (vol. ii, p. ). barring the phrase "world of _ideas_" (as against world of continuous experiencing) he need only have commenced at this point to have traveled straight and arrived somewhere. but it is absolutely impossible to hold both this view and that of the original independent existence of something given to and in thought and an independent existence of a thought-activity, thought-forms, and thought-contents. [ ] the criticism of bosanquet's theory of the judgment offered in this paper is from the standpoint of the theory of the judgment developed by professor john dewey, in his lectures on "the theory of logic." while the chief interest of the paper, as the title implies, is critical, it has been necessary to devote a portion of it to the exposition of the point of view from which the criticism is made.--h. b. t. [ ] the references throughout this paper are to the pages of vol. i of bernard bosanquet, _logic or the morphology of knowledge_, oxford, . [ ] f. h. bradley, _principles of logic_, p. . [ ] the difficulty, of course, is not a merely formal one, much less a verbal one. instinctively we grant to bosanquet his statement that reality is a continuous whole; we feel it almost captious to question his right to it. but why? because the _content of judgment_ is continuous; judgment is always engaged with the determination of a related totality. but if all content is ideal, and judgment is just the application of this content to reality in virtue of an isolated contact, surely it begs the entire question to say that reality apart from the content applied is continuous, and then to use this assertion to justify the objective validity of the judgment--its element of permanent truth. [ ] there is good reason for believing that mr. bosanquet escapes, in his own mind, the difficulty by the term "correspondence." "the name stands for these elements in the idea which _correspond_ in the separate worlds;" we may even be accused of injustice in confusing this correspondence with bare identity of existence. but if one idea corresponds to another in the sense of referring to it, what is this but the fact to be explained--how an existence can refer beyond itself? [ ] this conclusion is clearly recognized by bradley, _appearance and reality_, chap. . [ ] it would be suggestive to inquire in what sense conscious thought claims to know. is it a general claim which thought _qua_ thought puts forth, or is it the claim of the content of some particular thought? the former, of course, is a mere pious aspiration having no reference to specific validity or truth; the latter is precisely the problem under consideration. [ ] bosanquet would seem to have followed lotze in this insertion of a world of "meanings" intermediate between the individual idea as such and the real object as such. see the criticism already passed, pp. - . [ ] or, the situation as questioned is itself a fact, and a perfectly determinate (though not determined) one. see pp. , . [ ] of course, the distinction between the process of arriving as temporal, and the essential relation of subject and predicate as eternal, harks back to the notion of judgment as the process by which "we" reproduce, or make real for ourselves, a reality already real within itself. and it involves just the same difficulties. the relation of subject and predicate--this simultaneous distinction and mutual reference--has meaning only in an act of adjustment, of attempt to control, within which we distribute our conditions. when the act is completed, the relation of subject and predicate, as subject and predicate, quite disappears. an eternal relation of the two is meaningless; we might as well talk of an eternal reaching for the same distant object by the same hand. in such conceptions, we have only grasped a momentary phase of a situation, isolated it, and set it up as an entity. significant results would be reached by considering the "synthetic" character (in the kantian sense) of judgment from this point of view. all modern logicians agree that judgment must be ampliative, must extend knowledge; that a "trifling proposition" is no judgment at all. what does this mean save that judgment is developmental, transitive, in effect and purport? and yet these same writers conceive of reality as a _finished system of content in a complete and unchangeable single judgment_! it is impossible to evade the contradiction save by recognizing that since it is the business of judgment to transform, its test (or truth) is successful performance of the particular transformation it has set itself, and that transformation is temporal. [ ] it is worth considering whether this may not be the reality of royce's distinction between outer and inner meaning. an anticipation of experience is the working prerequisite of the control which will realize the idea, _i. e._, the experience anticipated. one is no more "inner" or "outer" than the other. [ ] _logik_, p. . [ ] de morgan, _budget of paradoxes_, pp. , ; quoted by welton, _logic_, vol. ii, p. . [ ] advanced grammarians treat this matter in a way which should be instructive to logicians. the hypothesis, says sweet (§ of _a new english grammar, logical and historical_, oxford, ), suggests an affirmation or negation "as objects of thought." "in fact, we often say _supposing_ (that is, 'thinking') _it is true_, instead of _if it is true_." in a word, the hypothetical judgment as such puts explicitly before us the content of thought, of the predicate or hypothesis; and in so far is a moment in judgment rather than adequate judgment itself. [ ] this carries with it, of course, the notion that "sensation" and "image" are not distinct psychical existences in themselves, but are distinguished logical forces. [ ] concerning the strict correlativity of subject and predicate, data and hypothesis, see p. . [ ] _novum organum_, vol. i, p. . [ ] newton's "rules for philosophizing" (_principia_, book iii) are as follows: rule i. "no more causes of natural things are to be admitted than such as are both true, and sufficient to explain the phenomena of those things." rule ii. "natural effects of the same kind are to be referred as far as possible to the same causes." rule iii. "those qualities of bodies that can neither be increased nor diminished in intensity, and which are found to belong to all bodies within reach of our experiments are to be regarded as qualities of all bodies whatever." rule iv. "in experimental philosophy propositions collected by induction from phenomena are to be regarded either as accurately true or very nearly true notwithstanding any contrary hypothesis, till other phenomena occur, by which they are made more accurate or are rendered subject to exceptions." [ ] book iii, chap. , sec. ; italics mine. the latter part of the passage, beginning with the words "if we did not often commence," etc., is quoted by mill from comte. the words "neither induction nor deduction would enable us to understand even the simplest phenomena" are his own. [ ] book iii, chap. , sec. . [ ] book iii, chap. , secs. and . [ ] william whewell, _the philosophy of the inductive sciences_, london, . [ ] the essential similarity between whewell's view and that of lotze, already discussed (see chap. ) is of course explainable on the basis of their common relationship to kant. [ ] _logic_, book iv, chap. , sec. ; italics mine. [ ] _ibid._ [ ] _ibid._, sec. ; in sec. he states even more expressly that any conception is appropriate in the degree in which it "helps us toward what we wish to understand." [ ] _ibid._, sec. ; italics mine. [ ] venn, _empirical logic_, p. . [ ] venn, _empirical logic_, p. ; italics mine. [ ] welton, _manual of logic_, vol. ii, chap. . [ ] w. s. jevons, _principles of science_, pp. , . [ ] b. erdmann, "zur theorie des syllogismus und der induktion," _philosophische abhandlungen_, vol. vi, p. . [ ] wundt, _logik_, d ed., vol. ii, p. . [ ] welton, _manual of logic_, vol. ii, p. . [ ] _op. cit._, vol. i, p. ff. [ ] _op. cit._, vol. i, pp. - . [ ] bosanquet, _logic_, vol. i, p. . [ ] bradley, _principles of logic_, p. . [ ] _op. cit._, vol. i, p. . [ ] bradley, _principles of logic_, p. . [ ] _op. cit._, vol. i, pp. , . [ ] bradley, _op. cit._, pp. - . [ ] _op. cit._, pp. , . [ ] this study may be regarded as in some sense a development of pp. - of _the necessary and the contingent in the aristotelian system_, published in by the university of chicago press. while quite independent in treatment, the two papers supplement each other. [ ] the best special illustration of this truth with which i am acquainted is presented for the science of chemistry in an article by f. wald, "die genesis der stöchiometrischen grundgesetze," in _zeitschrift für physikalische chemie_, vol. xviii ( ), pp. ff. [ ] [greek: xi] , . [ ] h . [ ] in allusion to fr. (diels). diels finds in fr. (fr. , bywater), [greek: oti sophon esti pantôn kechôrismenon] the thought that god is the absolute, comparing the [greek: nous] of anaxagoras and the [greek: chôristê idea] of plato and the [greek: ousia chôristê] of aristotle. he assumes that [greek: sophon]=[greek: logos] and concedes great significance to the fragment. but this interpretation is utterly incompatible with everything else that we know of heraclitus, and should be admitted only if it were the only one admissible. zeller discusses the fragment at length, vol. i, p. , . if diels's interpretation be accepted, the exposition above given of heraclitus's logical position must be abandoned. [ ] it has been, and in some quarters is still, the fashion to say that heraclitus is the originator of the doctrine of relativity; but zeller is quite right in denying the charge. no doubt his teachings lent themselves readily to such a development, but he did not so express himself. according to him the _contrarieties coexist in the process_. [ ] _cf._ ritter-preller, § _c_. [ ] this, in a word, is the burden of my study of _the necessary and the contingent in the aristotelian system_. [ ] i have in preparation a study of the problem of physical interaction in pre-socratic philosophy which deals with this question in all its phases. [ ] this statement is, of course, figurative, since empedocles denied the existence of a void. [ ] i cannot now undertake a defense of this statement, which runs counter to certain ancient reports, but must reserve a full discussion for my account of physical interaction. [ ] the motive for making this assumption was clearly the desire to make of the [greek: nous] the prime mover in the world while exempting it from reaction on the part of the world, which would have been unavoidable if its nature had contained parts of other things. it is the same problem of "touching without being touched in return" that led aristotle to a similar definition of god and of the rational soul. the same difficulty besets the absolutely "simple" soul of plato's _phaedo_ and the causality of the ideas. [ ] aristotle, _de generatione et corruptione_, ^b f. [ ] we have seen that this distinction was latent in anaximenes's process of rarefaction and condensation. for other matters see chaignet, _histoire de la psychologie_, vol. i, p. , whose account, however, needs to be corrected in some particulars. [ ] i say "perhaps" because ancient reports differ as to the precise relation of position and arrangement to the distinction between qualities, primary and secondary. [ ] this is only another instance of what mr. venn (_empirical logic_, p. ) has wittily alluded to as "screwing up the cause and the effect into close juxtaposition." [ ] simplicius says [greek: euthys meta to prooimion]; see diels, _die fragmente der vorsokratiker_ (berlin, ), p. , l. . [ ] fr. , diels. [ ] see diels, _fragmente der vorsokratiker_, p. , l. ; p. , l. . [ ] c f. [ ] considerations of space as well as circumstances attending the immediate preparation of this discussion for the press have precluded any but the most general and casual reference to the recent literature of the subject. much of this literature only imperfectly distinguishes the logical and psychological points of view, so that critical reference to it, unaccompanied by detailed restatement and analysis of the positions criticised, would be useless. [ ] in order to avoid complicating the problems, we have here employed the common notion that the physical world, physical object, and property may be taken for granted as possible adequate contents of judgment, and that the problem is only as to the objectivity of economic and ethical contents. of course we may, in the end, come to believe that the "physical" object is itself an economic construct, in the large sense of "economic;" that is, an instrument of an effective or successful experience. thus in terms of the illustration used above, in the attitude of entertaining in a general way the plan of building a house _of some sort or other_, one may have before him various building materials the ascertained qualities of which are, it may be, socially recognized as in a general way fitting them for such a use. there is doubtless so much of real foundation for the common notion here referred to. but along with the _definition_ of the plan in ethical and economic judgment, along with the determination actually to build a house, and a house of a certain specific kind, must go _further_ determination of the means in their physical aspects, a determination which all the while reacts into the process of determination of the end. see below, p. , note . [ ] in the moral life, as elsewhere, the distinction of deduction and induction is one of degree. there is but one _type_ or _method_ of inference, though some inferences may approach more closely than do others the limit of pure "subsumption." [ ] see iii below. [ ] it is no part of the present view that the ends which enter into economic conflict are incapable of becoming organic and intrinsically interrelated members of the provisional system of life. on the contrary, the very essence of our contention is that adjustment established between two such conflicting ends in economic judgment is in itself ethical and a member of the provisional system of the individual's ends of life, and will stand as such, subject to modification through changes elsewhere in the system, so long as the economic conditions in view of which it was determined remained unchanged. the "mutual exclusiveness" of the ends in ethical deliberation is simply the correlate of a relative fixity in certain of the conditions of life. a man's command over the means of obtaining such things as books and fuel varies much and often suddenly in a society like ours from time to time; but, on the other hand, his physical condition, his intelligence, his powers of sympathy, and his spiritual capacity for social service commonly do not. hence there can be and is a certain more or less definite and permanent comprehensive scheme of conduct morally obligatory upon him so far as the exercise of these latter faculties is concerned, but so far as his conduct depends upon the variable conditions mentioned, it cannot be prescribed in general terms, nor will any provisional ideal of moral selfhood admit any such prescriptions as integral elements into itself. the moral self is an ideal construct based upon these fixed conditions of life--conditions so fixed that the spiritual furtherance or deterioration likely to result from certain modes of conduct involving and affecting them can be estimated directly and with relative ease by the "ethical" method of judgment. implied in such a construct is, of course, a reference to certain relatively permanent social and also physical conditions. in so far as society and physical nature, and for that matter the individual's own nature, are _variable_, these are the subjects of "scientific" or "factual" judgments incidental to the determination of problems by the "economic" method--problems, that is, for which no _general_ answer, through reference to a more or less definite and stable working concept of the self, can be given. thus our knowledge of the physical universe is largely, if not chiefly, incidental to and conditioned by our economic experience. again, our economic judgments are in every case determinative of the self in situations in which, as presented by (perhaps even momentarily) variable conditions, physical, social, or personal, the ethical method is inapplicable. in a socialistic state, in which economic conditions might be more stable than in our present one, many problems in consumption which now are economic in one sense would be ethical because admitting of solution by reference to the type of self presupposed in the established state program of production and distribution. even now it is not easy to specify an economic situation the solution of which is absolutely indifferent ethically. there is a possibility of intemperance even in so "æsthetic" an indulgence as turkish rugs. [ ] accordingly there can be no distinction of ends, some as ethical, others as economic, but from an ethical standpoint indifferent, and yet others as amenable neither to ethical nor to economic judgment. the type of situation and the corresponding mode of judgment employed determines whether an end shall be for the time being ethical, economic, or of neither sort conspicuously. [ ] the right of prudence to rank among the virtues cannot, on our present view, be questioned. economic judgment, though it must be valuation of means, is essentially choice of ends--and, as would appear, choice of a sort peculiarly difficult by reason of the usually slight intrinsic relation between the ends involved and also by reason of the absence of effective points of view for comparison. culture, as emerson remarks, "sees prudence not to be a several faculty, but a name for wisdom and virtue conversing with the body and its wants." and again, "the spurious prudence, making the senses final, is the god of sots and cowards, and is the subject of all comedy.... [the true prudence] takes the laws of the world whereby man's being is conditioned, as they are, and keeps these laws that it may enjoy their proper good" (essay on _prudence_). [ ] here again we purposely use inaccurate language. strictly, the ends here spoken of as competing are such, we must say, only because they are as yet in a measure indeterminate, wanting in "clearness," and are not yet understood in their true economic character; likewise the means are wanting in that final shade or degree of physical and mechanical determinateness which they are presently to possess as means to a finally determinate economic end. thus economic judgment, by which is to be understood determination of an end of action by the economic method and in accordance with economic principles, involves in general physical re-determination of the means. the means which at the outset of the present economic judgment-process appear as physically available indifferently for either of the tentative ends under consideration are only in a general way the same means for knowledge as they will be when the economic problem has been solved. they are, so far as now determinate, the outcome of former physical judgment-processes incidental to the definition of economic ends in former situations like the present. [ ] in our discussion of this preliminary question there is no attempt to furnish what might be called an _analysis_ of the consciousness of objectivity. this has been undertaken by various psychologists in recent well-known contributions to the subject. for our purpose it is necessary only to specify the intellectual and practical attitude out of which the consciousness of objectivity arises; not the sensory "elements" or factors involved in its production as an experience. [ ] so, on the other hand, our vague organic sensations are possibly more instructive as they are, _for their own purpose_, than they would be if more sharply discriminated and complexly referred. for convenience we here meet the view under consideration with its own terminology; we by no means wish to be understood as indorsing this terminology as psychologically correct. the sense-quality of which we read in "structural psychology" is, we hold, not a structural unit at all, but in fact a highly abstract development out of that unorganized whole of sensory experience in which reflective attention begins. there is, for example, no such thing as the simple unanalyzable sense-quality "red" in consciousness until judgment has proceeded far enough to have constructed a definite and measured experience which may be symbolized as "object-before-me-possessing-the-attribute-red." in place of the original sensory total-experience we now have a more or less developed perceptual (_i. e._, judgmental) total-experience. it is an instance of the "psychological fallacy" to interpret what are really elements of _meaning_ in a perceived object constructed in judgment (for this is the true nature of the "simple idea of sensation" or "sense-element") as so many bits of psychical material which were isolated from each other at the outset, and have been externally joined together in their present combination. [ ] the phrase is külpe's and is used in his sense of consciousness taken as a whole, as, for example, attentive, apperceptive, volitional, rather than in the sense made familiar by spencer and others. [ ] the foregoing discussion is in many ways similar to brentano's upon the same subject. in discussing his first class of modes of consciousness, the _vorstellungen_, he says: "we find no contrasts between presentations excepting those of the objects to which the presentations refer. only in so far as warm and cold, light and dark, a high note and a low, form contrasts can we speak of the corresponding presentations as contrasted; and, in general, there is in any other sense than this no contrast within the entire range of these conscious processes" (_psychologie vom empirischen standpunkte_, bd. i, p. ). this may stand as against any attempt to find contrast between abstract sense-qualities taken apart from their objective reference. what is, however, the ground of distinction between the presented objects? apparently this must be answered in the last resort as above. in this sense we should need finally to interpret "sensuous" and "material" in terms of objectivity as above defined, rather than the reverse. they are cases in or specifications of the determination of adequate stimuli. [ ] in this connection reference may be made to the well-known disturbing effect of the forced introduction of attention to details into established sensori-motor co-ordinations, such as "typewriting," playing upon the piano, and the like. [ ] _cf._ professor baldwin's _social and ethical interpretations_, and professor mcgilvary's recent paper on "moral obligation," _philosophical review_, vol. xi, especially pp. f. [ ] manifestly, as indicated just above, this accepted value of the object implies fuller physical knowledge of the object than was possessed at the outset of the economic judgment. see above, p. , note; p. , note ; and p. , below. [ ] _types of ethical theory_, vol. ii, p. . [ ] see p. above. [ ] it is not so much the case that the object, on the one side, excites in the agent's consciousness, on the other, the "sensations of resistance" which have played such a part in recent controversy on the subject, as that ( ) the object in certain of its promptings is "resisting" certain other of its promptings, or that ( ) certain "positive" activities of the agent are being inhibited by certain "negative" activities, thereby giving rise to the "emotion of resistance." that "positive" and "negative" are here used in a teleological way will be apparent. it is surely misleading to speak of "_sensations_ of resistance" even in deprecatory quotation marks, except as "sensation" is used in its everyday meaning, viz., experience of strongly sensory quality. [ ] the general theory of emotion which is here presupposed, and indeed is fundamental to the entire discussion, may be found in professor dewey's papers on "the theory of emotion," _psychological review_, vol. i, p. ; vol. ii, p. . [ ] such is, in fact, the teaching of the various forms of ethical intuitionism, and we find it not merely implied, but explicitly affirmed, in a work in many respects so remote from intuitionism in its standpoint as green's _prolegomena to ethics_. see pp. - , and especially pp. - . [ ] sermon ii. [ ] not to imply of course that psychologically or logically the distinction of conditions and means is other than a convenient superficial one. [ ] manifestly we have here been approaching from a new direction the "recognition coefficient" of reality described above. see p. . [ ] this, if it were intended as an account of the genesis of psychology as a science and of the psychological interest on the part of the individual, would doubtless be most inadequate. we have, for one thing, made no mention of the part which error and resulting practical failure play in stimulating an interest in the _judgmental_ processes of observation and the like, and in technique of the control of these. here, as well as in the processes of _execution_ of our purposes, must be found many of the roots of psychology as a science. moreover, no explanation has been offered above for the appropriation by the "energetic" self of these phenomena of interruption and retardation of its energy as being, in fact, its own, or within itself. the problem would appear to be psychological, and so without our province, and we gladly pass it by. [ ] we can, of course, undertake no minute analysis of the psychological mechanism or concatenation of the process here sketched in barest outline. our present purpose is wholly that of description. slight as our account of the process of transition is, we give it space only because it seems necessary to do so in order to make intelligible the accounts yet to be given of the conscious valuation processes for which the movement here described prepares the way. it will be observed that we assume above that the purpose is _successful as planned_ and _by succeeding_ brings about the undesirable results. failure in execution of the purpose as such could only, in the manner already outlined, prompt a more adequate investigation of the _factual conditions_. [ ] the case is not essentially altered in logical character if for the levitical law be substituted the general principles of the new dispensation read off details by an authoritative church or by "private judgment." [ ] a remark may be added here by way of caution. the presented self, we have said, attenuates to a mere maxim or tacit presumption in favor of a certain type of logical procedure in dealing with the situation. it must be remembered that the presented self, like all other presentation, is and comes to be for the sake of its function in experience, and so is practical from the start. the process sketched above is therefore not from bare presented content as such to a methodological presumption, which, as methodological and not contentual, is qualitatively different from what preceded it. [ ] _recognized_ authority is, of course, not the same thing by any means as authority unrecognized because absolutely dominant. [ ] we may be pardoned for supplying from the history of ethics no illustrations of this slight sketch. [ ] in fact, as suggested above, the _prolegomena to ethics_ is in many respects essentially intuitional in spirit, though its intuitionism is of a modern discreetly attenuated sort. [ ] this would appear to be the logical value of functional psychology as a science of mental process. [ ] we have already given a slight sketch of the historical process here characterized in the barest logical terms. [ ] further consideration of the problem of factual judgment must be deferred to part v. [ ] the relation of the empirical self to the "energetic" and to standards will come in for statement in part v in the connection just referred to. [ ] it might be possible to construct a "logic" of these various types of working moral standard in such a way as to show that in each type there is implied the one next higher morphologically, and ultimately the highest--that is, some sort of concept of the "energetic" self. [ ] it matters not at all whether, in ethics or metaphysics, our universal be abstract or on the other hand "concrete," like green's conception of the self, or a "hegelian" absolute. its logical use in the determination of particulars must be essentially the same in either case. [ ] in this connection reference may be made to mr. taylor's recent work, _the problem of conduct_. mr. taylor reduces the moral life to terms of an ultimate conflict between the ideals of egoism and social justice, holding that the conflict is in theory irreconcilable. with this negative attitude toward current standards in ethical theory one may well be in accord without accepting mr. taylor's further contention that a theory of ethics is therefore impossible. because the "ethics of subsumption" is demonstrably futile it by no means follows that a method of ethics cannot be developed along the lines of modern scientific logic which shall be as valid as the procedure of the investigator in the sciences. mr. taylor's _logic_ is virtually the same as that of the ethical theories which he criticises; because an ethical _ideal_ is impossible, a theory of ethics is impossible also. one is reminded of mr. bradley's criticism of knowledge in the closing chapters of the _logic_ as an interesting parallel. [ ] mr. bosanquet's discussion of the place of the principle of teleology in analogical inference will be found suggestive in this connection (_logic_, vol. ii, chap. iii). [ ] see above, p. and p. _ad fin._ [ ] we use the expression "energy-_equivalent_" because the "excess" gained by the self through the past adjustment is not of importance at just this point. the essential significance of the means now is not that they "cost" less than they promised to bring in in energy, but that _because they required sacrifice the self will now lose unless they are allowed to fulfil the promise_. they are the logical equivalent of the established modes of consumption from the standpoint of conservation of the energies of the self, not the mathematical equivalent. it would be desirable, if there were space, to present a brief account of the psychological basis of the concepts of energy and energy-equivalence which here come into play, but this must be