c 
 
 ELEMENTS OF LOGIC AS A SCIENCE 
 OF PROPOSITIONS.
 
 PRINTED BY MORRISON AND GIBB, 
 FOR 
 
 T. & T. CLARK, EDINBURGH, 
 
 LONDON, * . . . . HAMILTON, ADAMS, AND CO. 
 
 DUBLIN, .... GEORGE HERBERT. 
 
 NEW YORK, .... SCRIBNER AND WELFORD.
 
 AS A 
 
 SCIENCE OF PROPOSITIONS. 
 
 BY 
 
 E. E. CONSTANCE JONES, 
 
 LECTURER IN MORAL SCIENCES, OIRTON COLLEGE, CAMBRIDGE ; 
 JOINT-TRANSLATOR AND EDITOR OF LOTZE'S " MICKOCOSMUS." 
 
 EDINBURGH: 
 
 T. & T. CLAEK, 38 GEORGE STREET. 
 1890.
 
 PREFACE. 
 
 THE following pages have grown out of an attempt to reach, 
 point by point, some solution of various questions in Logic, 
 which, both in learning and in teaching, I have felt to be 
 special sources of difficulty. The continued use of Jevons's 
 Elementary Lessons in Logic with beginners, has particularly 
 contributed to keep these problems before my mind ; for 
 Jevons's little book, though full of interest and suggestion, is 
 not free from inconsistencies and confusions in connection 
 with the questions referred to. 
 
 Having reached apparent solutions of some difficulties, 
 and finding that these solutions are, as it seems to me, 
 consistent among themselves, and in harmony with a 
 certain general view of Logic which I take, I am desirous 
 to submit what I have written to the test of publication. 
 
 I at first intended to call this collection of chapters 
 " Notes " ; but as objections to this name, which I could 
 not gainsay, were put before me, I have adopted the 
 present title ; meaning to convey by it, not that the follow- 
 ing pages are intended for beginners, but that they present 
 what is necessary for indicating the outlines of the Science 
 of Logic as I conceive it. What I most strongly feel the 
 need of, and what I should have preferred to attempt to 
 write, is an elementary handbook, corresponding in some 
 respects to Jevons's ; but I think that certain divergences 
 of my view from current views require an amount of 
 explanation and justification which would be out of place 
 in a book intended for beginners. 
 
 The very large number of references introduced is due 
 to two causes. First, to the wish to confirm my opinion by 
 that of accepted authorities when the two seem to accord ; 
 and secondly, to the desire to indicate as precisely as possible, 
 in cases of difference, the doctrines which I am combating. 
 
 2000697
 
 VI PREFACE. 
 
 I am greatly indebted to the kindness of Mr. W. E. 
 Johnson, of King's College, who read through most of my 
 sections as they originally stood in manuscript, and whose 
 judicious and penetrating criticism has enabled me to work 
 out some points in my own view more fully and clearly, to 
 avoid several inconsistencies, and to correct some serious 
 mistakes. It would take too long to specify in detail all 
 the cases referred to; but I ought to mention that Mr. 
 Johnson's views differ from mine on some points of funda- 
 mental importance. 1 
 
 I am also under very great obligations to Mr. J. N. 
 Keynes, of Pembroke College, who has been so kind as to 
 read the proofs of this book, and whose criticisms have been 
 most valuable to me, though I have not, in every case, been 
 able to accept them. This has (in part) necessarily resulted 
 from a general difference of view a difference which is 
 clearly seen by reference to Mr. Keynes's work on Formal 
 Logic, the name of which occurs so often in the following 
 pages. 
 
 I should like to say that I trace the distinction which 
 I have drawn between Independent and Dependent Cate- 
 gorical Propositions, and, indeed, I believe my whole view 
 of the Import of Categoricals, to a suggestion received from 
 some strictures on Locke's treatment of propositions, in a 
 lecture (heard several years ago) of Professor Sidgwick's. 
 And it was some remarks of Professor Sidgwick's, indicating 
 the confusion between logical and psychological points of 
 view in Mill, that first made me feel the necessity of treating 
 Logic as a non-psychological Science. 
 
 I must also mention that I am indebted to Mr. Alfred 
 Sidgwick for criticisms that have helped me to put several 
 points more clearly. 
 
 GIKTON COLLEGE, CAMBRIDGE, 
 November 30, 1889. 
 
 1 The Import of Hypothetical and Disjunctive Propositions, and some ques- 
 tions connected with Predication and Existence, should perhaps be specially 
 indicated.
 
 CONTENTS. 
 
 PAET I. IMPORT OF PROPOSITIONS. 
 
 (I.) OF TERMS AS ELEMENTS OF PROPOSITIONS. 
 
 SECTION I. (INTRODUCTORY). 
 
 DEFINITION OF LOGIC. 
 
 Logic may be defined as the Science of the Import and Relations of Propositions, 
 or more briefly, as the Science of Propositions. Logic is not psychological, 1 
 both because it is not subjective and because it is of universal application. It 
 starts from the standpoint of ordinary thought, and assumes reason in man 
 and trustworthiness in language, pp. 1-3 
 
 SECTION II. 
 
 NAMES AND TERMS. 
 
 Names are to be distinguished from Terms. In All R is P, the Terms are All 
 R, and P. All R, the Subject-term, consists of Term-name (or Term-sign) 
 (R)+ Term-indicator (All). A Name is a word or group of words applying 
 to a thing, or things. A Thing is whatever has Existence (Quantitiveness) 
 and Character (Qualitiveness). A Term is any word or combination of words 
 occurring in a Categorical Proposition, and applying to that of which some- 
 thing is asserted (S), or that which is asserted of it (P). Denomination of a 
 Name or Term corresponds to Quantitiveness of a Thing ; and Attribution 
 of a Name or Term corresponds to Qualitiveness of a Thing. All Names 
 have both Denomination and Attribution. Determination is Attribution in 
 as far as explicitly signified. Implication is Attribution in as far as only 
 implied. The Determination of any Name includes the Attribute of being 
 called by that Name. By Import of a Name or Term is signified its Denomi- 
 nation together with its Attribution. Things are either (1) Subjects of 
 Attributes, or (2) Attributes. The names which apply to (1) are Substantival 
 Names; those which apply to (2) are Attribute Names. The Characteriza- 
 tion of Attributes, as well as of Subjects, is largely effected by (3) Adjectival 
 Names, which can never occur as Subject, but only as Predicate, of a Cate- 
 
 1 For the distinction of Psychology from other Sciences, cf. Encyclopedia Britannica, 9th 
 edition, part 77, p. 38, article Psychology.
 
 Vlll CONTENTS. 
 
 gorical Proposition. Substantival Names are subdivided into (a) Common, 
 (b) Special, (c) Unique Names, pp. 3-15 
 
 Tables I. II. (Adjectival Terms), pp. 16, 17 
 
 Table III. (Names), p. 18 
 
 SECTION III. 
 
 TERMS. 
 
 The characteristics of terms often cannot be settled without reference to the 
 propositions of which they are terms. Still, many of the most important 
 distinctions in propositions depend upon differences in the terms, especially in 
 the Subject Terms. The widest distinction between terms is that between 
 Uni-terminal or Adjectival Terms terms which can only be used as Predi- 
 cates of propositions ; and Bi-terminal Terms terms which may be used 
 both as Subjects and as Predicates. The principal division of these is into 
 Attribute Terms and Substantive Terms. Among the further subdivisions 
 of terms a specially important one is that into Dependent or Systemic 
 (implying a dependence or relation of subjects of attributes connected in some 
 system, which may be of any degree of complexity, from the simplicity of a 
 class or of any two related subjects to the intricacy of a genealogical tree, or 
 even of the universe itself) and Independent. From a proposition containing 
 a Systemic Term e.g. E is equal- to -F a number of Immediate Infer- 
 ences can be drawn in addition to those which can be drawn from other pro- 
 
 positions, pp. 19-25 
 
 Tables IV. -XVI. (Terms), . . . ..."'. . . . pp. 25-34 
 
 SECTION IV. 
 
 NOTE ON DEFINITION AND CONNOTATION. 
 
 The definition of a name sets forth its meaning, and the meaning of a name is 
 said to be its Connotation. Connotation has been understood in various 
 senses ; but the best view seems to be that what a name connotes is those 
 attributes on account of which we apply the name, and in the absence of any 
 of which we should not apply it, . . . . . . pp. 35-37 
 
 SECTION V. 
 THE MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 
 
 An examination of the definitions and use of the terms Abstract and Concrete 
 by different logical writers reveals an inconsistency between the various state- 
 ments of the same writer and a divergence between different writers, that 
 indicate considerable difficulty in the distinction which is had in view. It 
 will not do to say that an Abstract Term, as opposed to a Concrete Term, 
 means a term the application of which presupposes a process of abstraction 
 for this is true of every significant term. And we do not escape difficulty by 
 saying that a Concrete Name is the name of a Subject of Attributes, while an 
 Abstract Name is the name of an Attribute of Subjects. Nor is it satisfactory 
 to restrict the application of Abstract Term to Concepts, whether Concept 
 means something complete in itsdf and isolated from all else, or the mental 
 equivalent of a general name, . pp. 37-44
 
 CONTENTS. ix 
 
 (II.) OF PROPOSITIONS AS WHOLES. 
 
 (A.) CATEGORICAL PROPOSITIONS. 
 
 SECTION VI. 
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 
 
 Formal (most General) Import of Categorical*. 
 
 Having treated Terms, the elements of Categorical Propositions, as applying 
 to things, and not to the mental process of apprehending things, it would 
 be incongruous to define a Categorical Proposition as the expression of a. 
 Judgment ; and, moreover, this would leave us still asking for the definition 
 of Judgment." A Categorical Proposition may be defined as A Proposition 
 which affirms, or negates ( = absolutely denies), Identity of Denomination in 
 Diversity of Determination. Or it might be defined more briefly as A 
 Proposition which asserts Identity (or Non-Identity) in Diversity (cf. Section 
 XXVII. By Non-Identity I mean Complete absence of Identity), pp. 44-54 
 
 Classification of Categorical Propositions. 
 
 The primary division of Categorical Propositions is into Adjectival and Coin- 
 cidental (cf. p. 21). Most of the further subdivisions of Categoricals are 
 summed up in Table XVII. p. 62, and the whole are given in detail in the 
 Tables, pp. 62-76. Important differences in use, depending on differences 
 of relation to other propositions, are connected with the differences of form 
 exhibited in the Tables, pp. 54-61 
 
 Tables XVII.-XXXI. (Categorical Propositions), . . . pp. 62-76 
 
 SECTION VII. 
 
 NOTE ON THE PREDICABLES. 
 
 In the doctrine of Predicables we are concerned with the matter of propositions. 
 In the accounts of Predicables we find confusion of points of view and of the 
 elements concerned ; and, in particular, confusion between Denomination and 
 Determination, pp. 76-78 
 
 SECTION VIII. 
 MILL'S VIEW OF THE IMPORT OF PROPOSITIONS. 
 
 Any general differences in ordinary Categorical Propositions, beyond those 
 already noticed, depend upon either I. Relations of Determination between 
 S-name and P-name, and under this head comes Mill's distinction between 
 Real and Verbal Propositions. Or II. Determination of S-name, or of 
 P-name, or of both. Under this head comes Mill's division of propositions 
 into Propositions of Existence, Co-existence, Sequence, Causation, and 
 Resemblance. Mill's application of these Categories to the Import of 
 Categorical Propositions is strained, and he confuses Formal and Material 
 (Non-Formal) points of view, pp. 79-81
 
 X CONTENTS. 
 
 SECTION IX. 
 
 SYSTEMIC (HI DEPENDENT PROPOSITIONS. 
 
 The characteristic which distinguishes Systemic or Dependent Propositions 
 from Independent Propositions is this : In Systemic Propositions such as, 
 D is equal to F, A is like B of the two terms (S and P) one applies to some 
 thing or group of things, and the other expresses the relation of that thing or 
 group to a second thing or group. Hence it is possible for a person knowing 
 the system referred to, to draw more inferences from Dependent Propositions 
 than from Independent Propositions. A fortiori arguments, and other 
 arguments containing Dependent Propositions, can, with the help of Im- 
 mediate Inferences, always be expressed in strict syllogistic form, pp. 82-84 
 
 SECTION X. 
 
 NOTE ON MATHEMATICAL PROPOSITIONS. 
 
 The copula in Mathematical Propositions is to be understood as meaning in 
 equal to (i.e. is exactly similar quantitatively) ; and since a thing cannot be 
 said to be equal to itself, the terms of Mathematical Propositions (taking = 
 as the copula) must have different denominations, i.e. they must apply to 
 different things. Hence the terms of Mathematical Propositions can be 
 quantified with any, only when they have the most abstract application 
 possible, i.e. when they apply to numbers generally, and are not understood 
 to refer to some assigned unit (cf. Sections IX. and XXVII.), . pp. 84-86 
 
 SECTION XI. 
 
 PREDICATION AND EXISTENCE. 
 
 The view that Universal Categoricals do not (while Particulars do] imply the 
 "existence" of what is referred to by S and P, and the interpretation of All 
 S is P, No S is P, to mean Sp = 0, SP = 0, respectively, are not to be 
 accepted, for first, if we take "existence" in the widest possible sense, to 
 deny that our terms do apply and are meant to apply to what has a minimum 
 of existence of some kind, implies the view that our terms do not apply, or 
 are not meant to apply, to things at all. It 'also cuts off all possibility of 
 positing or implying existence in general (except in what appears to me to be a 
 wholly arbitrary, and therefore inadmissible, way). But second, "existence" 
 may be taken to mean " membership of the Universe of Discourse." On such 
 a view, our Universe of Discourse may be (1) all-embracing, or (2) restricted. 
 Let X represent the Universe of Discourse. Then if (1), it follows that 
 Everything is X. But this by Obversion gives us Nothing is x. Here we 
 have transcended our Universe, so it was not all-embracing. And similarly 
 with restricted Universes, whenever we mention our Universe, we can tran- 
 scend it. And in interpreting All S is P, as Sp = 0, we do transcend it ; for 
 since is not X, it must be x. And when we transcend X, and talk of what 
 is x, there seems no reason why we should call X rather than x, or than X 
 -(- x, our Universe of Discourse. And Sp = must mean either SpX = 
 ( = SpX = x) in which case we have a contradiction in terms or Spx = x, 
 in which case both our terms refer to the region x and not to X. Among the 
 inconveniences involved by the view which this Section attempts to refute
 
 CONTENTS. XI 
 
 are the following : Universals and Particulars are to be differently inter- 
 preted, and no interpretation can be given to S is P, S is-not P ; Subversions 
 and Conversions of A are not valid inferences ; * All S is P and No S is P 
 may be asserted together, pp. 86-102 
 
 SECTION XII. 
 
 (B.) INFERENTIAL PROPOSITIONS. 
 
 An Inferential Proposition is a Proposition expressing a relation between Ante- 
 cedent and Consequent, such that an identity (or identities) expressed or 
 indicated by the Consequent is an inference from an identity (or identities) 
 expressed or indicated by the Antecedent. Inferential Propositions may be 
 (1) Hypothetical, or (2) Conditional. A Hypothetical Proposition is one in 
 which two (expressed or indicated) Categoricals (or combinations of Categoricals) 
 are combined in such a way as to express that one (Consequent) is an inference 
 from the other (Antecedent). A Conditional Proposition is one which asserts 
 that any object which is indicated by a given class-name and distinguished 
 in some particular way, may be inferred to have also some further distinction. 
 The import of an Inferential may be expressed in a Categorical of the form, G 
 is an inference from A. Hypothetical are either Self-contained or Keferential. 
 Conditionals are either Divisional or Quasi-Divisional. Conditionals (but 
 not all Hypothetical) are reducible to Categoricals of the form, Any E that 
 is F, is H ; and it is only Categoricals of this form that are reducible to 
 Conditionals, pp. 103-113 
 
 Tables XXXII., XXX III. (Hypothetical and Conditional Propositions), 
 
 pp. 114, 115 
 
 SECTION XIII. 
 
 (C.) ALTERNATIVE PROPOSITIONS. 
 
 Alternatives may have some element of unexclusiveuess, but must also have 
 some element of exclusiveness, otherwise there is no alternation. In as far as 
 "alternatives" are absolutely unexclusive, they are of the form A or A. 
 Where the Alternatives are Propositions, there must be some difference of 
 meaning in the Propositions, or there is no Alternation, and so far there is 
 exclusiveness ; but Alternatives may be true together, and so far there is 
 unexclusivcness. Where the Alternatives are Terms, there may be un- 
 exclusiveness of denomination, but there must be some exclusiveness of 
 determination. An Alternative Proposition may be denned as A Proposi- 
 tion in which a plurality of differing elements (connected by or, and called 
 the Alternatives) are so related that not all of them can be denied, because 
 the denial of some justifies the assertion of the rest. Alternative Proposi- 
 tions may be divided into Classificatory, Quasi-Divisional, and Contingent 
 (cf. Section XXVII.), pp. 115-121 
 
 Table XXXIV. (Alternative Propositions) p. 122 
 
 SECTION XIV. 
 
 NOTE ON CLASSIFICATION AND DIVISION. 
 
 Division and Classification are the same thing looked at from different points of 
 view : any table presenting a Division presents also a Classification. It is 
 
 1 The Quantification of A would also, I presume, be illegitimate.
 
 Xll CONTENTS. 
 
 desirable to distinguish Classification from Classing, and from Systematiza- 
 tion pp. 123, 124 
 
 SECTION XV. 
 
 QUANTIFICATION AND CONVERSION. 
 
 Quantification is a necessary stage in the Conversion of Categorical Propositions. 
 It is only Coincidentals that can be quantificated and converted. From the 
 view of the Import of Categoricals advocated in Section VI. it follows that 
 the Quantification of Common Categoricals is always possible, but is only to 
 be admitted as a transformation-stage. This view of Quantification is con- 
 firmed by a consideration of the traditional logical treatment of proposi- 
 tions, pp. 124-130 
 
 SECTION XVI. 
 
 THE MEANING OF SOME. 
 
 The special force and meaning of propositions in the stage of Quantification 
 depends principally upon the meaning given to Some. To define Some as 
 meaning "Some but not all," or "Some at least, it may be all," or " Not 
 none," is not satisfactory. It seems best to say that Some H means an inde- 
 finite quantity or number of R. Taking this meaning of Some, Quantification 
 by Some merely makes our terms explicitly indeterminate, and the function 
 of Quantification, on the whole, seems to be simply to bring into prominence 
 the quantitive (denominational) aspect of the Predicate, . pp. 130-132 
 
 PART II. RELATIONS OF PROPOSITIONS. 
 
 SECTION XVII. 
 
 GENERAL REMARKS ON THE RELATIONS OF PROPOSITIONS. 
 
 Two Propositions may be related to each other as Incompatible, or Unattached, 
 or Correlative, or Premissal. To any two Premissal Propositions a third pro- 
 position may be related, either as inferrible, or as non-inferrible, pp. 133-135 
 
 Table XXXV. (Eelations of Propositions) p. 136 
 
 SECTION XVIII. 
 
 INFERENCE. 
 
 One Proposition is an Inference from another or others, when the assertion of 
 the former is justified by the latter, and the latter is, in some respect, different 
 from the former. An "Inductive" Inference must be allowed to be formal, 
 as well as the Inferences commonly distinguished as "Deductive," and a 
 "Mediate" Inference only differs from an "Immediate" Inference in being 
 more complex, pp. 137-141 
 
 Table XXXVI. (Inferences), p. 142
 
 CONTENTS. xiii 
 
 SECTION XIX. 
 
 IMMEDIATE INFERENCES (EDUCTIONS). 
 
 When we pass from one proposition to another, and the latter is justified by the 
 former, and differs from it in some respect, the latter is an Immediate Infer- 
 ence (Eduction) from the former. Eductions may have I. Categoricals (a), 
 or Inferential (b), or Alternatives (c), for both educt and educend : these may 
 be called Pure Eductions, or Eversions. Or, II. they may have a Categorical 
 with an Inferential (a), or a Categorical with an Alternative (6), or an Inferen- 
 tial with an Alternative (c). These may be called Mixed Eductions or Trans- 
 versions. There are eight principal kinds of Categorical Eversions (cf. 
 Table, p. 150). The only Inferential Eversion may be most appropriately 
 called Contraversion. There seems to be only one strictly formal Alternative 
 Eversion, which may be called a Converse. In Transversion the most in- 
 teresting points are that all Inferentials and Alternatives may have their 
 meaning expressed in Categorical form ; that Conditionals and Categoricals 
 (of which S and P in the one correspond to A and C in the other) are re- 
 ciprocally educible ; that Inferentials are educible from Alternatives, and 
 Alternatives from Inferentials, and thus the Alternative answering to any 
 Inferential has a corresponding Categorical, educible from the Categorical 
 which answers to the Inferential, pp. 143-149 
 
 Table XXXVII. (Immediate Inferences or Eductions), . . p. 150 
 
 SECTION XX. 
 
 INCOMPATIBLE PROPOSITIONS. 
 
 Propositions are Incompatible when they cannot both be true. Two Pro- 
 positions are Contrary when they cannot both be true, but may both be 
 false ; they are Contradictwy when they cannot both be true and cannot 
 both be false, pp. 151-156 
 
 MEDIATE INFERENCES (SYLLOGISMS). 
 
 SECTION XXI. 
 
 (A.) CATEGORICAL SYLLOGISMS. 
 
 The Dictum de omni et nullo is merely a formulation of the truth that if any 
 object or objects belong to a class, what can be said about the class (dis- 
 tributively) can be said about it or them. It applies only in cases in which 
 we are dealing with A, E, I, or propositions. And Jevons's Rule of Infer- 
 ence is not satisfactory. If Syllogism means Formal Mediate Inference, 
 Categorical Syllogism may be defined as A combination of three categorical 
 propositions, one of which (the Conclusion) is inferred from the other two 
 taken together these two being called the Premisses, and having in common 
 one term-name which does not occur in the conclusion. The conclusion has 
 its S-name in common with one premiss, and its P-name in common with 
 the other premiss. And of such Categorical Syllogisms the following may 
 be accepted as Canon : If the denomination of two terms is identical (or
 
 XIV CONTENTS. 
 
 non-identical), 1 any third term which has a different term- name and is de- 
 nominationally identical with the whole (or a part) of one of those two, is 
 also identical (or n on -identical), in whole or part, with the denomination of 
 the other. The traditional rules of Categorical Syllogism may be condensed, 
 and amended in correspondence with the above Canon, . pp. 156-163 
 
 SECTION XXII. 
 
 (B.) INFERENTIAL SYLLOGISMS. 
 
 Inferential Syllogisms are Syllogisms which have an Inferential Premiss. A 
 Pure Inferential Syllogism (1) is A Syllogism of which the conclusion and 
 both the premisses are Inferential Propositions. A Mixed Inferential 
 Syllogism (2) is A Syllogism of which the major premiss is an Inferential 
 Proposition, the minor premiss and the conclusion being Categorical Pro- 
 positions. (1) May be Hypothetical (a), or Conditional (b) ; (2) may be 
 Hypothetico-Categorical (c), or Conditio-Categorical (d). There are separate 
 Canons for (a), (b), (c), (d), pp. 163-165 
 
 Table XXXVIII. (Inferential Syllogisms), p. 166 
 
 SECTION XXIII. 
 
 (C.) ALTERNATIVE SYLLOGISMS. 
 
 An Alternative Syllogism is A Syllogism of which one premiss is always an 
 Alternative Proposition or a combination of Alternative Propositions, and of 
 which one premiss and the conclusion, or both premisses, or both premisses 
 and the conclusion, may be alternative. Alternative Syllogisms may be 
 Pure (a) or Mixed, and Mixed subdivide into Categorico - Alternative (b), 
 Hypothetico-Alternative (c), and Conditio-Alternative (d). The four classes, 
 (a), (b), (c), (d), have distinct Canons, .... pp. 167, 168 
 
 Tables XXXIX., XL. (Alternative Syllogisms), ... pp. 169, 170 
 SECTION XXIV. 
 
 NOTE ON THE GROUND OF INDUCTION. 
 
 Cause, as defined by Mill, is a contradictory notion, and all Inductive Inference 
 is based upon the assumption of a certain constant coinherence of attributes 
 in the subjects concerned. In Induction we proceed upon the principle that 
 any subject of attributes that is like another in one respect is like it in a 
 plurality of respects (or that any attribute is one of a set recurring uniformly). 
 "With this are connected the further principles, that no subject of attributes 
 is unlike another (or its former self) in one respect only, that no two objects 
 or classes are alike in all respects, and that no two objects or classes are 
 unlike in all respects (cf. Section XXVII.), . , . pp. 171-175 
 
 SECTION XXV. 
 
 NOTE ON THE LAWS OF THOUGHT. 
 