omitted. [ ] putting it negatively, the renunciation of the new end involves a "greater" sacrifice than all the sacrifices which adherence to the present system of consumption can compensate. [ ] green, as is well known, allows that any formulation of the ideal self must be incomplete, but holds that it is not for this reason useless. but this is to assume that development in the ideal is never to be radically reconstructive, that the ideal is to expand and fill out along established and unchangeable lines of growth so that all increase shall be in the nature of accretion. the self as a system is fixed and all individual moral growth is in the nature of approximation to this absolute ideal. this would appear to be essentially identical in a logical sense with mr. spencer's hypothesis of social evolution as a process of gradual approach to a condition of perfect adaptation of society and the individual to each other in an environment to which society is perfectly adapted--a condition in which "perfectly evolved" individuals shall live in a state of blessedness in conformity to the requirements of "absolute ethics." for a criticism of this latter type of view see mr. taylor's above-mentioned work (chap. v, _passim_). [ ] for green's cautious defense of conscientiousness as a moral attitude see the _prolegomena to ethics_, book iv, chap. i; and for a statement of the present point of view as bearing upon green's difficulty, see dewey, _the study of ethics: a syllabus_, p. _ad fin._, and _philosophical review_, vol. ii, pp. , . [ ] along the line thus inadequately suggested might be found an answer to certain criticisms of the attempt to dispense with a metaphysical idea of the self. such criticisms usually urge that without reference to a metaphysical ideal no meaning attaches to such conceptions as "adjustment," "expansion," "furtherance," and the like as predicated of the moral acts of an agent in their effect upon the "energetic" self. anything that one may do, it is said, is expansive of the self, if it be something new, except as we judge it by a metaphysical ideal of a rightly expanded self. for an excellent statement of this general line of criticism see stratton, "a psychological test of virtue," _international journal of ethics_, vol. xi, p. . [ ] the polemic of certain recent writers (as, for example, ehrenfels in his _system der werttheorie_) against the objectivity of judgments of value appears to rest upon an uncritical acceptance of the time-honored distinction between "primary" and "secondary" qualities as equivalent to the logical distinction of subjective and objective. thus ehrenfels confutes "das vorurteil von der objectiven bedeutung des wertbegriffes" by explaining it as due to a misleading usage of speech expressive of "an impulse, deep-rooted in the human understanding, to objectify its presentations" and then goes on to say "we do not desire things because we recognize the presence in them of a mysterious impalpable essence of value but we ascribe value to them because we desire them." (_op. cit._, bd. i, p. .) this may serve to illustrate the easy possibility of confusing the logical and psychological points of view, as likewise does ehrenfels's formal definition of value. (bd. i., p. .) [ ] the essential dependence of factual judgment upon the rise of economic and ethical conflict is implied in the widely current doctrine of the teleological character of knowledge. it is indeed nowadays something like a commonplace to say in one sense or another that knowledge is relative to ends, but it is not always recognized by those who hold this view that an end never appears as such in consciousness alone. the end that guides in the construction of factual knowledge is an end in ethical or economic conflict with some other likewise indeterminate end in the manner above discussed. [ ] see above, pp. , . [ ] _cf._ schiller, _riddles of the sphinx_, chap. vii, §§ - . [ ] it would appear that the principle of the conservation of energy is valid only in the physical sphere; but the logical significance of this limitation cannot be here discussed. [ ] that the assumption mentioned is the essential basis of the twin theories of associationism in psychology and hedonism in ethics is shown by dr. warner fite in his article, "the associational conception of experience," _philosophical review_, vol. ix, pp. ff. _cf._ mr. bradley's remarks on the logic of hedonism in his _principles of logic_, pp. - . [ ] the "energetic" self is apparently mr. bradley's fourth "meaning of self," the self as monad--"something moving parallel with the life of a man, or, rather, something not moving, but literally _standing_ in relation to his successive variety" (_appearance and reality_ [ st ed.] p. , in chap. ix, "the meanings of the self"). mr. bradley's difficulty appears to come from his desiring a psychological content for what is essentially a logical conception--a confusion (if we may be permitted the remark) which runs through the entire chapter to which we refer and is responsible for the undeniable and hopeless incoherency of the various meanings of the self, as mr. bradley therein expounds them. "if the monad stands aloof," says mr. bradley, "either with no character at all or a private character apart, then it may be a fine thing in itself, but it is a mere mockery to call it the self of a man" (p. ). surely this is to misconstrue and then find fault with that very character of essential _logical_ apartness from any possibility of determination in point of descriptive psychological content which constitutes the whole value of the "energetic" self as a logical conception stimulative of the valuation-process and so inevitably of factual judgment. see pp. , , above. the reader may find for himself in mr. bradley's enumeration of meanings our concept of the empirical self. but surely the "energetic" and empirical selves would appear on our showing to have no necessary conflict with each other. [ ] in the first of these inseparable aspects valuation is determinative of rightness and wrongness; in the second it presents the object as good or bad. see p. , above. [ ] see, for example, wieser, _natural value_ (eng. trans.), p. . [ ] see pp. - above. [ ] the illustration, as also the general principle which it here is used to illustrate, was suggested some years since by professor g. h. mead in a lecture course on the "history of psychology," which the writer had the advantage of attending. [ ] the conservative function of valuation may be further illustrated by reference to the well-known principle of marginal utility of which we have already made mention (p. above), and which has played so great a part in modern economic theory. the value of the unit quantity of a stock of any commodity is, according to this principle, measured by the least important single use in the schedule of uses to which the stock as a whole is to be applied. manifestly, then, adherence to this valuation placed upon the unit quantity is in so far conservative of the whole schedule and the marginal value is a "short-hand" symbol expressive of the value of the whole complex purpose presented in the schedule. moreover, the increase of marginal value concurrently with diminution of the stock through consumption, loss, or reapplication is not indicative so much of a change of purpose as of determination to adhere to so much of the original program of consumption as may still be possible of attainment with the depleted supply of the commodity. [ ] thus except on this condition we should deny the propriety of speaking of the value of a friend or of a memento or sacred relic. the purpose of accurate definition of the function of such objects as these in the attainment of one's ends is foreign to the proper attitude of loving, prizing, or venerating them. we may ethically value the _act_ of sacrifice for a friend or of solicitous care of the memento, but the object of our sacrifice or solicitude has simply the direct or immediate "qualitative" emotional character appropriate to the kinds of activity to which it is the adequate stimulus. [ ] _history of philosophy_ (tuft's translation), p. . [ ] _cf._ professor j. r. angell's article, "relations of structural and functional psychology to philosophy," _decennial publications of the university of chicago_, vol. iii, pp. - ; also _philosophical review_, vol. xii, no. . _cf._ also mr. schiller's essay on "axioms as postulates" in _personal idealism_. [ ] from this point on this paper is an expansion of some paragraphs, pp. - , in an article on "existence, meaning, and reality," printed from vol. iii of the first series of the _decennial publications of the university of chicago_. [ ] p. . [ ] pp. , ; italics mine. [ ] p. . [ ] p. . [ ] p. ; italics mine. [ ] pp. , ; italics mine. [ ] p. . [ ] p. . [ ] p. ; italics mine. [ ] _cf._ p. ; also p. . [ ] p. . [ ] this warns us that in the phrase, "a plan of action," the term "action" must be more inclusive than it is in much current discussion. it must not be limited to gymnastic performance. it must apply to any sort of activity planned for, and which, when it arrives, fulfils the plan. this, i take it, is the import of the paragraph at the top of p. of professor james's _philosophical conceptions and practical results_. [ ] p. . [ ] pp. , . [ ] p. . [ ] p. . [ ] pp. , . [ ] see p. . [ ] p. ; italics mine. [ ] p. ; italics mine. [ ] it is worth noting in passing that here the universal appears to be located in finite experience, while the ground of the particular is in the absolute. [ ] p. . [ ] p. ; italics mine. [ ] p. . [ ] p. . [ ] p. . [ ] this ghost of subjectivism haunts the entire part of the essay in which the final fulfilment of finite ideas is found in "a certain absolute system of ideas." [ ] p. ; italics mine. [ ] p. . [ ] p. . [ ] p. . [ ] p. . [ ] this reduction of the purposive to the representative function carries with it an interesting implication concerning the whole character and relationship of thought and will. from beginning to end, on almost every page, mr. royce insists upon the idea as an expression of will. at the outset we read: "when we try to define the idea in itself, as a conscious fact, our best means is to lay stress upon the sort of will or active meaning which any idea involves for the mind that forms the idea" (p. ). again: "the idea is a will seeking its own determination. it is nothing else" (p. )--and so on throughout the lectures. and we have already seen how consistently this is worked out in the analysis of concrete acts, such as singing, etc. but now, as related to the absolute system, the will, as embodied in the idea, is to find its final determination in approximating the certain absolute system of ideas. this would seem to make will but little more than the mere form of representation itself. the idea is a will, but in its relation to truth its will is "to correspond even in its vagueness to its own final and completely individual expression." [ ] p. . [ ] p. . [ ] p. . [ ] _cf._ mr. gore's paper, above. [ ] _cf._ baldwin's _development and evolution_, pp. , , on the necessity of the submission of the "new experience" to the test of its ability to utilize habit. interpreted broadly, habit might here mean the whole mechanical side, including organism _and_ environment, and so include mr. baldwin's second or "extra-organic" test. [ ] p. . [ ] pp. , . [ ] see, above, professor dewey's study iii, pp. ff. [ ] p. . * * * * * transcriber's note: . footnotes have been renumbered and moved from the middle of a chapter to the end of the main text. . other than that, printer's inconsistencies in spelling, punctuation, hyphenation, and ligature usage have been retained. the art of logical thinking or the laws of reasoning by william walker atkinson l.n. fowler & company , imperial arcade, ludgate circus london, e.c., england the progress company chicago, ill. copyright by the progress company chicago, ill., u.s.a. contents i. reasoning ii. the process of reasoning iii. the concept iv. the use of concepts v. concepts and images vi. terms vii. the meaning of terms viii. judgments ix. propositions x. immediate reasoning xi. inductive reasoning xii. reasoning by induction xiii. theory and hypotheses xiv. making and testing hypotheses xv. deductive reasoning xvi. the syllogism xvii. varieties of syllogisms xviii. reasoning by analogy xix. fallacies chapter i. reasoning "reasoning" is defined as: "the act, process or art of exercising the faculty of reason; the act or faculty of employing reason in argument; argumentation, ratiocination; reasoning power; disputation, discussion, argumentation." stewart says: "the word _reason_ itself is far from being precise in its meaning. in common and popular discourse it denotes that power by which we distinguish truth from falsehood, and right from wrong, and by which we are enabled to combine means for the attainment of particular ends." by the employment of the reasoning faculties of the mind we compare objects presented to the mind as percepts or concepts, taking up the "raw materials" of thought and weaving them into more complex and elaborate mental fabrics which we call abstract and general ideas of truth. brooks says: "it is the thinking power of the mind; the faculty which gives us what has been called _thought-knowledge_, in distinction from _sense-knowledge_. it may be regarded as the mental architect among the faculties; it transforms the material furnished by the senses ... into new products, and thus builds up the temples of science and philosophy." the last-mentioned authority adds: "its products are twofold, _ideas_ and _thoughts_. an _idea_ is a mental product which when expressed in words does not give a proposition; a _thought_ is a mental product which embraces the relation of two or more ideas. the ideas of the understanding are of two general classes; abstract ideas and general ideas. the thoughts are also of two general classes; those pertaining to contingent truth and those pertaining to necessary truth. in contingent truth, we have _facts_, or immediate judgments, and _general truths_ including _laws_ and _causes_, derived from particular facts; in necessary truth we have _axioms_, or self-evident truths, and the truths derived from them by reasoning, called _theorems_." in inviting you to consider the processes of reasoning, we are irresistibly reminded of the old story of one of moliere's plays in which one of the characters expresses surprise on learning that he "had been talking prose for forty years without knowing it." as jevons says in mentioning this: "ninety-nine people out of a hundred might be equally surprised on hearing that they had been converting propositions, syllogizing, falling into paralogisms, framing hypotheses and making classifications with genera and species. if asked whether they were logicians, they would probably answer, no! they would be partly right; for i believe that a large number even of educated persons have no clear idea of what logic is. yet, in a certain way, every one must have been a logician since he began to speak." so, in asking you to consider the processes of reasoning we are not assuming that you never have reasoned--on the contrary we are fully aware that you in connection with every other person, have reasoned all your mature life. that is not the question. while everyone reasons, the fact is equally true that the majority of persons reason incorrectly. many persons reason along lines far from correct and scientific, and suffer therefor and thereby. some writers have claimed that the majority of persons are incapable of even fairly correct reasoning, pointing to the absurd ideas entertained by the masses of people as a proof of the statement. these writers are probably a little radical in their views and statements, but one is often struck with wonder at the evidences of incapacity for interpreting facts and impressions on the part of the general public. the masses of people accept the most absurd ideas as truth, providing they are gravely asserted by some one claiming authority. the most illogical ideas are accepted without dispute or examination, providing they are stated solemnly and authoritatively. particularly in the respective fields of religion and politics do we find this blind acceptance of illogical ideas by the multitude. mere assertion by the leaders seems sufficient for the multitude of followers to acquiesce. in order to reason correctly it is not merely necessary to have a good intellect. an athlete may have the proper proportions, good framework, and symmetrical muscles, but he cannot expect to cope with others of his kind unless he has learned to develop those muscles and to use them to the best advantage. and, in the same way, the man who wishes to reason correctly must develop his intellectual faculties and must also learn the art of using them to the best advantage. otherwise he will waste his mental energy and will be placed at a disadvantage when confronted with a trained logician in argument or debate. one who has witnessed a debate or argument between two men equally strong intellectually, one of whom is a trained logician and the other lacking this advantage, will never forget the impression produced upon him by the unequal struggle. the conflict is like that of a powerful wrestler, untrained in the little tricks and turns of the science, in the various principles of applying force in a certain way at a certain time, at a certain place, with a trained and experienced wrestler. or of a conflict between a muscular giant untrained in the art of boxing, when confronted with a trained and experienced exponent of "the manly art." the result of any such conflict is assured in advance. therefore, everyone should refuse to rest content without a knowledge of the art of reasoning correctly, for otherwise he places himself under a heavy handicap in the race for success, and allows others, perhaps less well-equipped mentally, to have a decided advantage over him. jevons says in this connection: "to be a good logician is, however, far more valuable than to be a good athlete; because logic teaches us to reason well, and reasoning gives us knowledge, and knowledge, as lord bacon said, is power. as athletes, men cannot for a moment compare with horses or tigers or monkeys. yet, with the power of knowledge, men tame horses and shoot tigers and despise monkeys. the weakest framework with the most logical mind will conquer in the end, because it is easy to foresee the future, to calculate the result of actions, to avoid mistakes which might be fatal, and to discover the means of doing things which seemed impossible. if such little creatures as ants had better brains than men, they would either destroy men or make them into slaves. it is true that we cannot use our eyes and ears without getting some kind of knowledge, and the brute animals can do the same. but what gives power is the deeper knowledge called science. people may see, and hear, and feel all their lives without really learning the nature of things they see. but reason is the mind's eye, and enables us to see why things are, and when and how events may be made to happen or not to happen. the logician endeavors to learn exactly what this reason is which makes the power of men. we all, as i have said, must reason well or ill, but logic is the science of reasoning and enables us to distinguish between the good reasoning which leads to truth, and the bad reasoning which every day betrays people into error and misfortune." in this volume we hope to be able to point out the methods and principles of correctly using the reasoning faculties of the mind, in a plain, simple manner, devoid of useless technicalities and academic discussion. we shall adhere, in the main, to the principles established by the best of the authorities of the old school of psychology, blending the same with those advanced by the best authorities of the new psychology. no attempt to make of this book a school text-book shall be made, for our sole object and aim is to bring this important subject before the general public composed of people who have neither the time nor inclination to indulge in technical discussion nor academic hair-splitting, but who desire to understand the underlying _working principles_ of the laws of reasoning. chapter ii. the process of reasoning the processes of reasoning may be said to comprise four general stages or steps, as follows: i. _abstraction_, by which is meant the process of _drawing off_ and _setting aside_ from an object, person or thing, _a quality or attribute_, and making of it a distinct object of thought. for instance, if i perceive in a _lion_ the quality of _strength_, and am able to think of this quality abstractly and independently of the animal--if the term _strength_ has an actual mental meaning to me, independent of the lion--then i have _abstracted_ that quality; the thinking thereof is an act of _abstraction_; and the thought-idea itself is an _abstract idea_. some writers hold that these abstract ideas are realities, and "not mere figments of fancy." as brooks says: "the rose dies, but my idea of its color and fragrance remains." other authorities regard abstraction as but an act of _attention_ concentrated upon but the particular quality to the exclusion of others, and that the abstract idea has no existence apart from the general idea of the object in which it is included. sir william hamilton says: "we can rivet our attention on some particular mode of a thing, as its smell, its color, its figure, its size, etc., and abstract it from the others. this may be called modal abstraction. the abstraction we have now been considering is performed on individual objects, and is consequently particular. there is nothing necessarily connected with generalization in abstraction; generalization is indeed dependent on abstraction, which it supposes; but abstraction does not involve generalization." ii. _generalization_, by which is meant the process of forming concepts or general ideas. it acts in the direction of apprehending the common qualities of objects, persons and things, and combining and uniting them into a single notion or _conception_ which will comprehend and include them all. a general idea or concept differs from a particular idea in that it includes within itself the qualities of the particular and other particulars, and accordingly may be applied to any one of these particulars as well as to the general _class_. for instance, one may have a _particular idea_ of some _particular_ horse, which applies only to that particular horse. he may also have a general idea of _horse_, in the generic or _class_ sense, which idea applies not only to the general class of _horse_ but also to each and every _horse_ which is included in that class. _the expression of generalization or conception is called a concept._ iii. _judgment_, by which is meant the process of comparing two objects, persons or things, one with another, and thus perceiving their agreement or disagreement. thus we may compare the two concepts _horse_ and _animal_, and perceiving a certain agreement between them we form the judgment that: "a _horse_ is an _animal_;" or comparing _horse_ and _cow_, and perceiving their disagreement, we form the judgment: "a _horse_ is not a _cow_." _the expression of a judgment is called a proposition._ iv. _reasoning_, by which is meant the process of comparing two objects, persons or things, through their relation to a third object, person or thing. thus we may reason (a) that all mammals are animals; (b) that a horse is a mammal; (c) that, _therefore_, a horse is an animal; the result of the reasoning being the statement that: "a horse is an animal." the most fundamental principle of reasoning, therefore, consists in the comparing of two objects of thought through and by means of their relation to a third object. _the natural form of expression of this process of reasoning is called a syllogism._ it will be seen that these four processes of reasoning necessitate the employment of the processes of analysis and synthesis, respectively. analysis means a separating of an object of thought into its constituent parts, qualities or relations. synthesis means the combining of the qualities, parts or relations of an object of thought into a composite whole. these two processes are found in all processes of reasoning. abstraction is principally analytic; generalization or conception chiefly synthetic; judgment is either or both analytic or synthetic; reasoning is either a synthesis of particulars in induction, or an evolution of the particular from the general in deduction. there are two great classes of reasoning; _viz._, ( ) inductive reasoning, or the inference of general truths from particular truths; and ( ) deductive reasoning, or the inference of particular truths from general truths. _inductive reasoning_ proceeds by discovering a general truth from particular truths. for instance, from the particular truths that individual men die we discover the general truth that "all men must die;" or from observing that in all observed instances ice melts at a certain temperature, we may infer that "all ice melts at a certain temperature." inductive reasoning proceeds from the _known to the unknown_. it is essentially a synthetic process. it seeks to discover general laws from particular facts. _deductive reasoning_ proceeds by discovering particular truths from general truths. thus we reason that as all men die, john smith, being a man, must die; or, that as all ice melts at a certain temperature, it follows that the particular piece of ice under consideration will melt at that certain temperature. deductive reasoning is therefore seen to be essentially an analytical process. mills says of inductive reasoning: "the inductive method of the ancients consisted in ascribing the character of general truths to all propositions which are true in all the instances of which we have knowledge. bacon exposed the insufficiency of this method, and physical investigation has now far outgrown the baconian conception.... induction, then, is that operation by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. in other words, induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times." regarding deductive reasoning, a writer says: "deductive reasoning is that process of reasoning by which we arrive at the necessary consequences, _starting from admitted or established premises_." brooks says: "the general truths from which we reason to particulars are derived from several distinct sources. some are intuitive, as the axioms of mathematics or logic. some of them are derived from induction.... some of them are merely hypothetical, as in the investigation of the physical sciences. many of the hypotheses and theories of the physical sciences are used as general truth for deductive reasoning; as the theory of gravitation, the theory of light; etc. reasoning from the theory of universal gravitation, leverrier discovered the position of a new planet in the heavens before it had been discovered by human eyes." halleck points out the interdependence of inductive and deductive reasoning in the following words: "man has to find out through his own experience, or that of others, the _major premises_ from which he argues or draws his conclusions. by induction we examine what seems to us a sufficient number of individual cases. we then conclude that the rest of these cases, which we have not examined, _will obey the same general laws_.... the premise, 'all cows chew the cud,' was laid down after a certain number of cows had been examined. if we were to see a cow twenty years hence, we should expect that she chewed her cud.... after induction has classified certain phenomena and _thus given us a major premise_, we proceed deductively to apply the inference to any new specimen that can be shown to belong to that class." the several steps of deductive reasoning shall now be considered in turn as we proceed. chapter iii. the concept in considering the process of thinking, we must classify the several steps or stages of thought that we may examine each in detail for the purpose of comprehending them combined as a whole. in actual thinking these several steps or stages are not clearly separated in consciousness, so that each stands out clear and distinct from the preceding and succeeding steps or stages, but, on the contrary, they blend and shade into each other so that it is often difficult to draw a clear dividing line. the first step or stage in the process of thinking is that which is called _a concept_. a concept is a mental representation of anything. prof. wm. james says: "the function by which we mark off, discriminate, draw a line around, and identify a numerically distinct subject of discourse is called _conception_." there are five stages or steps in each concept, as follows: i. _presentation._ before a concept may be formed there must first be a presentation of the material from which the concept is to be formed. if we wish to form the concept, _animal_, we must first have perceived an animal, probably several kinds of animals--horses, dogs, cats, cows, pigs, lions, tigers, etc. we must also have received impressions from the sight of these animals which may be reproduced by the memory--represented to the mind. in order that we may have a full concept of _animal_ we should have perceived every kind of animal, for otherwise there would be some elements of the full concept lacking. accordingly it is practically impossible to have a _full_ concept of anything. the greater the opportunities for perception the greater will be the opportunity for conception. in other books of this series we have spoken of the value and importance of the attention and of clear and full perception. without an active employment of the attention, it is impossible to receive a clear perception of anything; and unless the perception has been clear, it is impossible for the mind to form a clear concept of the thing perceived. as sir wm. hamilton has said: "an act of attention, that is an act of concentration, seems thus necessary to every exertion of consciousness, as a certain contraction of the pupil is requisite to every exertion of vision.... attention, then, is to consciousness what the contraction of the pupil is to sight, or to the eye of the mind what the microscope or telescope is to the bodily eye.... it constitutes the half of all intellectual power." and sir b. brodie said: "it is attention, much more than in the abstract power of reasoning, which constitutes the vast difference which exists between minds of different individuals." and as dr. beattie says: "the force with which anything strikes the mind is generally in proportion to the degree of attention bestowed upon it." ii. _comparison._ following the stage of presentation is the stage of comparison. we separate our general concept of _animal_ into a number of sub-concepts, or concepts of various kinds of animals. we compare the pig with the goat, the cow with the horse, in fact each animal with all other animals known to us. by this process we distinguish the points of resemblance and the points of difference. we perceive that the wolf resembles the dog to a considerable degree; that it has some points of resemblance to the fox; and a still less distinct resemblance to the bear; also that it differs materially from the horse, the cow or the elephant. we also learn that there are various kinds of wolves, all bearing a great resemblance to each other, and yet having marked points of difference. the closer we observe the various individuals among the wolves, the more points of difference do we find. the faculty of comparison evidences itself in inductive reasoning; ability and disposition to analyze, classify, compare, etc. fowler says that those in whom it is largely developed "reason clearly and correctly from conclusions and scientific facts up to the laws which govern them; discern the known from the unknown; detect error by its incongruity with facts; have an excellent talent for comparing, explaining, expounding, criticising, exposing, etc." prof. william james says: "any personal or practical interest in the results to be obtained by distinguishing, makes one's wits amazingly sharp to detect differences. and long training and practice in distinguishing has the same effect as personal interest. both of these agencies give to small amounts of objective difference the same effectiveness upon the mind that, under other circumstances, only large ones would make." iii. _abstraction._ following the stage of comparison is that of abstraction. the term "abstraction" as used in psychology means: "the act or process of separating from the numerous qualities inherent in any object, the particular one which we wish to make the subject of observation and reflection. or, the act of withdrawing the consciousness from a number of objects with a view to concentrate it on some particular one. the negative act of which attention is the positive." to _abstract_ is "to separate or set apart." in the process of abstraction in our consideration of _animals_, after having recognized the various points of difference and resemblance between the various species and individuals, we proceed to consider some special quality of animals, and, in doing so, we _abstract_, set aside, or separate the particular quality which we wish to consider. if we wish to consider the _size_ of animals, we abstract the quality of size from the other qualities, and consider animals with reference to size alone. thus we consider the various degrees of size of the various animals, classifying them accordingly. in the same way we may abstract the quality of shape, color or habits, respectively, setting aside this quality for special observation and classification. if we wish to study, examine or consider certain qualities in a thing we abstract that particular quality from the other qualities of the thing; or we abstract the other qualities until nothing is left but the particular quality under consideration. in examining or considering a class or number of things, we first abstract the qualities _possessed in common_ by the class or number of things; and also abstract or set aside the qualities _not common_ to them. for instance; in considering classes of animals, we abstract the combined quality of milk-giving and pouch-possessing which is possessed in common by a number of animals; then we group these several animals in a class which we name the _marsupialia_, of which the opossum and kangaroo are members. in these animals the young are brought forth in an imperfect condition, undeveloped in size and condition, and are then kept in the pouch and nourished until they are able to care for themselves. likewise, we may abstract the idea of the _placenta_, the appendage which connects the young unborn animal with the mother, and by means of which the foetus is nourished. the animals distinguished by this quality are grouped together as the placental mammals. the placental mammals are divided into various groups, by an abstraction of qualities or class resemblance or difference, as follows: the _edentata_, or toothless creatures, such as the sloths, ant-eaters, armadillos, etc.; the _sirenia_, so-named from their fancied resemblance to the fabled "sirens," among which class are the sea-cows, manatees, dugongs, etc.; the _cetacea_, or whale family, which although fish-like in appearance, are really mammals, giving birth to living young which they nourish with breast-milk, among which are the whales, porpoises, dolphins, etc.; the _ungulata_, or hoofed animals, such as the horse, the tapir, the rhinoceros, the swine, the hippopotamus, the camel, the deer, the sheep, the cow, etc.; the _hyracoidea_, having teeth resembling both the hoofed animals and the gnawing animals, of which the coney or rock-rabbit is the principal example; the _proboscidea_, or trunked animals, which family is represented by the various families of elephants; the _carnivora_, or flesh-eaters, represented by various sub-families and species; the _rodentia_, or gnawers; the _insectivora_, or insect feeders; the _cheiroptera_, or finger-winged; the _lemuroidea_, or lemurs, having the general appearance of the monkey, but also the long bushy tail of the fox; the _primates_, including the monkeys, baboons, man-apes, gibbons, gorillas, chimpanzees, orang-outangs and man. in all of these cases you will see that each class or general family possesses a certain _common quality_ which gives it its classification, and which quality is the subject of the abstraction in considering the particular group of animals. further and closer abstraction divides these classes into sub-classes; for instance, the family or class of the _carnivora_, or flesh-eaters, may be divided by further abstraction into the classes of seals, bears, weasels, wolves, dogs, lions, tigers, leopards, etc. in this process, we must first make the more general abstraction of the wolf and similar animals into the dog-family; and the lion, tiger and similar forms into the cat-family. halleck says of abstraction: "in the process of abstraction, we draw our attention away from a mass of confusing details, unimportant at the time, and attend only to qualities common to the class. abstraction is little else than centering the power of attention on some qualities to the exclusion of others." iv. _generalization._ arising from the stage of abstraction is the stage of generalization. _generalization_ is: "the act or process of generalizing or making general; bringing several objects agreeing in some point under a common or general name, head or class; an extending from particulars to generals; reducing or arranging in a genus; bringing a particular fact or series of facts into a relation with a wider circle of facts." as bolingbroke says: "the mind, therefore, makes its utmost endeavors to _generalize_ its ideas, beginning early with such as are most familiar and coming in time to those which are less so." under the head of abstraction we have seen that through abstraction we may generalize the various species into the various families, and thus, in turn, into the various sub-families. following the same process we may narrow down the sub-families into species composed of various individuals; or into greater and still greater families or groups. generalization is really the act of classification, or forming into classes all things having certain qualities or properties _in common_. the corollary is that _all things in a certain generalized class must possess the particular quality or property common to the class_. thus we know that all animals in the class of the _carnivora_ must eat flesh; and that all _mammals_ possess breasts from which they feed their young. as halleck says: "we put all objects having like qualities into a certain _genus_, or class. when the objects are in that class, _we know that certain qualities will have a general application to them all_." v. _denomination._ following closely upon the step of generalization or classification, is the step of denomination. by _denomination_ we mean "the act of naming or designating by a name." a name is the symbol by which we think of a familiar thing without the necessity for making a distinct mental image upon each occasion of thought. or, it may be considered as akin to a _label_ affixed to a thing. as in the case of the algebraic symbols, _a_, _b_, _c_, _x_, and _y_, by the use of which we are able to make intricate calculations easily and rapidly, so may we use these word symbols much more readily than we could the lengthy descriptions or even the mental images of the thing symbolized. it is much easier for us to think "_horse_" than it would be to think the full definition of that animal, or to think of it by recalling a mental picture of the horse each time we wished to think of it. or, it is much better for us to be able to glance at a label on a package or bottle than to examine the contents in detail. as hobbes says: "a word taken at pleasure to serve for a mark, which may raise in our minds a thought like to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker had or had not, before in his mind." mill says: "a name is a word (or set of words) serving the double purpose of a mark to recall to ourselves the likeness of a former thought and as a sign to make it known to others." some philosophers regard names as symbols of _our ideas of things_, rather than of the things themselves; others regard them as symbols of the things themselves. it will be seen that the value of a name depends materially upon the correct meaning and understanding regarding it possessed by the person using it. chapter iv. the use of concepts having observed the several steps or stages of a concept, let us now consider the use and misuse of the latter. at first glance it would appear difficult to misuse a concept, but a little consideration will show that people very commonly fall into error regarding their concepts. for instance, a child perceives a horse, a cow or a sheep and hears its elders apply the term "_animal_" to it. this term is perfectly correct, although symbolizing only a very general classification or generalization. but, the child knowing nothing of the more limited and detailed classification begins to generalize regarding the animal. to it, accordingly, an "animal" is identical with the dog or the cow, the sheep or the horse, as the case may be, and when the term is used the child thinks that _all animals_ are similar to the particular animal seen. later on, when it hears the term "animal" applied to a totally different looking creature, it thinks that a mistake has been made and a state of confusion occurs. or, even when a term is applied within narrower limits, the same trouble occurs. the child may hear the term "dog" applied to a mastiff, and it accordingly forms a concept of _dog_ identical with the qualities and attributes of the mastiff. later, hearing the same term applied to a toy-terrier, it becomes indignant and cries out that the latter is no "dog" but is something entirely different. it is not until the child becomes acquainted with the fact that there are many kinds of creatures in the general category of "dog" that the latter term becomes fully understood and its appropriate concept is intelligently formed. thus we see the importance of the step of presentation. in the same way the child might imagine that because some particular "man" had red hair and long whiskers, _all men_ were red-haired and long-whiskered. such a child would always form the concept of "man" as a creature possessed of the personal qualities just mentioned. as a writer once said, readers of current french literature might imagine that all englishmen were short, dumpy, red-cheeked and irascible, and that all englishwomen had great teeth and enormous feet; also that readers of english literature might imagine that all frenchmen were like monkeys, and all frenchwomen were sad coquettes. in the same way many american young people believe that all englishmen say "don't you know" and all englishwomen constantly ejaculate: "fancy!" also that every englishman wears a monocle. in the same way, the young english person, from reading the cheap novels of his own country, might well form the concept of all americans as long-legged, chin-whiskered and big-nosed, saying "waal, i want to know;" "i reckon;" and "du tell;" while they tilted themselves back in a chair with their feet on the mantelpiece. the concept of a western man, entertained by the average eastern person who has never traveled further west than buffalo, is equally amusing. in the same way, we have known western people who formed a concept of boston people as partaking of a steady and continuous diet of baked beans and studiously reading browning and emerson between these meals. halleck says: "a certain norwegian child ten years old had the quality _white_ firmly imbedded in his concept _man_. happening one day to see a negro for the first time, the child refused to call him a man until the negro's other qualities compelled the child to revise his concept and to eliminate whiteness. if that child should ever see an indian or a chinaman, the concept would undergo still further revision. a girl of six, reared with an intemperate father and brothers, had the quality of _drunkenness_ firmly fixed in her concept of _man_. a certain boy kept, until the age of eleven, _trustworthiness_ in his concept of man. another boy, until late in his teens thought that man was a creature who did wrong not from determination but from ignorance, that any man would change his course to the right path if he could but understand that he was going wrong. happening one day to hear of a wealthy man who was neglecting to provide comforts for his aged mother in her last sickness, the boy concluded that the man did not know his mother's condition. when he informed the man, the boy was told to mind his own business. the same day he heard of some politicians who had intentionally cheated the city in letting a contract and he immediately revised his concept. it must be borne in mind that most of our concepts are subject to change during our entire life; that at first they are made only in a tentative way; that experience may show us, at any time, that they have been erroneously formed, that we have, abstracted too little or too much, made this class too wide or too narrow, or that here a quality must be added or there one taken away." let us now consider the mental processes involved in the formation and use of a concept. we have first, as we have seen, the presentation of the crude material from which the concept must be formed. our attention being attracted to or directed toward an object, we notice its qualities and properties. then we begin a process of comparison of the object perceived or of our perception of it. we compare the object with other objects or ideas in our mind, noting similarities and differences and thereby leading towards classification with similar objects and opposed dissimilar ones. the greater the range of other objects previously perceived, the greater will be the number of relations established between the new object or idea and others. as we advance in experience and knowledge, the web of related objects and ideas becomes more intricate and complex. the relations attaching to the child's concept of horse is very much simpler than the concept of the experienced adult. then we pass on to the step of analysis, in which we separate the qualities of the object and consider them in detail. the act of abstraction is an analytical process. then we pass on to the step of synthesis, in which we unite the materials gathered by comparison and analysis, and thus form a general idea or concept regarding the object. in this process we combine the various qualities discerned by comparison and analysis, and grouping them together as in a bundle, we tie them together with the string of synthesis and thus have a true general conception. thus from the first general conception of _horse_ as a simple thing, we notice first that the animal has certain qualities lacking in other things and certain others similar to other things; then we analyze the various qualities of the horse, recognized through comparison, until we have a clear and distinct idea of the various parts, qualities and properties of the horse; then we synthesize, and joining together these various conceptions of the said qualities, we at last form a clear general concept of _the horse as he is_, with all his qualities. of course, if we later discover other qualities attached to the horse, we add these to our general synthesized concept--our concept of _horse_ is enlarged. of course these various steps in the formation and use of a concept are not realized as distinct acts in the consciousness, for the processes are largely instinctive and subconscious, particularly in the case of the experienced individual. the subconscious, or habit mind, usually attends to these details for us, except in instances in which we deliberately apply the will to the task, as in cases of close study, in which we take the process from the region of the involuntary and place it in the voluntary category. so closely related and blended are these various steps of the process, that some authorities have disputed vigorously upon the question as to which of the two steps, comparison or analysis, precedes the other. some have claimed that analysis must precede comparison, else how could one compare without having first analyzed the things to be compared. others hold that comparison must precede analysis, else how could one note a quality unless he had his attention drawn to it by its resemblance to or difference from qualities in other objects. the truth seems to lie between the two ideas, for in some cases there seems to be a perception of some similarity or difference before any analysis or abstraction takes place; while in others there seems to be an analysis or abstraction before comparison is possible. in this book we have followed the arrangement favored by the latest authorities, but the question is still an open one to many minds. as we have seen, the general concept once having been formed, the mind proceeds to classify the concept with others having general qualities in common. and, likewise, it proceeds to generalize from the classification, assuming certain qualities in certain classes. then we proceed to make still further generalizations and classifications on an ascending and widening scale, including seeming resemblances less marked, until finally we embrace the object with other objects in as large a class as possible as well as in as close and limited a sub-class as possible. as brooks says: "generalization is an ascending process. the broader concept is regarded as higher than the narrower concept; a concept is considered higher than a percept; a general idea stands above a particular idea. we thus go up from particulars to generals; from percepts to concepts; from lower concepts to higher concepts. beginning down with particular objects, we rise from them to the general idea of their class. having formed a number of lower classes, we compare them as we did individuals and generalize them into higher classes. we perform the same process with these higher classes, and thus proceed until we are at last arrested in the highest class, _being_. having reached the pinnacle of generalization, we may descend the ladder by reversing the process through which we ascend." from this process of generalization, or synthesis, we create from our simple concepts our _general concepts_. some of the older authorities distinguished between these two classes by terming the former "conceptions," and reserving the term "concepts" for the general concepts. brooks says of this: "the products of generalization are general ideas called _concepts_. we have already discussed the method of forming conceptions and now consider the nature of the concept itself.... a concept is a general idea. it is a general notion which has in it all that is common to its own class. it is a general scheme which embraces all the individuals of the class while it resembles in all respects none of its class. thus my conception of a _quadruped_ has in it all four-footed animals, but it does not correspond in all respects to any particular animals; my conception of a _triangle_ embraces all triangles, but does not agree in details with any particular triangle. the general conception cannot be made to fit exactly any particular object, but it teems with many particulars. these points may be illustrated with the concepts _horse_, _bird_, _color_, _animal_, etc." so we may begin to perceive the distinction and difference between a _concept_ and a _mental image_. this distinction, and the fact that _a concept cannot be imaged_, is generally difficult for the beginner. it is important that one should have a clear and distinct understanding regarding this point, and so we shall consider it further in the following chapter. chapter v. concepts and images as we have said, a concept cannot be imaged--cannot be used as the subject of a mental image. this statement is perplexing to the student who has been accustomed to the idea that every conception of the mind is capable of being reproduced in the form of a mental image. but the apparently paradoxical statement is seen as quite simple when a little consideration is given to it. for instance, you have a distinct general concept of _animal_. you know what you mean when you say or think, _animal_. you recognize an animal when you see one and you understand what is meant when another uses the word in conversation. but you cannot form a mental image of the concept, _animal_. why? because any mental image you might form would be either a picture of _some particular animal_ or else a composite of the qualities of several animals. your concept is too broad and general to allow of a composite picture of _all animals_. and, in truth, your concept is _not a picture of anything that actually exists_ in one particular, but an abstract idea embracing the qualities of all animals. it is like the algebraic _x_--a symbol for something that exists, but not the thing itself. as brooks says: "a concept cannot be represented by a concrete image. this is evident from its being general rather than particular. if its color, size or shape is fixed by an image, it is no longer general but particular." and halleck says: "it is impossible to image anything without giving that image individual marks. the best mental images are so definite that a picture could be painted from them. a being might come under the class _man_ and have a snub nose, blonde hair, scanty eyebrows, and no scar on his face. the presence of one of these individual peculiarities in the concept _man_ would destroy it. if we form an image of an apple, it must be either of a yellow, red, green, or russet apple, either as large as a pippin or as small as a crab-apple. a boy was asked what he thought of when '_apple_' was mentioned. he replied that he thought of 'a big, dark-red, apple with a bad spot on one side, near the top.' that boy could image distinctly, but his power of forming concepts was still in its infancy." so we see that while a mental image must picture the particular and individual qualities, properties and appearances of some particular unit of a class, a _concept_ can and must contain only the _class qualities_--that is, the qualities belonging to the entire class. the general concept is as has been said "a general idea ... a general notion which has in it all that is common to its own class." and it follows that a "general idea" of this kind cannot be pictured. a picture must be of some particular thing, while a concept is something above and higher than particular things. we may picture _a man_, but we cannot picture man the concept of the race. a concept is not a reproduction of the image of a _thing_, but on the contrary is _an idea of a class of things_. we trust that the student will consider this point until he arrives at a clear understanding of the distinction, and the reason thereof. but, while a concept is incapable of being pictured mentally as an image, it is true that _some particular representative of a class_ may be held in the mind or imagination as _an idealized object_, as a general representative of the class, when we speak or think of the general term or concept, providing that its real relation to the concept is recognized. these idealized objects, however, are not concepts--they are _percepts_ reproduced by the memory. it is important, however, to all who wish to convey their thought plainly, that they be able to convert their concepts into idealized representative objects. otherwise, they tend to become too idealistic and abstract for common comprehension. as halleck well says: "we should in all cases be ready to translate our concepts, when occasion requires, into the images of those individuals which the concept represents. a concept means nothing except in reference to certain individuals. without them it could never have had existence and they are entitled to representation. a man who cannot translate his concepts into definite images of the proper objects, is fitted neither to teach, preach, nor practice any profession.... there was, not long ago, a man very fond of talking about _fruit_ in the abstract; but he failed to recognize an individual cranberry when it was placed before him. a humorist remarked that a certain metaphysician had such a love for abstractions, and such an intense dislike for concrete things, as to refuse to eat a concrete peach when placed before him." in the beginning many students are perplexed regarding the difference between a _percept_ and a _concept_. the distinction is simple when properly considered. a percept is: "the object of an act of perception; that which is perceived." a concept is: "a mental representation." brooks makes the following distinction: "a _percept_ is the mental product of a real thing; a _concept_ is a mere idea or notion of the common attributes of things. a _percept_ represents some particular object; a _concept_ is not particular, but general. a _percept_ can be described by particulars; a _concept_ can be described only by generals. the former can usually be represented by an image, the latter cannot be imagined, _it can only be thought_." thus one is able to image the _percept_ of a particular horse which has been perceived; but he is unable to image correctly the concept of _horse_ as a class or generic term. in connection with this distinction between _perception_ and _conception_, we may as well consider the subject of _apperception_, a term favored by many modern psychologists, although others steadfastly decline to recognize its necessity or meaning and refuse to employ it. apperception may be defined as: "perception accompanied by comprehension; perception accompanied by recognition." the thing perceived is held to be comprehended or recognized--that is, _perceived in a new sense_, by reason of certain previously acquired ideas in the mind. halleck explains it as: "the perception of things in relation to the ideas which we already possess." it follows that all individuals possessed of equally active organs of perception, and equally active attention, will perceive the same thing in the same way and in the same degree. but the _apperception_ of each individual will differ and vary according to his previous experience and training, temperament and taste, habit and custom. for instance, the familiar story of the boy who climbed a tree and watched the passers-by, noting their comments. the first passer-by noticing the tree, says aloud: "that would make a good stick of timber." "good morning, mr. carpenter," said the boy. the next man said: "that tree has fine bark." "good morning, mr. tanner," said the boy. another said, "i bet there's a squirrel's nest up in that tree." "good morning, mr. hunter," said the boy. the woman sees in a bird something pretty and "cunning." the hunter sees in it something to kill. the ornithologist sees it as something of a certain genus and species, and perhaps also as something appropriate for his collection. the farmer perceives it to be something destructive of either insects or crops. a thief sees a jail as something to be dreaded; an ordinary citizen, something useful for confining objectionable people; a policeman, something in the line of his business. and so on, the apperception differing upon the previous experience of the individual. in the same way the scientist sees in an animal or rock many qualities of which the ordinary person is ignorant. our training, experience, prejudices, etc., affect our apperception. and so, we see that in a measure our _concepts_ are determined not only by our simple perceptions, but also materially by our apperceptions. we conceive things not only as they are apparent to our senses, but also as colored and influenced by our previous impressions and ideas. for this reason we find widely varying concepts of the same things among different individuals. only an absolute mind could form an absolute concept. chapter vi. terms in logic the words _concept_ and _term_ are practically identical, but in the popular usage of the terms there is a distinct difference. this difference is warranted, if we depart from the theoretical phase of logic, for the word _concept_ really denotes an _idea_ in the mind, while the word _term_ really denotes a _word_ or name of an idea or concept--the symbol of the latter. in a previous chapter we have seen that denomination, or "the act of naming or designating by a name" is the final step or stage in forming a concept. and it is a fact that the majority of the words in the languages of civilized people denote general ideas or concepts. as brooks says: "to give each individual or