 The Law of Identity is an expression of the permanence of things, of their 
 identity in diversity, and is better conveyed by the formula Every A is B 
 
 1 I take identical to mean completely coincident, and non-identical to mean altngether un- 
 coincident.
 
 CONTENTS. XV 
 
 [or not B] than by the strictly unmeaning A is A. If A is B, A is-not 
 non-B, or Two contradictory propositions cannot both Reaffirmed; and A is 
 either B or not-B, or Two contradictory propositions cannot both be denied, 
 seem the best formulae for the Laws of Contradiction and Excluded Middle 
 respectively. These three Laws may be called the Axioms of Logic, and 
 express the three principles (1) of the possibility of significant assertion, (2) 
 of consistency, (3) of inter-relation or reciprocity (of. p. 206), pp. 175-178 
 
 SECTION XXVI. 
 
 FALLACIES. 
 
 Confusion should be regarded not as itself Fallacy, but as a source of Fallacy. 
 All Fallacy consists (1) in identifying what is different, or (2) in differencing 
 what is identical ; thus we get a primary subdivision of Fallacies into those 
 of (1) professed Identification or Discontinuity, (2) professed Difference or 
 Tautology. Fallacy may be defined as The assertion or assumption of some 
 relation between (i.) Terms, or (ii.) Propositions, which does not hold between 
 them. Or taking the word in a narrower sense, there is Fallacy whenever we 
 conclude from one or more propositions to another, the conclusion not being 
 justified by the premiss or premisses. All Fallacies are reducible to Formal 
 Fallacies Elemental, or Eductive, or Syllogistic, or Circular (cf. Tables 
 XLL.XLII.), pp. 178-193 
 
 Tables XLI., XLII. (Fallacies), pp. 194, 195 
 
 SUPPLEMENT. 
 
 SECTION XXVII. 
 
 RECAPITULATORY. 
 
 This Section is, for the most part, a recapitulation, . . . pp. 196-208
 
 PABT I. 
 IMPOET OF PROPOSITIONS. 
 
 (I.-) OF TERMS AS ELEMENTS OF PROPOSITIONS. 
 
 SECTION I. (INTKODUCTOKY). 
 
 DEFINITION OF LOGIC. 
 
 To provide a satisfactory definition of Logic is admittedly 
 difficult. The definitions which have actually been given 
 differ among themselves ; and in many cases an author's 
 definition does not seem to apply directly and naturally to the 
 topics of which he subsequently treats. For instance, Jevons 
 says that Logic is the Science of Eeasoning, or the Science of 
 the Laws of Thought (Elementary Lessons in Logic, Less. I.), 
 and then proceeds to consider Terms, Propositions, Immediate 
 Inference, Fallacies, Method, Induction, Abstraction, etc., to 
 some of which subjects, certainly, the definition does not 
 obviously and without straining apply. 
 
 He suggests, however, another and, I think, a more satis- 
 factory definition when, in the Elementary Lessons (p. 69, 7th 
 edition; cf. also op. cit., Preface, p. vi.), he speaks of Logic 
 as treating of " the relations of the different propositions and 
 the inferences which can be drawn from them" (inferences, 
 of course, come under the head of relations). 1 In accordance 
 with this suggestion, I propose to define Logic as the Science 
 of the Import and Relations of Propositions, or more briefly, as 
 the Science of Propositions. 
 
 1 Cf. also Mill, Logic, Bk. i. ch. i. 2, aiid Boole, Laws of Thought, p. 7. 
 
 A
 
 2 IMPORT OF PROPOSITIONS. 
 
 All the subjects usually treated in handbooks of Logic come 
 simply and naturally under the above definition, and are con- 
 veniently classifiable. We may, I think, without any violence 
 include a consideration of Names and Terms, which are 
 elements of propositions ; a consideration of Predicables and 
 Categories, of Definition, of the meaning of Categorical and 
 other propositions, and of Quantification, comes under the 
 head of " Import of Propositions ; " Opposition and Immediate 
 Inference, Syllogism, Analogy, Induction, Scientific Explanation, 
 Fallacy, etc., would be included in " Eelations of Propositions." 
 
 Logic is objective, for it relates to objects of thought ; 
 universal, for it applies to all objects. As concerned with 
 objects known, it implies a knower. But all sciences imply 
 a knower, all deal with objects. It is because of an unique 
 characteristic pervading explicit reference of knoivn Object to 
 knowing Subject that Psychology is called " subjective " : 
 the knower qua knower is not the known even in Psycho- 
 logy. Logic, I think, just as much applies to and just as 
 little is Psychology, as it applies to or is any other science ; 
 and I do not see why, if we are studying the mental pro- 
 cesses concerned in Inference, etc., we should call our study 
 Logic and not Psychology. We can only tell in any case of 
 reasoning whether our processes have been right i.e. logical 
 by comparing the proposition which states our result with the 
 propositions which state our data. If we regard Logic as 
 concerned with the elements, import, and relations of asser- 
 tions expressed in language, we have assigned to it a sphere 
 coextensive with knowledge itself, and in accordance with the 
 general recognition of it as fundamental and of universal 
 application, and with its old name Science of Sciences. The 
 burden of proof lies with those who narrow this sphere, and 
 call it psychological, or metaphysical, or physical, or anything 
 else except logical. 
 
 Since, however, Logic is admittedly concerned with Truth, 
 with what we ought to think and propositions are valuable 
 only as a means of arriving at and expressing Truth, it might 
 be asked, Why not define it at once as the Science of Truth ?
 
 NAMES AND TERMS. 3 
 
 To this, I think, a twofold answer might be made ; for first, 
 the use of the word Propositions instead of Truth in the defini- 
 tion seems to simplify both the application and the articula- 
 tion of the science ; and second, there is no way of expressing 
 truth except in propositions, and no way of testing any truth 
 which is called in question except by comparing the proposi- 
 tion which expresses it with other propositions. 
 
 If Logic is the Science of Propositions, it must start from 
 the standpoint of ordinary thought, ascertained by reflexion on 
 ordinary language. Two assumptions which appear to be 
 involved in ordinary thought are, that (1) the meaning and 
 application of terms is uniform, and (2) that which is self- 
 evident ought to be believed. That is to say, ordinary thought 
 assumes reason in man, and trustworthiness in language. 
 These assumptions may in any given case turn out to be 
 unwarranted ; but in order to prove that they are so in that 
 particular case, in order even to doubt or to examine that 
 case, we are bound to assume them to some extent at least 
 provisionally. Thus it seems that a comparatively general 
 and permanent faith in the validity of these assumptions is 
 an indispensable condition of intelligent scepticism in any 
 particular instance. 
 
 The following pages are chiefly concerned with Formal 
 Logic Formal being taken to mean most general (cf. 
 Professor Sidgwick's History of Ethics, ch. iii. 1, p. 108, 
 first edition). 
 
 SECTION II. 
 
 NAMES AND TERMS. 
 
 Although we frequently see Names and Terms used syno- 
 nymously, it seems desirable to distinguish Names which are 
 Terms from Names which are not Terms, and even to 
 emphasize the distinction, since the failure to keep this
 
 4 IMPORT OF PROPOSITIONS. 
 
 distinction in view tends, I think, to confusion (cf. post, 
 Section on Categorical Syllogisms). For instance, it is very 
 unsatisfactory to find, in a treatise on Logic, in which a 
 Categorical Proposition is analysed into " two terms and the 
 copula," that S and P are referred to as the terms of such a 
 proposition as All S is P, while such syllogisms as 
 
 All P is M, 
 All M is S, 
 
 Some S is P ; 
 
 All men are animals, 
 All animals are mortals, 
 Some mortals are men ; 
 
 are spoken of as having " three and only three terms." ] 
 
 If a proposition contain nothing but two terms and a copula, 
 it is clear that the terms in the above propositions are All S 
 (Some) P, All P, (Some) M, All men, (Some) animals, and so 
 on. 2 Again, if in All birds are feathered, Tully is Cicero, the 
 terms are birds, feathered, Tully, Cicero, what are we to call 
 All birds ? Supposing we get out of the difficulty by saying 
 
 1 Cf. e.g. Jevons' Elementary Lessons in Logic, 7th edition, p. 183 foot, p. 
 124 ("whatever is predicated of a term distributed"), p. 127 (e.g. "Every 
 syllogism has three and only three terms "), etc. 
 
 * When Mill (Logic, ii. 383, 9th edition) says that Fallacies of Ratiocination 
 "generally resolve themselves into having more than three terms to the 
 syllogism, either avowedly, or in the covert mode of an undistributed middle 
 term, or an illicit process of one of the two extremes," he implicitly allows the 
 meaning of term advocated in this Section. And if the Subject and the Predi- 
 cate of a proposition are its terms, then this meaning which I wish to assign to 
 term is countenanced by Mill in the following passage (Logic, Bk. i. ch. i. 2, 
 vol. i. p. 19, 9th edition) : " In the proposition, the earth is round, the Predi- 
 cate 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." (Mill also uses Name in the sense in 
 which I wish to use Term (a sense which is frequently assigned to it) ; cf. 
 Logic, loc. cit., " The first glance at a proposition shows that it is formed 
 by putting together two names." " 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 distinction 
 which I draw between term and term-name is also taken by Mr. W. E. Johnson, 
 but with different terminology. Cf. Keynes, Formal Logic, p. 54, 35.
 
 NAMES AND TERMS. 5 
 
 that All birds consists of term + indicator, there remains the 
 objection that in one case the term applies to the whole of the 
 Subject, while in another case it applies to only a part of it. 
 And in such propositions as, Snowdon is the highest mountain 
 in Wales, These men are sailors, are we to say that highest 
 mountain in Wales or the highest mountain in Wales, that 
 men or these men are terms ? If $ is P is a form representative 
 of all affirmative Categoricals, and if, in it, S and P are terms, 
 I do not see how inconsistency of terminology can be escaped 
 if in such a proposition as, e.g., All birds are feathered, we 
 call birds a term. And the circumstance that in my opinion 
 an essential point in Categorical Propositions is the quantitive 
 identity of certain elements, is to me a further reason for 
 wishing to attach the appellation of term to those elements 
 rather than to what is very frequently only a constituent of 
 them. We might call M, P, S, Men, Animals, Mortals, the 
 Term-names or perhaps it might be better to use the expres- 
 sion Term-signs when we make letters stand for significant 
 words, reserving the expression Term-names for cases where 
 significant words are used. Thus in the above instances Men, 
 Animals, Mortals would be Term-names, M, P, S Term-signs. 
 We can, in this way, mark a distinction of Names as part of 
 Terms, both from the terms of propositions and from names in 
 the ordinary wide sense of that word, which allows us to use 
 it of isolated words or groups of words that apply to objects, 
 e.g. the nouns, etc., occurring in alphabetical order in dic- 
 tionaries and indexes. Many substantival words are commonly 
 or always modified when they occur as Subject-names of 
 propositions, by some characterization (expressed or implied) 
 that need not attach to them when they are in isolation ; e.g. 
 by the words all, some, one, certain, this, those. This con- 
 stituent of the Term may perhaps be called the Term-indicator, 
 or more briefly, the Indicator. In some cases Term and 
 
 Term < v are the same, e.g. in S is P, Tully is Cicero. 
 
 t -name j 
 
 Name may be defined as any word or group of words 
 applying to or indicating a Thing, or Things. By thing I
 
 6 IMPORT OF PROPOSITIONS. 
 
 mean whatever has Existence and Character. 1 Existence and 
 Character have a certain correspondence with Quantity and 
 Quality as sometimes used ; but since Quantity, Quality, and 
 their derivatives have in ordinary logical use also narrower 
 and somewhat different meanings, I should propose to use 
 Quantitiveness and Qualitiveness (with the corresponding 
 adverbs and adjectives). These words seem to me convenient 
 because they mark both a distinction from and a likeness to 
 Quantity and Quality as ordinarily used, and they are pre- 
 ferable to That-ness and What-ness (which are more unequi- 
 vocal in meaning), because they have corresponding adjectives 
 and adverbs. By Quantitiveness I mean that in virtue of which 
 anything is something, that which is involved in calling it some- 
 thing or anything just the bare minimum of existence of some 
 kind which justifies the application of a name (that is, of any 
 name at all). To attribute Quantitiveness to anything would 
 be simply to say tJiat it is. Thus Quantitiveness would have a 
 meaning nearly allied to that of Quantity in the phrase Quantity 
 of Propositions, meaning the Universality or Particularity of 
 their Subject-term, i.e. the application of that Term to all 
 or some of the things indicated by the Term-name. But 
 when we say that mathematical, as distinguished from logical, 
 propositions deal with Quantity, or are quantitative, Quantity 
 means Quality which is increased or decreased (but not altered 
 in intensity} by addition or subtraction of homogeneous parts. 
 I think it would be convenient to call this Extensive Quality 
 as contrasted with Quality in which increase or decrease of 
 amount involves alteration of intensity. This latter may 
 perhaps be called Intensive Quality. The peculiarity of 
 mathematical propositions is, that the whole characterization 
 of their Terms is concerned with what I venture to call 
 Extensive Quality. 
 
 1 Cf. Mr. Bradley's Principles of Logic, p. 3, "In all that is we can dis- 
 tinguish two sides (1) existence, and (2) content." (It is, of course, only as 
 thought of that things have names applied to them.) Cf. also Professor W. 
 James, The Psychology of Belief (Mind, Iv. 331), "In the strict and ultimate 
 sense of the word existence, everything which can be thought of at all exists as 
 some sort of object, whether mythical object, individual thinker's object, or 
 object in outer space and for intelligence at large."
 
 NAMES AND TERMS. 7 
 
 By Qualitiveness I mean that in virtue of which anything 
 is wliat it is. The Qualitiveness of a Thing includes all its 
 attributes, thus completely characterizing the kind of its 
 Quantitiveness ; and whatever we predicate of a thing expresses 
 some attribute of it. Quality is commonly used both in this 
 sense and also in a narrower sense, as, e.g., when we speak of 
 the Quality of Propositions, meaning their character as affirma- 
 tive or negative. And when we distinguish between (1) 
 Quantity and (2) Quality in an object, referring all the while 
 to its attributes as, e.g., between (1) the weight and (2) the 
 nutritive, etc., attributes of a loaf of bread Quantity means 
 Extensive Quality, and Quality means Intensive Quality (in 
 the sense indicated above). The use of Quality as meaning 
 the affirmative or negative character of propositions would 
 perhaps be justified by the consideration that this affirmative- 
 ness or negativeness is such an important characteristic as to 
 merit being called Quality tear e^o^v. But no confusion 
 need result if we add the qualification of propositions when 
 using Quality in this sense. 
 
 A Term is any combination of words occurring in a Cate- 
 gorical Proposition, and applying to that of which something 
 is asserted (S), or that which is asserted of it (P). 
 
 Attributes may be (1) Intrinsic or Essential, (2) Extrinsic 
 or Accidental. Either of these again may be Extensive, 
 Intensive, or Simple. An Intrinsic Attribute of anything 
 named is some attribute included in the meaning of its name ; 
 all other Attributes are Extrinsic. E.g. Carnivorousness, four- 
 footediiess, are Intrinsic Attributes of a lion ; being of a par- 
 ticular shade of colour, being born in Africa, having a tufted 
 tail, are Extrinsic Attributes. 
 
 Again, Intrinsic and Extrinsic Attributes may be either 
 Dependent (or Systemic) that is, attributes in which explicit 
 reference is made to something other than that which has 
 the attributes or Independent that is, not making such 
 reference. These differences come to be of consequence when 
 Adjectival Names are used in propositions, that is, when they 
 become Terms (Predicates). They are of consequence partly
 
 8 IMPOKT OF PEOPOSITIOXS. 
 
 with reference to the most general (or formal), and partly 
 with reference to the less general (or material), distinctions 
 between terms and propositions. We may therefore classify 
 Adjectival Terms (in accordance with the distinctions above 
 taken) as in Tables I. and II. It would seem that what- 
 ever is indicated by a name is thought as having what I have 
 called quantitiveness and qualitiveuess. And unless it has 
 quantitiveness and qualitiveness some continuity of exist- 
 ence x and some distinguishing attributes it must be wholly 
 characterless or a nonentity. 
 
 I propose to use the word Denomination (of a Name or 
 Term) as corresponding to Quantitiveness (of a Thing) ; and 
 Attribution (of a Name or Term) as corresponding to Qualitive- 
 ness (of a Thing). Denomination of a Name or Term will 
 therefore refer to the continued identical existence of the 
 things, whether Subjects or Attributes, which are indicated ; 
 and Attribution of a Name or Term will mean the distinctive 
 character of the things named. The Attribution of a Name 
 or Term in as far as explicitly signified may be called the 
 Determination; in as far as it is only implied, it may be called 
 the Implication : thus Attribution will mean Determination 
 + Implication? I agree with those logicians 3 who maintain 
 that every name or term has what I have called Denomination 
 and Determination (if we may admit as part of the Determi- 
 nation of a name the attribute of being called by that name). 
 Indeed it seems to me that Denomination and Attribution (of 
 which Determination is always a part) are mutually implicated 
 in terms, as inevitably as quantitiveness and qualitiveness in 
 the things indicated, or as lines and angles, or likeness and 
 difference. 
 
 In as far as a term is denominative, it applies (as I under- 
 stand denominative} to the quantitiveness, the mere undeter- 
 
 1 Cf. post, Section on the Laws of Thought. 
 
 2 I have avoided the words Denotation and Connotation, because they have, 
 as Fowler says, been "already employed with so much uncertainty" that it is 
 difficult to use them without some risk of confusion ; and indeed no use of 
 those terms that I am acquainted with corresponds to the distinction which I 
 have in view here. 
 
 3 Cf. e.g. Bradley, Principles of Logic, p. 156.
 
 NAMES AND TEEMS. 9 
 
 mined existence, of the thing of which it is the name 
 that identity which enables us to speak of a thing as one, 
 under whatever change of attributes. In as far as it is 
 determinative, it applies to the qualitiveness of the thing 
 including in qualitiveness the kind of its existence (material, 
 fictitious, ideational, etc.). 
 
 This difference of aspect in terms is possibly what Jevons 
 is thinking of when in the Elementary Lessons in Logic 
 (Lesson V.) he emphasizes the distinction between Intension 
 and Extension. The importance which he attributes to this, 
 saying that when it is once grasped there is little further 
 difficulty to be encountered in Logic, is hardly borne out by 
 his further treatment ; but if what he had in view corresponds 
 to what I have called Attribution and Denomination, the 
 importance he assigns to it is, I think, not exaggerated. 
 
 The following passages from Dr. Bain, Dr. Venn, and Mill, 
 seem to me confirmatory of that view of Existence and 
 Character in Things, and Denomination and Determination in 
 Names or Terms, which I have here taken. Dr. Bain says 
 (Logic, 2nd ed. i. 59), "Existence has no real opposite;" 
 (p. 107), "With regard to the predicate Existence, occurring 
 in certain propositions, we may remark no science, or depart- 
 ment of logical method, springs out of it. Indeed, all such 
 propositions are more or less abbreviated or elliptical, etc." 
 
 Dr. Venn (Empirical Logic, p. 232) says, "Though mere 
 logical existence cannot be intelligibly predicated, inasmuch as 
 it is presupposed necessary by the use of the term, yet the 
 special kind 1 of existence which we call objective or experi- 
 ential can be so predicated. It 1 is not implied by the use of 
 the term ; it l is not conveyed by the ordinary copula ; it is a 
 real restriction upon anything thus indicated, and therefore it is 
 a perfectly fit. subject 1 of logical predication." 
 
 Mill says (Logic, ii. 325, 9th ed.), "If the analysis of 
 
 qualities in the earlier part of this work be correct, names of 
 
 qualities and names of substances stand for the very same 
 
 sets of facts or phenomena ; whiteness and a white thing are 
 
 1 The italics are mine.
 
 10 IMPORT OF PROPOSITIONS. 
 
 only different phrases, required by convenience 1 for speaking 
 of the same external fact under different relations. Not such, 
 however, was the notion which this verbal distinction sug- 
 gested of old, either to the vulgar or to the scientific. White- 
 ness was an entity inhering or sticking in the white substance ; 
 and so of all other qualities. So far was this carried that 
 even concrete general terms were supposed to be, not names 
 of indefinite numbers of individual substances, but names of 
 a peculiar kind of entities termed Universal Substances. 
 Because we can think and speak of man in general, that is, 
 of all persons in so far as possessing the common attributes 
 of the species, without fastening our thoughts permanently on 
 some one individual person; therefore man in general was 
 supposed to be, not an aggregate of individual persons, but an 
 abstract or universal man, distinct from these." 
 
 It would, I think, be convenient to extend the sense of 
 Determination so that the determination of any name may 
 include the attribute of being called by that name. This is 
 certainly a part, and not an implicit part, of the attribution. 
 
 By Import I intend the Denomination together with the 
 Attribution of a name or term, i.e. the complete scope of 
 the term in its quantitive and qualitive aspects. To take 
 examples : Denomination of (1) Man is the more or less 
 permanent existence of all individuals of the human race 
 (Socrates, Plato, Aristotle, Shakespeare, and so on). (The 
 whole of the characteristics of Man is included in the attribu- 
 tion of the word. Existence and Character (Quantitiveness 
 and Qualitiveness) are, of course, inseparably bound up to- 
 gether, though we may think and speak of them separately. 
 The existence- of each thing is unique, but this uniqueness of 
 existence can only be made clear by its unique attribution 
 and the existence and the attribution involve each other.) 
 Denomination of (2) Triangularity is the mere existence of 
 the attribute named wherever it occurs. 
 
 Determination of (1) is the attributes of animality and 
 rationality, and (in accordance with the view suggested above) 
 
 1 The italics are mine.
 
 NAMES AND TERMS. 11 
 
 it also includes the attribute of being called Man ; of (2) is 
 the characteristics of having three angles, and being called 
 Triangularity. 
 
 Implication of (1) is that the things to which the name is 
 applied are Subjects of Attributes, have a particular external 
 form, etc. 1 Of (2) that that to which the name is applied is 
 (wherever occurring) an Attribute of Subjects, etc. 
 
 The Import of (1) is all creatures to which the name 
 applies, considered with reference both to quantitiveness and 
 qualitiveness, they being Subjects of Attributes, having the 
 characteristics of animality and rationality, and being called 
 by the name Man, etc. 
 
 Of (2) is the attribute Triangularity, as having quantitive- 
 ness, i.e. as occurring (wherever it does occur) and as having 
 definite qualitiveness (i.e. as differentiated from other Attri- 
 butes by having three angles, and by being called Triangularity, 
 and as differentiated qua Attribute of Subjects from Subjects 
 of Attributes, etc.). 
 
 The Denomination of (1) All the Greek poets [are celebrated] 
 means the quantitiveness (qua Subjects) of those things of 
 which All the Greek poets is the name i.e. of the individuals 
 Homer, ^schylus, Sophocles, and so on ; of (2) Whiteness [is 
 the colour of snow, sea-foam, privet-blossom, etc.] is the 
 quantitiveness (qua Attribute i.e. the occurrence in Subjects) 
 of that of which Whiteness is the name. (Most Attribute 
 Names do not take a plural, because in them determination 
 is most prominent, and denomination of the singular includes 
 every case of occurrence. The only exception is, groups of 
 Attributes which have such striking similarity that they 
 possess a name in common e.g. colour, virtue.) 
 
 1 It would generally be very difficult (not to say impossible) to state at length 
 the whole of the implications of any name used with intelligence. It is, I think, 
 to a great extent upon the fulness and vividness with which implications of 
 names are realized in thought, that the force and adequacy of our ideas depend ; 
 and the realization of some implications is indispensable for understanding. 
 Such implications seem to be had in view when it is said that our terms always 
 refer to a certain definite Universe of Discourse. This way of meeting the case, 
 however, does not appear to me to be satisfactory or useful (cf. post, Section on 
 Predication and Existence).
 
 12 IMPORT OF PROPOSITIONS. 
 
 The Determination of (1) is the attributes of belonging to 
 the Greek nation, of producing fine poetical compositions, of 
 being the only Greeks who did so, of being called All the 
 Greek poets. Of (2) is the attribute common to and dis- 
 tinctive of snow, sea-foam, privet -blossom, etc., and on 
 account of possessing which they are called white, and the 
 attribute of being called Whiteness. 
 
 In (1) the Implication is that the things named are 
 Subjects of Attributes, of a particular form, speaking a 
 particular language, etc. 
 
 The Implication of (2) is that the thing named is an 
 Attribute of Subjects, etc. 
 
 The Import of the above terms is given by combining, in 
 each case, the Denomination and Attribution of the term. 
 
 The broadest division of Things that language involves 
 and suggests is into I. Subjects of Attributes ; II. Attributes. 
 The names which apply to I. may be called Substantival 
 Names, and those which apply to II. may be called Attribute 
 Names. 
 