particular idea a name peculiar to itself would be impracticable and indeed impossible; the mind would soon become overwhelmed with its burden of names. nearly all the ordinary words of our language are general rather than particular. the individuals distinguished by particular names, excepting persons and places, are comparatively few. most objects are named only by common nouns; nearly all of our verbs express general actions; our adjectives denote common qualities, and our adverbs designate classes of actions and qualities. there are very few words in the language, besides the names of persons and places, that do not express general ideas." in logic the word _term_ is employed to denote _any word or words which constitute a concept_. the word _concept_ is employed strictly in the sense of _a subject of thought_, without reference to the words symbolizing it. the _concept_, or subject of thought, is the important element or fact and the _term_ denoting it is merely a convenient symbol of expression. it must be remembered that a _term_ does not necessarily consists of but a single word, for often many words are employed to denote the concept, sometimes even an entire clause or phrase being found necessary for the current _term_. for the purpose of the consideration of the subjects to be treated upon in this book, we may agree that: _a term is the outward symbol of a concept_; and that: _the concept is the idea expressed by the term_. there are three general parts or phases of deductive logic, namely: terms, propositions and syllogisms. therefore, in considering terms we are entering into a consideration of the first phase of deductive logic. unless we have a correct understanding of terms, we cannot expect to understand the succeeding stages of deductive reasoning. as jevons says: "when we join terms together we make a proposition; when we join propositions together, we make an argument or piece of reasoning.... we should generally get nothing but nonsense if we were to put together any terms and any propositions and to suppose that we were reasoning. to produce a good argument we must be careful to obey certain rules, which it is the purpose of logic to make known. but, in order to understand the matter perfectly, _we ought first to learn exactly what a term is, and how many kinds of terms there may be_; we have next to learn the nature of a proposition and the different kinds of propositions. afterwards we shall learn how one proposition may by reasoning be drawn from other propositions in the kind of argument called the syllogism." now, having seen that terms are the outward symbols or expression of concepts, and are the names of things which we join together in a proposition, let us proceed to consider the different kinds of terms, following the classifications adopted by the authorities. a _term_ may contain any number of nouns, substantive or adjective or it may contain but a single noun. thus in, "tigers are ferocious," the first term is the single substantive "tigers;" the second term is the single adjective "ferocious." and in the proposition, "the king of england is the emperor of india," there are two terms, each composed of two nouns, "king of england" being the first term and "emperor of india" being the second term. the proposition, "the library of the british museum is the greatest collection of books in the world," contains fifteen words but _only two terms_; the first term being "the library of the british museum," in which are two substantives, one adjective, two definite articles and one preposition; the second term being, "the greatest collection of books in the world," which contains three substantives, one adjective, two articles, and two prepositions. the above illustration is supplied by jevons, who adds: "a logical term, then, may consist of any number of nouns, substantive or adjective, with the articles, prepositions and conjunctions required to join them together; still _it is only one term if it points out, or makes us think of a single object, or collection, or class of objects_." (a substantive, is: "the part of speech which expresses something that exists, either material or immaterial.") the first classification of terms divides them into two general classes, _viz._, ( ) singular terms; and ( ) general terms. a _singular term_ is a term denoting a single object, person or thing. although denoting only a single object, person or thing, it may be composed of several words; or it may be composed of but one word as in the case of a proper name, etc. the following are singular terms, because they are terms denoting but a single object, person or thing: "europe; minnesota; socrates; shakespeare; the first man; the highest good; the first cause; the king of england; the british museum; the commissioner of public works; the main street of the city of new york." it will be noted that in all of the examples given, the singular term denotes a particular something, a specific thing, a something of which there is but one, and that one possesses particularity and individuality. as hyslop says: "_oneness of kind_ is not the only or distinctive feature of singular terms, but _individuality_, or singularity, as representing a concrete individual whole." a _general term_ is a term which applies, in the same sense, to each and every individual object, person or thing in a number of objects, persons or things of the same kind, or to the entire class composed of such objects persons or things of the same kind. for instance, "horse; man; biped; mammal; trees; figures; grain of sand; matter," etc. hyslop says, regarding general terms: "in these instances the terms denote more than one object, and apply to all of the same kind. their meaning is important in the interpretation of what are called universal propositions." another general classification of terms divides them into two respective classes, as follows: ( ) collective terms; and ( ) distributive terms. hyslop says of this classification: "this division is based upon the distinction between aggregate wholes of the same kind and class terms. it partly coincides with the division into singular and general terms, the latter always being distributive." a _collective term_ is one which denotes an aggregate or collected whole of objects, persons or things of the same or similar kind, _which collective whole is considered as an individual_, although composed of a totality of separate individual objects, persons or things. thus the following terms: "regiment; congregation; army; family; crowd; nation; company; battalion; class; congress; parliament; convention;" etc. are collective terms, because they denote collective, aggregate or composite wholes, considered as an individual. a _distributive term_ is a term which denotes _each and every individual object, person or thing in a given class_. for example, are the terms: "man; quadruped; biped; mammal; book; diamond; tree." as hyslop says: "general terms are always distributive." also: "it is important also to keep clear the distinction between _class_ wholes and _collective_ wholes.... they are often confused so as to call a term denoting a _class_ a collective term." another general classification of terms divides them into the following two respective classes; ( ) concrete terms; and ( ) abstract terms. a _concrete term_ is a term denoting either a definite object, person or thing which is subject to perception and experience, and may be considered as actually existent concretely, as for instance: horse; man; mountain; dollar; knife; table; etc., or else an attribute thought of and used solely as an attribute, as for instance: "beautiful, wise, noble, virtuous, good," etc. an _abstract term_ is a term denoting the attribute, quality or property _considered as apart from the object, person or thing_ and as having an abstract existence, as for instance: "beauty; wisdom; nobility; goodness; virtue," etc. as we have seen elsewhere, these qualities have no real existence _in themselves_, but are known and thought of only in connection with concrete objects, persons and things. thus we cannot know "beauty," but may know _beautiful things_; we cannot know "virtue," but we may know virtuous people, etc. an _attribute or quality_ is _concrete_ when expressed as an _adjective_; and _abstract_ when expressed as a _noun_; as for instance, "beautiful" and "beauty," respectively, or "virtuous" and "virtue," respectively. the distinction may be summed up as follows: a concrete term is _the name of a thing or of a quality of a thing expressed as an adjective and as merely a quality_; while an abstract term is the name of a quality of a thing, _expressed as a noun and as a "thing" in itself_. certain terms may be used as either concrete terms or as abstract terms, and certain authorities have seen fit to classify them as _mixed terms_, as for instance the terms: "government; religion; philosophy;" etc. another general classification of terms divides them into two respective classes as follows: ( ) _positive terms_; and ( ) _negative terms_. a _positive term_ is a term which denotes its own qualities, as for instance: "good, human, large, square, black, strong," etc. these terms indicate the presence of the quality denoted by the term itself. a _negative term_ is a term denoting the absence of a quality, as for instance: "inhuman, inorganic, unwell, unpleasant, non-conducive," etc. these terms _deny_ the presence of certain qualities, rather than _asserting_ the presence of an opposite quality. they are essentially negative in nature and in form. jevons says: "we may usually know a negative term by its beginning with one of the little syllables un-, in-, a-, an-, non-, or by its ending with -less." hyslop says: "the usual symbols of negative terms are _in_, _un_, _less_, _dis_, _a_, or _an_, _anti_, _mis_, and sometimes _de_, and _non_ and _not_." jevons adds: "if the english language were a perfect one, every term ought to have a negative term exactly corresponding to it, so that all adjectives and nouns would be in pairs. just as _convenient_ has its negative _inconvenient_; metallic, non-metallic; logical, illogical; and so on; so blue should have its negative, non-blue; literary, non-literary; paper, non-paper. but many of these negative terms would be seldom or never used, and if we happen to want them, we can make them for the occasion by putting not-, or non-, before the positive term. accordingly, we find in the dictionary only those negative terms which are much employed." the last named authority also says: "sometimes the same word may seem to have two or even more distinct negatives. there is much difference between _undressed_ and _not-dressed_, that is 'not in evening dress.' both seem to be negatives of 'dressed,' but this is because the word has two distinct meanings." some authorities insist upon closer and further classification, as for instance, in the case of what they call a _privative term_, denoting the absence of qualities once possessed by the object, person or thing, as: "deaf, dead, blind, dark," etc. hyslop says that these terms "are positive in form and negative in matter or meaning." also in the case of what they call a _nego-positive term_, denoting "the presence of a positive quality expressed in a negative manner," as: disagreeable, inhuman, invaluable, etc. these last mentioned classes however are regarded by some as the result of "carrying too far" the tendency toward classification, and the two general classes, positive and negative, are thought sufficient for the purpose of the general student. the same objection applies to a classification occasionally made _i.e._, that which is called an _infinitated term_, denoting a term the intent of which is to place in a distinct category every object, person or thing other than that expressed in the corresponding positive term. the intent of the term is to place the positive idea in one class, and all else into a separate one. examples of this class of terms are found in: "not-i, not-animal, not-tree, unmoral," etc. hyslop says of these terms: "they are not always, if ever, recognized as rhetorically elegant, but are valuable often to make clear the really negative, or infinitatively negative nature of the idea in mind." another general classification of terms divides them into two respective classes, as follows: ( ) absolute terms; and ( ) relative terms. an _absolute term_ is a term denoting the presence of qualities intrinsic to the object, and not depending upon any relation to any other object, as for instance: "man; book; horse; gun;" etc. these terms _may be_ related to many other terms, but are _not necessarily_ related to any other. a _relative term_ is a term denoting certain _necessary_ relations to other terms, as for instance: "father; son; mother; daughter; teacher; pupil; master; servant;" etc. thus it is impossible to think of "child" except in relation to "parent," or _vice versa_. the one term implies the existence of its related term. hyslop says of the above classification: "relative terms suggest the thought of other individuals with the relation involved as a part of the term's meaning, while absolute terms suggest only the qualities in the subject without a relation to others being necessarily involved." some authorities also classify terms as _higher and lower_; also as _broad and narrow_. this classification is meant to indicate the content and extent of the term. for instance, when we classify, we begin with the individuals which we then group into a small class. these classes we then group into a larger class, according to their resemblances. these larger classes then go to form a part of still larger classes, and so on. as these classes advance they form _broader_ terms; and as we retreat from the general class into the less general and more particular, the term becomes _narrower_. by some, the _broader_ term which includes the narrower is called the _higher term_, and the narrower are called the _lower terms_. thus _animal_ would be a higher and broader term than dog, cat or tiger because it includes the latter. brooks says: "since a concept is formed by the union of the common attributes of individuals, it thus embraces both attributes and individuals. the attributes of a concept constitute what is called its _content_; the individuals it embraces constitute its _extent_." accordingly, the feature of including objects in a concept or term is called its _extension_; while the feature of including attributes or qualities is called its intension. it follows as a natural consequence that the greater the _extension_ of a term, the less its _intension_; the greater its _intension_, the less its _extension_. we will understand this more clearly when we consider that the more individuals contained in a term, the fewer _common_ properties or qualities it can contain; and the more common properties, the fewer individuals. as brooks says: "the concept _man_ has more _extension_ than _poet_, _orator_ or _statesman_, since it embraces more individuals; and less _intension_, since we must lay aside the distinctive attributes of poet, orator and statesman in order to unite them in a common class _man_." in the same way the general term _animal_ is quite extended for it includes a large number of individual varieties of very different and varied characteristics and qualities; as for instance, the lion, camel, dog, oyster, elephant, snail, worm, snake, etc. accordingly its intension must be small for it can include only the qualities common to all animals, which are very few indeed. the definition of the term shows how small is its _intension_, as: "_animal._ an organic being, rising above a vegetable in various respects, especially in possessing sensibility, will and the power of voluntary motion." another narrows the intension still further when he defines _animal_ as: "a creature which possesses, or has possessed, life." halleck says: "_animal_ is very narrow in intension, very broad in extension. there are few qualities common to all animals, but there is a vast number of animals. to give the full meaning of the term in _extension_, we should have to name every animal, from the microscopic infusoria to the tiger, from the angleworm to the whale. when we decrease the extension to one species of animal, _horse_, the individuals are fewer, the qualities more numerous." the importance of forming clear and distinct concepts and of grouping, classifying and generalizing these into larger and broader concepts and terms is recognized by all authorities and is generally regarded as forming the real basis of all constructive thought. as brooks says: "generalization lies at the basis of language: only as man can form general conceptions is it possible for him to form a language.... nearly all the ordinary words in our language are general rather than particular.... this power of generalization lies also at the basis of science. had we no power of forming general ideas, each particular object would be a study by itself, and we should thus never pass beyond the very alphabet of knowledge. judgments, except in the simplest form, would be impossible; and it is difficult to see how even the simplest form of the syllogism could be constructed. no general conclusion could be drawn from particulars, nor particular conclusions from generals; and thus neither inductive nor deductive reasoning would be possible. the classifications of science could not be made; and knowledge would end at the very threshold of science." chapter vii. the meaning of terms every term has its _meaning_, or _content_, as some authorities prefer to call it. the word or words of which the term is composed are merely vocal sounds, serving as a symbol for the real _meaning_ of the term, which _meaning_ exists only in the mind of the person understanding it. to one not understanding the meaning of the term, the latter is but as a meaningless sound, but to one understanding it the sound awakens mental associations and representation and thus serves its purpose as a symbol of thought. each concrete general term has two _meanings_, ( ) the actual concrete thing, person or object to which the term is applied; and ( ) the qualities, attributes or properties of those objects, persons or things in consequence of which the term is applied. for instance, in the case of the concrete term _book_, the first meaning consists of the general idea of the thing which we think of as _a book_, and the second meaning consists of the various qualities which go to make that thing a book, as the printed pages, the binding, the form, the cover, etc. not only is that particular thing _a book_, but every other thing having the same or similar properties also must be _a book_. and so, whenever i call a thing _a book_ it must possess the said qualities. and, whenever i combine the ideas of these qualities in thought, i must think of _a book_. as jevons says: "in reality, every ordinary general term has a double meaning: it means the things to which it is applied, ... it also means, in a totally different way, the qualities and peculiarities _implied_ as being in the things. logicians say that the number of things to which a term applies is the _extension_ of the term; while the number of qualities or peculiarities implied is the _intension_." the extension and intension of terms has been referred to in the previous chapter. the general classification of the degrees of _extension_ of a general term is expressed by the two terms, _genus_ and _species_, respectively. the classification of the character of the _intension_ of a term is expressed by the term, _difference_, _property_ and _accident_, respectively. _genus_ is a term indicating: "a class of objects containing several species; a class more extensive than a species; a universal which is predicable of several things of different species." _species_ is a term denoting: "a smaller class of objects than a genus, and of two or more of which a genus is composed; a predicable that expresses the whole essence of its subject in so far as any common term can express it." an authority says: "the names _species_ and _genus_ are merely relative and the same common term may, in one case, be the species which is predicated of an individual, and in another case the individual of which a species is predicated. thus the individual, george, belongs to the logical species man, while man is an individual of the logical species animal." jevons says: "it is desirable to have names by which to show that one class is contained in another, and accordingly we call the class which is divided into two or more smaller ones, the _genus_, and the smaller ones into which it is divided, the _species_." _animal_ is a _genus_ of which _man_ is a _species_; while _man_, in turn, is a _genus_ of which _caucasian_ is a _species_; and _caucasian_, in turn, becomes a _genus_ of which _socrates_ becomes a species. the student must avoid confusing the _logical_ meaning of the terms _genus_ and _species_ with the use of the same terms in natural history. _each class is a "genus" to the class below it in extension; and each class is a "species" to the class above it in extension._ at the lowest extreme of the scale we reach what is called the _infima species_, which cannot be further subdivided, as for instance "socrates"--this lowest species must always be an individual object, person or thing. at the highest extreme of the scale we reach what is _summum genus_, or highest genus, which is never a species of anything, for there is no class higher than it, as for instance, "being, existence, reality, truth, the absolute, the infinite, the ultimate," etc. hyslop says: "in reality there is but one _summum genus_, while there may be an indefinite number of _infimae species_. all intermediate terms between these extremes are sometimes called _subalterns_, as being either genera or species, according to the relation in which they are viewed." passing on to the classification of the character of the _intension_ of terms, we find: _difference_, a term denoting: "the mark or marks by which the species is distinguished from the rest of the genus; the specific characteristic." thus the color of the skin is a _difference_ between the negro and the caucasian; the number of feet the _difference_ between the biped and the quadruped; the form and shape of leaves the _difference_ between the oak and the elm trees, etc. hyslop says: "whatever distinguishes one object from another can be called the _differentia_. it is some characteristic in addition to the common qualities and determines the species or individual under the genus." _property_, a term denoting: "a peculiar quality of anything; that which is inherent in or naturally essential to anything." thus a _property_ is a distinguishing mark of a class. thus black skin is a _property_ of the negro race; four feet a _property_ of quadrupeds; a certain form of leaf a _property_ of the oak tree. thus a _difference_ between two species may be a _property_ of one of the species. _accident_, a term denoting: "any quality or circumstance which may or may not belong to a class, accidentally as it were; or, whatever does not really constitute an essential part of an object, person or thing." as, for instance, the redness of a rose, for a rose might part with its redness and still be a rose--the color is the _accident_ of the rose. or, a brick may be white and still be a brick, although the majority of bricks are red--the redness or whiteness of the brick are its _accidents_ and not its essential _properties_. whately says: "_accidents_ in logic are of two kinds--separable and inseparable. if walking be the _accident_ of a particular man, it is a separable one, for he would not cease to be that man though he stood still; while, on the contrary, if spaniard is the _accident_ connected with him, it is an inseparable one, since he never can cease to be, ethnologically considered, what he was born." arising from the classification of the meaning or content of terms, we find the process termed "definition." _definition_ is a term denoting: "an explanation of a word or term." in logic the term is used to denote the process of analysis in which the _properties_ and _differences_ of a term are clearly stated. there are of course several kinds of definitions. for instance, there is what is called a _real definition_, which whately defines as: "a definition which explains the nature of the thing by a particular name." there is also what is called a _physical definition_, which is: "a definition made by enumerating such parts as are actually separable, such as the hull, masts, etc., of a ship." also a _logical definition_, which is: "a definition consisting of the genus and the difference. thus if a planet be defined as 'a wandering star,' _star_ is the genus, and _wandering_ points out the difference between a planet and an ordinary star." an _accidental definition_ is: "a definition of the _accidental_ qualities of a thing." an _essential definition_ is: "a definition of the essential _properties_ and _differences_ of an object, person or thing." crabbe discriminates between a definition and an explanation, as follows: "a _definition_ is correct or precise; an _explanation_ is general or ample. the _definition_ of a word defines or limits the extent of its signification; it is the rule for the scholar in the use of any word; the _explanation_ of a word may include both definition and illustration; the former admits of no more words than will include the leading features in the meaning of any term; the latter admits of an unlimited scope for diffuseness on the part of the explainer." hyslop gives the following excellent explanation of the _logical definition_, which as he states is the proper meaning of the term in logic. he states: "the rules which regulate logical definition are as follows: . a definition should state the essential attributes of the species defined. . a definition must not contain the name of word defined. otherwise the definition is called _a circulus in definiendo_. . the definition must be exactly equivalent to the species defined. . a definition should not be expressed in obscure, figurative, or ambiguous language. . a definition must not be negative when it can be affirmative." a correct definition necessarily requires the manifestation of the two respective processes of analysis and synthesis. _analysis_ is a term denoting: "the separation of anything into its constituent elements, qualities, properties and attributes." it is seen at once that in order to correctly define an object, person or thing, it is first necessary to analyze the latter in order to perceive its essential and accidental properties or differences. unless the qualities, properties and attributes are clearly and fully perceived, we cannot properly define the object itself. _synthesis_ is a term denoting: "the act of joining or putting two or more things together; in logic: the method by composition, in opposition to the method of resolution or analysis." in stating a definition we must necessarily join together the various essential qualities, properties and attributes, which we have discovered by the process of analysis; and the synthesized combination, considered as a whole, is the definition of the object expressed by the term. chapter viii. judgments the first step in the process of reasoning is that of conception or the forming of concepts. the second step is that of judgment, or the process of perceiving the agreement or disagreement of two conceptions. _judgment_ in logic is defined as: "the comparing together in the mind of two notions, concepts or ideas, which are the objects of apprehension, whether complex or incomplex, and pronouncing that they agree or disagree with each other, or that one of them belongs or does not belong to the other. judgment is therefore affirmative or negative." when we have in our mind two concepts, we are likely to compare them one with the other, and to thus arrive at a conclusion regarding their agreement or disagreement. this process of comparison and decision is what, in logic, is called _judgment_. in every act of judgment there must be at least two concepts to be examined and compared. this comparison must lead to a judgment regarding their agreement or disagreement. for instance, we have the two concepts, _horse_ and _animal_. we examine and compare the two concepts, and find that there is an agreement between them. we find that the concept _horse_ is included in the higher concept of _animal_ and therefore, we assert that: "_the horse is an animal._" this is a statement of _agreement_ and is, therefore, a _positive judgment_. we then compare the concepts _horse_ and _cow_ and find a disagreement between them, which we express in the statement of the judgment that: "_the horse is not a cow._" this judgment, stating a disagreement is what is called a _negative judgment_. in the above illustration of the comparison between the concepts _horse_ and _animal_ we find that the second concept _animal_ is broader than the first, _horse_, so broad in fact that it includes the latter. the terms are not equal, for we cannot say, in truth, that "an animal is the horse." we may, however, include a _part_ of the broader conception with the narrower and say: "some animals are horses." sometimes both concepts are of equal rank, as when we state that: "man is a rational animal." in the process of judgment there is always the necessity of the choice between the positive and the negative. when we compare the concepts _horse_ and _animal_, we must of necessity decide either that the horse _is_ an animal, or else that it is _not_ an animal. the importance of the process of judgment is ably stated by halleck, as follows: "were isolated concepts possible, they would be of very little use. isolated facts are of no more service than unspun wool. we might have a concept of a certain class of three-leaved ivy, as we might also of poisons. unless judgment linked these two concepts and decided that this species of ivy is poisonous, we might take hold of it and be poisoned. we might have a concept of bread and also one of meat, fruit and vegetables. if we also had a concept of food, unrelated to these, we should starve to death, for we should not think of them as foods. a vessel, supposing itself to be far out at sea, signaled another vessel that the crew were dying of thirst. that crew certainly had a concept of drinkable things and also