 In the present connection it may perhaps be allowed to 
 distinguish Subject of Attributes and Attributes as follows : 
 
 A Subject is that of which the differentia is to liave charac- 
 teristics and not to be a characteristic. 
 
 An Attribute is that of which the differentia is to be a 
 characteristic. That it may also have characteristics does not 
 destroy its nature as Attribute, any more than being a father 
 abrogates a man's relation as son to his own father. 
 
 If we start with Tilings simply, every characterization of 
 any Thing will without difficulty be allowed to be effected by 
 the attribution of the terms applied to it. But I see no 
 reason why, if we start with Things that are Subjects and 
 Things that are Attributes, we may not (if it is convenient) 
 reckon that in this case Attribution begins with such charac- 
 terization as sets forth the distinctive kind of Attribute, or the 
 distinctive kind of Subject. I do not see what objection can 
 be made to this, as far as Attributes are concerned (and no 
 one, as far as I know, objects to it with regard to Subjects),
 
 NAMES AND TERMS. 13 
 
 by any one who allows that Attributes have distinctive 
 character, to which corresponds Attribution of names. And 
 if any Attribute can have Attributes ascribed to it (and 
 ordinary language certainly countenances, perhaps even 
 necessitates, such a reference), it must be in virtue of its 
 quantitiveness. Any Attribute capable of further character- 
 ization by attribution, must be capable of it in virtue of its 
 as yet to some extent uncharacterized existence or quantitive- 
 ness, not in virtue of the characterization by attribution which 
 it has already received. 
 
 The characterization of Attributes, as well as of Subjects, 
 is largely effected by names of a third kind, which may be 
 called III. Adjectival Names. In these names the qualitive- 
 ness of the object named is most prominent and some definite 
 characteristics are determined, as in white, fragrant, organized, 
 beautiful. Adjectival Names have several important charac- 
 teristics. (1) They always refer to some Thing (Subject of 
 Attributes or Attribute) previously named, which they help to 
 characterize, and can occur as P of a Categorical Proposition 
 which has either an Attribute Term, or a Substantival Term 
 for S ; while an Attribute Term can be predicated only of an 
 Attribute Term, and a Substantival Term only of a Sub- 
 stantival Term. (2) They can occur only as P, never as S, 
 of a Categorical Proposition. 1 (3) Attribution (as already 
 implied) is prominent in them. It is interesting, with refer- 
 ence to this consideration, to notice that in, e.g., modern 
 English, 2 adjectives do not take the sign of the plural, 
 although the things which they qualify may be many. (4) 
 They are applied because of certain characteristics in the 
 things to which they apply. In (3) Adjectival Names 
 resemble Attribute Names ; in (4) they resemble Attribute 
 Names and Common Names (cf. Table III.). 
 
 What is primary in a Subject is that it is ; what is primary 
 in an Attribute is what it is : an Attribute Name always 
 
 1 Cf. also German in such propositions as, e.g., Diese Lieder sind wunderschiin, 
 Wir sind's nicht gewohnt. 
 
 2 Cf. Stock, Deductive Loyic, 88.
 
 14 IMPORT OF PROPOSITIONS. 
 
 characterizes the Attribute which it applies to so fully that 
 any affirmative Categorical Proposition having Complete Attri- 
 bute Terms for both S and P must be a Nominal Proposition. 
 A Subject Name may determine nothing more than that what 
 it applies to is called by that name. 
 
 Substantival Names are names in which (in isolation or 
 as Subjects) the quantitiveness of what is named is most 
 prominent. 1 Here the determination may include definite 
 characteristics, sufficient to enable us to define and apply 
 the name, as in, e.g., bird, fairy, accident. Or we may have 
 some characteristics determined, but not enough to enable 
 us to define or apply the name, as the eldest son of Charles I. 
 Or it may only be (i.) determined that the thing called by 
 a name has the attribute of being called by that name; 
 (ii.) implied that the thing has, 1st, what is common to all 
 Subjects of Attributes; 2nd, unique individuality; 3rd, an 
 unique name as in, e.g., Tom Smith. 
 
 Substantival Names may be divided into (a) Common 
 Names, i.e. names of which the application is restricted by 
 the determination only, as man, fairy, Ragged Robin. 
 
 (b) Special Names, i.e. names the application of which has 
 some definite degree of further restriction, but is not confined to 
 only one object or group, as Predicables, Admiral of the Fleet, 
 Czar of Russia, Friday, September. Special Names have 
 always more than the minimum of Determination ; and there 
 may be an indefinite number of Fridays, Admirals, etc. ; but 
 there can be only one Friday in the week, and fifty-two in 
 a year, and, at any given time, only three Admirals of our 
 Fleet, only one Czar of Eussia, and so on. 
 
 (c) Unique Names, i.e. names of which the application may 
 be said to be restricted to one object or group of objects, 
 as, the sun, father of D., this boy, Julius Ccesar, Mary, Tom, 
 Quellyn Youde, Vancouver's Island, 1888 A.D., the children of 
 King Charles I. 
 
 Unique names may have a maximum of determination, as 
 
 1 When a Substantival Name is used as P of a proposition, the qualitiveness 
 of what is named becomes most prominent.
 
 NAMES AND TERMS. 15 
 
 the sun, or a minimum, as Gordon. Such names as Gordon, 
 Tom, Muriel, of course may be, and are, applied to many 
 individuals, but they may still be called Unique, being given 
 in every case with the intention of distinguishing an unique 
 individual an object of which (without further knowledge 
 than the name affords) we can only predicate (1) what is 
 common to all Subjects of Attributes, (2) unique individuality, 
 (3) an unique name, (4) what that name is. If a " proper 
 name " conveys more to us than this, it is because either (1) 
 we have special knowledge of the individual named, or (2) 
 because the name has, so far, ceased to be a Proper Name. 
 
 I have adopted the above distinctions of names in prefer- 
 ence to those ordinarily given in logical handbooks for the 
 following among other reasons. The old distinctions form 
 independent couples (e.g. General and Singular, Collective and 
 Distributive, Positive and Negative), and they do not lend them- 
 selves to a satisfactory classification. Some of them are of no 
 logical importance, e.g. Collective (a name that is not collective 
 may be used collectively), Positive and Negative, Eelative and 
 Absolute ; and the distinction between Categorematic and 
 Syncategorematic is a distinction purely of words, and not 
 even of names, much less of terms (though Jevons, Elementary 
 Lessons in Logic, 7th ed. p. 26, uses it as applying to terms). 
 The distinction between Abstract and Concrete is inconsist- 
 ently treated by logicians, and is, in my opinion, untenable, 
 since it seems impossible to arrive at any valid justification 
 for the adoption of those particular words in their logical use, 
 or at any satisfactory test by which to determine their appli- 
 cation. My reasons for this opinion and some discussion of 
 the subject are given in a short consideration of the terms 
 Abstract and Concrete. On the other hand, the division of 
 names which I have adopted appears to correspond to impor- 
 tant distinctions either in the objects named or in the aspect 
 of them with which we are concerned ; there are no cross- 
 divisions, and a formally good classification is possible. , All 
 of them are, I think, of further consequence when we come 
 to the divisions of Terms and of Categorical Propositions.
 
 16 
 
 IMPORT OF PROPOSITIONS. 
 
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 03 
 
 fe 
 
 < ?'s "i .2 
 
 g kS "O "o ~~^ 
 
 ^ S)<^ (M fg'C 3 
 
 W J- o fjO 
 
 ' = 0^o 
 
 O2 r-l ^2 (Cl 
 
 ' ^ S M <? 9 
 
 W 43 cs 
 
 S 3 S '" 
 
 ^ 'c "" *" B"3 S H 
 
 -H Ifilifl 
 
 sJUJs* 
 
 ef\ v *r ^r 4 >< t^*4 r_i . 
 
 >> 
 f-1 
 
 'C'-O 
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 OD * 8 
 
 w 2 
 z a 
 
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 N 
 
 j G 
 
 3 *B @ 
 
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 "
 
 TERMS. 1 9 
 
 SECTION III. 
 
 TERMS. 
 
 If we consider Names qud nominal and not qud terminal (cf. 
 Table of Names, p. 18), we shall find some broad distinctions 
 corresponding to differences in the things named, or in the 
 aspect of them which is emphasized differences which are 
 of importance when we come to the classification of Terms 
 and Propositions. As regards Terms, however, we frequently 
 cannot fully settle their character as Attribute Terms, Sub- 
 stantival Terms, etc., until we have considered what their 
 special force is in the propositions to which they belong. 
 An isolated name can generally be classed on mere inspection 
 as primarily adjectival or substantival, and so on; but the 
 terms of any proposition must be regarded as parts of that 
 proposition, and only then, it may be, can they have their 
 character definitely and fully determined this character, of 
 course, depending on the character of the thing named. For 
 instance, if I am asked to characterize the name Whiteness, I 
 have no hesitation in calling it an Attribute Name ; but if 
 the word Whiteness is given to me as a Term or part of a 
 Term, and I am required to characterize it, I can only say, 
 Until I know the proposition in which it occurs, I am unable 
 to do so. If, e.g., the proposition is, Whiteness is a colour, 
 then Whiteness is an Attribute Term; if the proposition is, 
 This table-cloth is whiteness itself, then I should say that 
 Whiteness is part of an Adjectival Term (whiteness itself being 
 equivalent to as white as white can be) ; if the proposition is, 
 This whiteness is death-like, I should say that whiteness is 
 perhaps part of an Attribute Term, this whiteness (this white- 
 ness meaning this pallor of countenance for an exactly similar 
 colour on china or on silk, etc., need not be death-like). 
 
 It will be found, however, that most of the important 
 distinctions in propositions depend upon differences in their 
 Terms, especially the Subject Terms e.g. any proposition
 
 20 IMPORT OF PROPOSITIONS. 
 
 beginning with a class-name qualified by No is an Universal 
 .Proposition ; any proposition beginning with a class-name 
 qualified by Some is a particular proposition. I therefore 
 proceed to consider Terms before discussing Propositions. 
 
 The accompanying Tables of Terms, pp. 2534 (containing 
 many important distinctions in addition to those which 
 correspond to the distinctions of names already noticed), 
 exhibit the distinctions of Terms in schemes of Division. 
 The remarks which follow here will be made with reference 
 to these Tables. 
 
 The first distinction I have taken is that between what I 
 have called (1) Uni-terminal and (2) Si-terminal Terms. 
 (1) Are terms which can only be used as P of Categorical 
 Propositions ; (2) are Terms which may be used as either 
 S or P of Categorical Propositions. 
 
 All Uni - terminal Terms are Adjectival, and the first 
 subdivision here is into what may be called Vernacular 
 Terms, e.g. red, like X, and Specific Terms, e.g. lanceolate, 
 pinnate, Chartist, aesthetic, " intense." (These would include 
 what Dr. Venn calls Special or Technical Terms (Empirical 
 Logic, p. 281). He goes so far as to say that it is philosophi- 
 cally more correct to call these terms, not English, but another 
 tongue, op. cit. p. 282.) Each of these again may be sub- 
 divided into Dependent or Systemic (implying a dependence 
 or relation of objects connected in some system, which may 
 be of any degree of complexity, from the simplicity of a class 
 or of any two related objects to the intricacy of a genealogical 
 tree, or even of the universe itself) and Independent. Any 
 one who has a knowledge of the system referred to by a 
 Systemic or Dependent Term can draw from a proposition 
 containing it a greater variety of inferences than is possible 
 in the case of propositions which contain only Independent 
 Terms (compare, e.g., E is F, and E is equal to F}; hence the 
 logical importance of this distinction, and hence also the 
 hopelessness of constructing a " Logic of Relatives." A 
 fortiori arguments are simply arguments of which some 
 terms are " dependent." All kinds of Terms are divisible
 
 TERMS. 2 1 
 
 into Dependent and Independent. Dependent Adjectivals are 
 such as like B, before C, equal to D, less pinnatifid tlian E,, 
 out-heroding Herod. 
 
 To the division into Urn-terminal and Bi- terminal Terms 
 there corresponds a very important division of Categorical 
 Propositions, namely, that into what I propose to call (1) 
 Adjectival Propositions and (2) Coincidental Propositions. (1) 
 are Categorical Propositions which have a Uni- terminal Term 
 for P, and cau neither be converted nor quantified ; (2) are 
 Categorical Propositions which have Bi-terminal Terms for 
 both S and P ; most of them can be converted, and those 
 unquantified Coincidentals which have Common Names for 
 Term-names can be both quantified and converted. This 
 distinction will be further considered with reference to 
 Quantification. 
 
 The subdivisions of (1) and (2) correspond. It is therefore 
 not necessary to consider them under both heads, and I have 
 accordingly in the Tables of Categorical Propositions (Tables 
 IV. XVI.) aimed at carrying out the division under one head 
 only, choosing (2) rather than (1) because all (1) are reducible 
 to (2), and it is with (2) that we are concerned in the logical 
 processes of Conversion, Reduction, etc. 
 
 The principal division of Bi-terminal Terms is into Attri- 
 bute Terms and Substantive Terms. Attribute Terms are 
 further divisible into (1) Vernacular and (2) Specific Terms ; 
 (1) and (2) subdivide into Complete Terms e.g. Steadfastness, 
 Stupidity and Partial Terms. The latter may be Definite 
 or Indcjlnite Singular e.g. His heroism, Some sestheticism ; 
 and Definite or Indefinite Particular e.g. Their hard-hearted- 
 ness, Much affection. Particulars are Distributive or Collective. 
 All the above species are Independent and Dependent. 
 
 Under Substantive Terms we have the species (1) Common 
 Terms, (2) Special Terms, (3) Unique Terms. Common Terms are 
 divisible into Vernacular and Specific Terms. The Vernacular 
 Common Terms of any language include Universal Terms 
 corresponding to every Term-name ; have determination (can 
 be defined), their determination being a sufficient guide to
 
 22 IMPORT OF PROPOSITIONS. 
 
 their application ; and are understood by any persons who are 
 said to know the language, without special training or informa- 
 tion, whether scientific, artistic, professional, or peculiar to any 
 trade, or section of society, and so on. Vernacular Names 
 form the bulk of any language, and we expect to find them 
 fully enumerated in any good ordinary dictionary. Specific 
 Names (including Technical Names, Slang and Cant words, 
 and so on) also have a maximum of Determination and may 
 be Universal, but to understand them needs some special 
 training or information. We find them partly in special 
 treatises and vocabularies, dictionaries of Slang, of History, of 
 Biography, in local Vocabularies, the Encyclopaedia, Inquire 
 Within, Hone's Day Book, etc. ; but they are to a large extent 
 unstatutable language. Of such expressions as cesthetic, Philis- 
 tine, take the bun, masker, Parnellite, we should not know where 
 to look for a printed explanation ; and such words are specially 
 difficult to translate, while Technical Names are probably the 
 easiest of any. Technical Names supply the material of 
 scientific Nomenclature and Terminology. 
 
 The Vernacular words of any language may be recruited 
 from time to time from Specific words, and the departments 
 of the latter, on the other hand, sometimes appropriate Vulgar 
 Terms. 
 
 Propositions having Specific Terms may be reduced to pro- 
 positions having Vernacular Terms, but many of the latter 
 cannot be reduced to the former. It is in this circumstance 
 that I find the justification for introducing this distinction in 
 a logical division. It is with reference to Specific Terms that 
 the case for Universes of Discourse seems to me most plausible. 
 It may no doubt conduce to clearness and conciseness that 
 in vocabularies of, e.g., Architectural Terms, Terms of Sport, 
 Slang, and so on, a limitation is expressly introduced once for 
 all (cf., however, post, Section on Predication and Existence). 
 But this limitation is itself limited, and the cases in which it 
 applies are generally indicated by a difference of type or some 
 similar device. 
 
 Vernacular Terms are divisible into Partial and Total ;
 
 TERMS. 23 
 
 Partial into Singular and Particular ; Singular into Definite 
 and Indefinite ; Definite and Indefinite (and every other 
 penultimate class) into Independent and Dependent. Par- 
 ticular Terms divide into Definite and Indefinite, and each of 
 these into Collective and Distributive. Total Terms ( Universals) 
 subdivide into Definite (Distributive and Collective) and 7ft- 
 definite (Distributive}. The Subdivisions of Specific Terms 
 correspond to those of Vernacular Terms. Examples of all 
 these classes, and of those which follow, are given in the 
 Tables of Terms. 
 
 By a Partial Term, is meant a Term of which the applica- 
 tion is not ex vi termini the whole sphere of the Term-name ; 
 by a Total Term, is meant a term of which the application is 
 ex vi termini the whole sphere of the Term-name. All E 
 includes every E, whether we look to determination or appli- 
 cation ; some E may happen to apply to all the Es, but cannot 
 have the same determination. 
 
 It may be noticed that many technical and other terms 
 which have the form have not the force of Dependent Terms ; 
 e.g. Fibres of Corti, Basis of Division, Consilience of Inductions, 
 Man-of-war, will of iron. 
 
 By Special Terms I mean such terms as Predicables, Conic 
 Sections, the days of the week, which resemble Common Terms 
 in that they are fully determinative, and may be used uni- 
 versally as in, All Conic Sections are curves and resemble 
 Unique Terms in being members of a limited, and as it 
 were organic system ; as in The five Predicables are Genus, 
 Species, Difference, Property, and Accident. Unique Terms 
 are different; for though, e.g., Apostle, Continent are fully 
 determinative, and we can say All Apostles, All continents, 
 we cannot regard Apostles and continents as being related 
 to the ttvelve Apostles, the five continents, in the same way as 
 all Predicables are related to the five Predicables, all Conic 
 Sections to the four Conic Sections. 
 
 Special Terms are divisible into Total and Partial ; these 
 into Simple (similar to Common Terms) and Synoptical (re- 
 garded as indicating members of limited groups). Simple
 
 24 IMPORT OF PROPOSITIONS. 
 
 Totals (Universals} are divided into Definite (Distributive 
 and Collective) and Indefinite (Distributive). Synoptical Totals 
 (Generals) may be (1) Summary or (2) Enumerative ; (1) 
 subdivides into Definite (Distributive and Collective} and In- 
 definite (Distributive) ; (2) subdivides into Distributive and 
 Collective. Partial Simple Terms are Singular (Definite and 
 Indefinite) and Particular (Definite and Indefinite, Distributive 
 and Collective) ; Partial Synoptical Terms are Unitary (Definite 
 and Indefinite} and Plurative ; Plurative are Summary (Definite 
 and Indefinite, Distributive and Collective) and Enumerative 
 (Distributive and Collective}. The final division, as before 
 remarked, is into Independent and Dependent in each case. 
 
 Unique Terms are subdivided into Whole ((a) having the 
 application of Term and Term-name the same, or (&) no 
 distinction between Term and Term-name) and Partial; 
 Whole into (b) Individual and (a) Total ; Individual into 
 Appellative, Descriptive, and Mixed; Totals (Generals] into 
 Summary and Enumerative; Total Summary into Appella- 
 tive, Descriptive, and Mixed (Definite and Indefinite), and the 
 Definites into Distributives and Collectives ; Total Enumeratives 
 into Appellative, Descriptive, and Mixed (Distributive and Collec- 
 tive}. Partial Terms are divided into Unitary and Plurative; 
 Unitary into Appellative, Descriptive, and Mixed (Definite and 
 Indefinite} ; Plurative divide into (1) Summary and (2) 
 Enumerative; (1) into Appellative, Descriptive, and Mixed 
 (Definite and Indefinite, Distributive and Collective} ; (2) into 
 Appellative, Descriptive, and Mixed (Distributive and Collective}. 
 All Enumeratives are, of course, Definite. 
 
 All Definite Partial Terms have an unique application. 
 Special Terms are (as already indicated) not limited in 
 application to one object or group of objects, or one or some 
 of a particular group, differing in this point from Unique 
 Terms. By Descriptive Terms, I mean Terms of which the 
 Term-names determine the distinctive characteristics of the 
 objects to which they apply ; by Appellative Terms, Terms 
 of which the Term-names are of the nature of (so-called) 
 Proper Names. A Mixed Term is a term which is partly
 
 TEEMS. 
 
 25 
 
 Descriptive and partly Appellative ; as the Shield of Achilles, 
 George Smith's brother. Any other (unexplained) names used 
 in this classification are, I hope, self-explanatory. I think 
 that the reason why such names as Gold, Water, the number 
 6, the half-sovereign, the word " and" the word " symbol" etc., 
 are always or mostly used in the singular number, is because 
 these names apply to things of which the intrinsic quality 
 does not vary from instance to instance. (Compare the 
 corresponding plural use of such names as peas, beans, etc.) 
 Attribute Names (cf. ante, p. 11) seldom take a plural, but 
 the denomination of Attribute Terms may be limited by the 
 term-indicator which, however, can never be numerical. 
 
 TABLE IV.] 
 
 TERMS. 
 
 UNI-TKRMINAL TERMS. 
 ADJECTIVAL TERMS. 
 
 ATTRIBUTE TERMS. 
 
 Bl-TERMINAL TERMS. 
 
 SUBSTANTIVE TERMS. 
 
 COMMON 
 TERMS. 
 
 SPECIAL 
 TERMS. 
 
 UNIQt'E 
 
 TJSKM.S. 
 
 TABLE V.] 
 
 ADJECTIVAL TERMS (VERNACULAR AND SPECIFIC). 
 
 Independent. 
 
 e.rj. "White ; 
 Strong ; 
 pinnatifid ; 
 non-connotative ; 
 quantified ; 
 hedonistic ; 
 Socratic ; 
 Aberdonian ; 
 Chartist. 
 
 Dependent. 
 
 e.g. more lanceolate than Lastrea 
 
 Dilatata ; 
 
 out-heroding Herod ; 
 more Chartist than Frost ; 
 like summer ; 
 true as steel.
 
 IMPORT OF PROPOSITIONS. 
 
 
 
 C- 
 02 
 
 Q 
 
 to 
 
 O 
 
 i 
 21 
 
 a * IT a .. S a 
 
 "S SO",- S &> 
 
 B 2-o 
 
 * 
 
 
 ! p ._ W CO 
 
 s^ 1:'3 
 
 ! ^ 'f- 1 -ij '-*.
 
 TERMS. 
 
 27 
 
 > *to M 
 
 _e_!*f! 
 
 s 
 
 2,2 .->"2 
 
 3.2.T* X co 
 
 = g 
 
 llillSp II 
 
 l?^n a ||3 ^^ 
 >> o 8 h2 ^ ""^^ 
 
 sai2-si?3j 
 
 :o- H^g^J^i^' 
 
 m J? i .5; u H *3 
 
 s i i!ft* fi l "j^i. 
 
 a " S " 2 5- > ^oitE 
 
 dill 
 
 ^^ |6|IS|^iS^5 
 
 ^2a5* g f|I f 
 
 ^oS^gr^ S 
 P -^ S^'p. H
 
 28 
 
 IMPORT OF PROPOSITIONS. 
 
 
 tr JB 
 
 J & ** 
 
 C - 
 O 
 
 SB. 
 
 N &. 1 " 
 
 TK 
 TE 
 
 nde 
 
 Ter 
 
 33 ""* O 
 
 gJT 
 
 c to 
 
 >:; 
 
 '.2 bj~ r 
 
 .a" g'4S^, 
 
 H*o S SI 
 
 ^ S el 
 
 cS*. 
 Sf.s * x 
 <O t to <a 
 
 S 2 ^ r^.S "S 
 
 5 -^ PT5---S 1^ 
 _| g EH g o o *^ 
 
 - y. /._; ~ 
 
 g os a o '" >>-=, 
 g c ^2-217* g> 
 
 "S 2 ' 'j2 .2 to S 
 S ~ -2 e'O ! n 9 f- 
 
 V o rs fc< .^ to cs 
 
 a J3 y "i ^ -M .
 
 TERMS. 
 
 29 
 
 . 
 
 ft ^ 
 
 - w 35- 
 
 1-3 SL| 
 
 r 
 
 a 
 
 -2 3- 
 
 s -2 Sl.S'* 
 "^ "** 5 Q' . ^ 1 "r"'-*- a ^ 
 
 .a-la* .2 *! 
 