of water. to the surprise of the first, the second vessel signaled back, 'draw from the sea and drink. you are at the mouth of the amazon.' the thirsty crew had not joined the concept _drinkable_ to the concept of water over the ship's side. a man having taken an overdose of laudanum, his wife lost much valuable time in sending out for antidotes, because certain of her concepts had not been connected by judgment. she had good concepts of coffee and of mustard; she also knew that an antidote to opium was needed; but she had never linked these concepts and judged that coffee and mustard were antidotes to opium. the moment she formed that judgment she was a wiser woman for her knowledge was related and usable.... judgment is the power revolutionizing the world. the revolution is slow because nature's forces are so complex, so hard to be reduced to their simplest forms and so disguised and neutralized by the presence of other forces.... fortunately judgment is ever silently working and comparing things that, to past ages, have seemed dissimilar; and it is continually abstracting and leaving out of the field of view those qualities which have simply served to obscure the point at issue." judgment may be both analytic or synthetic in its processes; and it may be neither. when we compare a narrow concept with a broader one, as a part with a whole, the process is synthetic or an act of combination. when we compare a part of a concept with another concept, the process is analytic. when we compare concepts equal in rank or extent, the process is neither synthetic nor analytic. thus in the statement that: "a horse is an animal," the judgment is synthetic; in the statement that: "some animals are horses," the judgement is analytic; in the statement that: "a man is a rational animal," the judgment is neither analytic nor synthetic. brooks says: "in one sense all judgments are synthetic. a judgment consists of the union of two ideas and this uniting is a process of synthesis. this, however, is a superficial view of the process. such a synthesis is a mere mechanical synthesis; below this is a thought-process which is sometimes analytic, sometimes synthetic and sometimes neither analytic nor synthetic." the same authority states: "the act of mind described is what is known as _logical judgment_. strictly speaking, however, every intelligent act of the mind is accompanied with a _judgment_. to know is to discriminate and, therefore, to judge. every sensation or cognition involves a knowledge and so a judgment that it exists. the mind cannot think at all without judging; to think is to judge. _even in forming the notions which judgment compares, the mind judges._ every notion or concept implies a previous act of judgment to form it: in forming a concept, we compare the common attributes before we unite them; and comparison is judgment. it is thus true that 'every concept is a contracted judgment; every judgment an expanded concept.' this kind of judgment, by which we affirm the existence of states of consciousness, discriminate qualities, distinguish percepts and form concepts, is called _primitive or psychological judgment_." in logical judgment there are two aspects; _i.e._, judgment by extension and judgment by intension. when we compare the two concepts _horse_ and _animal_ we find that the concept _horse_ is contained in the concept _animal_ and the judgment that "_a horse is an animal_" may be considered as a judgment by extension. in the same comparison we see that the concept _horse_ contains the _quality of animality_, and in attributing this quality to the _horse_, we may also say "_the horse is an animal_," which judgment may be considered as a judgment by intension. brooks says: "both views of judgment are correct; the mind may reach its judgment either by extension or by intension. the method by extension is usually the more natural." when a judgment is expressed in words it is called a proposition. there is some confusion regarding the two terms, some holding that a judgment and a proposition are identical, and that the term "proposition" may be properly used to indicate the judgment itself. but the authorities who seek for clearness of expression and thought now generally hold that: "_a proposition is a judgment expressed in words._" in the next chapter, in which we consider propositions, we shall enter into a more extended consideration of the subject of judgments as expressed in propositions, which consideration we omit at this point in order to avoid repetition. just as the respective subjects of concepts and terms necessarily blend into each other, so do the respective subjects of judgments and propositions. in each case, too, there is the element of the mental process on the one hand and the verbal expression of it on the other hand. it will be well to keep this fact in mind. chapter ix. propositions we have seen that the first step of deductive reasoning is that which we call concepts. the second step is that which we call propositions. in logic, a _proposition_ is: "a sentence, or part of a sentence, affirming or denying a connection between the terms; limited to express assertions rather than extended to questions and commands." hyslop defines a proposition as: "any affirmation or denial of an agreement between two conceptions." _examples of propositions_ are found in the following sentences: "the rose is a flower;" "a horse is an animal;" "chicago is a city;" all of which are affirmations of agreement between the two terms involved; also in: "a horse is not a zebra;" "pinks are not roses;" "the whale is not a fish;" etc., which are denials of agreement between the terms. the _parts of a proposition_ are: ( ) the _subject_, or that of which something is affirmed or denied; ( ) the _predicate_, or _the something_ which is affirmed or denied regarding the _subject_; and ( ) the _copula_, or the verb serving as a link between the subject and the predicate. * * * * * in the proposition: "man is an animal," the term _man_ is the subject; the term _an animal_ is the predicate; and the word _is_, is the copula. the copula is always some form of the verb _to be_, in the present tense indicative, in an affirmative proposition; and the same with the negative particle affixed, in a negative proposition. the copula is not always directly expressed by the word _is_ or _is not_, etc., but is instead expressed in some phrase which implies them. for instance, we say "he runs," which implies "he is running." in the same way, it may appear at times as if the predicate was missing, as in: "god is," by which is meant "god is existing." in some cases, the proposition is inverted, the predicate appearing first in order, and the subject last, as in: "blessed are the peacemakers;" or "strong is truth." in such cases judgment must be used in determining the matter, in accordance with the character and meaning of the terms. an _affirmative proposition_ is one in which the predicate is _affirmed_ to agree with the subject. a _negative proposition_ is one in which the agreement of the predicate and subject is _denied_. examples of both of these classes have been given in this chapter. another classification of propositions divides them in three classes, as follows ( ) categorical; ( ) hypothetical; ( ) disjunctive. a _categorical proposition_ is one in which the affirmation or denial is made without reservation or qualification, as for instance: "man is an animal;" "the rose is a flower," etc. the fact asserted may not be _true_, but the statement is made positively as a statement of reality. a _hypothetical proposition_ is one in which the affirmation or denial is made to depend upon certain conditions, circumstances or suppositions, as for instance: "if the water is boiling-hot, it will scald;" or "if the powder be damp, it will not explode," etc. jevons says: "hypothetical propositions may generally be recognized by containing the little word 'if;' but it is doubtful whether they really differ much from the ordinary propositions.... we may easily say that 'boiling water will scald,' and 'damp gunpowder will not explode,' thus avoiding the use of the word 'if.'" a _disjunctive proposition_ is one "implying or asserting an alternative," and usually containing the conjunction "or," sometimes together with "either," as for instance: "lightning is sheet or forked;" "arches are either round or pointed;" "angles are either obtuse, right angled or acute." another classification of propositions divides them in two classes as follows: ( ) universal; ( ) particular. a _universal proposition_ is one in which the _whole quantity_ of the subject is involved in the assertion or denial of the predicate. for instance: "all men are liars," by which is affirmed that _all_ of the entire race of men are in the category of liars, not _some_ men but _all_ the men that are in existence. in the same way the proposition: "no men are immortal" is universal, for it is a _universal denial_. a _particular proposition_ is one in which the affirmation or denial of the predicate involves only a _part or portion_ of the whole of the subject, as for instance: "_some_ men are atheists," or "_some_ women are not vain," in which cases the affirmation or denial does not involve _all_ or the _whole_ of the subject. other examples are: "a _few_ men," etc.; "_many_ people," etc.; "_certain_ books," etc.; "_most_ people," etc. hyslop says: "the signs of the universal proposition, when formally expressed, are _all_, _every_, _each_, _any_, _and whole_ or words with equivalent import." the signs of particular propositions are also certain adjectives of quantity, such as _some_, _certain_, _a few_, _many_, _most_ or such others as denote _at least a part_ of a class. the subject of the distribution of terms in propositions is considered very important by logicians, and as hyslop says: "has much importance in determining the legitimacy, or at least the intelligibility, of our reasoning and the assurance that it will be accepted by others." some authorities favor the term, "qualification of the terms of propositions," but the established usage favors the term "distribution." the definition of the logical term, "distribution," is: "the distinguishing of a universal whole into its several kinds of species; the employment of a term to its fullest extent; the application of a term to its fullest extent, so as to include all significations or applications." a term of a proposition is _distributed_ when it is employed in its fullest sense; that is to say, _when it is employed so as to apply to each and every object, person or thing included under it_. thus in the proposition, "all horses are animals," the term _horses_ is distributed; and in the proposition, "some horses are thoroughbreds," the term _horses_ is not distributed. both of these examples relate to the distribution of the _subject_ of the proposition. but the predicate of a proposition also may or may not be distributed. for instance, in the proposition, "all horses are animals," the predicate, _animals_, is not distributed, that is, _not used in its fullest sense_, for all _animals_ are not _horses_--there are _some_ animals which are not horses and, therefore, the predicate, _animals_, not being used in its fullest sense is said to be "_not distributed_." the proposition really means: "all horses are _some_ animals." there is however another point to be remembered in the consideration of distribution of terms of propositions, which brooks expresses as follows: "distribution generally shows itself in the form of the expression, but sometimes it may be determined by the thought. thus if we say, 'men are mortal,' we mean _all men_, and the term men is distributed. but if we say 'books are necessary to a library,' we mean, not 'all books' but 'some books.' the _test of distribution_ is whether the term applies to '_each and every_.' thus when we say 'men are mortal,' it is true of each and every man that he is mortal." the rules of distribution of the terms of proposition are as follows: . all _universals_ distribute the _subject_. . all _particulars_ do not distribute the _subject_. . all _negatives_ distribute the _predicate_. . all _affirmatives_ do not distribute the _predicate_. the above rules are based upon logical reasoning. the reason for the first two rules is quite obvious, for when the subject is _universal_, it follows that the _whole subject_ is involved; when the subject is _particular_ it follows that _only a part_ of the subject is involved. in the case of the third rule, it will be seen that in every _negative_ proposition the _whole of the predicate_ must be denied the subject, as for instance, when we say: "some _animals_ are _not horses_," the whole class of _horses_ is cut off from the subject, and is thus _distributed_. in the case of the fourth rule, we may readily see that in the affirmative proposition the whole of the predicate _is not denied_ the subject, as for instance, when we say that: "horses are animals," we do not mean that horses are _all the animals_, but that they are merely a _part or portion_ of the class animal--therefore, the predicate, _animals_, is not distributed. in addition to the forms of propositions given there is another class of propositions known as _definitive or substitutive propositions_, in which the subject and the predicate are exactly alike in extent and rank. for instance, in the proposition, "a _triangle_ is a _polygon of three sides_" the two terms are interchangeable; that is, may be substituted for each other. hence the term "substitutive." the term "definitive" arises from the fact that the respective terms of this kind of a proposition necessarily _define_ each other. all logical definitions are expressed in this last mentioned form of proposition, for in such cases the subject and the predicate are precisely equal to each other. chapter x. immediate reasoning in the process of judgment we must compare two concepts and ascertain their agreement of disagreement. in the process of reasoning we follow a similar method and compare two judgments, the result of such comparison being the deduction of a third judgment. the simplest form of reasoning is that known as immediate reasoning, by which is meant the deduction of one proposition from another which _implies_ it. some have defined it as: "_reasoning without a middle term_." in this form of reasoning _only one proposition is required for the premise_, and from that premise the conclusion is deduced directly and without the necessity of comparison with any other term of proposition. the two principal methods employed in this form of reasoning are; ( ) opposition; ( ) conversion. _opposition_ exists between propositions having the same subject and predicate, but differing in quality or quantity, or both. the laws of opposition are as follows: i. ( ) if the universal is true, the particular is true. ( ) if the particular is false, the universal is false. ( ) if the universal is false, nothing follows. ( ) if the particular is true, nothing follows. ii. ( ) if one of two contraries is true, the other is false. ( ) if one of two contraries is false, nothing can be inferred. ( ) contraries are never both true, but both may be false. iii. ( ) if one of two sub-contraries is false, the other is true. ( ) if one of two sub-contraries is true, nothing can be inferred concerning the other. ( ) sub-contraries can never be both false, but both may be true. iv. ( ) if one of two contradictories is true, the other is false. ( ) if one of two contradictories is false, the other is true. ( ) contradictories can never be both true or both false, but always one is true and the other is false. in order to comprehend the above laws, the student should familiarize himself with the following arrangement, adopted by logicians as a convenience: {universal {affirmative (a) { {negative (e) propositions { { {affirmative (i) {particular {negative (o) examples of the above: universal affirmative (a): "all men are mortal;" universal negative (e): "no man is mortal;" particular affirmative (i): "some men are mortal;" particular negative (o): "some men are not mortal." the following examples of abstract propositions are often used by logicians as tending toward a clearer conception than examples such as given above: (a) "all a is b." (i) "some a is b." (e) "no a is b." (o) "some a is not b." these four forms of propositions bear certain logical relations to each other, as follows: a and e are styled _contraries_. i and o are _sub-contraries_; a and i and also e and o are called _subalterns_; a and o and also i and e are styled _contradictories_. a close study of these relations, and the symbols expressing them, is necessary for a clear comprehension of the laws of opposition stated a little further back, as well as the principles of conversion which we shall mention a little further on. the following chart, called the square of opposition, is also employed by logicians to illustrate the relations between the four classes of propositions: a contraries e +------------------------+ |\ / | | \ /s | | c\ /e | | o\ /i | | n\ /r | | t\ /o | s| r\ /t |s u| a\ /c |u b| \ /i |b a| \ /d |a l| \ / |l t| / \ |t e| / d\ |e r| / i\ |r n| /a c\ |n s| /r t\ |s | /t o\ | | /n r\ | | /o i\ | | /c e\ | | / s\ | |/ \ | +------------------------+ i sub-contraries o _conversion_ is the process of immediate reasoning by which we infer from a given proposition another proposition having the predicate of the original for its subject and the subject of the original for its predicate; or stated in a few words: _conversion is the transposition of the subject and predicate of a proposition_. as brooks states it: "propositions or judgments are _converted_ when the subject and predicate change places in such a manner that the resulting judgment is an inference from the given judgment." the new proposition, resulting from the operation or conversion, is called the converse; the original proposition is called the convertend. _the law of conversion_ is that: "no term must be distributed in the converse that is not distributed in the convertend." this arises from the obvious fact that nothing should be affirmed in the derived proposition than there is in the original proposition. there are three kinds of conversion; _viz_: ( ) simple conversion; ( ) conversion by limitation; ( ) conversion by contraposition. in _simple conversion_ there is no change in either quality or quantity. in _conversion by limitation_ the quality is changed from universal to particular. in conversion by negation the quality is changed but not the quantity. referring to the classification tables and symbols given in the preceding pages of this chapter, we may now proceed to consider the application of these methods of conversion to each of the four kinds of propositions; as follows: _the universal affirmative_ (symbol a) proposition is converted by limitation, or by a change of quality from universal to particular. the predicate not being "distributed" in the convertend, we must not distribute it in the converse by saying "_all_." thus in this case we must convert the proposition, "all men are mortal" (a), into "some mortals are men" (i). _the universal negative_ (symbol e) is converted by simple conversion, in which there is no change in either quality or quantity. for since both terms of "e" are distributed, they may both be distributed in the converse without violating the law of conversion. thus "no man is mortal" is converted into: "no mortals are men." "e" is converted into "e." _the particular affirmative_ (symbol i) is also converted by simple conversion in which there is no change in either quality or quantity. for since neither term is distributed in "i," neither term may be distributed in the converse, and the latter must remain "i." for instance; the proposition: "some men are mortal" is converted into the proposition, "some mortals are men." _the particular negative_ (symbol o) is converted by conversion by negation, in which the quality is changed but not the quantity. thus in converting the proposition: "some men are not mortal," we must _not_ say "some mortals are not men," for in so doing we would distribute _men_ in the predicate, where it is not distributed in the convertend. avoiding this, _we transfer the negative particle from the copula to the predicate_ so that the convertend becomes "i" which is converted by simple conversion. thus we transfer "some men are not mortal" into "some men are not-mortal" from which we easily convert (by simple conversion) the proposition: "some not-mortals are men." it will be well for students, at this point, to consider the three following fundamental laws of thought as laid down by the authorities, which are as follows: _the law of identity_, which states that: "the same quality or thing is always the same quality or thing, no matter how different the conditions in which it occurs." _the law of contradiction_, which states that: "no thing can at the same time and place both be and not be." _the law of excluded middle_, which states that: "everything must either be or not be; there is no other alternative or middle course." of these laws, prof. jevons, a noted authority, says: "students are seldom able to see at first their full meaning and importance. all arguments may be explained when these self-evident laws are granted; and it is not too much to say that the whole of logic will be plain to those who will constantly use these laws as the key." chapter xi. inductive reasoning inductive reasoning, as we have said, is the process of discovering general truth from particular truths, or inferring general laws from particular facts. thus, from the experience of the individual and the race regarding the particular truth that each and every man under observation has been observed to die sooner or later, it is inferred that _all_ men die, and hence, the induction of the general truth that "all men must die." or, as from experience we know that the various kinds of metals expand when subjected to heat, we infer that _all_ metals are subject to this law, and that consequently we may arrive by inductive reasoning at the conclusion that: "all metals expand when subjected to heat." it will be noticed that the conclusion arrived at in this way by inductive reasoning forms the fundamental premise in the process of deductive reasoning. as we have seen elsewhere, the two processes, inductive and deductive reasoning, respectively are interdependent--resting upon one another. jevons says of inductive reasoning: "in deductive reasoning we inquire how we may gather the truth contained in some propositions called premises, and put into another proposition called the conclusion. we have not yet undertaken to find out how we can learn what propositions really are true, but only _what propositions are true when other ones are true_. all the acts of reasoning yet considered would be called _deductive because we deduce, or lead down the truth from premises to conclusion_. it is an exceedingly important thing to understand deductive inference correctly, but it might seem to be still more important to understand _inductive inference_, by which we gather the truth of general propositions from facts observed as happening in the world around us." halleck says: "man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. by induction we examine what seems to us a sufficient number of individual cases. we then conclude that the rest of these cases, which we have not examined, will obey the same general law.... only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed." strange as may now appear, it is a fact that until a comparatively recent period in the history of man, it was held by philosophers that the only way to arrive at all knowledge was by means of deductive reasoning, by the use of the syllogism. the influence of aristotle was great and men preferred to pursue artificial and complicated methods of deductive reasoning, rather than to reach the truth by obtaining the facts from nature herself, at first hand, and then inferring general principle from the facts so gathered. the rise of modern scientific methods of reasoning, along the lines of inductive inference, dates from about - . roger bacon was one of the first to teach that we must arrive at scientific truth by a process of observation and experimentation on the natural objects to be found on all sides. he made many discoveries by following this process. he was ably seconded by galileo who lived some three hundred years later, and who also taught that many great general truths might be gained by careful observation and intelligent inference. lord francis bacon, who lived about the same time as galileo, presented in his _novum organum_ many excellent observations and facts regarding the process of inductive reasoning and scientific thought. as jevons says: "inductive logic inquires by what manner of reasoning we can gather the laws of nature from the facts and events observed. such reasoning is called induction, or inductive inquiry, and, as it has actually been practiced by all the great discoverers in science, it consists in four steps." the _four steps in inductive reasoning_, as stated by jevons, are as follows: _first step._--preliminary observation. _second step._--the making of hypotheses. _third step._--deductive reasoning. _fourth step._--verification. it will be seen that the process of inductive reasoning is essentially _a synthetic process_, because it operates in the direction of combining and uniting particular facts or truths into general truths or laws which comprehend, embrace and include them all. as brooks says: "the particular facts are united by the mind into the general law; the general law embraces the particular facts and binds them together into a unity of principle and thought. induction is thus a process of thought from the parts to the whole--a synthetic process." it will also be seen that the process of inductive reasoning is essentially _an ascending process_, because it ascends from particular facts to general laws; particular truths to universal truths; from the lower to the higher, the narrower to the broader, the smaller to the greater. brooks says of inductive reasoning: "the relation of induction to deduction will be clearly seen. induction and deduction are the converse, the opposites of each other. deduction derives a particular truth from a general truth; induction derives a general truth from particular truths. this antithesis appears in every particular. deduction goes from generals to particulars; induction goes from particulars to generals. deduction is an analytic process; induction is a synthetic process. deduction is a descending process--it goes from the higher truth to the lower truth; induction is an ascending process--it goes from the lower truth to the higher. they differ also in that deduction may be applied to necessary truths, while induction is mainly restricted to contingent truths." hyslop says: "there have been several ways of defining this process. it has been usual to contrast it with deduction. now, deduction is often said to be reasoning from general to particular truths, from the containing to the contained truth, or from cause to effect. induction, therefore, by contrast is defined as reasoning from the particular to the general, from the contained to the containing, or from effect to cause. sometimes induction is said to be reasoning from the known to the unknown. this would make deduction, by contrast, reasoning from the unknown to the known, which is absurd. the former ways of representing it are much the better. but there is still a better way of comparing them. deduction _is reasoning in which the conclusion is contained in the premises_. this is a ground for its certitude and we commit a fallacy whenever we go beyond the premises as shown by the laws of the distribution of terms. in contrast with this, then, we may call inductive reasoning _the process by which we go beyond the premises in the conclusion_.... the process here is to start from given facts and to infer some other probable facts more general or connected with them. in this we see the process of going beyond the premises. there are, of course, certain conditions which regulate the legitimacy of the procedure, just as there are conditions determining deduction. they are _that the conclusion shall represent the same general kind as the premises_, with a possibility of accidental differences. but it goes beyond the premises in so far as _known_ facts are concerned." the following example may give you a clearer idea of the processes of inductive reasoning: _first step._ preliminary observation. _example_: we notice that all the particular _magnets_ which have come under our observation _attract iron_. our mental record of the phenomena may be stated as: "a, b, c, d, e, f, g, etc., and also x, y, and z, all of which are _magnets_, in all observed instances, and at all observed times, _attract iron_." _second step._ the making of hypotheses. _example_: upon the basis of the observations and experiments, as above stated, and applying the axiom of inductive reasoning, that: "what is true of the many, is true of the whole," we feel justified in forming a hypothesis or inference of a general law or truth, applying the facts of the particulars to the general, whole or universal, thus: "_all_ magnets attract iron." _third step._ deductive reasoning. _example_: picking up a magnet regarding which we have had no experience and upon which we have made no experiments, we reason by the syllogism, as follows: ( ) _all_ magnets attract iron; ( ) _this thing_ is a magnet; therefore ( ) _this thing_ will attract iron. in this we apply the axiom of deductive reasoning: "whatever is true of the whole is true of the parts." _fourth step._ verification. _example_: we then proceed to test the hypothesis upon the particular magnet, so as to ascertain whether or not it agrees with the particular facts. if the magnet does not attract iron we know that either our hypothesis is wrong and that _some_ magnets do _not_ attract iron; or else that our _judgment_ regarding that particular "thing" being a magnet is at fault and that it is _not_ a magnet. in either case, further examination, observation and experiment is necessary. in case the particular magnet _does_ attract iron, we feel that we have verified our hypothesis and our judgment. chapter xii. reasoning by induction the term "induction," in its logical usage, is defined as follows: "(a) the process of investigating and collecting facts; and (b) the deducing of an inference from these facts; also (c) sometimes loosely used in the sense of an inference from observed facts." mill says: "_induction_, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. in other words, _induction_ is the process by which we conclude that what is true of certain individuals of a class, is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times." the _basis of induction_ is the axiom that: "_what is true of the many is true of the whole_." esser, a well known authority, states this axiom in rather more complicated form, as follows: "that which belongs or does not belong to many things of the same kind, belongs or does not belong to all things of the same kind." this basic axiom of induction rests upon the conviction that nature's laws and manifestations are regular, orderly and _uniform_. if we assume that nature does not manifest these qualities, then the axiom must fall, and all inductive reason must be fallacious. as brooks well says: "induction has been compared to a ladder upon which we ascend from facts to laws. this ladder cannot stand unless it has something to rest upon; and this something is our faith in the constancy of nature's laws." some authorities have held that this perception of the uniformity of nature's laws is in the nature of an _intuitive_ truth, or an inherent law of our intelligence. others hold that it is in itself an _inductive_ truth, arrived at by experience and observation at a very early age. we are held to have noticed the uniformity in natural phenomena, and almost instinctively infer that this uniformity is continuous and universal. the authorities assume the existence of two kinds of induction, namely: ( ) perfect induction; and ( ) imperfect induction. other, but similar, terms are employed by different authorities to designate these two classes. _perfect induction_ necessitates a knowledge of _all_ the particulars forming a class; that is, _all_ the individual objects, persons, things or facts comprising a class must be known and enumerated in this form of induction. for instance, if we _knew positively_ all of brown's children, and that their names were john, peter, mark, luke, charles, william, mary and susan, respectively; and that each and every one of them were freckled and had red hair; then, in that case, instead of simply _generalizing_ and stating that: "john, peter, mark, luke, charles, william, mary and susan, who are _all_ of brown's children, are freckled and have red hair," we would save words, and state the inductive conclusion: "all brown's children are freckled and have red hair." it will be noticed that in this case _we include in the process only what is stated in the premise itself_, and we do not extend our inductive process beyond the actual data upon which it is based. this form of induction is sometimes called "logical induction," because the inference is a logical necessity, without the possibility of error or exception. by some authorities it is held not to be induction at all, in the strict sense, but little more than a simplified form of enumeration. in actual practice it is seldom available, for it is almost impossible for us to know all the particulars in inferring a general law or truth. in view of this difficulty, we fall back upon the more practical form of induction known as: _imperfect induction_, or as it is sometimes called "practical induction," by which is meant the inductive process of reasoning in which we assume that the particulars or facts actually known to us correctly represent those which are not actually known, and hence the whole class to which they belong. in this process it will be seen that _the conclusion extends_ beyond the data upon which it is based. in this form of induction we must actually employ the principle of the axiom: "what is true of the many is true of the whole"--that is, must _assume_ it to be a fact, not because we _know_ it by actual experience, but because we infer it from the axiom which also agrees with past experience. the conclusion arrived at may not always be true in its fullest sense, as in the case of the conclusion of perfect induction, but is the result of an inference based upon a principle which gives us a reasonable right to assume its truth in absence of better knowledge. in considering the actual steps in the process of inductive reasoning we can do no better than to follow the classification of jevons, mentioned in the preceding chapter, the same being simple and readily comprehended, and therefore preferable in this case to the more technical classification favored by some other authorities. let us now consider these four steps. _first step._ preliminary observation. it follows that without the experience of oneself or of others in the direction of observing and remembering particular facts, objects, persons and things, we cannot hope to acquire the preliminary facts for the generalization and inductive inference necessary in inductive reasoning. it is necessary for us to form a variety of clear concepts or ideas of facts, objects, persons and things, before we may hope to generalize from these particulars. in the chapters of this book devoted to the consideration of concepts, we may see the fundamental importance of the formation and acquirement of correct concepts. concepts are the fundamental material for correct reasoning. in order to produce a perfect finished product, we must have perfect materials, and a sufficient quantity of them. the greater the knowledge one possesses of the facts and objects of the outside world, the better able is he to reason therefrom. concepts are the raw material which must feed the machinery of reasoning, and from which the final product of perfected thought is produced. as halleck says: "there must first be a presentation of materials. suppose that we wish to form the concept _fruit_. we must first perceive the different kinds of fruit--cherry, pear, quince, plum, currant, apple, fig, orange, etc. before we can take the next step, we must be able to form distinct and accurate images of the various kinds of fruit. if the concept is to be absolutely accurate, not one kind of fruit must be overlooked. practically this is impossible; but many kinds should be examined. where perception is inaccurate and stinted, the products of thought cannot be trustworthy. no building is firm if reared on insecure foundations." in the process of preliminary observation, we find that there are two ways of obtaining a knowledge of the facts and things around us. these two ways are as follows: i. by _simple observation_, or the perception of the happenings which are manifested without our interference. in this way we perceive the motion of the tides; the movement of the planets; the phenomena of the weather; the passing of animals, etc. ii. by the _observation of experiment_, or the perception of happenings in which we interfere with things and then observe the result. an _experiment_ is: "a trial, proof, or test of anything; an act, operation, or process designed to discover some unknown truth, principle or effect, or to test some received or reputed truth or principle." hobbes says: "to have had many _experiments_ is what we call _experience_." jevons says: "experimentation is observation with something more; namely, regulation of the things whose behavior is to be observed. the advantages of experiment over mere observation are of two kinds. in the first place, we shall generally know much more certainly and accurately with what we are dealing, when we make experiments than when we simply observe natural events.... it is a further advantage of artificial experiments, that they enable us to discover entirely new substances and to learn their properties.... it would be a mistake to suppose that the making of an experiment is inductive reasoning, and gives us without further trouble the laws of nature. _experiments only give us the facts upon which we may afterward reason...._ experiments then merely give facts, and it is only by careful reasoning that we can learn when the same facts will be observed again. _the general rule is that the same causes will produce the same effects._ whatever happens in one case will happen in all like cases, provided that they are really like, and not merely apparently so.... when we have by repeated experiments tried the effect which all the surrounding things might have on the result, we can then reason with much confidence as to similar results in similar circumstances.... in order that we may, from our observations and experiments, learn the law of nature and become able to foresee the future, we must perform the process of generalization. to generalize is to draw a general law from particular cases, and to infer that what we see to be true of a few things is true of the whole genus or class to which these things belong. it requires much judgment and skill to generalize correctly, because everything depends upon the number and character of the instances about which we reason." having seen that the first step in inductive reasoning is preliminary observation, let us now consider the next steps in which we may see what we do with the facts and ideas which we have acquired by this observation and experiment. chapter xiii. theory and hypotheses following jevons' classification, we find that the second step in inductive reasoning is that called "the making of hypotheses." a _hypothesis_ is: "a supposition, proposition or principle _assumed or taken for granted_ in order to draw a conclusion or inference in proof of the point or question; a proposition assumed or taken for granted, though not proved, for the purpose of deducing proof of a point in question." it will be seen that a hypothesis is merely held to be _possibly or probably true_, and _not certainly true_; it is in the nature of a _working assumption_, whose truth must be tested by observed facts. the assumption may apply either to the _cause_ of things, or to the _laws_ which govern things. akin to a hypothesis, and by many people confused in meaning with the latter, is what is called a theory. a _theory_ is: "a verified hypothesis; a hypothesis which has been established as, apparently, the true one." an authority says "_theory_ is a stronger word than _hypothesis_. a _theory_ is founded on principles which have been established on independent evidence. a _hypothesis_ merely assumes the operation of a cause which would account for the phenomena, but has not evidence that such cause was actually at work. metaphysically, a theory is nothing but a hypothesis supported by a large amount of probable evidence." brooks says: "when a hypothesis is shown to explain all the facts that are known, these facts being varied and extensive, it is said to be verified, and becomes a theory. thus we have the theory of universal gravitation, the copernican theory of the solar system, the undulatory theory of light, etc., all of which were originally mere hypotheses. this is the manner in which the term is usually employed in the inductive philosophy; though it must be admitted that it is not always used in this strict sense. discarded hypotheses are often referred to as theories; and that which is actually a theory is sometimes called a hypothesis." the steps by which we build up a hypothesis are numerous and varied. in the first place we may erect a hypothesis by the methods of what we have described as perfect induction, or logical induction. in this case we proceed by simple generalization or simple enumeration. the example of the freckled, red-haired children of brown, mentioned in a previous chapter, explains this method. it requires the examination and knowledge of every object or fact of which the statement or hypothesis is made. hamilton states that it is the only induction which is absolutely necessitated by the laws of thought. it does not extend further than the plane of experience. it is akin to mathematical reasoning. far more important is the process by which hypotheses are erected by means of inferences from imperfect induction, by which we reason from the known to the unknown, transcending experience, and making true inductive inferences from the axiom of inductive reasoning. this process involves the subject of causes. jevons says: "the cause of an event is that antecedent, or set of antecedents, from which the event always follows. people often make much difficulty about understanding what the cause of an event means, but it really means nothing beyond _the things that must exist before in order that the event shall happen afterward_." causes are often obscure and difficult to determine. the following five difficulties are likely to arise: i. the cause may be out of our experience, and is therefore not to be understood; ii. causes often act conjointly, so that it is difficult to discover the one predominant cause by reason of its associated causes; iii. often the presence of a counteracting, or modifying cause may confuse us; iv. often a certain effect may be caused by either of several possible causes; v. that which appears as a _cause_ of a certain effect may be but a co-effect of an original cause. mill formulated several tests for ascertaining the causal agency in particular cases, in view of the above-stated difficulties. these tests are as follows: ( ) the method of agreement; ( ) the method of difference; ( ) the method of residues; and ( ) the method of concomitant variations. the following definitions of these various tests are given by atwater as follows: _method of agreement_: "if, whenever a given object or agency is present without counteracting forces, a given effect is produced, there is a strong evidence that the object or agency is the cause of the effect." _method of difference_: "if, when the supposed cause is present the effect is present, and when the supposed cause is absent the effect is wanting, there being in neither case any other agents present to effect the result, we may reasonably infer that the supposed cause is the real one." _method of residue_: "when in any phenomena we find a result remaining after the effects of all known causes are estimated, we may attribute it to a residual agent not yet reckoned." _method of concomitant variations_: "when a variation in a given antecedent is accompanied by a variation of a given consequent, they are in some manner related as cause and effect." atwater adds: "whenever either of these criteria is found free from conflicting evidence, and especially when several of them concur, the evidence is clear that the cases observed are fair representatives of the whole class, and warrant a valid inductive conclusion." jevons gives us the following valuable rules: i. "whenever we can alter the quantity of the things experimented on, we can apply _a rule for discovering which are causes and which are effects_, as follows: we must vary the quantity of one thing, making it at one time greater and at another time less, and if we observe any other thing which varies just at the same times, it will in all probability be an _effect_." ii. "when things vary regularly and frequently, there is _a simple rule, by following which we can judge whether changes are connected together as causes and effects_, as follows: those things which change in exactly equal times are in all likelihood connected together." iii. "it is very difficult to explain how it is that we can ever reason from one thing to a class of things by generalization, _when we cannot be sure that the things resemble each other in the important points_.... upon what grounds do we argue? we have to get a general law from particular facts. this can only be done by going through all the steps of inductive reasoning. having made certain observations, we must frame hypotheses as to the circumstances, or laws from which they proceed. then we must reason deductively; and after verifying the deductions in as many cases as possible, we shall know how far we can trust similar deductions concerning future events.... it is difficult to judge when we may, and when we may not, safely infer from some things to others in this simple way, without making a complete theory of the matter. _the only rule_ that can be given to assist us is that _if things resemble each other in a few properties only, we must observe many instances before inferring that these properties will always be joined together in other cases_." chapter xiv. making and testing hypotheses the older philosophers and logicians were often at a loss how to reasonably account for the origin of hypotheses. it will be seen, after giving the matter a little thought, that the actual formation of the hypothesis is more than a mere grouping together or synthesis of facts or ideas--there is another mental process which actually evolves the hypothesis or theory--which gives _a possible reason_. what is this mental process? let us consider the matter. brooks well says: "the hypotheses of science originate in what is called anticipation. they are not the result of a mere synthesis of facts, for no combination of facts can give the law or cause. we do not see the law; we see the facts and _the mind thinks the law_. by the power of anticipation, the mind often leaps from a few facts to the cause which produces them or the law which governs them. many hypotheses were but _a happy intuition of the mind_. they were the result of what la place calls 'a great guess,' or what plato so beautifully designates as 'a sacred suspicion of truth.' the forming of hypotheses requires a suggestive mind, a lively fancy, a philosophic imagination, that catches a glimpse of the idea through the form, or sees the law standing behind the fact." the student of the new psychology sees in the mental operation of the forming of the hypothesis--"the mind thinking the law"--but an instance of the operation of the activities of the subconscious mind, or even the superconscious mind. (see the volume on the subconscious mind in this series.) not only does this hypothesis give the explanation which the old psychology has failed to do, but it agrees with the ideas of others on the subject as stated in the above quotation from brooks; and moreover agrees with many recorded instances of the formation of great hypotheses. sir wm. hamilton discovered the very important mathematical law of quaternions while walking one day in the dublin observatory. he had pondered long on the subject, but without result. but, finally, on that eventful day he suddenly "felt the galvanic circle of thought" close, and the result was the realization of the fundamental mathematical relations of the problem. berthelot, the founder of synthetic chemistry, has testified that the celebrated experiments which led to his remarkable discoveries were seldom the result of carefully followed lines of conscious thought or pure reasoning processes; but, instead, came to him "of their own accord," so to speak, "as from a clear sky." in these and many other similar instances, the mental operation was undoubtedly purely subjective and subconscious. dr. hudson has claimed that the "subjective mind" cannot reason inductively, and that its operations are purely and distinctly deductive, but the testimony of many eminent scientists, inventors and philosophers is directly to the contrary. in this connection the following quotation from thomson is interesting: "the system of anatomy which has immortalized the name of oken is the consequence of a flash of anticipation which glanced through his mind when he picked up in a chance walk the skull of a deer, bleached and disintegrated by the weather, and exclaimed after a glance, 'it is part of a vertebral column!' when newton saw the apple fall, the anticipatory question flashed through his mind, 'why do not the heavenly bodies fall like this apple?' in neither case had accident any important share; newton and oken were prepared by the deepest previous study to seize upon the unimportant fact offered to them, and to show how important it might become; and if the apple and the deer-skull had been wanting, some other falling body, or some other skull, would have touched the string so ready to vibrate. but in each case there was a great step of anticipation; oken thought he saw a type of the whole skeleton in a single vertebra, while newton conceived at once that the whole universe was full of bodies tending to fall.... the discovery of goethe, which did for the vegetable kingdom what oken did for the animal, that the parts of a plant are to be regarded as metamorphosed leaves, is an apparent exception to the necessity of discipline for invention, since it was the discovery of a poet in a region to which he seemed to have paid no especial or laborious attention. but goethe was himself most anxious to rest the basis of this discovery upon his observation rather than his imagination, and doubtless with good reason.... as with other great discoveries, hints had been given already, though not pursued, both of goethe's and oken's principles. goethe left his to be followed up by others, and but for his great fame, perhaps his name would never have been connected with it. oken had amassed all the materials necessary for the establishment of his theory; he was able at once to discover and conquer the new territory." it must not be supposed, however, that all hypotheses flashing into the field of consciousness from the subconsciousness, are necessarily true or correct. on the contrary many of them are incorrect, or at least only partially correct. the subconsciousness is not infallible or omniscient--it merely produces results according to the material furnished it. but even these faulty hypotheses are often of value in the later formation of a correct one. as whewell says: "to try wrong guesses is with most persons the only way to hit upon right ones." kepler is said to have erected at least twenty hypotheses regarding the shape of the earth's orbit before he finally evolved the correct one. as brooks says: "even incorrect hypotheses may be of use in scientific research, since they may lead to more correct suppositions." the supposition of the circular motions of the heavenly bodies around the _earth_ as a center, which lead to the conception of epicycles, etc., and at last to the true theory is an illustration of this. so the 'theory of phlogiston' in chemistry, made many facts intelligible, before the true one of 'oxidation' superseded it. and so, as thomson says, "with the theory that 'nature abhors a vacuum,' which served to bring together so many cognate facts not previously considered as related. even an incorrect conception of this kind has its place in science, so long as it is applicable to the facts; when facts occur which it cannot explain, we either correct it or replace it with a new one. the pathway of science, some one remarks, is strewn with the remains of discarded hypotheses." halleck says regarding the danger of hasty inference: "men must constantly employ imperfect induction in order to advance; but great dangers attend inductive inferences made from too narrow experience. a child has experience with one or two dogs at his home. because of their gentleness, he argues that all dogs are gentle. he does not, perhaps, find out the contrary until he has been severely bitten. his induction was too hasty. he had not tested a sufficiently large number of dogs to form such a conclusion. from one or two experiences with a large crop in a certain latitude, a farmer may argue that the crop will generally be profitable, whereas it may not again prove so for years. a man may have trusted a number of people and found them honest. he concludes that people as a rule are honest, trusts a certain dishonest man, and is ruined. the older people grow, the more cautious they generally become in forming inductive conclusions. many instances are noted and compared; but even the wisest sometimes make mistakes. it once was a generally accepted fact that all swans were white. nobody had ever seen a dark swan, and the inference that all swans were white was regarded as certainly true. black swans were, however, found in australia." brooks says regarding the probability of hypotheses: "the probability of a hypothesis is in proportion to the number of facts and phenomena it will explain. the larger the number of facts and phenomena that it will satisfactorily account for, the greater our faith in the correctness of our supposition.... if there is more than one hypothesis in respect to the facts under consideration, that one which accounts for the greatest number of facts is the most probable.... in order to verify a hypothesis it must be shown that it will account for all the facts and phenomena. if these facts are numerous and varied, and the subject is so thoroughly investigated that it is quite certain that no important class of facts has been overlooked, the supposition is regarded as true, and the hypothesis is said to be verified. thus the hypothesis of the 'daily rotation' of the earth on its axis to account for the succession of day and night is accepted as absolutely true. this is the view taken by dr. whewell and many other thinkers in respect to the verification of a hypothesis. some writers, however, as mill and his school, maintain that in order to verify a hypothesis, we must show not only that it explains all the facts and phenomena, but that there is no other possible hypothesis which will account for them.... the former view of verification is regarded as the correct one. by the latter view, it is evident that a hypothesis could never be verified." jevons says: "in the fourth step (verification), we proceed to compare these deductions with the facts already collected, or when necessary and practicable, we make new observations and plan new experiments, so as to find out whether the hypothesis agrees with nature. if we meet with several distinct disagreements between our deductions and our observations, it will become likely that the hypothesis is wrong, and we must then invent a new one. in order to produce agreement it will sometimes be enough to change the hypothesis in a small degree. when we get hold of a hypothesis which seems to give results agreeing with a few facts, we must not at once assume that it is certainly correct. we must go on making other deductions from it under various circumstances, and, whenever it is possible, we ought to verify these results, that is, compare them with facts observed through the senses. when a hypothesis is shown in this way to be true in a great many of its results, especially when it enables us to predict what we should never otherwise have believed or discovered, it becomes certain that the hypothesis itself is a true one.... sometimes it will happen that two or even three quite different hypotheses all seem to agree with certain facts, so that we are puzzled which to select.... when there are thus two hypotheses, one as good as the other, we need to discover some fact or thing which will agree with one hypothesis and not with the other, because this immediately enables us to decide that the former hypothesis is true and the latter false." in the above statements regarding the _verification_ of hypotheses we see references made to the testing of the latter upon the "facts" of the case. these _facts_ may be either the observed phenomena or facts apparent to the perception, or else _facts_ obtained by deductive reasoning. the latter may be said to be facts which are held to be true if the hypothesis be true. thus if we erect the hypothesis that "all men are mortal," we may reason deductively that it will follow that each and every thing that is a _man_ must die sooner or later. then we test our hypotheses upon _each and every man_ whom we may subject to observation and experiment. if we find a single man who does not die, then the test disproves our hypotheses; if on the contrary all men (the "facts" in the case) prove to be mortal, then is our hypotheses proven or established. the deductive reasoning in this case is as follows: "_if_ so-and-so is true regarding such-and-such a class; and if this particular thing belongs to that class; then it will follow that so-and-so is true regarding this particular thing." this argument is expressed in what is called a hypothetical proposition (see chapter ix), the consideration of which forms a part of the general subject of deductive reasoning. therefore as jevons has said, "deductive reasoning is the third step in inductive reasoning, and precedes verification", which we have already considered. halleck says: "after induction has classified certain phenomena and thus given us a major premise, we may proceed _deductively_ to apply the inference to any new specimen that can be shown to belong to that class. induction hands over to deduction a ready-made major premise.... deduction takes that as a fact, making no inquiry about its truth.... only after general laws have been laid down, after objects have been classified, after major premises have been formed, can _deduction_ be employed." in view of the above facts, we shall now proceed to a consideration of that great class of reasoning known under the term--deductive reasoning. chapter xv. deductive reasoning we have seen that there are two great classes of reasoning, known respectively, as ( ) inductive reasoning, or the discovery of general truth from particular truths; and ( ) deductive reasoning, or the discovery of particular truths from general truths. as we have said, deductive reasoning is the process of discovering particular truths from a general truth. thus from the general truth embodied in the proposition "all horses are animals," when it is considered in connection with the secondary proposition that "dobbin is a horse," we are able to deduce the particular truth that: "dobbin is an animal." or, in the following case we deduce a particular truth from a general truth, as follows: "all mushrooms are good to eat; this fungus is a mushroom; therefore, this fungus is good to eat." a deductive argument is expressed in a deductive syllogism. jevons says regarding the last stated illustration: "here are three sentences which state three different facts; but when we know the two first facts, we learn or gather the third fact from the other two. when we thus learn one fact from other facts, we _infer or reason_, and we do this in the mind. reasoning thus enables