 S v*< *fi * c* ") ^ 
 
 -^ oi~** K ^ o 3 
 
 "' O c3 c3 -*a cS 
 
 ^ 03 aJ 1 ' fl ^^= 
 
 V ^3 OQ ^ ^Q ^j L '^ J ^3 
 
 ^ -^ 
 
 s S 
 
 to g o ^ o 
 
 * "T^ ^ yntt ^ Kn 
 
 2.33s 
 
 Pi 
 
 ft S 
 
 *>_, 
 
 .2 * 
 
 3 i 
 
 W_ 
 
 
 o 
 
 -t> !-c 
 
 o > 
 
 H 
 
 
 
 
 
 h4 
 
 
 <4- 05 
 
 .2 
 
 <S 
 
 5 
 
 
 O'x 
 
 1 ' <o 
 
 
 PARTI 
 
 a5 
 M 
 
 a 
 
 ill 
 
 S 
 
 11 
 
 
 Cr-n 
 
 Ii 
 
 3 
 
 M 
 
 O 
 
 
 
 H 
 
 
 q 
 
 V 0? 
 
 rC 
 
 9*!*, *" 
 
 <4-> X ^4**H 
 
 O O^'O 
 
 p 
 
 HH 
 
 
 
 
 
 S 
 
 
 ft 
 
 
 !-* 00 
 
 03 
 
 
 03 
 
 
 c 
 
 H^ 
 
 o 
 
 
 
 
 
 
 
 S 
 
 S 
 
 *5 
 
 
 
 
 Q 
 
 v 
 
 03 
 
 ^ || 
 
 
 
 
 K 
 
 1 
 
 C c 
 
 *3 o> 
 
 
 
 ri 
 
 
 
 gO'g 
 
 >5 
 
 
 
 i 
 
 
 C,,^ S- 
 
 O5 2 
 
 
 
 a 
 
 5 
 
 
 53 M 
 
 
 
 M 
 
 
 ^j o> 
 
 
 
 
 H 
 
 ^ 
 
 5 
 
 c^3 
 
 
 IS 
 
 H 
 
 
 C L 
 
 
 
 X 
 
 P 
 
 2 
 3 
 
 H 
 
 H 
 
 1 
 
 Dependent 
 
 -il'S 
 
 - 
 Efia a 
 
 ,H^ 
 
 S 4l^ 
 J&j 
 
 
 
 
 T3 
 
 
 
 
 4 
 
 
 
 
 
 1 7" 
 
 H 
 
 
 
 
 
 k j -H 
 
 d 3 
 
 
 <D 
 
 c8 
 
 'o o 
 
 H i 
 
 'Tji 
 
 o'S 
 
 .2 5 
 
 <o % 
 
 1 
 
 -1 
 
 .2 S 
 
 SS" 
 
 ' /-. 
 
 H 4s; .^.s 2 s 5- 
 
 J^ 1 - i;> -* a 's S-aj 
 
 *- -5 S S 1 H &|S 
 
 O - tct- * H 7-1 '-C ;i. fl 
 
 ..
 
 30 
 
 IMPORT OF PROPOSITIONS. 
 
 *> * ' ~-fc3 Q) . , 
 
 ff K * >* C > < "aj 1 S 
 
 IfL 1 .ll!l|J 
 
 SJS S | 5l2"? J 
 
 gH | d j - *":3.S 
 
 ^ jR ? 8 8^ <u ^ 
 
 H P * 1 fl s A! A 
 
 <.Sg^ li^rfSA*^ 
 
 
 o . _ i 
 
 
 
 
 W H fi ^ o 
 
 g ^1^ I > 
 
 05 
 
 p tc a "ts <u 
 
 tS 1 "" 1 '" S 
 
 M 
 H 
 
 H n ^ P- ^ * -'^ 
 
 <a S, * 
 
 -Ct3 3 g 3 fci 
 
 
 S H fK^**^ 
 
 
 i 
 
 E 
 
 Q 5 "^JJ 
 
 S * ^|||lc 
 
 02 
 
 
 -rH . 
 
 1 
 
 09 
 
 J3-i "8 <u o e8 < 
 a rs "* > o 
 
 ^ c sS.,^ 
 
 -3 .) , 2 
 
 o 
 
 
 
 S5 
 
 W ^ &* S ^*'^ yi ^ (-* 
 
 C S >> oo J; **>~5 
 
 pfc 
 
 
 a, | c c i i"ce c 
 
 52. 
 
 S S If^"^^ ^'o'S 
 
 ^ su <J o ^^5 
 
 2 
 1 
 
 i. co ^ ^j 1 " 1 tao S Si 1 ' 
 
 g9. S ozSo-s.s 
 
 sr S"'"S c'g^; 
 
 "* * QJ O p^ ^ 
 
 EC O GO O 
 
 fa 
 
 ^^ 
 
 
 m 
 
 
 
 B 
 
 o5 * J "i s 
 
 ^ ^7 > ^'s|| [ ^^ 
 
 02 
 
 5 co 4 
 
 "^ ^ ^ H =* s 1 '^ H *" L 
 
 S 
 
 f" 1 a | ^g-S c 
 
 1,^5'oS "S o ^*o 
 
 M 
 
 PI oo Hw " r <"Ho 
 
 /^? t"^ OS ' ~* m ' "' ^ *~^ 
 
 H S Q H ^ ^ ^',2 r-=i 
 
 toj " " * 1^ o^c-^^- " 
 
 jj S w ^ ^ ** 2 s 
 
 5T t, ^ Q 'w>'3) ^ 5* 
 
 ^J *3 ^H C^- oo *2 
 
 ^^ '^ *l -1 "* C" -2 Oi r ~ l ^ 
 
 H => _K_ 
 
 
 o cc 
 
 
 H <u o o 
 
 ij P " 5 * 3 
 
 * J 
 
 ~ Q g5 |sa-2 t iT*i 
 
 1 ~' E aJ 
 
 ^^ 03 Q^ ft ^ bD O *"' 
 
 o ^ ^ -G ^^ ^ 
 
 HH Q; d "^ 'J O ^ O 
 G. F-H S6-I ^ S v 
 
 QK i 3 ^ 
 
 yj ^ Oi,-* to C g p^, 
 
 ^3> - 43 S '5 '*-' 
 
 Sll 
 
 5<J *) O Q <r^ 
 
 i-3- 1 Sl 
 
 -i^iS = 
 
 ^ & "S Agr*! 
 
 " S g* 5 ! * "^ B . 
 
 H g_a,| c 1 ^.! 
 
 1 p fl""*^^ a,'*^ 
 
 
 S "Sc 5 j 
 
 S "^ "g "S g ci --"S 
 
 cc 
 
 l_4 H ^ ^ ^> ^ ** S 
 
 ^ ^. S f3 FH P 
 
 a 
 
 ^2 . . <u' * O* 
 
 c? w <s 2'a"S eS t 5 > 
 
 w 
 
 c Q ri 'S "3 A 
 
 *~ ' tn ." o o ^ S ^ 
 
 f-l 
 
 S5 
 
 
 J 
 
 
 
 S 
 
 "S * ^ 
 
 ^ ^,0 0^5 ^ 
 
 i 
 
 E 
 
 02 
 
 H S 5 '3 u o 
 
 
 
 ^ Ed 'W *u ^ 
 
 ^S R E^ i2 Z'-^ 
 
 1 
 
 o N ? a 
 
 H S" |SJ 
 
 g *|||.| 
 
 - S 
 
 _^_ 
 
 
 K> CO * 4) , o 
 
 n g w 5 u ^ . 
 
 *> g S ^v'S S- * 
 
 ri H E > "e PH^OOV 
 
 f 00 S 2 c? ^ u_i ' ^* ^ <~ 
 
 > M H , g ti^ _ C 
 
 -|3 ce ll ) 7^ - fi i 
 
 o 3
 
 TERMS. 
 
 31 
 
 TABLE XL] 
 
 INDIVIDUAL TERMS (UNIQUE). 
 (APPELLATIVE, MIXED, AND DESCRIPTIVE.) 
 
 Independent Terms. 
 
 e.g. The last man ; the pre- 
 sent Prime Minister ; the 
 greatest poet ; the sun. 
 
 Julius Caesar; Mary; Conrad ; 
 The Iliad ; Athena ; George 
 Eliot ; Sir Walter Scott ; Van- 
 couver's Island ; " Long- 
 shanks ; " Melpomene [was the 
 Muse of tragic poetry]. 
 
 Dependent Terms. 
 
 e.g. The circumference of 
 the earth ; the Last of the 
 Mohicans ; Jarues Thompson's 
 second brother. 
 
 The Inferno of Dante ; 
 George Eliot's Dorothea; 
 the CEdipus Tyranuus of 
 Sophocles. 
 
 TABLE XII.] 
 
 UNIQUE UNITARY TERMS. 
 (APPELLATIVE, MIXED, AND DESCRIPTIVE.) 
 
 DEFINITE TERMS. 
 
 INDEFINITE TERMS. 
 
 Independent 
 Terms. 
 
 Dependent 
 Terms. 
 
 Independent 
 Terms. 
 
 Dependent 
 Terms. 
 
 c. g. This 
 
 e.g. That son 
 
 6.0.-) 
 
 e.g. One of the 
 
 Apostle ( = this 
 one of the 
 
 of Jacob ( = that 
 one of the sons of 
 
 One, 1 of the 
 Some j Apostles. 
 
 sons of Jacob. 
 One of Hesiod's 
 
 Apostles). 
 
 Jacob). 
 
 one i 
 
 Muses. 
 
 This Muse (- 
 
 That Muse of 
 
 One of the 
 
 
 this one of the 
 
 Hesiod (= that 
 
 Muses. 
 
 
 Muses) ; Euphro- 
 
 one of Hesiod's 
 
 
 
 syne [was one of 
 
 Muses). 
 
 
 
 the Graces]. 
 
 

 
 32 
 
 IMPORT OF PROPOSITIONS. 
 
 55. 
 
 S 
 
 02 S 
 
 g 
 
 H 8 
 
 H 
 ! 
 
 tf 
 & 
 
 nJ 
 PH 
 
 H 
 & 
 
 O" 
 i i 
 
 Sq 
 & 
 
 Rc~ 
 
 E j*i i ^ 
 
 ^ ^-? 
 
 4_t4-4-tl 
 
 2 o S 
 
 'J3 fe ,X o 2 
 
 ^uL^s O tS'43 
 !^ &>^ 1 '3 
 
 |^ EH 
 
 S*" < 
 
 3
 
 TERMS. 
 
 33 
 
 TABLE XIV.] 
 
 UNIQUE PLURATIVE TERMS (ENUMERATIVE). 
 APPELLATIVE, MIXED, AND DESCKIPTIVK. 
 
 I 
 DISTRIBUTIVE TERMS. 
 
 I 
 COLLECTIVE TERMS. 
 
 Independent 
 Terms. 
 
 Dependent 
 Terms. 
 
 Independent 
 Terms. 
 
 Dependent 
 Terms. 
 
 e.g. The nearest 
 
 e.g. The nearest 
 
 e.g. The largest 
 
 e.g. The nearest 
 
 and the farthest 
 
 and second near- 
 
 and second largest 
 
 and the farthest 
 
 of the planets 
 
 est of the planets 
 
 of the Continents 
 
 of the planets of 
 
 [have elliptical 
 
 of our Sun [are 
 
 [have together an 
 
 our Sun [are Mer- 
 
 orbits]. 
 
 between the Sun 
 
 area of 28 million 
 
 cury and Nep- 
 
 A g 1 a i a and 
 
 and the Earth]. 
 
 square miles]. 
 
 tune] ; the eldest 
 
 Thalia [were 
 
 M n e m e and 
 
 A g 1 a i a and 
 
 and the youngest 
 
 Graces]. 
 
 Melete of Mt. 
 
 Thalia [were two 
 
 sons of Jacob 
 
 
 Helicon [were 
 
 of the Graces], 
 
 [were Reuben and 
 
 
 worshipped by 
 
 
 Benjamin]. 
 
 
 the Boeotians]. 
 
 
 M n e m e and 
 
 
 
 
 Melete of Mt. 
 
 
 
 
 Helicon [were two 
 
 
 
 
 of the Bceotian 
 
 
 
 
 Muses]. 
 
 TABLE XV.] 
 
 UNIQUE TOTAL TERMS (ENUMERATIVE). 
 APPELLATIVE, MIXED, AND DESCRIPTIVE. 
 
 DISTRIBUTIVE TERMS. 
 
 COLLECTIVE TERMS. 
 
 Independent 
 Tirms. 
 
 Dependent 
 Terms. 
 
 Independent 
 Terms. 
 
 Dependent 
 Terms. 
 
 e.g. The largest, 
 
 e.g. The first, 
 
 e.g. The largest, 
 
 e.g. The first, 
 
 second largest 
 
 second . . . and 
 
 second largest 
 
 second . . . and 
 
 . . . and smallest 
 
 seventh days of 
 
 . . . and smallest 
 
 seventh days of 
 
 of the planets 
 
 last week [were 
 
 of the planets 
 
 last week [were 
 
 [have each an 
 
 rainy days]. 
 
 [are the satellites 
 
 the seven most 
 
 elliptical orbit]. 
 
 The Agamem- 
 
 of our sun] ; the 
 
 wretched days of 
 
 Aglaia, Thalia, 
 
 non, Choephori, 
 
 daughters of 
 
 my life]. 
 
 and Euphrosyne 
 
 and Eumenides 
 
 Apollo [were Clio, 
 
 The Agamem- 
 
 [were daughters 
 
 of ^Eschylus [are 
 
 Melpomene, etc.]. 
 
 non, Choephori, 
 
 of Apollo]. 
 
 magnificent 
 
 Aglaia, Thalia, 
 
 and Eumenides 
 
 
 plays]. 
 
 and Euphrosyne 
 
 of jEschylus 
 
 
 
 [were the three 
 
 [form the 
 
 
 
 Graces]. 
 
 Oresteia].
 
 34 
 
 IMPORT OF PROPOSITIONS. 
 
 S W-S 
 
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 f=* 
 
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 Is 
 
 L 
 
 
 
 
 Lg 
 
 
 Q 
 
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 q^ 
 
 2n 
 
 B 
 
 5 
 
 
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 PH 
 
 
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 W 
 
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 y. 
 
 
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 J 
 
 
 
 
 
 
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 O 
 
 &T 
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 ^o 
 
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 PH 
 
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 8-1 
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 64 05 T3 _fi e r3 K S 
 
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 NOTE ON DEFINITION AND CONNOTATION. 35 
 
 SECTION IV. 
 
 NOTE ON DEFINITION AND CONNOTATION. 
 
 The Definition of a word, it is said, sets forth its meaning ; 
 and the Meaning of a word, as distinguished from its 
 application, is frequently said to be its " connotation." 
 
 But what is the connotation of a word or name ? According 
 to some, it is the whole of the attributes common to the things 
 called by that name. This is the view of Jevons and some 
 other writers, and, according to Dr. Venn (Empirical Logic, 
 p. 183), it is shared by Dr. Bain. Mr. Keynes, however 
 (cf. Formal Logic, 2nd ed. p. 26), thinks Dr. Bain's opinion to 
 be that the connotation of a word comprises, not all the 
 attributes common to the things to which it applies, but 
 only those which are independent of one another. The 
 difficulty, not to say impossibility, of deciding what qualities 
 (if any) are independent, seems to be an insuperable objection 
 to this latter view. The opinion that any name of which we 
 know the application (cf. Jevons, Elementary Lessons in Logic, 
 Less, v., etc.) connotes all the " peculiar qualities and circum- 
 stances" which we know to belong to the thing named, 
 involves the admission that proper names are among the 
 most connotative of any ; and this admission Jevons makes, 
 or rather insists upon. But the proper name of a person not 
 known individually, must be allowed, even by Jevons him- 
 self, to have only a minimum of connotation, while a class- 
 name applied to any object not known individually may 
 convey a maximum of connotation. Jevons confuses (1) the 
 information conveyed by a name, without any individual 
 knowledge concerning the very thing or things named, and 
 (2) the information gained by individual knowledge of the 
 very thing or things indicated by a name, and consequently 
 associated with and suggested by the name. The view that 
 (2) is included in connotation involves as a consequence that 
 the same name may have different connotations to different
 
 36 IMPORT OF PROPOSITIONS. 
 
 people. And there is indeed a further confusion here, besides 
 the one mentioned above a confusion, namely, between (1) 
 the qualities which a thing is 'known to possess, and (2) the 
 qualities which it actually does possess (cf. Keynes, Formal 
 Logic, 2nd ed. p. 27, distinction between intension, connotation, 
 and comprehension}. Taking connotation to include (2), it is 
 clear that we do not, and cannot, know the whole connotation 
 of any name whatever. And it is plainly absurd that the 
 meaning of a name should be said to be something which no 
 person has ever understood to be conveyed by it. 
 
 In the case of any class-name, if it is said that it connotes 
 all the attributes known to be possessed in common by the 
 things to which it is applied, it follows that no universal 
 synthetic propositions are possible ; and worse than this, that 
 a multitude of significant names must have such a voluminous 
 meaning, and so many words the same meaning, as would 
 make language hopelessly unmanageable and confused. Since 
 our thought is discursive must proceed by successive steps of 
 intuition we need corresponding conditions in language; 
 that is, we need limited definitions and clearly marked 
 differences of meaning in different words. 
 
 It seems best to say that what a name connotes (what is 
 included in its determination) is, those attributes on account of 
 which we apply the name, and in the absence of any of which 
 we should not apply it. (Cf. Mill, Logic, Bk. i. ch. ii. 5, 
 p. 38, 9th ed., and Bk. i. ch. viii. 3, p. 156 ; also Keynes, 
 Formal Logic, 2nd ed. p. 25.) It may happen, and generally 
 does happen, that the attributes connoted by a name are in 
 our experience inseparably connected with other attributes 
 which it does not connote ; but it is not on account of these 
 latter that we apply the name in question. I believe, indeed, 
 that it is probable that every attribute is one of an unique 
 set, all of which are inseparably connected (cf. Section on 
 Ground of Induction}, and that the more our knowledge 
 grows, the fuller and surer will be the suggestions which, 
 from association, each name carries with it. But this increase 
 of knowledge concerning the things indicated by any name is
 
 MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 37 
 
 quite different from increase of the connotation of the name 
 itself; and increase of the former kind takes place to a far 
 greater extent than of the latter kind ; though, no doubt, there 
 can hardly be change of connotation except as the result 
 of an increase of knowledge. 
 
 SECTION V. 
 
 THE MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 
 
 ^Reference to the various definitions of Abstract and Concrete 
 Terms given in logical handbooks is sufficient to show that 
 the distinction is one involving some difficulty. In Tfie 
 Oxford Elements of Logic (1816) adjectives only e.g. white, 
 round, long are recognised as Concrete Terms (cf. p. 16); 
 such names as man, house, fairy, are not classed under the 
 head either of Abstract or Concrete. Dr. Abbott in his 
 Elements of Logic (1883, cf. pp. 4, 5, 83, 84, etc.) seems 
 undecided how to class adjectives ; Jevons, in Studies in 
 Deductive Logic (2nd ed. p. 4), omits them altogether ; but in 
 his Elemental- if Lessons in Logic (p. 21, 7th ed.) he says that 
 we must " carefully observe that adjectives are concrete, not 
 abstract." Again, while in Studies in Deductive Logic (p. 1) 
 lie allows only names that can stand as the Subject of a 
 proposition to be Categorematic, thus by implication excluding 
 adjectives from the category of terms altogether, in the 
 Elementary Lessons (p. 18) he admits adjectives among the 
 words " which stand, or appear to stand, alone as complete 
 terms." He explicitly says (Elementary Lessons in Logic, 
 p. 21 ; Studies in Deductive Logic, ch. i. 2, pp. 1, 2) that 
 lie was conscious of a difficulty, and the presence of this to 
 his mind is clearly betrayed by these inconsistent and con- 
 fused statements. Jevons' conclusion seems to be that 
 abstractness must be considered " a question of degree " (cf. 
 Studies, p. 2). No doubt it is a question of degree if by
 
 38 IMPORT OF PROPOSITIONS. 
 
 an abstract term is meant a term, the application of which 
 presupposes a process of abstraction every adjective, every 
 common term, every term applying to an attribute, is applied 
 as a result of abstraction ; even a " proper name " is in this 
 sense abstract, for, though not applicable to more than one 
 individual in the same sense, it is applicable to that one at 
 different times and under different circumstances, and in using 
 it as a permanent appellation, abstraction is made from these 
 times and circumstances. This is not, of course, the sense in 
 which Abstract is understood when used in antithesis to 
 Concrete. According to Mill (Logic, i. 29, 9th ed.), "A 
 concrete name is a name which stands for a thing ... as 
 John, the sea, this table . . . white." " An abstract name 
 is a name which stands for an attribute of a thing," e.g. white- 
 ness. Here the distinction seems to depend on discriminating 
 between a Subject of Attributes and Attributes of a Subject. 
 It seems clear that by thing as used here, Mill means just a 
 subject of attributes. But what reason is there for calling a 
 term which applies to attributes Abstract, while a term which 
 applies to a subject is called Concrete ? Attribute implies 
 subject as much as subject implies attributes as much as 
 parent implies child, or half implies whole. As Mill himself 
 says (op. cit. i. 5 3), " the condition of belonging to a substance " 
 (subject) is " precisely what constitutes an attribute." In 
 what respect is the term redness, which applies to an attribute 
 of red things, more abstract than the term red thing, which 
 applies to a thing which has the attribute ? A further 
 difficulty on Mill's view would arise with reference to the 
 predicates of such propositions as, e.g., Perseverance is admir- 
 able. If adjectives are concrete, we have here a " concrete " 
 Predicate asserted of an " abstract " Subject. Mr. Stock, Deduc- 
 tive Logic (1888, pp. 28, 29), says, " 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." " Those terms
 
 MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 39 
 
 only are called abstract which cannot be applied to substances 
 at all." (Op. cit. p. 27. The italics are mine.) Compare 
 also what is said on pp. 24, 25. 
 
 If \ve fall back upon Whately (Logic, 9th ed. p. 81), we 
 find that he describes Abstract Term as a term which is 
 applied to a "notion derived from the view taken of any 
 object " when not considered " with a reference to, or as in 
 conjunction with, the object that furnished the notion." As 
 a term applying to an attribute is, ex vi termini, considered 
 with such " reference " and " conjunction," we seem driven to 
 the conclusion that what Whately ought to mean, and what 
 must be meant by Abstract Term as distinguished from Con- 
 crete, if there is a consistent meaning in the distinction, is that 
 an Abstract Term is the .name of a logical " Concept " some- 
 thing complete in itself and isolated from all else totus teres 
 atque rotundus, involving no reference to attributes, as a term 
 applying to a subject does, and no reference to a subject, as 
 a term applying to an attribute does. Here there is indeed 
 a very marked distinction between the objects indicated by 
 Abstract Terms and by other terms. But it remains to ask 
 whether it is possible that Terms that is, the Subjects 
 and Predicates of propositions can indicate such logical 
 Concepts. 
 
 The meaning here assigned to Concept is substantially that 
 recognised by Mansel, who, in common with some other 
 logicians, holds that Logic is concerned with Concepts, and 
 Concepts only. Locke's " Abstract Idea " seems to correspond 
 to Mansel's " Concept," and he says that the " names of 
 abstract ideas" are "abstract words" (Essay, Bk. iii. ch. 8, 
 1). But, according to Locke, "all our affirmations . . . 
 are only in concrete " (loc. cit). With this view I agree, only 
 going so far beyond it as to hold that not only our affirmations, 
 but also our negations, are " only in concrete." For of such a 
 " concept " nothing but itself could be asserted, and nothing 
 could be denied but the negative of itself ; if isolated and 
 independent, it could have no relations whatever to things 
 in space and time. It would be like one of Leibnitz's Monads,
 
 40 IMPORT OF PROPOSITIONS. 
 
 having " no windows " by which anything could get into or 
 out of it ; a closed, solitary, impregnable whole, incapable of 
 diminution, increase, or division, or alteration of any kind. 
 
 It seems indisputable that a " concept " as thus denned (cf. 
 Mansel, etc.) must be quite incapable of alteration. Altera- 
 tion of any " concept " ABC would mean that some other 
 " concept "-^e.g. AB, or ABCD is substituted for it. If not 
 isolated and independent, it would, of course, be related to all 
 other things, like any ordinary idea. Again, if a " concept " 
 were something complete, the name applying to it and deter- 
 mining its character would have to indicate relations to every- 
 thing in the world, for such relations are among the attributes 
 of every constituent of the universe. Indeed, one such name 
 would describe the universe and all things in it, and there 
 need be only one name at all, and no propositions. But, 
 without pushing the thing to such an extreme, it must be 
 allowed that if all terms applied to independent or complete 
 concepts, all propositions would be reduced to the A is A 
 type ; any illustration, any bringing into connection, any 
 movement of thought at all would be impossible. Indeed, 
 assertion itself would be impossible ; for A is A, taken strictly, 
 has absolutely no predicative force, and merely attempts to 
 assert a necessary presupposition of all significant assertion 
 (cf. post, p. 52), and even, I think, of thought itself. 
 