us to ascertain the nature of a thing without actual trial. if we always needed to taste a thing before we could know whether it was good to eat or not, cases of poisoning would be alarmingly frequent. but the appearance and peculiarities of a mushroom may be safely learned by the eye or the nose, and reasoning upon this information and the fact already well known, that mushrooms are good to eat, we arrive without any danger or trouble at the conclusion that the particular fungus before us is good to eat. _to reason, then, is to get some knowledge from other knowledge._" the student will recognize that deductive reasoning is essentially _an analytic process_, because it operates in the direction of analyzing a universal or general truth into its particulars--into the particular parts which are included within it--and asserting of them that "what is true of the general is true of the particular." thus in the general truth that "all men are mortal," we see included the particular truth that "john smith is mortal"--john smith having been discovered to be a man. we deduce the particular truth about john smith from the general truth about "all men." we analyze "all men" and find john smith to be one of its particular parts. therefore, "deduction is an inference from the whole to its parts; that is, an analytic process." the student will also recognize that deductive reasoning is essentially _a descending process_, because it operates in the direction of a descent from the universal to the particular; from the higher to the lower; from the broader to the narrower. as brooks says: "deduction descends from higher truths to lower truths, from laws to facts, from causes to phenomena, etc. given the law, we can by deduction descend to the facts that fall under the law, even if we have never before seen the facts; and so from the cause we may pass down to observed and even unknown phenomena." the general truths which are used as the basis of deductive reasoning are discovered in several ways. the majority arise from inductive reasoning, based upon experience, observation and experiment. for instance in the examples given above, we could not truthfully assert our belief that: "all horses are animals" unless we had previously studied both the horse and animals in general. nor without this study could we state that "dobbin is a horse." nor could we, without previous study, experience and experiment truthfully assert that: "all mushrooms are good to eat;" or that "this fungus is a mushroom;" and that "therefore, this fungus is good to eat." even as it is, we must be sure that the fungus really is a mushroom, else we run a risk of poisoning ourselves. general truths of this kind are _not intuitive_, by any means, but are based upon our own experience or the experience of others. there is a class of general truths which are called _intuitive_ by some authorities. halleck says of these: "some psychologists claim that we have knowledge obtained neither through induction nor deduction; that we recognize certain truths the moment we perceive certain objects, without any process of inference. under the head of intuitive knowledge are classified such cases as the following: we perceive an object and immediately know that it is a time relation, as existing now and then. we are said to have an intuitive concept of time. when we are told that the whole is greater than a part; that things equal to the same thing are equal to each other; that a straight line cannot enclose space, we _immediately_, or intuitively, recognize the truth of these statements. attempts at proof do not make us feel surer of their truth.... we say that it is self-evident, or that we know the fact intuitively. the axioms of mathematics and logic are said to be intuitive." another class of authorities, however, deny the nature of intuitive knowledge of truth, or intuitive truths. they claim that all our ideas arise from sensation and reflection, and that what we call "intuition" is merely the result of sensation and reflection _reproduced by memory or heredity_. they hold that the _intuitions_ of animals and men are simply the representation of experiences of the race, or individual, arising from the impressions stored away in the subconsciousness of the individual. halleck states regarding this: "this school likens intuition to instinct. it grants that the young duck knows water instinctively, plunges into it, and swims without learning. these psychologists believe that there was a time when this was not the case with the progenitors of the duck. they had to gain this knowledge slowly through experience. those that learned the proper aquatic lesson survived and transmitted this knowledge through a modified structure, to their progeny. those that failed in the lesson perished in the struggle for existence.... this school claims that the intuition of cause and effect arose in the same way. generations of human beings have seen the cause invariably joined to the effect; hence, through inseparable association came the recognition of their necessary sequence. the tendency to regard all phenomena in these relations was with steadily increasing force transmitted by the laws of heredity to posterity, until the recognition of the relationship has become an intuition." another class of general truths is merely hypothetical. hypothetical means "founded on or including a hypothesis or supposition; assumed or taken for granted, though not proved, for the purpose of deducing proofs of a point in question." the hypotheses and theories of physical science are used as general truths for deductive reasoning. hypothetical general truths are in the nature of premises assumed in order to proceed with the process of deductive reasoning, and without which such reasoning would be impossible. they are, however, as a rule not mere assumptions, but are rather in the nature of assumptions rendered plausible by experience, experiment and inductive reasoning. the law of gravitation may be considered hypothetical, and yet it is the result of inductive reasoning based upon a vast multitude of facts and phenomena. the _primary basis of deductive reasoning_ may be said to rest upon the logical axiom, which has come down to us from the ancients, and which is stated as follows: "_whatever is true of the whole is true of its parts_." or, as later authorities have expressed it: "whatever is true of the general is true of the particular." this axiom is the basis upon which we build our deductive reasoning. it furnishes us with the validity of the deductive inference or argument. if we are challenged for proof of the statement that "this fungus is good to eat," we are able to answer that we are justified in making the statement by the self-evident proposition, or axiom, that "whatever is true of the general is true of the particular." if the general "mushroom" is good to eat, then the particular, "this fungus" being a mushroom, must also be good to eat. all horses (general) being animals, then according to the axiom, dobbin (particular horse) must also be an animal. this axiom has been stated in various terms other than those stated above. for instance: "whatever may be affirmed or denied of the whole, may be denied or affirmed of the parts;" which form is evidently derived from that used by hamilton who said: "what belongs, or does not belong, to the containing whole, belongs or does not belong, to each of the contained parts." aristotle formulated his celebrated dictum as follows: "whatever can be predicated affirmatively or negatively of any class or term distributed, can be predicated in like manner of all and singular the classes or individuals contained under it." there is another form of deductive reasoning, that is a form based upon another axiom than that of: "whatever is true of the whole is true of the parts." this form of reasoning is sometimes called mathematical reasoning, because it is the form of reasoning employed in mathematics. its axiom is stated as follows: "things which are equal to the same thing, are equal to one another." it will be seen that this is the principle employed in mathematics. thus: "x equals y; and y equals ; therefore, x equals ." or stated in logical terms: "a equals b; b equals c; therefore, a equals c." thus it is seen that this form of reasoning, as well as the ordinary form of deductive reasoning, is strictly _mediate_, that is, made through the medium of a third thing, or "two things being compared through their relation to a third." brooks states: "the real reason for the certainty of mathematical reasoning may be stated as follows: first, its ideas are definite, necessary, and exact conceptions of quantity. second, its definitions, as the description of these ideas are necessary, exact, and indisputable truths. third, the axioms from which we derive conclusions by comparison are all self-evident and necessary truths. comparing these exact ideas by the necessary laws of inference, the result must be absolutely true. or, stated in another way, using these definitions and axioms as the premises of a syllogism, the conclusion follows inevitably. there is no place or opportunity for error to creep in to mar or vitiate our derived truths." in conclusion, we wish to call your attention to a passage from jevons which is worthy of consideration and recollection. jevons says: "there is a simple rule which will enable us to test the truth of a great many arguments, even of many which do not come under any of the rules commonly given in books on logic. this rule is that _whatever is true of one term is true of any term which is stated to be the same in meaning as that term_. in other words, we may always _substitute one term for another if we know that they refer to exactly the same thing_. there is no doubt that a horse is some animal, and therefore the head of a horse is the head of some animal. this argument cannot be brought under the rules of the syllogism, because it contains four distinct logical terms in two propositions; namely, horse, some animal; head of horse, head of some animal. but it easily comes under the rule which i have given, because we have simply to put 'some animal' instead of 'a horse'. a great many arguments may be explained in this way. gold is a metal; therefore a piece of gold is a piece of metal. a negro is a fellow creature; therefore, he who strikes a negro, strikes a fellow creature." the same eminent authority says: "when we examine carefully enough the way in which we reason, it will be found _in every case to consist in putting one thing or term in place of another, to which we know it to have an exact resemblance in some respect_. we use the likeness as a kind of bridge, which leads us from a knowledge of one thing to a knowledge of another; thus _the true principle of reasoning may be called the substitution of similars, or the passing from like to like_. we infer the character of one thing from the character of something which acts as a go-between, or third term. when we are certain there is an exact likeness, our inference is certain; when we only believe that there probably is, or guess that there is, then our inferences are only probable, not certain." chapter xvi. the syllogism the third and highest phase or step in reasoning--the step which follows after those styled conception and judgment--is generally known by the general term "reasoning," which term, however, is used to include the two precedent steps as well as the final step itself. this step or process consists of the comparing of two objects, persons or things, through their relation to a third object, person or thing. as, for instance, we reason (a) that all mammals are animals; (b) that a horse is a mammal; and (c) that, _therefore_, a horse is an animal. the most fundamental principle of this step or reasoning consists in the comparing of two objects of thought through and by means of their relation to a third object. the natural form of expression of this process of reasoning is called a "syllogism." the process of reasoning which gives rise to the expression of the argument in the form of a syllogism must be understood if one wishes to form a clear conception of the syllogism. the process itself is very simple when plainly stated, although the beginner is sometimes puzzled by the complicated definitions and statements of the authorities. let us suppose that we have three objects, a, b and c, respectively. we wish to compare c and b, but fail to establish a relation between them at first. we however are able to establish a relation between a and b; and between c and a. we thus have the two propositions ( ) "a equals b; and ( ) c equals a". the next step is that of inferring that "if a equals b, and c equals a, then it must follow, logically, _that c equals b_." this process is that of indirect or mediate comparison, rather than _immediate_. c and b are not compared directly or immediately, but indirectly and through the medium of a. a is thus said to _mediate_ between b and c. this process of reasoning embraces three ideas or objects of thought, in their expression of propositions. it comprises the fundamental or elemental form of reasoning. as brooks says: "the simplest movement of the reasoning process is the comparing of two objects through their relation to a third." the result of this process is an argument expressed in what is called a syllogism. whately says that: "a syllogism is an argument expressed in strict logical form so that its conclusiveness is manifest from the structure of the expression alone, without any regard to the meaning of the terms." brooks says: "all reasoning can be and naturally is expressed in the form of the syllogism. it applies to both inductive and deductive reasoning, and is the form in which these processes are presented. its importance as an instrument of thought requires that it receive special notice." in order that the nature and use of the syllogism may be clearly understood, we can do no better than to at once present for your consideration the well-known "rules of the syllogism," an understanding of which carries with it a perfect comprehension of the syllogism itself. the rules of the syllogism state that in order for a syllogism to be a _perfect_ syllogism, it is necessary: i. _that there should be three, and no more than three, propositions._ these three propositions are: ( ) the _conclusion_, or thing to be proved; and ( and ) the premises, or the means of proving the conclusion, and which are called the major premise and minor premise, respectively. we may understand this more clearly if we will examine the following example: _major premise_: "man is mortal;" (or "a is b"). _minor premise_: "socrates is a man;" (or "c is a"). therefore: _conclusion_: "socrates is mortal" (or "c is b"). it will be seen that the above syllogism, whether expressed in words or symbols, is logically valid, because the conclusion must logically follow the premises. and, in this case, the premises being true, it must follow that the conclusion is true. whately says: "a syllogism is said to be valid when the conclusion logically follows from the premises; if the conclusion does not so follow, the syllogism is invalid and constitutes a fallacy, if the error deceives the reasoner himself; but if it is advanced with the idea of deceiving others it constitutes a sophism." the reason for rule i is that only three propositions--a major premise, a minor premise, and a conclusion--are needed to form a syllogism. if we have more than _three_ propositions, then we must have more than two premises from which to draw one conclusion. the presence of more than two premises would result in the formation of two or more syllogisms, or else in the failure to form a syllogism. ii. _that there should be three and no more than three terms._ these terms are ( ) the predicate of the conclusion; ( ) the subject of the conclusion; and ( ) the middle term which must occur in both premises, being the connecting link in bringing the two other terms together in the conclusion. the _predicate of the conclusion_ is called the _major_ term, because it is the greatest in extension compared with its fellow terms. the _subject of the conclusion_ is called the _minor_ term because it is the smallest in extension compared with its fellow terms. the major and minor terms are called the _extremes_. the middle term operates between the two extremes. the _major term_ and the _middle term_ must appear in the _major premise_. the _minor term_ and the _middle term_ must appear in the _minor premise_. the _minor term_ and the _major term_ must appear in the _conclusion_. thus we see that _the major term_ must be the predicate of the conclusion; the _minor term_ the subject of the conclusion; the _middle term_ may be the subject or predicate _of either of the premises_, but _must always be found once in both premises_. the following example will show this arrangement more clearly: in the syllogism: "man is mortal; socrates is a man; therefore socrates is mortal," we have the following arrangement: "mortal," the major term; "socrates," the minor term; and "man," the middle term; as follows: _major premise_: "man" (_middle term_) is mortal (_major term_). _minor premise_: "socrates" (_minor term_) is a man (_major term_). _conclusion_: "socrates" (_minor term_) is mortal (_major term_). the reason for the rule that there shall be "_only three_" terms is that reasoning consists in comparing _two terms_ with each other through the medium of a _third term_. there _must be_ three terms; if there are _more_ than three terms, we form two syllogisms instead of one. iii. _that one premise, at least, must be affirmative._ this, because "from two negative propositions nothing can be inferred." a negative proposition asserts that two things differ, and if we have two propositions so asserting difference, we can infer nothing from them. if our syllogism stated that: ( ) "man is _not_ mortal;" and ( ) that "socrates is _not_ a man;" we could form no conclusion, either that socrates _was_ or _was not_ mortal. there would be no logical connection between the two premises, and therefore no conclusion could be deduced therefrom. therefore, at least one premise must be affirmative. iv. _if one premise is negative, the conclusion must be negative._ this because "if one term agrees and another disagrees with a third term, they must disagree with each other." thus if our syllogism stated that: ( ) "man is _not_ mortal;" and ( ) that: "socrates is a man;" we must announce the negative conclusion that: ( ) "socrates is _not_ mortal." v. _that the middle term must be distributed; (that is, taken universally) in at least one premise._ this "because, otherwise, the major term may be compared with one part of the middle term, and the minor term with another part of the latter; and there will be actually no common middle term, and consequently no common ground for an inference." the violation of this rule causes what is commonly known as "the undistributed middle," a celebrated fallacy condemned by the logicians. in the syllogism mentioned as an example in this chapter, the proposition "_man_ is mortal," really means "_all_ men," that is, man in his universal sense. literally the proposition is "all men are mortal," from which it is seen that socrates being "_a_ man" (or _some_ of _all_ men) must partake of the quality of the universal man. if the syllogism, instead, read: "_some_ men are mortal," it would not follow that socrates _must_ be mortal--he might or might not be so. another form of this fallacy is shown in the statement that ( ) white is a color; ( ) black is a color; hence ( ) black must be white. the two premises _really_ mean "white is _some_ color; black is _some_ color;" and not that either is "_all_ colors." another example is: "men are bipeds; birds are bipeds; hence, men are birds." in this example "bipeds" is not distributed as "_all_ bipeds" but is simply not-distributed as "_some_ bipeds." these syllogisms, therefore, not being according to rule, must fail. they are not true syllogisms, and constitute fallacies. to be "_distributed_," the middle term must be the subject of a universal proposition, or the predicate of a negative proposition; to be "_undistributed_" it must be the subject of a particular proposition, or the predicate of an affirmative proposition. (see chapter on propositions.) vi. _that an extreme, if undistributed in a premise, may not be distributed in the conclusion._ this because it would be illogical and unreasonable to assert more in the conclusion than we find in the premises. it would be most illogical to argue that: ( ) "all horses are animals; ( ) no man is a horse; therefore ( ) no man is an animal." the conclusion would be invalid, because the term _animal_ is distributed in the conclusion, (being the predicate of a negative proposition) while it is not distributed in the premise (being the predicate of an affirmative proposition). as we have said before, any syllogism which violates any of the above six syllogisms is invalid and a fallacy. there are two additional rules which may be called derivative. any syllogism which violates either of these two derivative rules, also violates one or more of the first six rules as given above in detail. the _two derivative rules of the syllogism_ are as follows: vii. _that one premise at least must be universal._ this because "from two particular premises no conclusion can be drawn." viii. _that if one premise is particular, the conclusion must be particular also._ this because only a universal conclusion can be drawn from two universal premises. the principles involved in these two derivative rules may be tested by stating syllogisms violating them. they contain the essence of the other rules, and every syllogism which breaks them will be found to also break one or more of the other rules given. chapter xvii. varieties of syllogisms the authorities in logic hold that with the four kinds of propositions grouped in every possible order of arrangement, it is possible to form nineteen different kinds of valid arguments, which are called the _nineteen moods of the syllogism_. these are classified by division into what are called _the four figures_, each of which figures may be known by the position of the middle term in the premises. logicians have arranged elaborate and curious tables constructed to show what kinds of propositions when joined in a particular order of arrangement will make sound and valid syllogisms. we shall not set forth these tables here, as they are too technical for a popular presentation of the subject before us, and because they are not necessary to the student who will thoroughly familiarize himself with the above stated laws of the syllogism and who will therefore be able to determine in every case whether any given argument is a correct syllogism, or otherwise. in many instances of ordinary thought and expression the _complete_ syllogistic form is omitted, or not stated at full length. it is common usage to omit one premise of a syllogism, in ordinary expression, the missing premise being inferred by the speaker and hearer. a syllogism with one premise unexpressed is sometimes called an _enthymene_, the term meaning "in the mind." for instance, the following: "we are a free people, therefore we are happy," the major premise "all free people are happy" being omitted or unexpressed. also in "poets are imaginative, therefore byron was imaginative," the minor premise "byron was a poet" is omitted or unexpressed. jevons says regarding this phase of the subject: "thus in the sermon on the mount, the verses known as the beatitudes consist each of one premise and a conclusion, and the conclusion is put first. 'blessed are the merciful: for they shall obtain mercy.' the subject and the predicate of the conclusion are here inverted, so that the proposition is really 'the merciful are blessed.' it is evidently _understood_ that 'all who shall obtain mercy are blessed,' so that the syllogism, when stated at full length, becomes: 'all who shall obtain mercy are blessed; all who are merciful shall obtain mercy; therefore, all who are merciful are blessed.' this is a perfectly good syllogism." whenever we find any of the words: "_because_, _for_, _therefore_, _since_," or similar terms, we may know that there is an argument, and usually a syllogism. we have seen that there are three special kinds of propositions, namely, ( ) categorical propositions, or propositions in which the affirmation or denial is made without reservation or qualification; ( ) hypothetical propositions, in which the affirmation or denial is made to depend upon certain conditions, circumstances, or suppositions; and ( ) disjunctive propositions, in which is implied or asserted an _alternative_. the forms of reasoning based upon these three several classes of propositions bear the same names as the latter. and, accordingly the respective syllogisms expressing these forms of reasoning also bear the class name or term. thus, a categorical syllogism is one containing only categorical propositions; a hypothetical syllogism is one containing one or more hypothetical propositions; a disjunctive syllogism is one containing a disjunctive proposition in the major premise. _categorical syllogisms_, which are far more common than the other two kinds, have been considered in the previous chapter, and the majority of the examples of syllogisms given in this book are of this kind. in a categorical syllogism the statement or denial is made positively, and without reservation or qualification, and the reasoning thereupon partakes of the same positive character. in propositions or syllogisms of this kind it is asserted or assumed that the premise is true and correct, and, if the reasoning be logically correct it must follow that the conclusion is correct, and the new proposition springing therefrom must likewise be categorical in its nature. _hypothetical syllogisms_, on the contrary, have as one or more of their premises a hypothetical proposition which affirms or asserts something provided, or "if," something else be true. hyslop says of this: "often we wish first to bring out, if only conditionally, the truth upon which a proposition rests, so as to see if the connection between this conclusion and the major premise be admitted. the whole question will then depend upon the matter of treating the minor premise. this has the advantage of getting the major premise admitted without the formal procedure of proof, and the minor premise is usually more easily proved than the major. consequently, one is made to see more clearly the force of the argument or reasoning by removing the question of the material truth of the major premise and concentrating attention upon the relation between the conclusion and its conditions, so that we know clearly what we have first to deny if we do not wish to accept it." by joining a hypothetical proposition with an ordinary proposition we create a hypothetical proposition. for instance: "_if_ york contains a cathedral it is a city; york _does_ contain a cathedral; therefore, york is a city." or: "if _dogs_ have four feet, they are quadrupeds; dogs _do_ have four feet; therefore dogs _are_ quadrupeds." the hypothetical syllogism may be either affirmative or negative; that is, its hypothetical proposition may either hypothetically _affirm_ or hypothetically _deny_. the part of the premise of a hypothetical syllogism which conditions or questions (and which usually contains the little word "if") is called the antecedent. the major premise is the one usually thus conditioned. the other part of the conditioned proposition, and which part states what will happen or is true under the conditional circumstances, is called the consequent. thus, in one of the above examples: "if dogs have four feet" is the antecedent; and the remainder of the proposition: "they are quadrupeds" is the consequent. the antecedent is indicated by the presence of some conditional term as: _if_, _supposing_, _granted that_, _provided that_, _although_, _had_, _were_, etc., the general sense and meaning of such terms being that of the little word "_if_." the consequent has no special indicating term. jevons gives the following clear and simple _rules regarding the hypothetical syllogism_: i. "if the antecedent be affirmed, the consequent may be affirmed. if the consequent be denied, the antecedent may be denied." ii. "avoid the fallacy of affirming the consequent, or denying the antecedent. this is a fallacy because of the fact that the conditional statement made in the major premise _may not be the only one_ determining the consequent." the following is an example of "affirming the consequent:" "_if_ it is raining, the sky is overclouded; the sky _is_ overclouded; therefore, it _is raining_." in truth, the sky may be overclouded, and still it may _not_ be raining. the fallacy is still more apparent when expressed in symbols, as follows: "_if_ a is b, c is d; c _is_ d; therefore, a is b." the fallacy of denying the antecedent is shown by the following example: "_if_ radium were cheap it would be useful; radium is _not_ cheap; therefore radium _is not_ useful." or, expressed in symbols: "_if_ a is b, c is d; a is _not_ b; therefore c _is not_ d." in truth radium may be useful although not cheap. jevons gives the following examples of these fallacies: "if a man is a good teacher, he thoroughly understands his subject; but john jones thoroughly understands his subject; therefore, he is a good teacher." also, "if snow is mixed with salt it melts; the snow on the ground is _not_ mixed with salt; therefore it does _not_ melt." jevons says: "to affirm the consequent and then to infer that we can affirm the antecedent, is as bad as breaking the third rule of the syllogism, and allowing an undistributed middle term.... to deny the antecedent is really to break the fourth rule of the syllogism, and to take a term as distributed in the conclusion which was not so in the premises." hypothetical syllogisms may usually be easily reduced to or converted into categorical syllogisms. as jevons says: "in reality, hypothetical propositions and syllogisms are not different from those which we have more fully considered. _it is all a matter of the convenience of stating the propositions._" for instance, instead of saying: "if radium were cheap, it would be useful," we may say "cheap radium would be useful;" or instead of saying: "if glass is thin, it breaks easily," we may say "thin glass breaks easily." hyslop gives the following _rule for conversion_ in such cases: "regard the antecedent of the hypothetical proposition as the subject of the categorical, and the consequent of the hypothetical proposition as the predicate of the categorical. in some cases this change is a very simple one; in others it can be effected only by a circumlocution." the third class of syllogisms, known as _the disjunctive syllogism_, is the exception to the law which holds that all good syllogisms must fit in and come under the rules of the syllogism, as stated in the preceding chapter. not only does it refuse to obey these rules, but it fails to resemble the ordinary syllogism in many ways. as jevons says: "it would be a great mistake to suppose that all good logical arguments must obey the rules of the syllogism, which we have been considering. only those arguments which connect two terms together by means of a middle term, and are therefore syllogisms, need obey these rules. a great many of the arguments which we daily use are of this nature; but there are a great many other kinds of arguments, some of which have never been understood by logicians until recent years. one important kind of argument is known as the disjunctive syllogism, though it does not obey the rules of the syllogism, or in any way resemble syllogisms." the disjunctive syllogism is one having a disjunctive proposition in its major premise. the disjunctive proposition also appears in the conclusion when the disjunction in the major premise happens to contain more than two terms. a disjunctive proposition, we have seen, is one which possesses alternative predicates for the subject in which the conjunction "_or_" (sometimes accompanied by "_either_") appears. as for instance: "lightning is sheet _or_ forked;" or, "arches are _either_ round or pointed;" or, "angles are either obtuse, or right angled, or acute." the different things joined together by "or" are called alternatives, the term indicating that we may choose between the things, and that if one will not answer our purpose we may take the other, or one of the others if there be more than one _other_. the _rule regarding the use of disjunctive syllogisms_ is that: "if one or more alternatives be denied, the rest may still be affirmed." thus if we say that "a is b or c," or that "a is either b or c," we may _deny_ the b but still affirm the c. some authorities also hold that "if we affirm one alternative, we must deny the remainder," but this view is vigorously disputed by other authorities. it would seem to be a valid rule in cases where the term "either" appears as: "a is _either_ b _or_ c," because there seems to be an implication that one or the other alone can be true. but in cases like: "a is b _or_ c," there may be a possibility of _both being true_. jevons takes this latter view, giving as an example the proposition: "a magistrate is a justice-of-the-peace, a mayor, or a stipendiary magistrate," but it does not follow that one who is a justice-of-the-peace may not be at the same time a mayor. he states: "after affirming one alternative we can only deny the others _if there be such a difference between them that they could not be true at the same time_." it would seem that both contentions are at the same time true, the example given by jevons illustrating his contention, and the proposition "the prisoner is either guilty or innocent" illustrating the contentions of the other side. a _dilemma_ is a conditional syllogism whose major premise presents some sort of alternative. whately defines it as: "a conditional syllogism with two or more antecedents in the major, and a disjunctive minor." there being two mutually exclusive propositions in the major premise, the reasoner is compelled to admit one or the other, and is then caught between "the two horns of the dilemma." chapter xviii. reasoning by analogy what is called reasoning by analogy is one of the most elementary forms of reasoning, and the one which the majority of us most frequently employ. it is a primitive form of hasty generalization evidencing in the natural expectation that "things will happen as they have happened before in like circumstances." the term as used in logic has been defined as "resemblance of relations; resemblances of any kind on which an argument falling short of induction may be founded." brooks says: "analogy is that process of thought by which we infer that if two things resemble each other in one or more particulars, they will resemble each other in some other particular." jevons states the _rule for reasoning by analogy_, as follows: "if two or more things resemble each other in many points, they will probably resemble each other also in more points." others have stated the same principle as follows: "when one thing resembles another in known particulars, it will resemble it also in the unknown;" and "if two things agree in several particulars, they will also agree in other particulars." there is a difference between generalization by induction, and by analogy. in inductive generalization the rule is: "what is true of the many is true of all;" while the rule of analogy is: "things that have some things in common have other things in common." as jevons aptly remarks: "reasoning by analogy differs only in degree from that kind of reasoning called 'generalization.' when _many things_ resemble each other in a _few properties_, we argue about them by generalization. when a _few things_ resemble each other in _many properties_, it is a case of analogy." illustrating analogy, we may say that if in a we find the qualities, attributes or properties called _a_, _b_, _c_, _d_, _e_, _f_, _g_, respectively, and if we find that in b the qualities, etc., called _a_, _b_, _c_, _d_, _e_, respectively, are present, then we may reason by analogy that the qualities _f_ and _g_ must also belong to b. brooks says of this form of reasoning: "this principle is in constant application in ordinary life and in science. a physician, in visiting a patient, says this disease corresponds in several particulars with typhoid fever, hence it will correspond in _all_ particulars, and _is_ typhoid fever. so, when the geologist discovers a fossil animal with large, strong, blunt claws, he infers that it procured its food by scratching or burrowing in the earth. it was by analogy that dr. buckland constructed an animal from a few fossil bones, and when subsequently the bones of the entire animal were discovered, his construction was found to be correct." halleck says: "in argument or reasoning we are much aided by the habit of searching for hidden resemblances.... the detection of such a relation cultivates thought. if we are to succeed in argument, we must develop what some call a sixth sense of such relations.... the study of poetry may be made very serviceable in detecting analogies and cultivating the reasoning powers. when the poet brings clearly to mind the change due to death, using as an illustration the caterpillar body transformed into the butterfly spirit, moving with winged ease over flowering meadows, he is cultivating our apprehension of relations, none the less valuable because they are beautiful." but the student must be on guard against the deceptive conclusions sometimes arising from reasoning by analogy. as jevons says: "in many cases reasoning by analogy is found to be a very uncertain guide. in some cases unfortunate mistakes are made. children are sometimes killed by gathering and eating poisonous berries, wrongly inferring that they can be eaten, because other berries, of a somewhat similar appearance, have been found agreeable and harmless. poisonous toadstools are occasionally mistaken for mushrooms, especially by people not accustomed to gathering them. in norway mushrooms are seldom seen, and are not eaten; but when i once found a few there and had them cooked at an inn, i was amused by the people of the inn, who went and collected toadstools and wanted me to eat them also. this was clearly a case of mistaken reasoning by analogy. even brute animals reason in the same way in some degree. the beaten dog fears every stick, and there are few dogs which will not run away when you pretend to pick up a stone, even if there be no stone to pick up." halleck says: "many false analogies are manufactured, and it is excellent thought training to expose them. the majority of people think so little that they swallow these false analogies just as newly fledged robins swallow small stones dropped into their open mouths.... this tendency to think as others do must be resisted somewhere along the line, or there can be no progress." brooks says: "the argument from analogy is plausible, but often deceptive. thus to infer that since american swans are white, the australian swan is white, gives a false conclusion, for it is really black. so to infer that because john smith has a red nose and is a drunkard, then henry jones who also has a red nose is also a drunkard, would be a dangerous inference.... conclusions of this kind drawn from analogy are frequently fallacious." regarding the _rule for reasoning from analogy_, jevons says: "there is no way in which we can really assure ourselves that we are arguing safely by analogy. the only rule that can be given is this; that the more closely two things resemble each other, the more likely it is that they are the same in other respects, especially in points closely connected with those observed.... in order to be clear about our conclusions, we ought in fact never to rest satisfied with mere analogy, but ought to try to discover the general laws governing the case. in analogy we seem to reason from one fact to another fact without troubling ourselves either with deduction or induction. but it is only by a kind of guess that we do so; it is not really conclusive reasoning. we ought properly to ascertain what general laws of nature are shown to exist by the facts observed, and then infer what will happen according to these laws.... we find that reasoning by analogy is not to be depended upon, unless we make such an inquiry into the causes and laws of the things in question, that we really employ inductive and deductive reasoning." along the same lines, brooks says: "the inference from analogy, like that from induction, should be used with caution. its conclusion must not be regarded as certain, but merely as reaching a high degree of probability. the inference from a part to a part, no more than from a part to the whole, is attended with any rational necessity. to attain certainty, we must show that the principles which lie at the root of the process are either necessary laws of thought or necessary laws of nature; both of which are impossible. hence analogy can pretend to only a high degree of probability. it may even reach a large degree of certainty, but it never reaches necessity. we must, therefore, be careful not to accept any inference from analogy as true until it is proved to be true by actual observation and experiment, or by such an application of induction as to remove all reasonable doubt." chapter xix. fallacies a _fallacy_ is: "an unsound argument or mode of arguing, which, while appearing to be decisive of a question, is in reality not so; an argument or proposition apparently sound, but really fallacious; a fallacious statement or proposition, in which the error is not apparent, and which is therefore likely to mislead or deceive; sophistry." in deductive reasoning, we meet with two classes of fallacies; namely, ( ) fallacious premise; and ( ) fallacious conclusion. we shall now consider each of these in turn. _fallacious premise_ is in effect _an unwarranted assumption of premises_. one of the most common forms of this kind of fallacy is known as "_begging the question_," the principle of which is the assumption of a fundamental premise which is not conceded; the unwarrantable assumption of that which is to be proved; or the assumption of that by which it is to be proved, without proving it. its most common form is that of boldly stating some unproven fact, authoritatively and positively, and then proceeding to use the statement as the major premise of the argument, proceeding logically from that point. the hearer perceiving the argument proceeding logically often fails to remember that _the premise has been merely assumed_, without warrant and without proof and omitting the hypothetical "_if_." one may proceed to argue logically from the premise that "the moon is made of green cheese," but the whole argument is invalid and fallacious because of the fact that the person making it has "begged the question" upon an unwarranted premise. hyslop gives a good example of this form of fallacy in the case of the proposition "church and state should be united." proof being demanded the advocate proceeds to "beg the question" as follows: "good institutions should be united; church and state are good institutions; therefore, church and state should be united." the proposition that "good institutions should be united" is fallacious, being merely assumed and not proven. the proposition sounds reasonable, and few will feel disposed to dispute it at first, but a little consideration will show that while _some_ good institutions may well be united, it is _not_ a general truth that _all_ should be so. "begging the question" also often arises from _giving a name to a thing_, and then assuming that we have _explained_ the thing. this is a very frequent practice with many people--they try to _explain_ by merely applying names. an example of this kind is had in the case of the person who tried to explain why one could see through a pane of glass by saying "because it is transparent." or when one explains that the reason a certain substance breaks easily is "because it is brittle." moliere makes the father of a dumb girl ask why his daughter is dumb. the physician answers: "nothing is more easy than to explain it; it comes from her having lost the power of speech." "yes, yes," objects the father, "but the cause, if you please, why she has lost the power of speech." the physician gravely replies: "all our best authors will tell you that it is the impeding of the action of the tongue." jevons says: "the most frequent way, perhaps, in which we commit this kind of fallacy is to employ names which imply that we disapprove of something, and then argue that because it is such and such, it must be condemned. when two sportsmen fall out in some manner relating to the subject of game, one will, in all probability, argue that the act of the other was 'unsportsmanlike,' and therefore should not have been done. here is to all appearance a correct syllogism: "no unsportsmanlike act should be done; john robinson's act was unsportsmanlike: therefore, john robinson's act should not have been done. "this is quite correct in form; but it is evidently the mere semblance of an argument. 'unsportsmanlike' means _what a sportsman should not do_. the point to be argued was whether the act fell within the customary definition of _what was unsportsmanlike_." arising from "begging the question," and in fact a class of the latter, is what is called "reasoning in a circle." in this form of fallacy one assumes as proof of a proposition the proposition itself; or, uses the conclusion to prove the premise. for instance: "this man is a rascal because he is a rogue; and he is a rogue because he is a rascal." or, "it is warm because it is summer; and it is summer because it is warm." or "he never drinks to excess, because he is never intemperate in drinking." brooks says: "thus to argue that a party is good because it advocates good measures, and that certain measures are good because they are advocated by so excellent a party, is to reason in a circle. so when persons argue that their church is the true one, because it was established by god, and then argue that since it is the true church it must have been founded by god, they fall into this fallacy. to argue that 'the will is determined by the strongest motive' and to define the strongest motive as 'that which influences the will,' is to revolve in a circle of thought and prove nothing. plato commits this error when he argues the immortality of the soul from its simplicity, and afterwards attempts to prove its simplicity from its immortality." it needs care to avoid this error, for it is surprising how easily one falls into it. hyslop says: "the fallacy of reasoning in a circle occurs mostly in long arguments where it can be committed without ready detection.... when it occurs in a long discourse it may be committed without easy discovery. it is likely to be occasioned by the use of synonyms which are taken to express more than the conception involved when they do not." what is called a vicious circle is caused when the conclusion of one syllogism is used for a proposition in another syllogism, which in its turn comes to be used as a basis for the first or _original syllogism_. _fallacious conclusion_ is in effect _an unwarranted or irrelevant assumption of a logical conclusion_. there are many forms of this fallacy among which are the following: _shifting ground_, which consists in the pretence of proving one thing while in reality merely a similar or related thing is being proved. in this class is the argument that because a man is profane he must necessarily be dishonest; or that because a man denies the inspiration of the scriptures he must be an atheist. _fallacious questioning_, in which two or more related questions are asked, and the answer of one is then applied to the other. for instance: "you assert that the more civilized a community, the more silk-hats are to be found in it?" "yes." "then, you state that silk-hats are the promoters and cause of civilization in a community?" a question of this kind is often so arranged that an answer either in the affirmative or the negative will lead to a false or fallacious inference. for instance, the question once asked a respectable citizen on the witness stand: "have you stopped beating your mother?" an answer of either "yes" or "no," was out of the question, for it would have placed the witness in a false position, for he had never beaten his mother, nor been accused of the same. _partial proof_, in which the proof of a partial or related fact is used to infer a proof of the whole fact or a related one. for instance, it is fallacious to argue that a man has been guilty of drunkenness by merely proving that he was seen entering a saloon. _appeal to public opinion_, in which the prejudices of the public are appealed to rather than its judgment or reason. in politics and theological argument this fallacy is frequent. it is no argument, and is reprehensible. _appeal to authority, or reverence_, in which the reverence and respect of the public for certain persons is used to influence their feelings in place of their judgment or reason. for instance: "washington thought so-and-so, and therefore it must be right;" or "it is foolish to affirm that aristotle erred;" or "it has been believed by men for two thousand years, that, etc;" or "what our fathers believed must be true." appeals of this kind may have their proper place, but they are fallacies nevertheless, and not real argument. _appeal to profession_, in which an appeal is made to practices, principles or professions of the opponent, rather than to reason or judgment. thus we may argue that a certain philosophy or religion cannot be sound or good, because certain people who hold it are not consistent, or not worthy, moral or sober. this argument is often used effectively against an opponent, and is valid against him personally. but it is no valid argument against his philosophy or belief, because he may act in violation of them, or he may change his practices and still adhere to his beliefs--the two are not joined. _appeal to general belief_, in which an appeal is made to general or universal belief, although the same may be unsupported by proof. this is quite common, but is no real argument. the common opinion may be erroneous, as history proves. a few centuries ago this argument could have been used in favor of the earth being flat, etc. a half-century ago it was used against darwin. today it is being used against other new ideas. it is a fallacy by its very nature. _appeal to ignorance_, in which an appeal is made to the ignorance of the opponent that his conviction may follow from his inability to prove the contrary. it is virtually no argument that: "so-and-so must be true, _because you cannot prove that it is not_." as brooks says: "to argue that there is no material world, because we cannot explain how the mind knows it to exist, is the celebrated fallacy of hume in philosophy. the fact that we cannot find a needle in a haystack is no proof that it is not there." _introduction of new matter_, also called _non sequitur_, in which matter is introduced into the conclusion that is not in the premises. hyslop gives the following example of it: "all men are _rational_; socrates is a man; therefore, socrates is _noble_." de morgan gives the following more complex example: "episcopacy is of scripture origin; the church of england is the only episcopal church in england; therefore, the church established is the church that ought to be supported." other fallacies, resembling in some respects those above mentioned, are as follows: _fallacy of ambiguous terms_, in which different meanings of the same word are used to produce the fallacious argument. as jevons says: "a word with two distinct meanings _is really two words_." _confusion between collective and general meanings of a term_, of which jevons says: "it would be obviously absurd to argue that because _all_ the books in the british museum library are sure to give information about king alfred, therefore any particular book will be sure to give it. by '_all_ the books in the british museum library,' we mean all _taken together_. there are many other cases where the confusion is not so evident, and where great numbers of people are unable to see the exact difference." _arguing from the collective to the general_, in which the fallacy consists of arguing that because something is true of the whole of a group of things, therefore it is true of any of those things. jevons says: "_all_ the soldiers in a regiment may be able to capture a town, but it is absurd to suppose that therefore _every_ soldier in the regiment could capture the town single handed. white sheep eat a great deal more than black sheep; but that is because there are so many more of them." _uncertain meaning of a sentence_, from which confusion arises and fallacious argument may spring. jevons says: "there is a humorous way of proving that a cat must have three tails: because a cat has one tail more than _no_ cat; and _no cat_ has two tails; therefore, _any_ cat has three tails." here the fallacy rests upon a _punning_ interpretation of "no." _proving the wrong conclusion_, in which the attempt to confuse conclusions is made, with the result that some people will imagine that the case is established. jevons says: "this was the device of the irishman, who was charged with theft on the evidence of three witnesses, who had seen him do it; he proposed to call _thirty_ witnesses who had _not_ seen him do it. equally logical was the defense of the man who was called a materialist, and who replied, 'i am not a materialist; i am a barber.'" _fallacy of unsuccessful argument_, in which is attempted the illogical conclusion that _because a certain argument has failed the opposite conclusion is proven_. this fallacy is quite common, especially in cases of juries. one side fails to prove certain contentions, and the jury leaps to the conclusion that the opposite contention must be correct. this is clearly fallacious, for there is always the possibility of a _third_ explanation. in the case of a claim of _alibi_ juries are apt to fall into this fallacy. the failure of the attempt to establish an _alibi_ is often held to be in the nature of proof of the guilt of the accused. old trial lawyers assert that a failure to establish a claimed _alibi_ tends to injure the chance of the accused more than direct evidence against him. yet, as all logical reasoners will see, there is no logical validity in any such inference. as jevons has well said: "_no number of failures in attempting to prove a proposition really disprove it_." at the end of each failure the case simply stands in the same position as before the attempt; _i.e._, "not proven." _all violations of the rules of the syllogism_ constitute fallacies, as may be seen by forming a syllogism in violation of one or more of the rules. the logicians, particularly those of ancient times, took great pains to discover and _name_ new variations of fallacies, many of which were hair-splitting in nature, and not worthy of being considered seriously. some of those which we have enumerated may possibly be open to the same criticism, but we have omitted many of the worst offenders against practical common sense. an understanding of the fundamental laws of reasoning is sufficient to expose and unmask all fallacies, and such understanding is far more valuable than the memorizing of the _names_ of hair-splitting fallacies which would not deceive a child. in addition to the above stated fallacies of deductive reasoning, there are other fallacies which are met with in _inductive reasoning_. let us briefly consider them. _hasty and false generalization_ is a common fallacy of this class. persons sometimes see certain qualities in a few individuals of a class, and mistakenly infer that _all_ the individuals in that class must possess these same qualities. travelers frequently commit this fallacy. englishmen visiting the united states for a few weeks have been known to publish books upon their return home making the most ridiculous generalizations regarding the american people, their assertions being based upon the observation of a few scattered individuals, often not at all representative. americans traveling abroad commit similar errors. a flying trip through a country does not afford the proper opportunity for correct generalization. as brooks says: "no hypothesis should be accepted as true until the facts are so numerous that there can be no doubt of its being proved." _fallacies of observation_ result from incorrect methods of observation among which may be mentioned the following: ( ) _careless observation_, or inexact perception and conception; ( ) _partial observation_, in which one observes only a part of the thing or fact, omitting the remainder, and thus forming an incomplete and imperfect concept of the thing or fact; ( ) _neglect of exceptions and contradictory facts_, in which the exceptions and contradictory facts are ignored, thereby giving undue importance to the observed facts; ( ) _assumption of facts_ which are not real facts, or the assumption of the truth of things which are untrue; ( ) _confusing of inferences with facts_, which is most unwarrantable. _fallacies of mistaken cause_ result from the assumption of a thing as a cause, when it is not so, of which the following are familiar examples: _substituting the antecedent for the cause_, which consists in assuming a mere antecedent thing for a _cause_ of another thing. thus one might assume that the crowing of the cock was the _cause_ of daybreak, because it _preceded_ it; or that a comet was the cause of the plague which followed its appearance; or in the actual case in which a child reasoned that doctors _caused_ deaths, because observation had shown that they always visited persons before they died; or that crops failed because a president of a certain political party had been inaugurated a few months before. some fallacies of everyday reasoning are quite as illogical as those just mentioned. _substituting the symptom for the cause_, which consists in assuming as a _cause_ some mere symptom, sign or incident of the real cause. to assume that the pimples of measles were the _cause_ of the disease, would be to commit a fallacy of this kind. we have mentioned elsewhere the fallacy which would assume silk-hats to be the cause of civilization, instead of being a mere incident of the latter. politicians are fond of assuming certain incidents or signs of a period, as being the _causes_ of the prosperity, culture and advancement of the period, or the reverse. one might argue, with equal force, that automobiles were the causes of national prosperity, pointing to the fact that the more automobiles to be seen the better the times. or, that straw hats produced hot weather, for similar reasons. _the fallacy of analogy_ consists in assuming a resemblance or identity, where none exists. we have spoken of this in another chapter. brooks says, also: "it is a fallacy to carry an analogy too far; as to infer from the parable of the praying of the importunate woman that god resembles the unjust judge." in conclusion, we would call your attention to the following words from jevons, in which he expresses the gist of the matter: "it is impossible too often to remind people that, on the one hand, _all correct reasoning consists in substituting like things for like things_, and inferring that what is true of one will be true of all which are similar to it in the points of resemblance concerned in the matter. on the other hand, _all incorrect reasoning consists in putting one thing for another where there is not the requisite likeness_. it is the purpose of the rules of deductive and inductive logic to enable us to judge as far as possible when we are thus rightly or wrongly reasoning from some things to others." finis. transcriber's note: obvious typos and printer errors have been corrected without comment. in addition to obvious errors, the following changes have been made: page : "idea" changed to "ideas" in the phrase, "... forming concepts or general ideas." page : "infuoria" changed to "infusoria" in the phrase, "... the microscopic infusoria...." page : "disciple" changed to "discipline" in the phrase, "... necessity of discipline for invention...." other than the above changes, no attempt has been made to correct common spelling, punctuation, grammar, etc. the author's usage is preserved as printed in the original publication. studies and exercises in formal logic john neville keynes london macmillan and co., limited new york: the macmillan company because of nature of the source material, it was decided that a text version was impractical.