 I think that not only must it be impossible for names 
 applying to monadic concepts to be the terms of propositions, 
 but also that such concepts could not be objects of thought at 
 all. This seems to follow directly from the acceptance (1) of 
 the Law of Relativity (Semper idem sentire et non sentire ad 
 idem recidunt), and (2) of that definition of concept according 
 to which it is totus and teres something complete in itself 
 and wholly unrelated. Nothing is an object of knowledge 
 unless it is an identity in diversity, a permanent amid change, 
 and unless it is like some things and unlike other things. 
 Whatever is comparable with other things must be connected 
 with them in some system, e.g. in space ; but members of a 
 system are doubly related, namely, both to one another and to
 
 MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 41 
 
 the unity of which they are members, hence the members of a 
 system can never consist of such essentially isolated entities 
 as concepts. 
 
 But the name Concept may be differently defined, e.g. 
 as the " mental equivalent of a general name." Of the 
 existence of such mental objects there can be no doubt. But 
 I should demur to this definition, because I should maintain 
 that it draws an arbitrary distinction between the mental 
 equivalent of Common Names and that of other names, e.g. 
 Proper Names. Have I not an idea as truly general, corre- 
 sponding to, e.g., Alfred Tennyson, as to snow or horse ? My 
 idea of him must be one that applies throughout all variety 
 of time, place, and circumstance, just as my idea of snow or 
 horse applies under a variety of individual manifestations. 
 And there seem many reasons in support of the view that 
 Common (and Proper) names are not the names of concepts 
 (in the sense of mental equivalents}. For if they are (1) we 
 are left without any term for the object from seeing (or in 
 some way knowing) which we have got the idea. (2) When 
 a familiar object, e.g. a bird, is seen, some such mental equiva- 
 lent must accompany the sight of it as accompanies the hear- 
 ing of the word, otherwise it could not be recognised. 
 
 (3) In the case of a word having two distinct applications 
 e.g. box, page we determine which of the applications we are 
 to take by reference, not to a concept, but to a thing of which 
 we may have a concept ; because what any concept is must be 
 determined by what the thing is of which it is the concept. 
 
 (4) The idea called up in the mind by a Common or other 
 name, is an idea which differs widely in different minds, and 
 in the same mind under different circumstances (as of context, 
 interest, etc.). Thus the same name would have an indefinite 
 multitude of different meanings. If we say that in every 
 unit of all this multitude there is some element of similarity, 
 and that it is this which is meant by mental equivalent, that a 
 concept is a kind of mental type, e.g. a kind of Bird-in-itself, 
 I would ask, Can it be recognised as a type unless considered 
 in conjunction with its ectypes, the copies in which it is
 
 42 IMPORT OF PROPOSITIONS. 
 
 exemplified ? I should say that the person whose mental 
 equivalent of a name (common or other) is most perfect and 
 adequate, is the person in whose mind that name calls up the 
 greatest fulness of well-ordered particulars, so connected and 
 arranged as to give most prominence to what is most important ; 
 so presented, in fact, as to exhibit clearly the law or type 
 common to all ; here the element or elements of similarity 
 are exhibited in the greatest fulness of relationship. It would 
 be generally allowed, I think, that an expert in any subject 
 is likely to have more perfect mental equivalents of the names 
 special to that subject than those who are comparatively 
 unacquainted with it ; or that any one has a better mental 
 equivalent of the name of a person whom he knows well than 
 he has of those with whom his acquaintance is but slight. 
 It seems to me that, for instance, I myself have beyond com- 
 parison a clearer, more satisfactory, and, I suppose, truer idea 
 called up by names of things or persons that I am well 
 acquainted with, than by those of things or persons that I do 
 not know, or know but slightly, or am only learning to know. 
 And the superiority seems to consist in the greater fulness and 
 completeness of the corresponding ideas in the first case. 
 Things with which one is familiar become clearer and more 
 real in proportion as one knows more about them the unity 
 of a system becomes more striking in proportion as one 
 realizes more fully the inter-relations of the plurality which 
 it embraces. This is quite compatible with the fact that 
 an influx of fresh information, especially in an unfamiliar 
 region, may sometimes involve one in great confusion. 
 
 As to the mental equivalents which actually occur to people's 
 minds in using names, experiment seems to show that 
 these differ exceedingly in different cases. Such a word as 
 animal, for instance, will call up to one person's mind the 
 name simply printed, or written in a particular handwriting, 
 or printed on the outside of a particular book ; or it may call 
 up the image of a " picture alphabet " with illustrations of 
 animals, or some story of animal intelligence, or a pet animal, 
 or the first animal one cared for, or the cat of the house, or
 
 MEANING OF ABSTRACT AND CONCRETE, AND OF CONCEPT. 43 
 
 an idea of the movements made in speaking the word, or some 
 striking delineation of an animal seen in a magic-lantern 
 exhibition or a picture gallery, or Noah's ark, or a mere shape- 
 less moving mass. If one dwells upon the word, an immense 
 succession of ideas may occur to one; in rapid reading or 
 speaking, probably only one or two. What seems very often 
 to happen in the latter case is, that one just thinks very 
 transiently of the word itself, with a satisfactory, though 
 evanescent, consciousness of understanding its meaning and 
 application. If in reading or listening one meets a word of 
 which one does not know the meaning, one is instantly 
 arrested by a feeling of dissatisfaction, due to the recognition 
 of a hindrance to comprehension. As an illustration of what 
 I mean, I may refer to what happens when, in looking 
 rapidly through a passage in some' tolerably familiar language 
 with a view to translating it, one comes here and there upon 
 words of which one does not know the meaning. The trans- 
 lator, the moment he sees the other words, and without any 
 pause to realize their full import, is aware that he knows 
 their signification ; and he is aware, just as instantaneously, 
 that he does not know the meaning of the strange words. 
 What perhaps often happens to some people, in connection 
 with Common and Proper names, is that these call up in the 
 mind a kind of " generic image." E.g. the word horse may 
 suggest a sort of vague image, like a horse seen at a little 
 distance in a fog, which is definite enough not to be mistaken 
 for any other creature, but not definite enough to be identified as 
 of this or that breed, colour, size, etc., much less as a definite 
 individual : quadruped may suggest merely four vague elemen- 
 tary legs, supporting an elementary body, like a child's draw- 
 ing and so on. Our image of many acquaintances, and even 
 friends, may be very vague, just definite enough to enable us 
 to know them when we see them, but by no means definite 
 enough to enable us to accurately draw or describe them, or 
 perhaps even to say by what sign or signs we recognise them. 
 Butler (Sermon I. note 2) puts the case of a man whom 
 he supposes to " go through some laborious work, upon promise
 
 44 IMPORT OF PROPOSITIONS. 
 
 of a great reward, without any distinct knowledge what the 
 reward would be." The state of this man's mind with refer- 
 ence to the reward must, I imagine, correspond in essentials 
 with the state of mind of a person dwelling on a Common 
 Name withdrawn from context ; but, of course, names ordinarily 
 occur to us with a context which helps to determine their 
 mental equivalent. 
 
 (II.) OF PROPOSITIONS AS WHOLES. 
 (A. ) C ATEGOKICAL PROPOSITIONS. 
 
 SECTION VI. 
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 
 Formal (most General) Import of Catcgoricah. 
 
 It seems convenient to discuss Propositions in immediate 
 connection with Terms, the constituents of all Propositions. 
 Proposition may perhaps be defined quite generally as a 
 sentence or significant combination of words affirming or 
 altogether denying unity (in difference). 
 
 Each of the principal forms of Proposition has, of course, 
 its own special definition. Propositions may be divided into 
 (1) Categorical, (2) Inferential, and (3) Alternative ; (2) may 
 be subdivided * into Hypothetical, e.g. If D is E, D (or F) is 
 G ; and Conditional, e.g. If any D is E, that D is F. The 
 division is exhibited in tabular form, thus : 
 
 PROPOSITIONS. 
 
 I ! I 
 
 Categorical Propositions. Inferential Propositions. Alternative Propositions. 
 
 I ! 
 
 Hypothetical Propositions. Conditional Propositions. 
 
 1 Cf. Keynes, Formal Logic, 2nd edition, pp. 64, 65 ; also post, Section on 
 Inferential Propositions.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 45 
 
 I assume that any proposition would be admitted to be the 
 expression of a judgment, and capable of being defined as 
 such. This mode of definition is, however, subject to two 
 inconveniences ; for, in the first place, until a definition of 
 judgment has been given, we have defined ignotum per 
 irjnotum ; and, in the second place, it tends to a confusion 
 of standpoints if, after having treated Terms, the elements of 
 Propositions, as applying to Things, we define Proposition as 
 the mere expression of a psychological process. Unless we 
 apprehended things we could, of course, have neither ideas of 
 them nor names of them ; unless we judged we could neither 
 think Propositions nor express them; and it is true that 
 Logic is concerned with "what we ought to think." But 
 Apprehension and Judgment, considered as mental processes, 
 are the concern of Psychology, and Logic is concerned with 
 what we ought to think only because we ought to think of 
 things as they are. There is no more reason for defining Pro- 
 position by reference to Judgment, than for defining Term by 
 reference to Apprehension. If Terms are concerned with 
 things, Propositions are concerned with the same things. Our 
 things may, of course, be thoughts, or thoughts of thoughts, 
 and so on, to any degree of " Re-representation," but at any 
 point in the regress what our terms apply to is surely the 
 objects thought about, and not the apprehension of those 
 objects ; what our Propositions import is surely something 
 about those things other than the fact (however indisputable) 
 that we frame a judgment concerning them. However re- 
 representative the objects to which our terms apply, our 
 thought of the thing named would be impossible without our 
 having an idea which is something other than the thing 
 intended to be indicated by the name. The presence of 
 such an idea is as inevitable as the nervous change which 
 is supposed to accompany all change of consciousness. For 
 instance, let my term be King's College Chapel, Cambridge. 
 Here the object named is a construction of stone and mortar 
 distant, perhaps, more than a hundred miles from my present 
 position in space. But without an idea present to my mind
 
 46 IMPORT OF PROPOSITIONS. 
 
 and other than the object named, I could not hear or use the 
 term with intelligence. And if my term is, the thought which 
 I had two minutes ago of King's College Chapel, the object 
 named, and the accompanying idea, though not so diverse 
 as in the previous case, are equally distinct. 
 
 A Categorical Proposition might be defined as, A Proposi- 
 tion which affirms (or negates) Identity of Denomination in 
 Diversity of Attribution, and is of the form 
 
 S copula P. 1 
 
 But this definition would admit Propositions of the form 
 A is A, 
 
 because the second A differs from the first A in implication, 
 since it is predicated, while the first A is predicated of. A is 
 A, however, is a locution which has only the form and not the 
 force of a Proposition. A significant Categorical Proposition, 
 a Proposition in which the Predicate adds something to the 
 Subject, may be defined as, A Proposition which affirms (or 
 negates) Identity of Denomination in Diversity of Determina- 
 tion. (Or if we consider directly the Things which are named 
 by our terms rather than the terms themselves, we may define 
 as follows : A Categorical Proposition is a Proposition which 
 affirms (or negates) quantitive Identity in qualitive Diversity.) 
 
 Thus a Categorical Proposition asserts complete coincidence 
 or absolute non-coincidence of S and P. 
 
 It will perhaps not be superfluous to illustrate the applica- 
 tion of my definition by a few simple examples. In All 
 birds are animals a proposition which (understood with an 
 implication of the knowledge which we possess concerning the 
 
 1 In a class there is also one-in-many or many-in-one, namely, a qualitive 
 one in a quantitive many, or similarity of character in a plurality of things. 
 There is a third kind of one-in-many, where we have a system of Subjects of 
 Attributes related to each other and to a common whole (a quantitive many in a 
 quantitive one). Mill (Logic, ii. 395) considers the importance of the dis- 
 tinction upon which my definition turns the distinction, namely, between a 
 thing being identical (numero tantum), and things being similar (specie tantum). 
 The same distinction is discussed by Dr. James Ward (Encycl. Brit. 9th ed., 
 part 77, p. 81a, art. "Psychology "), who uses the terms individual identity and 
 indistinguishable, resemblance.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 47 
 
 relation between the classes Birds and Animals) might be 
 represented as in the first diagram what is asserted is that 
 the denomination of All birds is the very same 
 as the denomination of animals. But not of 
 all animals, but only of those animals included 
 by circle B that is, some animals. The 
 denomination of All birds is found to coincide 
 with, to be in short, the denomination of the 
 some animals of the proposition under con- 
 sideration. This coincidence of denomination 
 of S and P might be represented thus : 
 
 That the determination of All birds is differ- 
 ent from that of [so??i] animals is obvious. 
 
 Take again, Some vertebrates are quadrupeds (understood, 
 as the previous example, in its full material signification). 
 
 The continued identical existence of 
 the things indicated by Some vertebrates 
 is just the same as that of the things 
 indicated by [some] quadrupeds that is, 
 the denomination of S and P is iden- 
 tical. The determination of Some verte- 
 brates is, of course, different from that of [som] quad- 
 rupeds. In the proposition, Those men are my three 
 brothers, the S denominates the quantitive- 
 ness the continued identical existence of 
 certain individuals, say, AB, CD, and XY; 
 and the P denominates the very same 
 quantitiveness, the same continued exist- 
 ence under whatever change of attributes 
 i.e. the quantitiveness of the identical persons, AB, CD, 
 and XY. Hence, wherever two terms have identical 
 denomination, their application is the same ; 
 what the one term is the name of, the 
 other term is the name of. The determina- 
 tion of Those men differs, of course, from 
 the determination of My three brothers. 
 Again in, This musician is a painter, the
 
 48 
 
 IMPORT OF PROPOSITIONS. 
 
 denomination of S is the denomination of P ; hence S 
 and P apply to one and the same person. 
 The determination is again different. In 
 Perseverance is admirable, Courage is 
 valour, there is the same identity of 
 denomination and diversity of determina- 
 tion as in the previous examples. The 
 last example differs from the others in 
 this, that (if not interpreted as a defi- 
 nition) the determination of S differs 
 from that of P in name only. In S is 
 not P, what is denominated by S is declared 
 to be not what is denominated by P, the determination 
 of S differs ex vi termini from the determination of P. 
 
 In Some E is not Q, what is 
 asserted is, that the denomination 
 of Some H is wholly nncoincident 
 with the denomination of Q. The 
 determination of Some R and of 
 Q is, of course, different. In, There is no rose without 
 a thorn, what is asserted is that the denomination of all 
 
 roses is wholly unidentical with 
 the denomination of without a 
 thorn. And the determination 
 of all roses is different from that 
 of without a thorn. 
 A consideration of the extreme case 
 
 A is A (A is-not not-A) 
 
 confirms this analysis. For though A is A conveys abso- 
 lutely nothing more than mere A does (and this appears 
 to me to be nothing at all, for a mere isolated name is a 
 complete nonentity), the exigencies of assertion introduce 
 difference of position in space or order in time between the 
 Subject A and the Predicate A, in addition to the implication 
 that the SA is what is predicated of, while the PA is what is 
 predicated. Unless we could speak or write A twice over
 
 IMPORT AND CLASSIFICATION OF CATEGOEICAL PROPOSITIONS. 49 
 
 we could not assert A to be A. Thus in A is A there is 
 a formal though valueless diversity of attribution, and this 
 valuelessness becomes if possible more obvious when we 
 use significant terms. And that both A's have an identical 
 denomination (and thus both apply to an identical thing) 
 seems so evident as to be incapable of proof. 
 
 If the denomination of SA were different from the denomi- 
 nation of PA, this would have to be expressed by saying 
 that 
 
 (S)A is-not (P)A. 
 
 The proposition, A is not-A, is comparable to the terms 
 Aa (a = not-A), Round -Square, or any other complex of 
 contradictions. 
 
 And while in A is A the diversity of attribution had 
 shrunk to such a degree as to be purely a matter of form, 
 and incapable of imparting any value to the predication, in 
 A is not-A the diversity has become so extreme as to destroy 
 the identity implied by the affirmative copula. In A is-not 
 A, though there is a formal diversity of attribution between 
 S and P, the determination is precisely similar, and hence 
 the denomination is identical. The proposition is therefore 
 self-contradictory, the identity involved by the terms being 
 negatived by the copula. 
 
 Unless we admit an indefinite variety of different copulas, 
 I do not see that any insuperable objection can be brought 
 against the above account of Categorical Propositions. This 
 account, involving as it does the view that all terms have 
 both denomination and determination, seems to me of 
 fundamental importance. I have tried to give some 
 further justification of it, both in later passages of this 
 Section and also in the Section on Quantification and Con- 
 
 1 I should like to refer here to some passages of De Morgan, Dr. Venn, Mr. 
 Bradley, and Mr. Bosanquet, which seem to me confirmatory or elucidatory 
 of the view of the Import of Categorical Propositions which I advocate. De 
 Morgan says (Formal Logic, pp. 49, 50), "Speak of names and say 'man t'a 
 animal ;' the is is here an is of applicability ; to whatsoever (idea, object, etc.) 
 
 D
 
 50 IMPORT OF PROPOSITIONS. 
 
 Propositions of the form : 
 
 There is X, There are Y's, 
 are reducible to either 
 
 (1) X is in that place ; 
 
 Y's are in that place 
 
 For instance, if X = Newton's statue, then There is X 
 Newton's statue is there ( = in some indicated place) ; 
 if Y's = blackberries, then There are Y's = Blackberries 
 are there ( =: in some indicated place) 
 
 or (2) X is existent ; 
 Y's are existent. 
 
 For instance, if Y's = Green roses, then There are Y's may 
 mean, Green roses are existent. 1 Such propositions as, 
 
 It is raining, It is cold, 
 are already in the form S is P it apparently being meant to 
 
 man is a name to be applied, to that same (idea, object, etc.) animal is a name 
 to be applied. . . . As to absolute external objects, the is is an is of identity, 
 the most common and positive use of the word. Every man in one of the 
 animals ; touch him, you touch an animal ; destroy him, you destroy an 
 animal." 
 
 Dr. Venn (Empirical Logic, p. 212) says, " What the statement [Plovers are 
 Lapwings, Clematis Vitalba is Traveller's Joy] really means is that a certain 
 object has two different names belonging to it." (The italics are mine.) 
 
 The next quotation is from Mr. Bradley (Principles of Logic, p. 28) : " The 
 doctrine of equation, or identity of the terms, has itself grasped a truth, a truth 
 turned upside down and not brought to the light, but for all that a deep 
 fundamental principle." 
 
 " Turned upside down and made false it runs thus: the object of judgment is, 
 despite their difference in meaning, to assert the identity of subject and pre- 
 dicate [when taken in extension]." This " upside down " doctrine if for despite 
 we read through is exactly what seems to me to be the true account of the 
 import of Categorical Propositions (explaining identity to mean tantum numero). 
 Mr. Bradley's condemnation of this interpretation seems to me to depend on a 
 confusion between identity and similarity, for he goes on to say (p. 29), " In 
 ' S = P ' we do not mean to say that S and P are identical [ = ? ]. We mean 
 to say that they are different, that the diverse attributes S and P are united iu 
 one subject. " If in S is P the attributions of S and P are diverse, but are 
 "united in one subject," this is exactly what I mean by S and P being identical 
 (where S and P are Substantive Terms). 
 
 Mr. Bosanquet says (Logic, i. 96), "The content of a judgment is always 
 ... a recognised identity in differences." 
 
 1 Is the there in this case a corruption of they ? If the original form was, 
 e.g. Green roses, they are = Green roses exist, or are to be found (cf. an old
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 51 
 
 indicate something vaguely conceived as a causal agent to 
 which P is attributed as effect, or, more vaguely still, a 
 subject to which P is assigned as attribute. 
 
 According to the above definition of significant Categoricals 
 (as has been already repeated and illustrated to perhaps a 
 tedious degree), the S and P of an affirmative proposition have 
 always the same denomination and different determinations. 
 If it is allowed that the S and P in any Categorical have 
 denomination, it seems clear that in affirmative propositions 
 they must both have the same (= identical) denomination 
 and in negative propositions different (= non-identical) denomi- 
 nations. If my S is the name of something having its own 
 quantitiveness, the P which I assert that S is must certainly 
 have the same quantitiveness, and therefore be the same thing 
 (subject or attribute, as the case may be) as S, and have the 
 same denomination as S. Of negative propositions the con- 
 verse holds. The assertion that the S and P of the Categorical 
 must have different determinations is perhaps more likely to 
 be disputed than the assertion that they must, if affirmative, 
 have the same denomination, and if negative a different 
 denomination. (Terms having the same determination must 
 have also the same denomination, therefore the above assertion 
 concerning different determinations holds with reference to 
 negative as well as to affirmative propositions.) In trying, 
 just above, to apply my definition to " Propositions " of the 
 form A is A, A is-not not-A, I came to the conclusion that 
 this form of words can have no predicative force. I wish to 
 set forth a little further the reasons for this conclusion, and 
 will therefore ask, What can A is A, A is-not not-A, stand for ? 
 What thought, what truth, or what assertion is it that can 
 correspond to, or be expressed by, these forms of speech ? 
 
 There seems to be prima facie a case for special examina- 
 tion of these (which have been called Identical) " Propositions " 
 
 form of inscription in books, e.g. Stephen Thorp, his book), it may have passed 
 to They are, (i.e.) green roses (are) ; and then, perhaps for euphony's sake and 
 with some oblivion of the primary meaning and a vague reference to there in 
 sense (2), There are green roses. There seems sometimes to be pleonastic, as in 
 There is frost to-night, There is nothing to be seen from my window.
 
 52 IMPORT OF PROPOSITIONS. 
 
 for A is A, and A is-not not-A differ in the following 
 respects from ordinary propositions of the S is P, S is-not P 
 type (1) they can have no intelligible contradictory; (2) they 
 cannot be divided into Adjectival and Coincidental Proposi- 
 tions ; (3) any word or combination of words or symbols may 
 stand for S, and for P ; (4) S and P in A is A must be 
 precisely similar; in A is-not not-A, S and P differ in being 
 the precise negatives of each other. 
 
 Let us take a sentence of the form A is A, in which A 
 is significant and since A is-not not-A is reducible to the 
 affirmative form, it need hardly be examined here separately. 
 Let the sentence be, e.g., Whiteness is whiteness, or This tree 
 is this tree. In using these forms of words how do I go 
 beyond what is involved in the mere enunciation of the words 
 whiteness, this tree ? That whiteness and this tree should BE 
 whiteness and this tree respectively seems not a significant 
 assertion, but a presupposition of all significant assertion 
 as extension is a presupposition of colour, or ears of sound. 
 And if, in perceiving whiteness or thinking of this tree, I ever 
 need to assert that whiteness is whiteness, or that this tree is 
 this tree, do I not just as much need to assert the same 
 sentence separately for both S and P in each case ? And at 
 what point is the process to stop ? And if identity needs 
 to be asserted for the terms, does it not equally need to be 
 asserted for the copula ? If we need to declare that whiteness 
 is whiteness, etc., do we not also need to declare that Is is Is ? 
 Unless we can start by accepting terms and copula as having 
 simply and certainly a constant signification, I do not see how 
 we are ever to start at all. 
 
 The analysis involved in my definition of Categorical Pro- 
 positions I believe to be both ultimate and absolutely general, 
 and also to contain the maximum that can be asserted with 
 absolute generality. When the Proposition is analysed into 
 (1) Subject and (2) Predication, there are always two elements 
 distinguishable in (2) ; namely, (a) a constant element (the 
 copula) significant of identity or non-identity, (b) a changing 
 element (the predicate). E.g. in (a) He sleeps, (/3) He will
 
 IMPOKT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 53 
 
 sleep, (a) = He (is) sleeping in present time, (/8) = He (is) 
 to sleep in future time. Hence the analysis into Subject and 
 Predication fails of being ultimate. Hobbes' account of 
 Categorical Proposition that the Predicate is a name of the 
 same thing of which the Subject is a name furnishes an 
 absolutely general but a deficient and superficial definition 
 (cf. Mill, Logic, i. 99). The Class Inclusion and Exclusion 
 view is neither ultimate nor formal (strictly general). If we 
 say that 
 
 R is Q (1), 
 
 R is not Q (2), 
 
 may mean respectively 
 
 R is included in Q (3), 
 R is excluded from Q (4), 
 
 we give an account which needs explanation even more than 
 that which it professes to explain. For the relation between 
 R and included in Q, excluded from Q, in (3) and (4), is pre- 
 cisely the same as that between E and Q (1), not-Q (2) ; 
 and the justification for adding included in to the copula in 
 (1) is not clear. Again, this explanation is not properly 
 formal ; for there are a multitude of propositions to which 
 it cannot be made to apply at all, e.g. Tully is Cicero, Courage 
 is Valour, The word quadruped is a word that means having 
 four legs. And in the cases where it does apply, it refers to 
 a relation not between the Terms, but between the Term- 
 names, for the " relation " indicated by the copula between 
 the Terms (Subject and Predicate) of a Categorical Proposi- 
 tion is that of Identity or Non-Identity. And R is included 
 in Q is not even compatible with 
 
 Ris Q, 
 
 for what R is Q means is, that R and Q are coincident or 
 identical. 
 
 As regards Mathematical Equations, they also may be 
 analyzed into 
 
 S copula P (cf. Section X.).
 
 54 IMPORT OF PROPOSITIONS. 
 
 The interpretation which makes 
 
 (All S is P) = (Sp = 0) 
 
 and Mill's view of the Import of Propositions will be dis- 
 cussed in Sections XL and VIII. 
 
 That view of the Import of a Categorical Proposition, 
 according to which it asserts a connection between two ideas 
 (which is one of the views discussed and rejected by Mill, 
 Logic, Bk. i. ch. v.), results from a particular theory of the 
 import of Terms. 
 
 Classification of Categorical Propositions. 
 
 In the Tables of Categorical Propositions (pp. 62-76), the 
 first distinction taken is that between (1) Adjectival Proposi- 
 tions and (2) Coincidental Propositions. As before remarked 
 (p. 21), (1) are Propositions which have a Uni-terminal Term 
 for P, and they cannot, as Adjectival Propositions, be con- 
 verted ; but Adjectival Propositions can always be replaced by 
 Coincidental Propositions, which are susceptible of conversion. 
 And as all the subdivisions of Adjectivals and Coincidentals 
 correspond, I have in the Tables of Categorical Propositions 
 confined myself to Coincidentals. These are propositions 
 which have Bi-terminal Terms for S and P, and they are 
 susceptible of conversion. I have adopted the name Coinci- 
 dental because it seemed a convenient word, and is, besides, 
 suggestive of the identity of denomination which holds between 
 the S and P of all affirmative Categorical Propositions, and is 
 perhaps specially obvious in those in which both terms are 
 bi-terminal. 
 
 Coincidental Propositions may be either (1) Attribute 
 Propositions, i.e. propositions which have an Attribute Term 
 for S ; or (2) Substantive Propositions, i.e. propositions which 
 have a Substantive Term for S. 
 
 Attribute Propositions subdivide into Complete and Partial 
 Propositions, and Partial into Singular (Definite and Inde- 
 finite}. Particulars are Distributive or Collective. Each of
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 55 
 
 the above, again, may be Vernacular or Specific; and each 
 of all these subdivisions (in common with every penultimate 
 division in the classification) subdivides into .Independent 
 and Dependent. A Dependent Proposition is a Proposition 
 which has at least one Dependent Term. 
 
 The majority of the subdivisions of Attribute Terms seem, 
 however, to be most appropriately, and perhaps even most 
 usually, expressed as Complete Propositions {i.e. Propositions 
 which predicate concerning the Attribute in its completeness), 
 the modification on which a distinction depends appearing as 
 part of the content of the Predicate. E.g. instead of saying, 
 Some perseverance is mischievous, it might (and perhaps 
 most frequently would) be said, Perseverance is sometimes 
 mischievous, or, Perseverance is mischievous in some cases. 
 The corresponding Common Proposition here would be, Some 
 cases (or instances) of perseverance are mischievous. We 
 can say, That courage was remarkable, Some kindness is cruel ; 
 but, That instance of courage was remarkable, Kindness is 
 sometimes cruel, are perhaps preferable. Attribute Names 
 have properly no plural, and Particular Definites frequently 
 cannot be expressed as (Particular) Attribute Propositions. 
 E.g. Those instances of laziness are nothing out of the 
 common. 
 
 In Coincidental Propositions which have Attribute Terms 
 for S and for P, conversion takes place without any modi- 
 fication of the terms ; e.g. Courage is valour, Generosity 
 is not justice, convert quite simply to Valour is courage, Justice 
 is not generosity. In such propositions as Courage is Valour, 
 the terms have not only the same denomination but also a 
 determination similar in every point except in this, that the 
 object is called by different names in S and P (unless we 
 regard the proposition as making an assertion about the word 
 which is the Subject). 
 
 In my Table of Categorical Propositions (Table XVII.) the 
 first division is into Whole and Partial. Whole Propositions 
 include Complete Propositions (cf. above), Individual Proposi- 
 tions, and Total Propositions.
 
 56 IMPORT OF PROPOSITIONS. 
 
 Individual Propositions are divided into Descriptive, Appel- 
 lative, and Mixed (partly Descriptive and partly Appellative). 
 Total Propositions may be Universal (or Unlimited] and General 
 (or Limited}. Universals are Common and Special, and the 
 Common are Vernacular and Specific. Each of these classes 
 of Universals may be Definite (Collective and Distributive) or 
 Indefinite (Distributive). 
 
 (All equations of the kind commonly called Mathematical 
 or Quantitative propositions are Dependent.) 
 
 The Generals are (1) Special, (2) Unique. (1) Subdivide 
 into Summary (Definite and Indefinite) and Enumerating 
 (which here and elsewhere are all Definite). The Definites 
 may be Distributive or Collective ; the Indefinite Generals 
 are (here and elsewhere, like the Indefinite Universals) all 
 Distributive. (2) Unique Generals may be Summary or 
 Enumerative, and these again may be Descriptive, Appellative, 
 or Mixed. Those which are Summary further subdivide into 
 Definite and Indefinite, Distributive and Collective ; the 
 Enumeratives may be Distributive or Collective. 
 
 Partial Propositions (i.e. Propositions of which the S has a 
 Term-indicator which is not Universal nor General) are divided 
 into Single (referring to one individual, species, or specimen of 
 a class or quantity) and Multiple (referring to more than one 
 such individual, species, or specimen). Single Propositions 
 subdivide into Singular (Attribute, Common, and Special) and 
 Unitary (Special and Unique). Common Singulars may be 
 Vernacular or Specific, and each of these and Special Singulars 
 subdivide into Definite and Indefinite. Unique Unitaries may 
 be Descriptive, Appellative, or Mixed, and each of these, and 
 Special Unitary Propositions, may be Definite or Indefinite. 
 Multiple Propositions are Particular (Attribute, Common, and 
 Special) and Plurative (Special and Unique). Such propositions 
 as, Some bread is unwholesome, Some air is bracing, Some 
 gas has escaped, should, I think, be classed rather as Multiple 
 than as Single, since where the Some is not equivalent to 
 certain kinds, certain specimens, or certain (somehow indicated) 
 quantities, it can always be said that what is referred to is
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 57 
 
 quantity that may be divided without losing its specific 
 character, and that it may therefore be regarded as Multiple 
 rather than Single. 
 
 Particular Common Propositions may be either Vernacular 
 or Specific, and each of these is subdivided into Definite and 
 Indefinite, and these into Distributive and Collective. The 
 subdivisions of Particular Special Propositions are the same 
 as those of Vernacular and Specific Particulars. 
 
 Plurative Propositions are Special and Unique, and both 
 subdivide into Summary and Euumerative. The Special 
 Summary Pluratives are Definite and Indefinite, Distributive 
 and Collective. The Enumeratives are either Distributive or 
 Collective. 
 
 Unique Plurative Propositions are Summary and Enumera- 
 tive. Each of these may be Descriptive, Appellative, or 
 Mixed. 
 
 The different kinds of Summary Propositions subdivide into 
 Definite and Indefinite, Distributive and Collective ; the 
 Enumerative Propositions into Distributive and Collective. 
 A Distributive Enumerative Proposition may be looked at as 
 a combination of propositions (cf. Jevons' Elementary Lessons 
 in Logic, 7th ed. p. 90 a " compound " sentence, consisting 
 of " co-ordinate propositions "). 
 
 Important differences in use, depending on differences of 
 relation to other propositions, are connected with the differences 
 that are apparent on a mere inspection in the propositions of 
 the Tables, pp. 6276. The following may be noticed here A 
 Distributive Universal Proposition is the only one from which 
 both Universals and Particulars can be deduced by Immediate 
 Inference (Collective Universals have the form without the 
 force of Universals). It is only Distributive Universals 
 such as, All particles of matter attract each other and Special 
 Generals such as, The three angles of a triangle (the three 
 angles of any one triangle) are equal to two right angles (a pro- 
 position which, though Collective in form, has distributive 
 force) that are capable of expressing a Law, a Law being 
 a statement of some uniformity of coexistence or succession
 
 58 IMPORT OF PROPOSITIONS. 
 
 (depending on coexistence) in things. In expressing Uni- 
 versality these propositions express also Necessity, since the 
 rule which has not at any time or place an exception, states 
 something which cannot anyhow be otherwise- while con- 
 versely, what must be, is something to which there is nowhere 
 an exception. Every Categorical Syllogism expressing a 
 so-called " Inductive " reasoning a reasoning in which by 
 help of particular instances we reach and establish a new 
 law has an Universal proposition for major premiss and 
 conclusion (cf. post, Section XVIII. 3rd note, and Table 
 XXXVI.) ; every Syllogism by which any law is deduced 
 from other laws has Universals or Special Generals for 
 premisses and conclusion. Indefinite Universals (e.g. Any 
 E is Q) are not directly subject to the ordinary rules of 
 Immediate Inference and Opposition. Any R is Q converts 
 most naturally to Some Q's are R's. There is no negative 
 form specially corresponding to this Indefinite Universal. It 
 is, of course, denied in Some R is not Q (contradictorily), and 
 in No R is Q (contrarily) ; but these forms are the recog- 
 nised correspondents of All R is Q, the Definite Affirmative 
 Universal. In General, as in Universal Propositions the 
 S-term applies to all the objects to which the S-name applies ; 
 but in Generals the sphere of the S-name is restricted. As 
 regards the Term-names of the Unique Terms, their application 
 is fixed and limited once for all, but as regards Special Names, 
 it may increase under certain conditions. For instance, the 
 application of Muse or picture ~by Rembrandt can never be 
 increased, while that of, e.g., Sunday, or April, or picture by J. E. 
 Millais, may. It is only to Definite Distributive Universals 
 and Indefinite Distributive Particulars that the ordinary rules 
 for Conversion, and therefore, of course, for Keduction also, 
 apply ; and the forms of Syllogism (Barbara, Celarent, etc.) 
 recognised by the traditional Formal Logic are concerned with 
 these only. To Singular Propositions (though they can be 
 treated in some respects as Definite Universals) the same 
 rules of Conversion and Opposition do not apply ; and with 
 regard to propositions of the form Some Q is R, understood as
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 59 
 
 Singular e.g. Some jockey broke his horse's back over the 
 first fence (1), similar remarks may be made. Some (= a, 
 one, a certain) jockey broke, etc., may perhaps be denied by a 
 proposition of this form, Some (= a, one, a certain) jockey 
 did not break, etc. (2), but this could not be said of, e.g., 
 
 Some jockeys are rascals, 
 
 which no one could hold to be incompatible with 
 Some jockeys are not rascals. 
 
 I admit that (1) would be most ordinarily and naturally 
 negatived by 
 
 No jockey broke, etc. (3), 
 
 but (1) might be incompatible, I think, with (2) ; the reason 
 for denying (1) by (3) rather than by (2) appears to be that 
 while (1) is the most indefinite form of affirmation concerning 
 an individual that can be used, implying that he is merely 
 pointed out as just one of a class, (3) is the most indefinite 
 possible form of negation concerning an individual in it the 
 denial is made of him simply as a member of the class 
 whereas (2) rather implies reference to an individual indi- 
 cated more specially than as a mere member of his class. 
 
 When General (Definite) and Plurative Propositions are 
 converted, the Predicate Terms of the new propositions got 
 by this conversion must have indicators which are the same 
 as, or equivalent to, those which they had as Subject-Terms 
 of the old (converted) propositions ; e.g., 
 
 All of my pupils have passed, converts to Some who have 
 passed are all my pupils ; The, planets are bodies having an 
 elliptical orbit, converts to Some bodies having an elliptical 
 orbit are the planets ; Some of Rembrandt's pictures are master- 
 pieces, converts to Some masterpieces are some of Rembrandt's 
 pictures. The converses of General and Plurative propositions 
 differ from Particular Propositions in this, that if in any 
 converse of the former the Term-Indicator of the new predi- 
 cate is omitted, the force of the proposition is quite altered. 
 
 In the common examples of what is called Inductive
 
 60 IMPORT OF PROPOSITIONS. 
 
 Syllogism, 1 or Perfect Induction, the Minor Premiss is a 
 Collective Enumerative Proposition, and the Major Premiss a 
 Distributive Enumerative Proposition ; the conclusion being 
 Summary and Distributive ; e.g., 
 
 Sunday, Monday, . . . and Saturday are all (omnes) twenty- 
 four hours in length ; 
 
 Sunday, Monday, . . . and Saturday are all (cuncti) the 
 days of the week ; 
 
 . . All (omnes) the days of the week are twenty-four hours 
 in length. 
 
 It may be remarked that this Syllogism is incorrect in 
 form, the Minor Term being taken collectively in its premiss, 
 distributively in the conclusion. I do not remember to have 
 seen this inaccuracy noticed. Mansel (Mansel's Aldrich, 4th 
 ed. p. 221), Whately (Logic, 9th ed. p. 152), and Jevons 
 (Elementary Lessons, 7th ed. pp. 214, 215), among others, 
 offer as instances of Perfect or Aristotelian Induction, argu- 
 ments exactly corresponding in form to the one I have given, 
 without any remark on their formal incorrectness. 
 
 To reach by Inference (Mediate or Immediate) an Universal 
 Proposition, we must always start from an Universal ; and 
 to reach a General we must always start from a General. 
 Particulars are immediately deducible from Universals and 
 Particulars, and Pluratives from Generals and Pluratives ; 
 Singulars from Universals or Particulars or Singulars ; Unitary 
 Propositions from General or Plurative or Unitary pro- 
 positions. From Individual or Singular Propositions only 
 Individuals and Singulars, and from Particular Propositions 
 only Particulars and Singulars can be obtained. Complete 
 Propositions can be got only from Complete Propositions or 
 their 'converses ; and these, and Singular and Individual 
 Propositions, convert quite simply, and admit of only one 
 mode of negation. In Traduction as described and illustrated 
 by Jevons (cf. Elementary Lessons in Logic, 7th ed. pp. 211, 
 
 1 1 should propose to call this (in an amended form) a Limited Deductive 
 (Categorical) Syllogism.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 61 
 
 222), both of the premisses and the conclusion are Singular 
 or Individual Propositions. I should like to extend the 
 application of the term so as to include Syllogisms of which 
 either (a) all the terms are Singular or Individual, or (b) the 
 Subjects of both premisses are Definite Partial Terms. 
 
 Although in Universal and General Propositions the dis- 
 tributive all may have the same force as any in the majority 
 of propositions, yet there are certain differences for any may 
 occur as Subject - indicator in a proposition in which, by 
 determination of S or P, the application of the Subject is 
 restricted to one individual. E.g. Any one who wins this 
 race will have a silver cup, Any person whom the Committee 
 choose will be appointed Secretary, Any one may have my 
 ticket (we could not here replace any by all}. Any is equi- 
 valent to the a or an in many proverbial sayings e.g. A 
 woman's mind and winter's wind change oft, An honest miller 
 has a golden thumb, An ill plea should be well pleaded. 
 The force of any X seems to be this: A thing, and the 
 only condition of acceptance is Xness. Hence it follows that 
 any is equivalent to all, wherever more than one is in ques- 
 tion. From the statement that any X is Y it follows that all 
 X's are Y (if there be more than one X), because Xness is 
 connected with Yness. And, conversely, from all X's are Y 
 it follows that any X is Y, because from every X being Y 
 there may be inferred a connection between Xness and Yness. 
 
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 IMPORT OF PROPOSITIONS. 
 
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 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 63 
 
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 H |1 
 
 S>*5 S 
 
 
 
 
 O OH S 
 
 i5 ft. 55, 
 
 e ^ a> 
 
 |i|j 
 
 -T 
 
 
 d 
 
 ^ ^ 
 
 . j=^= 
 
 j 
 
 
 ai 55 
 
 
 . CO C^ '*^ 
 
 fa 
 
 
 * 2 
 
 *-* 
 
 * S "^^ g 
 
 
 H 
 
 
 is 
 
 ^' 
 
 
 K 
 
 
 
 
 09 i 
 
 
 ^ Q 
 
 v> 
 
 03 c8 
 
 Q 
 
 -^- ' 
 
 (^ 
 
 
 B 
 
 * 
 
 PH 
 
 ^ 
 
 <C ^ 
 
 A 
 
 
 03 "^ 
 
 2. O 
 43 !>, O 
 
 < 
 
 
 W O "-V . 
 
 3 "&4-W P< 
 
 b 
 
 
 ^S 11 
 
 " S H 
 
 !~?1 Bi- 
 
 o 
 
 ^ ' 
 
 
 
 ;.-S3g w 2^ 
 
 I 1 !! 1 ?!.!!! 
 
 ^.2 2i^cg^ 
 S -era fe o es 
 
 I 
 
 
 .2 c g 
 ^ ' 2 
 
 o co _ c8 B 
 
 - fi O 
 
 a o o m 
 'S^ 
 
 ss 
 ol 
 
 
 om 
 is 
 ; 
 iou 
 
 suiiii 
 
 S53-S.S>
 
 IMPORT OF PROPOSITIONS. 
 
 TABLE XIX.] 
 
 INDIVIDUAL PROPOSITIONS (APPELLATIVE, 
 DESCRIPTIVE, AND MIXED) 
 
 INDEPENDENT 
 PROPOSITIONS. 
 
 e.g. The sun is not a 
 planet ; the present Czar is 
 a tyrant ; Praise -God Bare- 
 bones is one of Sir Walter 
 Scott's characters ; Mon- 
 mouthshire is not a "Welsh 
 county ; Aglaia was a Greek 
 goddess ; Jack is a fidgety 
 child ; Tom Smith, the boy 
 I speak of, has a ferret. 
 
 DEPENDENT 
 PROPOSITIONS. 
 
 e.g. The CEdipus Tyrannic 
 of Sophocles is an unsur- 
 passed tragedy ; the Inferno 
 of Dante has not been satis- 
 factorily translated into 
 English; the year 1888 A.D. 
 was a year remarkable for its 
 bad weather ; the youngest 
 child of that poor woman 
 has just died of whooping- 
 cough ; Jane Smith's eldest 
 boy has scarlet fever ; the 
 P.S. to your letter yesterday 
 was not of much conse- 
 quence ; the circumference of 
 the earth is about 24,000 
 miles ; Bacon of Verulam 
 seems to be the denomina- 
 tion by which Francis Bacon 
 is commonly known to Ger- 
 mans ; the greatest poet of 
 the Elizabethan age was 
 Shakspeare.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 65 
 
 ! "3 =- 
 
 g a 3 "I Hi a 
 
 E o | I, S ""< .2 . 
 
 > a 
 
 
 P? ! 1 
 
 o (f -S 
 
 |B~I ^ 
 
 K 02 S ' 
 
 s 
 
 0. 
 
 -S - 
 ca 
 &S 
 
 25 
 
 ^ 
 &1 1. 
 
 - 
 
 II 
 
 
 S-Si 
 
 
 
 
 o cj i 2 
 
 < K S -S' 
 
 "S ^* g . ' 
 
 " o 
 
 1 - 
 
 
 08 oM '43 o 
 
 i-r 
 
 s -J s
 
 '66 
 
 IMPORT OF PROPOSITIONS. 
 
 TABLE XXI.] 
 
 UNIVERSAL PROPOSITIONS (SPECIAL). 
 
 DEFINITE PROPOSITIONS. 
 
 DISTRIBUTIVE 
 PROPOSITIONS. 
 
 Independent 
 Propositions. 
 
 e.g. All conic sec- 
 tions are m a t h e- 
 matical figures ; no 
 elements are com- 
 pounds ; no English 
 Decembers are warm 
 months ; no March 
 could be more wintry 
 than this July ; genus 
 includes specie* 
 ( = every genus, etc. ). 
 
 COLLECTIVE 
 PROPOSITIONS. 
 
 Independent 
 Propositions. 
 
 e.g. All circles are 
 fewer than all conic 
 sections. 
 
 INDEFINITE 
 
 PROPOSITIONS 
 
 (DISTRIBUTIVE). 
 
 Independent 
 Proposition*. 
 
 e.g. Any circle is 
 a figure with equal 
 radii ; any Predicable 
 is out of place here ; 
 any Predicable will 
 do for illustration. 
 
 Dependent 
 Proposition*. 
 
 e.g. All Figures of 
 Syllogism are valid 
 forms of reasoning. 
 
 Dependent 
 Propositions. 
 
 e.g. All Syllogisms 
 in the first Figure 
 do not include all 
 valid Syllogisms. 
 
 Dependent 
 Propositions. 
 
 e.g. Any Figure of 
 Syllogism is a valid 
 form of reasoning ; 
 any April in England 
 is an uncertain 
 month with regard 
 to weather; any 
 Friday in Lent is a 
 fast day.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 67 
 
 00* CT^ <0 
 
 s % o a 
 .2 .&-. 2 
 "2 13 a, g 
 
 If 
 
 5 "is 
 
 El 
 
 s a^^ 2 
 
 
 ~ 5E O - 1 
 
 ^ ci- 
 
 . & 1 -- 2 
 
 H 
 
 w "2 "3 S. ' " 
 
 i 
 
 - 1 ^ cT ^ 1 
 
 & 
 
 
 -- s5 J , 
 
 
 .s 
 
 '~\ ^" SfcHtSc3> a Scoa-'+J- < -' 
 
 HPM S r ooC J g>,SS'? 
 
 * -< 
 
 S "^^ 
 S b -I 
 
 rQ 
 
 B fl 
 
 g.2 
 
 - 
 
 5, 5s 
 
 ,-^ tt) CO W 
 
 <S C is 
 ee *-
 
 68' 
 
 IMPORT OF PROPOSITIONS. 
 
 TABLE XXIII.] 
 
 GENERAL PROPOSITIONS (UNIQUE SUMMARY). 
 (DESCRIPTIVE, MIXED, AND APPELLATIVE.) 
 
 DEFINITE PROPOSITIONS. 
 
 DISTRIBUTIVE 
 PROPOSITIONS. 
 
 Independent 
 Propositions. 
 
 e.g. All the patri- 
 archs were sons of 
 Jacob ; all the planets 
 have an elliptical or- 
 bit ; all the days of 
 my life are [few and] 
 i-vil ; all the Greek 
 heroes were men of 
 courage ; each of the 
 nine Muses was a 
 daughter of Apollo ; 
 all of those cattle are 
 Kyloes ; all of the 
 birds in that aviary 
 are parrots. 
 
 COLLECTIVE 
 PROPOSITIONS. 
 
 Independent 
 Propositions. 
 
 e.g. The twelve pat- 
 riarchs were Reuben, 
 Simeon, Levi, Judah, 
 Issachar, Zebulon, 
 Joseph, Benjamin, 
 Dan, Naphtali, Gad, 
 and Asher. The three 
 Furies were Tisiphone, 
 Alecto, and Megsera. 
 
 INDEFINITK 
 (DISTRIBUTIVE) 
 PROPOSITIONS. 
 
 Independent 
 Propositions. 
 
 e.g. Any of the 
 patriarchs was a son 
 of Jacob. 
 
 Any of the Graces 
 was a daughter of 
 Apollo. 
 
 Dependent 
 Propositions. 
 
 e.g. All the gods 
 of Greek mythology 
 were anthropomorphic 
 beings ; all the wheels 
 that go to Croyland 
 are shod with silver. 
 
 All the Muses of 
 Homer were dwellers 
 in Olympus. 
 
 Dependent 
 Propositions. 
 
 e.g. The heroes of 
 Greek mythology were 
 Achilles, Ulysses, etc. ; 
 all the days of my life 
 are few [and evil]. 
 
 The Muses of Hesiod 
 were nine in number. 
 
 Dependent 
 Proposition*. 
 
 e.g. Any god of 
 Greek mythology was 
 an anthropomorphic 
 being ; any of B's set 
 is a person not to be 
 trusted ; any of Rem- 
 brandt's pictures is a 
 masterpiece. 
 
 Any of the Muses 
 of Hesiod was a 
 daughter of Zeus.
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 69 
 
 TABLE XXIV.] 
 
 GENERAL PROPOSITIONS (UNIQUE ENUMERATIVE). 
 (DESCRIPTIVE, MIXED, AND APPELLATIVE.) 
 
 DISTRIBUTIVE PROPOSITIONS. 
 
 COLLECTIVE PROPOSITIONS. 
 
 Independent Proposition*. 
 
 e.g. The largest, second largest 
 . . . and smallest of the planets 
 have each an elliptical orbit. 
 
 Aglaia, Thalia, and Euphrosyne 
 were daughters of Apollo. 
 
 Independent Propositions. 
 
 e.g. The largest, second largest 
 . . . and smallest of the planets 
 are the satellites of our sun ; the 
 first, second, third, and fourth of 
 the Cardinal Virtues were Wisdom, 
 Courage, Justice, and Temperance. 
 
 Aglaia, Thalia, and Euphrosyne 
 were the three Graces. 
 
 Dependent Propositions. 
 
 e.g. The first, second . . . and 
 seventh days of last week were 
 rainy days. 
 
 The Agamemnon, Choephone, and 
 Eumenides of ^Eschylus are splendid 
 plays. 
 
 Dependent Propositions. 
 
 e.g. The first, second . . . and 
 seventh days of last week were the 
 seven most wretched days of my 
 life ; the daughters of Henry VIII. 
 were Mary and Elizabeth. 
 
 The Agamemnon, Choephorae, and 
 Eumenides of ^Eschylus fonn the 
 Oresteia.
 
 70 
 
 IMPORT OF PROPOSITIONS. 
 
 sec. 
 o D o~- 
 
 
 -3 
 
 a, 
 
 2 ,-, 
 
 l g 
 
 I 
 
 3 
 
 a. 
 
 
 02 
 
 
 
 " o 3) j3 "X; 
 
 
 ~~ > -~ -i"S ec -" : ;: 
 
 2; 
 
 
 
 ^5 aj a 5 * j; 
 
 
 ogjj % G"* S~ 
 
 O 
 
 
 
 S 3 h^- ~ 
 -*a o ^ . T* o 
 
 
 ^^-= '5 -c 
 
 H 
 
 
 
 5 "*' & E ^ 
 
 
 ^~u - c 'f'Sci" M 
 
 H-t 
 
 55 
 
 
 
 rf ^ * <pa S "o * 
 
 
 CJ3 "oi^S-5^ 
 
 O 
 
 
 
 
 
 C o '^. *** ^ bo ^ 
 
 PH 
 
 
 
 C o S ^ ^A * 
 
 
 ^ ^ 03 08 M E ' r ~ 
 
 SINGULAR PRO 
 
 ONS (VERNACULAR AND SPECIFIC). 
 
 i 
 INDEFINITE PROPOSITIONS. 
 
 1 
 
 Independent Propositions. 
 
 e.</. One prisoner has escaped ; one 
 , a ) si>y has been tak< 
 recovered ; Qne J- m f litia . man i? not , 
 
 a gold medal as big as a crown piece is t 
 A Master in Lunacy was summone 
 Court; an Asplenium Lanceolatum was 
 frost ; one Cystopteris is a sickly plant ; a 
 was then on the throne of Germany 
 Jacqueminot is not mentioned. 
 
 Dependent Propositions. 
 
 e.y. One warder of a prison is missing 
 of an artillery regiment is a prisoner ; 
 friends is not a ratepayer ; a spire of 
 been struck by liglltning. 
 A guardian of the poor ought to be a 
 ing person ; a frond of Allosorus t'ri-tpi' 
 preserved specimen in my collection ; 
 from Gower sang at the Eisteddfod ; a 
 Baroko must be reduced ; a colonel of i 
 prisoner ; one reduction from the 4th 1 
 1st has not beon attempted. 
 
 * _ 5 
 
 3 O ^ S jr 
 
 x5gwr.*t 
 111! NX 
 
 S a <o 3 ^ * c 
 s t5-^s2 s L.' s 
 .Soooo-asS'S, 
 
 g a eo^'-g | 
 
 H S- 2 . *:>< 
 <.Q <u ~ o) o . 
 
 *?2 H"i 55 J 
 
 . M 
 

 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. "71 
 
 TABLE XXVI. ] 
 
 UNITARY PROPOSITIONS. 
 
 SPECIAL PROPOSITIONS 
 (SYNOPTICAL). 
 
 UNIQUE PROPOSITIONS 
 (DESCRIPTIVE, MIXED, AND 
 
 
 
 DBF 
 PROPOS 
 
 APPELL 
 
 ATIVE). 
 
 DEFINITE 
 PROPOSITIONS. 
 
 INDEFINITE 
 PROPOSITIONS. 
 
 NITE 
 ITIONS. 
 
 INDEFINITE 
 PROPOSITIONS. 
 
 Independent 
 Proposition*. 
 
 Independent 
 Propositions. 
 
 Indep 
 Propo 
 
 undent 
 titions. 
 
 Independent 
 Propositions. 
 
 e.g. This one 
 of the Predi- 
 cables is Pro- 
 perty. 
 
 e.g. One of the 
 elements is Sele- 
 nium ; one of the 
 elements must be 
 heavier than any 
 compound. 
 
 e.g. This planet 
 is Mars. 
 This Fury is 
 Alecto. 
 
 e.g. One planet 
 is Jupiter. 
 One of tin; 
 Furies is Alecto. 
 
 Dependent 
 Propositions. 
 
 e.g. That day 
 of the week is 
 Monday. 
 
 Dependent 
 Propositions. 
 
 e.g. One finger 
 of the hand is 
 called the index 
 finger. 
 
 Dependent 
 Propositions. 
 
 e.g. This satel- 
 lite of Jupiter is 
 not so large as 
 the moon. 
 
 This Muse of 
 Hesiod is Terpsi- 
 chore. 
 
 Dependent 
 Proposition*. 
 
 e.g. One see 
 of an English 
 bishop is not a 
 well - endowed 
 see. 
 
 One of Hesiod's 
 Muses is Terpsi- 
 chore.
 
 72 
 
 IMPORT OF PROPOSITIONS. 
 
 TABLE XXVII.] 
 
 PARTICULAR PROPOSITIONS (COMMON). 
 (VERNACULAR AND SPECIFIC.) 
 
 DBF 
 
 [NITE 
 
 INDEFI 
 
 XITK 
 
 PROPOSITIONS. 
 
 1 r 
 
 PROPOSI 
 
 noNs. 
 
 1 
 
 DISTRIBUTIVE 
 PROPOSITIONS. 
 
 1 
 COLLECTIVE 
 PROPOSITIONS. 
 
 1 
 DISTRIBUTIVE 
 PROPOSITIONS. 
 
 1 
 COLLECTIVE 
 PROPOSITIONS. 
 
 1 
 
 1 
 
 I 
 
 1 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Propositions, 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 e.g. These 
 
 e.g. These fields 
 
 e.g. Some men are 
 
 e.g. Some trees 
 
 men are mer- 
 
 have together 
 
 geniuses ; some un- 
 
 are oaks and 
 
 chants ; these 
 
 an area of 50 
 
 educated men have 
 
 beeches. Some 
 
 persons are 
 
 acres; those 
 
 gifted sons ; some 
 
 Polypodiums are 
 
 .spies. 
 
 men are 56 in 
 
 trees have been cut 
 
 Vulgare and 
 
 These Ophio- 
 
 number ; those 
 
 down ; some men are 
 
 Cambricum. 
 
 </lossacece are 
 
 lish weigh alto- 
 
 not trustworthy ; 
 
 
 vigorous plants ; 
 
 gether 20 Ibs. 
 
 few elephants are 
 
 
 those Hohen- 
 
 Those Poly- 
 
 " rogues ; " some 
 
 
 /ollerns are 
 
 podiums are 
 
 bread is bitter food. 
 
 
 descended from 
 
 Vulgare and 
 
 Some Polypodiums 
 
 
 Frederick of 
 
 Cambricum ; 
 
 are very hardy ferns ; 
 
 
 Snabia. 
 
 these Hohen- 
 
 some Hegelians are 
 
 
 
 zollerns were dis- 
 
 not understood ; some 
 
 
 
 tinguished mili- 
 
 Polypodiums have 
 
 
 
 tary leaders ; 
 
 the sori exposed ; 
 
 
 
 those Israelites 
 
 some Lady Ferns are 
 
 
 
 were in great 
 
 to be found in this 
 
 
 
 distress. 
 
 neighbourhood. 
 
 
 Dependent 
 
 Dependent 
 
 Dependent 
 
 Dependent 
 
 Propositions. 
 
 Propositions. 
 
 Proposition*. 
 
 Proposition^. 
 
 e.g. Those 
 
 e.g. Those 
 
 e.g. Some officers 
 
 e.g. Somegreat 
 
 officers of a man- 
 
 officers of a man- 
 
 of men - of - war are 
 
 poets among our 
 
 of-war were 
 
 of-war number 
 
 prisoners ; some sons 
 
 contemporaries 
 
 taken prisoners. 
 
 six. 
 
 of uneducated men 
 
 are Browning 
 
 These fronds 
 
 These Conser- 
 
 have been geniuses. 
 
 and Tennyson. 
 
 of Polypodium 
 
 vative Unionists 
 
 Some prime donne 
 
 Some Conser- 
 
 Cambricum are 
 
 of Monmouth- 
 
 at the London Opera 
 
 vative Unionists 
 
 good specimens ; 
 
 shire are John 
 
 Houses make good 
 
 of Monmouth- 
 
 those Liberal 
 
 Allen Rolls and 
 
 incomes ; some sul- 
 
 shire are A. B. 
 
 Unionists of 
 
 George Griffin 
 
 phites of soda are not 
 
 and C. D. 
 
 Glamorganshire 
 
 Griffin ; these 
 
 poisons ; some sori 
 
 
 have not done 
 
 pinnae of Hy- 
 
 of Polypodiacece are 
 
 
 much. 
 
 menophyllum 
 
 without indusia ; 
 
 
 
 are deflexed. 
 
 few nervous systems 
 
 
 
 
 of vertebrates are so 
 
 
 
 
 complex as that of 
 
 
 
 
 the elephant. 

 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 73 
 
 TABLE XXVIII.] 
 
 PARTICULAR PROPOSITIONS (SPECIAL). 
 
 DEFINITE PROPOSITIONS. 
 
 INDEFINITE PROPOSITIONS. 
 
 
 | 
 
 DISTRIBUTIVE 
 
 COLLECTIVE 
 
 DISTRIBUTIVE 
 
 COLLECTIVE 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 e. g. These 
 
 e. g. Those 
 
 e.g. Some Pre- 
 
 e.g. Some 
 
 I'redicables are 
 
 months were a 
 
 dicables are not 
 
 conic sections 
 
 inappropriate 
 
 wretched time ; 
 
 easy to classify ; 
 
 rilled up the 
 
 terms. 
 
 those circles are 
 
 some Lents are 
 
 blackboard. 
 
 
 as many as 
 
 very cold seasons. 
 
 
 
 twenty. 
 
 
 
 Dependent 
 Propositions. 
 
 e. g. Those 
 Sundays in April 
 were happy days; 
 these sections of 
 a cone are badly 
 drawn. 
 
 Dependent 
 Proposition*. 
 
 e. g. Those 
 Fridays in 
 December were 
 only two alto- 
 gether ; those 
 sections of a cone 
 are fewer than 
 they ought to be. 
 
 Dependent 
 Propositions. 
 
 e.g. Some days 
 in November will 
 probably be 
 gloomy days ; 
 some Kamadans 
 of the Moham- 
 medans are kept 
 more strictly 
 than othecs. 
 
 Dependent 
 Propositions. 
 
 e.g. A few days 
 in December 
 were all the 
 holiday he had ; 
 ten days in June 
 is not much.
 
 74 
 
 IMPORT OF PROPOSITIONS. 
 
 
 T3 o "^'3 
 53 B = 5 
 
 o^j 
 
 a5 
 
 .2 d o5 
 
 ^ c 
 
 s g 
 
 
 aH-S * 
 ^S E e 9 * S 
 
 S ^ ^ ' 
 
 
 
 R 
 
 O 
 
 L 
 
 2$ 
 
 1 
 COLLECT 
 PROPOSITI 
 
 l^-S^^^o 5 
 
 |l|-ss s i 
 
 2! H ^j! 
 
 *> S, u 0. 
 
 ft- SH r. 'n ^ ' 
 
 S 
 PH E 
 
 
 S s o>"S 2 
 15 o2O75 
 
 "||' 
 
 
 w w 
 
 H J 
 
 
 B S B Z -K 
 
 ^^3 
 
 3 
 5 
 
 w 
 
 ENUMERA 
 (AL 
 
 1 
 DISTRIBUTIVE 
 PROPOSITIONS. 
 
 ^ *3 
 
 lis:l||l 
 
 ^3*-! C -**-! Ci * ' 
 
 S-^ s^^S^^ 
 
 -iti.i*s^ 
 
 ffa| & 5, 
 
 SO, . S % 
 ^ S a o 
 
 > P 0) 08 g 
 
 <J'aSS^ 
 
 Dependent 
 Propositions, 
 e.g. The thumb a 
 first finger of a ha 
 are its most use! 
 
 PH 
 
 
 
 
 ss. 
 
 
 
 
 
 
 S fl a! 
 
 O 03 't i 
 
 ED 
 
 
 a 3 1 
 
 ^3 B 
 
 ^ 
 
 
 ^9 
 
 ~*^ ^ -** 
 
 O 
 
 H S 
 
 ~2"- 
 
 
 
 S 
 
 e 1 
 
 2"o 
 
 S-I 5" 
 
 PROPOS 
 1 
 
 g 
 
 
 
 M 
 
 (C 
 
 1 
 COLLECI 
 PROPOSIT 
 
 s * ^ Stl 
 
 N~L( . -V 
 
 * 
 
 ft'lM * 
 
 . c J= 
 
 
 o 
 
 
 
 
 w 
 
 S 
 
 
 t S 
 
 ^J y ^ 
 
 
 o 
 
 
 flj cS 
 
 OB 
 
 2 
 
 9 
 
 
 
 
 H 
 
 PH 
 
 
 
 
 ^J 
 
 
 
 
 Q) 0> 
 
 03 CO 
 
 P3 
 
 B 
 
 
 5 >- 
 
 
 p 
 
 B 
 
 
 * 
 
 r-3 
 
 g 
 
 E 
 
 K & 
 
 " ** fi 
 
 ** 8 *0 'I "** 
 
 m 
 
 a 
 
 H ^ 
 
 'S -2 o 
 
 . fe 
 
 
 y^ 
 
 B 
 
 ~ HO !-> Q3 
 
 ^J ^ *^ 
 
 
 
 CO I-C 
 
 
 
 
 1-1 H M 
 
 00 - - 
 g ^ 
 
 a o S > 
 * Ss o ^ 
 1 ^ O2 ^ 
 
 II 1 ^ 
 
 
 S cc O 
 
 o t-< ft* 
 
 
 i^ ^- Q 0) 
 
 
 Q(S 
 
 Sf ^ (i-2'2 
 
 to> ^ 
 
 
 
 
 
 
 
 
 o ^ 
 
 , 
 
 
 
 O 
 
 rs o 
 
 - 
 
 2 s 
 
 S^ 
 .3 
 
 ! O "o'S 
 
 are us 
 argumen 
 
 o s 
 
 }{l|
 
 IMPORT AND CLASSIFICATION OF CATEGORICAL PROPOSITIONS. 75 
 
 TABLE XXX.] 
 
 PLURATIVE PROPOSITIONS (UNIQUE SUMMARY). 
 (DESCRIPTIVE, MIXED, AND APPELLATIVE.) 
 
 DEFI 
 
 
 
 FINITE 
 
 KITE 
 
 INDE 
 
 PROPOS 
 
 ITIONS. 
 
 PROPOS 
 
 UTIONS. 
 
 DISTRIBUTIVE 
 
 COLLECTIVE 
 
 DISTRIBUTIVE 
 
 COLLECTIVE 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 PROPOSITIONS. 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Independent 
 
 Proposition*. 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 e.g. Those 
 
 e.g. Those two 
 
 e.g. Some of 
 
 e.g. Some of 
 
 planets are eacli 
 
 planets are Ju- 
 
 the planets are 
 
 the planets are 
 
 larger than the 
 
 piter and Saturn ; 
 
 larger than the 
 
 Jupiter, Saturn, 
 
 earth; those 
 
 those English 
 
 earth ; some of 
 
 and Venus. 
 
 ancient Greeks 
 
 bishoprics are 
 
 the elements are 
 
 Some of the 
 
 were heroes ; two 
 
 Durham and 
 
 very heavy sub- 
 
 Sirens were heard 
 
 of the planets are 
 
 Chester. 
 
 stances ; some of 
 
 singing together. 
 
 nearer to the sun 
 
 Those Graces 
 
 those prisoners 
 
 
 than the earth is. 
 
 are Thalia and 
 
 are spies ; several 
 
 
 Those Muses 
 
 Aglaia. 
 
 of these trees 
 
 
 are frequently re- 
 
 
 have been struck 
 
 
 ferred to by poets. 
 
 
 by lightning. 
 
 
 
 
 Some of the 
 
 
 
 
 Muses are not 
 
 
 
 
 very important 
 
 
 
 
 personages in my- 
 
 
 
 
 thology. 
 
 
 Dependent 
 
 Dependent 
 
 Dependent 
 
 Dependent 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 Proposition*. 
 
 f.rj. Those two 
 
 e.g. Those con- 
 
 e.g. Some of 
 
 e.g. Some of 
 
 of the continents 
 
 tinents of the 
 
 the great rivers 
 
 the great rivers 
 
 of the Eastern 
 
 "Western hemi- 
 
 of America are 
 
 of Europe are 
 
 hemisphere are 
 
 sphere are North 
 
 larger than, any 
 
 the Volga, the 
 
 immensely larger 
 
 and South 
 
 in Europe ; some 
 
 Danube, the 
 
 than Australia ; 
 
 America ; those 
 
 of his pupils are 
 
 Rhine, and the 
 
 three members of 
 
 grandsons of 
 
 not geniuses. 
 
 Loire. 
 
 the present Cabi- 
 
 Queen Victoria 
 
 Some of the 
 
 Some of the 
 
 net are D.C.L.'s; 
 
 are soldiers and 
 
 Muses of Hesiod 
 
 Muses of Hesiod 
 
 these plays of 
 
 sailors. 
 
 are better known 
 
 were Clio, Mel- 
 
 Euripides are 
 
 Those Muses of 
 
 than the others. 
 
 pomene and Terp- 
 
 masterpieces. 
 
 Hesiod are Clio 
 
 
 sichore. 
 
 Those Muses 
 
 and Euterpe. 
 
 
 
 of Hesiod are 
 
 
 
 
 favourite deities 
 
 
 
 
 of the poets. 
 
 

 
 IMPORT OF PROPOSITIONS. 
 
 TABLE XXXI. ] 
 
 PLURATIVE PROPOSITIONS (UNIQUE ENUMERATIVE). 
 (DESCRIPTIVE, MIXED, AND APPELLATIVE.) 
 
 DISTRIBUTIVE PROPOSITIONS. 
 Independent Propositions. 
 
 e.g. The largest and second largest 
 of the planets both exceed the earth 
 iu bulk. 
 
 Aglaia and Thalia were daughters 
 of Apollo. 
 
 Dependent Propositions. 
 
 e.g. The largest and the smallest 
 of the continents of the Eastern 
 hemisphere have immense rivers. 
 
 The Agamemnon and Choephone 
 of jEschylus are fine plays. 
 
 COLLECTIVE PROPOSITIONS. 
 Independent Propositions. 
 
 e.g. The greatest and second 
 greatest of German poets are Goethe 
 and Schiller. 
 
 Aglaia and Thalia were two of the 
 Graces. 
 
 Dependent Propositions. 
 
 e.g. The largest and the smallest 
 of the independent States of Europe 
 are Russia and San Marino. 
 
 The Agamemnon and Choephorse 
 of jEsehylus are two out of the three 
 plays which form the Oresteia. 
 
 SECTION VII. 
 
 NOTE ON THE PREDICABLES. 
 
 In the doctrine of Predicables we are concerned with the 
 matter of propositions, since it is impossible to say of pro- 
 positions expressed in symbols, under which Predicable-head 
 the Predicates come. This subject of Predicables is full of 
 confusion, and emphatically illustrates Carlyle's saying that 
 " mixing things up is the great bad." 
 
 It does not seem to me possible to reduce the accounts of 
 Predicables to a form that would have practical or theoretical 
 value ; but it may clear up the subject a little to indicate 
 the different elements and points of view which, with- 
 out clearly discriminating one from another, they seem to 
 include. We may distinguish (1) a division of Predicates 
 regarded from a particular point of view i.e. in relation to
 
 NOTE ON THE PEEDICABLES. 77 
 
 their Subjects or, more accurately, a division of Predicate- 
 names regarded in relation to their Subject-names. (2) A 
 scheme of division, and subdivision by dichotomy (" the 
 matchless beauty of the Eamean tree "), from which a series 
 of definitions " per genus et differentiam " and the relations 
 of the positive members in a hierarchical classification are 
 deducible. (3) A view of the relations between classes of 
 natural objects and between individuals and their classes, 
 resulting from and only compatible with a peculiar doctrine 
 of the constitution of nature. (4) The relation between 
 what the Subject-name applies to and what the Predicate- 
 name applies to. (Cf. Genus and Species, which refer to 
 relations between classes : cf. also Aristotle's division into 
 Predicates which are (a) convertible (Definition and Property), 
 (b) not-convertible (Genus and Accident) with the Subject ; 
 in (a) there is identity, in (&) there is not identity of denomi- 
 nation of S-name and P-name.) (5) The relation between 
 what the Subject-name denominates and what the Predicate- 
 name determines (cf. Difference, Property, Accident, which 
 refer to relations of Subjects and their Attributes cf. Mill 
 (Logic, i. p. 134, 9th ed.), confusion between class-relations 
 and relation of Subject and Attribute) ; (6) A division of 
 General Names corresponding to differences of classes (cf. 
 Mill, Logic, Bk. i. ch. viii. 21. 134, 9th ed.). 
 
 If we take the Tree of Porphyry, and make a table of Pre- 
 dicates according to the suggestion which it affords, we get an 
 intelligible division of Predicates into 
 
 (a) Genus (wider containing class). 
 
 (&) Species (narrower contained class). 
 
 (c) Difference (mark by which Species is distinguished 
 from Genus). 
 
 But except on the Realist view, or where the Difference is 
 unique, Genus is not distinguishable, in predication, from 
 Difference (as in, e.g., 
 
 All men are rational, 
 
 All men are animals) ; 
 
 unless we say that Genus is understood to refer to denomina-
 
 78 IMPORT OF PROPOSITIONS. 
 
 tion and Species to determination. Genus + Difference, when 
 predicated of Species, give the Definition e.g. Man is a 
 rational animal here there is identity of the classes referred 
 to. The omission of this head of Predicables seems a defect 
 in the Scholastic account of Predicables. 
 
 If I say, Ccesar is a man, I predicate Species Species 
 prjfidicabilis. But if I say, This animal is a man, what is it 
 that I predicate (on any view of the Predicables) ? I do not 
 see under which head of Predicables this Predicate is to be 
 brought. If I say, All negroes are men, I predicate Species 
 too, on the Realist (or on Mill's) view. But if we are to take 
 this view, nothing but exhaustive knowledge can enable us to 
 know in any case under which Predicable-head our Predicate 
 comes. If I say, All men are animals, I predicate Genus, 
 and All men is a Species subjicibilis. In, These animals are 
 rational animals, I do not know what Predicable I predicate. 
 And if I say, All rational animals are men, what is my 
 Predicate ? Not Genus (that would be animals). Not Species, 
 for that would be rational animals, Species it is said consisting 
 of Genus and Difference. Not Difference, because rational 
 would be the Difference. Not Definition, because here the 
 Definition of the Predicate is given by the Subject. Not 
 Property (for Property flows from essence, and men contains 
 the whole of the essence). Not Accident (because men is 
 essential). 
 
 Coincidence of two classes in extension (of two class-names 
 in application) can hardly be called a relation of classes (i.e. a 
 relation of the extension of classes or application of class- 
 names) at all (cf. post, p. 80, note 1). 
 
 Difference, Property, and Accident either do not express 
 class-relations (which are relations of extension), or they are 
 resolvable into Genus or Species. Genus and Species are pro- 
 perly understood in denomination (quantitively) ; but Differ- 
 ence, Property, and Accident are properly taken (if they are 
 distinctive at all) in determination (qualitively). (Cf. Jevons, 
 Principles of Science, p. 699, 9th ed. "Difference, it is 
 evident, can be interpreted in intension only.")
 
 MILL'S VIEW OF THE IMPORT OF PROPOSITIONS. 
 
 79 
 
 SECTION VIII. 
 MILL'S VIEW OF THE IMPORT OF PROPOSITIONS. 
 
 Any further general differences in (unquantified) Categorical 
 Propositions, beyond those already noticed, depend, I think, 
 wholly upon determination, upon 
 
 1. Eelations of determination between S-nanie and P- 
 nanie here we get the distinctions between Analytic and 
 Synthetic, Real and Verbal. Mill says that Verbal Proposi- 
 tions only inform us as to the meaning of names ; and I 
 should like to take him as nearly as possible at his word, 
 and restrict the term " verbal " to Definitions and Proposi- 
 tions asserting Synonymity of names. Such a Proposition as 
 Courage is Valour (1) may mean (a) The word Courage is a 
 word having the same application as the word Valour (in 
 which case it is verbal), or (&) The thing named ~by the word 
 Courage is ike, same as the thing named by the word Valour. 
 I should propose to group together (a) and (&) with Defini- 
 tions, as Nominal Propositions, thus : 
 
 NOMINAL PROPOSITIONS. 
 
 Verbal Propositions. 
 
 Definitional 
 Propositions. 
 
 e.g. Man is a ra- 
 tional animal. 
 
 (a) Synonymous 
 Propositions. 
 
 e.g. Courage is 
 Valour ( = The word 
 
 (//) Quasi-Tautologous 
 Propositions. 
 
 e.g. Courage is 
 Valour (= The thiny 
 
 Courage is a word, -named by the word 
 etc.) ; Marguerite is Courage, etc.). 
 Daisy. 
 
 Understood as (a), (1) is plainly a question of names ; 
 understood as (6), not only is the denomination of S and P 
 the same, but also no difference can be pointed out in the 
 determination of S and P respectively, except that the object
 
 80 IMPOKT OF PROPOSITIONS. 
 
 named is referred to by one name in S and by a different 
 name in P. 1 
 
 2. Determination of S-name or P-naine, or both. Under 
 this head must certainly be reckoned Mill's division of pro- 
 positions into Propositions of 
 
 Existence. 
 
 Coexistence. 
 
 Sequence. 
 
 Causation. 
 
 Eesemblance. 
 
 (Cf. Mill, Logic,- i. 116, 9th ed.) With reference to this list, 
 Prof. Bain says that Mill " enumerates five ultimate predicates, 
 or classes of predications" (Bain, Logic, i. 106, 2nd ed.) ; 
 but though it seems to me to be true that Coexistence, etc., 
 and such Existence as can be expressed, are most commonly 
 expressed in the Predicate of a proposition, Mill's account of 
 the heads of Coexistence and Succession is by no means in 
 accordance with this view. He analyses, as an example 
 apparently of both Coexistence and Sequence, the proposi- 
 tion, " A generous person is worthy of honour " (cf. Logic, i. 
 110-112). What he here means by Coexistence (? and 
 Sequence), and declares to be the " most common . . . mean- 
 ing which propositions are ever intended to convey," would 
 appear to be Coexistence of Attributes ; 2 and since Attributes 
 cannot coexist (or exist) except in a Subject, this account 
 of the import of propositions conies very near to the one I 
 have proposed, only that it does not apply without modifica- 
 
 1 In all cases of coincident denomination of S-name and P-name in a Cate- 
 gorical, the only "relation " between the Term-names is a relation of determina- 
 tion, a relation within the one class which is indicated by each of them. In 
 denomination, the S-name and the P-namc are not related, but identical. This 
 remark applies both to Nominal Propositions and also to what are commonly 
 called Synthetic or Real Propositions, e.g. All food-cookers are risible creatures 
 (cf. ante, p. 79). 
 
 * This, which may be accepted as Mill's view of the Formal Import of Pro- 
 positions (in as far as it is to be gathered from the Logic), appears to be con- 
 nected with his view of Logic generally, as concerned pre-eminently with 
 Induction, with passing to new truths, for it is only by fresh enlightenment as 
 to the connections of attributes that an increase of knowledge respecting classes 
 of objects can be gained.
 
 MILL'S VIEW OF THE IMPORT OF PROPOSITIONS. 8 1 
 
 tion to what I have called Quasi-Tautologous Propositions, 1 
 and that Mill (though somewhat doubtfully) interprets partly 
 in Sequence as well as in Coexistence (cf. op. cit. i. pp. 113, 
 114, 6). Again, according to Mill (op. cit. i. p. 116), this 
 proposition, " The sensation I feel is one of tightness," is 
 among the propositions which assert Resemblance. But this 
 proposition does not seem to have any distinctive character- 
 istic justifying that title. The Category of Causation he 
 reduces to Sequence. As one example of a proposition assert- 
 ing "a sequence accompanied with causation," Mill gives 
 "Prudence is a virtue" (pp. 119, 120). Here we may 
 perhaps say, that if this proposition asserts " a sequence 
 accompanied with causation," then of any proposition with 
 Common or Attribute Terms we may give the same account. 
 
 Mill's application of his Categories to the Import of Pro- 
 positions seems to me extremely strained, and the mixture 
 here of Formal and Material (non-formal) points of view very 
 confusing. Categorical Propositions which in any ordinary 
 sense would be said to assert Coexistence, Sequence, Causa- 
 tion or Resemblance, assert it in virtue of the content of the 
 terms (generally of the Predicate) ; and thus understood, there 
 are other Categories which might make good their claim to 
 be added to Mill's list ; e.g. the Categories of Inclusion, Ex- 
 clusion, Intersection, Coincidence, etc. Then there are the 
 Categories of Identity (and Non-identity) and Diversity, 
 which apply directly to all Categorical Propositions without 
 exception ; the Categories of Inherence and Subsistence, 
 which apply to all Adjectival propositions, such as, e.g., Trees 
 are green; the Category of Inference, which applies to all 
 Hypothetical and Conditional Propositions ; the Categories of 
 Relations of Magnitude, Part and Whole, and so on. 
 
 1 According to Mill himself, its application would be very much more 
 restricted.
 
 82 IMPORT OF PROPOSITIONS. 
 
 SECTION IX. 
 
 SYSTEMIC OR DEPENDENT PROPOSITIONS. 
 
 I mentioned above (of. ante, p. 20) the connection between 
 what are called a fortiori arguments and Dependent or 
 Systemic Terms. A proposition which has one such term 
 for S or P or both, besides the ordinary purely formal 
 Immediate Inferences which can be drawn from it in just the 
 same way as from Independent Propositions, furnishes other 
 Immediate Inferences to any one acquainted with the system 
 to which it refers. These inferences are not purely formal, 
 inasmuch as they cannot be drawn except by a person know- 
 ing the " system ; " on the other hand, they are not material 
 in the ordinary sense, since no knowledge is needed of the 
 objects referred to, except a knowledge of their place in the 
 system, and this knowledge is in many cases almost coexten- 
 sive with intelligence itself; consider, e.g., the relations of 
 magnitude of objects in space, of the successive parts of time, 
 of family connections, of number. From such a proposition as 
 
 The son of C is the father of D, 
 
 iti addition to the purely formal inferences which may be 
 drawn (the father of D is the son of C, etc.), it is possible for 
 any one having the most elementary knowledge of family 
 relationship to infer further that 
 
 C is the grandfather of D, 
 C is the father of D's father, 
 D is the son of C's son, 
 D is the grandson of C, etc. 
 From 
 
 C is equal to D (besides Something equal to D is C, etc.) 
 it can be inferred that 
 
 D is equal to C, 
 
 C is not less than D,
 
 SYSTEMIC OR DEPENDENT PROPOSITIONS. 83 
 
 D is not greater than C, 
 C is not greater than D, 
 Whatever is greater than C is greater than D, 
 
 and so on. (Cf. also, C is an inference from D, etc.) 
 
 In each of the above examples we are not dealing solely 
 with one object or group in the same way as in Independent 
 Propositions, e.g. 
 
 All men are mortal, 
 
 Tully is Cicero, 
 
 The sky is blue 
 
 we are considering, besides the identity of denomination of S 
 and P, two objects quantitively distinct, namely C and D. 
 The S and P of each proposition have, of course, as just 
 remarked, the same denomination, but an inspection of the 
 Terms (where they are understood) enables us to know that 
 in each case we are concerned with two things (two Subjects 
 or two Attributes) related in a certain way, while of the 
 examples last given this cannot be said. In each of the 
 Dependent Propositions given, what is predicated of S is its 
 relation to another object, and we are able to take that other 
 object and predicate of it its relation to the first object. And 
 where we have two Dependent Propositions as premisses, we 
 are concerned with three distinct objects, and the relations 
 between them ; and the point of union may be in one of the 
 objects, to which both of the others are related. These con- 
 siderations seem to me to account for the reputed anomalous 
 character of a fortiori, etc., arguments. Every such argu- 
 ment can, I think, be expressed (at greater or less length) by 
 help of Immediate Inference or by rigid Syllogism, or by a 
 combination of both, propositions being used that state 
 explicitly principles or laws of the systems referred to, 
 which, in the ordinary conveniently abbreviated form, are 
 only implied. E.g. in 
 
 A is greater than B, 
 B is greater than C, 
 A is greater than C
 
 84 IMPORT OF PROPOSITIONS. 
 
 (where we have four term-names), the reasoning may be 
 expressed by a Conditional Syllogism, thus : 
 
 If any thing (A) is greater than a second thing (B), which 
 (B) is greater than a third thing (C) ; that thing (A) is greater 
 than (C) : 
 
 A thing (A) is greater than a second thing (B), which (B) 
 is greater than a third thing (C) : 
 
 That thing (A) is greater than (C). 
 
 This Conditional may, of course, but with increase of 
 awkwardness, be reduced to Categorical form. 
 
 When Mansel says that a fortiori, etc., arguments as 
 they stand are material, i.e. are arguments in which the 
 conclusion follows from the premisses solely by the force of 
 the terms (Hansel's Aldrich, pp. 198, 199), but that they 
 are reducible to strict syllogistic form, he appears to me to 
 be right. 
 
 Among the most important of Dependent Propositions are 
 Mathematical or Quantitative Propositions. 
 
 SECTION X. , 
 
 NOTE ON MATHEMATICAL PROPOSITIONS. 
 
 My question here is, What is the quantity of the terms, and 
 what the force of the copula, in Mathematical Propositions ? 
 Take, e.g., 
 
 (a) {2 + 3 = 6 1} , and let 2 + 3 and 6 1 mean, 2 + 3 
 and 6 1 of an assigned unit. 
 
 Taking = as signifying is equal to, and 2 + 3, etc., as 
 signifying 2 units together with 3 units, etc., may we read 
 (a), with the subject taken distributively, as 
 
 any (2 + 3)=some (6 1) 
 (i.e. any 2 + 3 is equal to some 6-1, of the assigned unit) ?
 
 NOTE ON MATHEMATICAL PROPOSITIONS. 85 
 
 We cannot have 
 
 any (2 + 3)=any (6-1), 
 
 because the objects denoted by the Predicate in that case 
 might be the very same objects denoted by the Subject, in 
 which case the copula = would be inappropriate, since a thing 
 cannot be said to be equal to itself. 
 
 And if, taking S and P collectively, we interpret (a) to mean 
 
 all (2 + 3) = all (6 - 1), 
 on this view we might have 
 
 1 = (1 + 2 + 3+ etc.) 
 
 (1 + 1) = 1 (cf. Boole), and so on ; 
 
 for all 1's taken collectively embraces all units, however 
 grouped. 
 
 But this would not be admissible in Mathematics, and the 
 appropriate copula here (cf. the Multiplication Table) would 
 be is, not =. (But cf. Monck, Introduction to Logic, p. 19.) 
 
 If, however, we say (cf. ante, p. 84) that (a) means 
 
 any (2 + 3) = some (6 1), 
 
 there arises the difficulty that Simple Conversion (as com- 
 monly applied with the copula = ) would give us a pro- 
 position of this form, 
 
 some (6 1) = any (2 + 3), 
 
 which would not be valid, for the reason which prevented our 
 accepting 
 
 any (2 + 3) = any (6 1). 
 We might have 
 
 some (2 + 3) = some (6 1-), 
 or 
 
 these (2 + 3) = (those 6 1), etc. 
 
 But here the universality which we attribute to Mathe- 
 matical propositions is wanting.
 
 86 IMPORT OF PROPOSITIONS. 
 
 If we interpret = as meaning is-equal-to-or-identical-with, 
 then we can say 
 
 any (2 + 3) -any (6-1), 
 
 and our proposition is true, universal, and convertible. 
 It may be remarked that the copula 
 
 is-equal-to-or-identical-with 
 
 has the same force as 
 
 is-or-is-equal-to. 
 
 If, on the other hand, we hold the figures in question to 
 have the most general or abstract application possible, and take 
 
 2+3=6-1 
 to mean 
 
 The numbers 2 -f 3 = the numbers 6 1 ; 
 
 the difficulties above referred to do not arise. Thus under- 
 stood, 2 + 3 = 6 1 is equivalent to 
 
 any (2 -j- 3) is equal to any (6 1). 
 
 I take equal to mean exactly similar quantitatively, and 
 identical to mean the very same quantitively (numero tantum}. 
 Thus a thing would be equal to some other thing, identical 
 with itself. (Cf. post, Section XXVII.) 
 
 SECTION XL 
 
 PREDICATION AND EXISTENCE. 
 
 The point discussed under this heading is indicated by Dr. 
 Venn (Symbolic Logic, p. 128) as the question whether a 
 " logician who utters a proposition of the form ' All X is Y ' 
 can reasonably refuse to say Yes or No to the question, Do 
 you thereby imply that there is any X and Y ? " (cf. below, 
 " assert or imply "). 1 
 
 1 The subject here considered is treated of by the following writers (among 
 others) : Jevons, Deductive Logic, pp. 141, 142; Dr. Venn, Symbolic Logic,
 
 PREDICATION AND EXISTENCE. 87 
 
 I wish to inquire, first, what can this question mean, and 
 what answer can be given to it, as long as we do not mean 
 by " existence " merely membership of the Universe of Discourse? 
 (cf. Keynes, Formal Logic, 2nd ed. pp. 137, 138). 
 
 If we say that evert/ term is the name of something, or if 
 we say with Mill (Logic, Bk. i. chs. ii., iii.), that whatever can 
 have a name given to it is a Thing, and that all names are 
 names of Things, then we must either answer Yes to Dr. 
 Venn's question, or we must say that there may be Thing* 
 nameable and named which are absolutely non - existent. 
 That this latter answer should be given is perhaps suggested 
 in the question, " Whether when we utter the proposition ' All 
 X is Y ' we either assert or imply that there are such things 
 as X or Y, that is, that such things exist in some sense or 
 other?" 1 (Symbolic Logic, -p. 126). It is, at any rate, Dr. 
 Venn's view (cf. Symbolic Logic, ch. vi. e.g. pp. 130, 131, 
 136, 137) that Universal Categorical Propositions do not 
 (while Particulars do) imply the " existence " of what is re- 
 ferred to by S and P. (The view that the meaning of " All 
 X is Y " is expressed by Xy = adopting Jevons' notation 
 refers the non-existence which is here predicated not to 
 X or to Y, but to Xy.) 
 
 I should maintain that the Things spoken of must exist in 
 some sense or other, and that those who assert the contrary 
 may reasonably be called upon to produce and justify a 
 definition of Thing which excludes existence in every sense, 
 whatever. Indeed Dr. Venn himself in his most recent work 2 
 seems to allow this, for he says (Empirical Logic, p. 232) that 
 " mere logical existence cannot be intelligibly predicated, inas- 
 much as it is presupposed necessary by the use of the term." 
 Mere logical existence means, I suppose, merely such exist- 
 ence as is involved in a thing's being thought about and 
 
 ch. vi., and Empirical Logic, chs. ix., x. ; Mr. Keynes, Formal Logic, Part ii. 
 ch. viii. ; Mr. Bradley, Principles of Logic, note at end of ch. v. of Bk. i. 
 
 1 The italics are mine. 
 
 2 In which, however, he by implication confirms the account of Predication 
 and Existence given in the Symbolic Logic (cf. Empirical Logic, pp. 230, 
 257).
 
 IMPORT OF PROPOSITIONS. 
 
 named, which seems to necessitate some reference beyond the 
 momentary thought of the thinker. 1 Dr. Venn also says 
 (Empirical Logic, p. 141), "I incline therefore to say de- 
 cisively with Mill that the reference of names is to be carried 
 beyond the notion or concept to the objects or things from 
 which the notions are derived or should be derived." And 
 again, p. 158, "Each separate word, whatever the sense 
 through which it is conveyed, is to be taken as an indivisible 
 whole, and referred directly to the corresponding idea, or 
 rather ... to the phenomenon itself." Again, " People do 
 not speak with an intention to mislead, nor do ordinary 
 adults talk habitually of nonentities" (p. 275). It is but 
 the barest minimum of " existence " of any kind whatever 
 mere That-ness that I contend for (no other more deter- 
 minate existence could be involved in the use of all terms), 
 and " logical existence " must certainly involve this minimum. 2 
 Whoever affirms that any term can be devoid of denomination 
 (and hence have no application, not be the name of anything), 
 would allow, I suppose, that such a term must have deter- 
 mination (meaning) ; but I am quite unable to see how a 
 term can have determination and not denomination that is 
 to say, that it can signify character a combination of attri- 
 butes but not " existence ; " this seems like saying that it 
 can signify some kind of existence but not existence itself. I 
 can only conceive of the world as consisting of Subjects (more 
 or less permanent) and Attributes (more or less transient), 
 each having at least a minimum of " existence " by which I 
 understand a capacity of affecting or being affected : such a 
 capacity belongs to even the most fleeting idea of the feeblest 
 mind. No term, it appears to me, can be the name of any- 
 
 1 Cf. Bosanquet, Logic, i. 18, 19: "A name always refers to something." 
 " That which is named is recognised as having a significance beyond the infini- 
 tesimal moment of the present and beyond the knowledge of the individual 
 ... It is, in short, characterized as an object of knowledge." 
 
 a The "existence " that I mean is, I think, what is meant by Professor William 
 James when he says, " In the strict and ultimate sense of the word existence, 
 everything which can be thought of at all exists as some sort of object, whether 
 mythical object, individual thinker's object, or object in outer space and for 
 intelligence at large" (Mind, Jv. 331).
 
 PREDICATION AND EXISTENCE. 89 
 
 thing other than some of these Subjects or Attributes, and to 
 some of these Subjects or Attributes any term must apply. 
 It might be said, I suppose, that when I mentally construct 
 the plan of a building, a picture, a story, I am merely putting 
 together " combinations of attributes " which have no " exist- 
 ence ; " I should say, however, that so far from having no 
 existence, these objects of thought may have an extremely 
 potent and influential existence, for they may be the arche- 
 types and part-causes of constructions having a visible and 
 tangible existence. It appears to me that they may have 
 more energy of existence, and therefore more reality, than 
 visible and tangible objects which once had physical existence, 
 but which, in the form in which they are thought about, have 
 altogether ceased to be, except in thought. And indeed the 
 same may be said of objects of thought which are not arche- 
 typal of any constructions in the material world. The exist- 
 ence of anything, and the thought of that existence, are of 
 course two distinct things, and also existence in one case may 
 differ in character from existence in another case ; but these 
 admissions are not inconsistent with the view that all thought 
 is of something to which some existence is ascribed, and 
 which actually has some existence though it may very well 
 be that the existence ascribed to it may be a different kind 
 of existence from that which it has. 
 
 If by terms having determination and not denomination is 
 meant terms which apply to concepts logical (or monado- 
 logical) concepts, that are complete in themselves and 
 altogether isolated it appears to me that even supposing 
 such concepts to exist as ideas, and to have names by which 
 they are called, these names could never be the terms of 
 propositions. (Cf. ante, Section V.) 
 
 If it is admitted that all terms are names of something, 
 but maintained that the Things which are named may be 
 " non-existent," the answer to Dr. Venn's question with 
 which we started may, of course, be in the negative. But 
 (besides the difficulty as to the meaning of Thing, and 
 besides the difficulty there seems in affirming or denying
 
 90 IMPORT OF PROPOSITIONS. 
 
 anything of what has absolutely no existence whatever, or in 
 making one affirmation or denial in preference to another) 
 how, on this view, are we ever to posit existence pure and 
 simple at all ? Unless an implication of existence is con- 
 tained in the mere enunciation of the S and P of a proposi- 
 tion, I do not see how it can be " implied or asserted." It is 
 not existence pure and simple which is ever asserted in the 
 P of any proposition, 1 but only some mode of existence, that 
 is, some characteristic ; the bare " existence " of which, of 
 course, depends upon the " existence " of that of which it is 
 the characteristic. E.g. if I say 
 
 Fairies are non-existent, 
 
 the existence that I deny is not existence of every kind, since 
 fairies have a certain kind of existence in fairy tales and in 
 imagination. This existence in imagination is, of course, dis- 
 tinct from the so-called mental image which accompanies not 
 only our comprehension of the terms of propositions which we 
 understand, but also our apprehension of objects which we 
 recognise. What is denied to them in the above proposition 
 is (perhaps) " ordinary phenomenal existence and at the time 
 present." 
 If I say 
 
 Ideals of conduct exist, 
 
 the existence that I affirm is not bare existence, nor, e.g., the 
 kind of existence just denied to fairies, but existence in 
 men's thoughts. Unless it is admitted that mere existence 
 is intended to be implied in the very enunciation of the 
 terms of a proposition, the interpretation of our proposition 
 
 1 Cf. Bain, Logic, i. 59, IJ)7, 2nd ed. : "There is nothing correlative to the 
 supposed Universe, existence, the absolute ; nothing affirmed when the sup- 
 posed entity is denied." "With regard to the predicate Existence occurring 
 in certain propositions, we may remark that no science, or department of logical 
 method, springs out of it. Indeed all such propositions are more or less 
 abbreviated or elliptical. " 
 
 Cf. also Venn, Empirical Logic, p. 198 : "Existence, in every case where it 
 need be taken into account, can be regarded as being of the nature of an attri- 
 bute." A " special kind of existence " is not "implied by the use of the term ; 
 is not conveyed by the ordinary copula ; it is a real restriction . . . and there- 
 fore it is a perfectly fit subject of logical predication " (op. cit. p. 232).
 
 PREDICATION AND EXISTENCE. 91 
 
 is liable to involve us in an infinite reress ; we have no TTOV 
 
 Take a proposition of the form 
 All E is Q 
 
 interpreted on the view that Predication (at any rate in the 
 case of an Universal proposition) is not intended to involve 
 existence. 
 
 All K is Q (1), 
 
 it is said, is equivalent to 
 
 Eq = O (2) * 
 = There is no Eq (3). 
 
 If we remove the ambiguity of is, (3) appears to be equiva- 
 lent to 
 
 No Eq is existent (4), 
 (4) = All Eq is non-existent (5), 
 
 and (5), interpreted in the same way as (1), is equivalent to 
 No Eq-existent is existent (6), 
 
 and this process may be carried on indefinitely (compare the 
 result of interpreting S is P to mean S is P is true}. Besides 
 which, (6) is a contradiction in terms. 
 
 It is said that in reducing All R is Q to Rq 0, Subject 
 and Predicate are taken strictly in extension (" denotation "). 
 But since All R is (some) Q is pronounced to be equivalent 
 to (not 
 
 All-E-not-(some)-Q = 
 but) 
 
 Eq=0, 
 
 1 It seems to me that in just that "existence" of the things named by 
 a term which is "presupposed necessary by the use of the term," the "refer- 
 ence to reality " is involved, of which Mr. Bosanquet speaks (Logic, Bk. i. 
 ch. i. 2) as essential in judgment. And then every proposition by its very 
 nature and constitution lays claim to be true it cannot help itself and it can 
 only be called in question or contradicted by another proposition also claiming 
 to be true. But unless the terms of propositions are the names of something 
 having some kind of existence or other, one does not understand how this inevit- 
 able claim of propositions can have even so much significance as to be capable 
 of being rejected. 
 
 3 Cf. Venn, Symbolic Logic, pp. 25, 144, etc.
 
 92 IMPORT OF PROPOSITIONS. 
 
 it is clear (1) that it is R and Q, and not All R, (some) Q, 
 that have been dealt with ; (2) that R and Q have been taken 
 in determination. 1 
 
 A further point is, that unless the very positing of a term 
 signifies the existence of something named by the term, we 
 could never say, S is P, since the mere symbol S is certainly 
 not the symbol P. And when our terms are synonyms, or 
 our proposition declares a definition, as in, e.g., 
 
 Courage is valour, 
 
 The word man is a word meaning rational animal, 
 
 the analysis into Sp = seems peculiarly inappropriate. 
 
 I think that some of the difficulty of this subject arises 
 from the circumstance that there is often confusion between 
 the following two questions : (1) Does a term necessarily 
 imply some " existence " of something to which it refers ? 
 (2) Do people when they use terms mean to imply that 
 those terms apply to things having the characteristics usually 
 attributed to the things named by the terms (or their con- 
 stituents) ? In particular, it seems that a confusion about 
 time is often involved ; for instance, when it is said that any 
 assertion, All R is Q, leaves (or is meant to leave) the exist- 
 ence of E doubtful, it is not always clear whether the doubt 
 refers to all (any) time, or some particular time. If the 
 doubt does refer to all time, we are simply taken back to the 
 question about bare existence, and can only ask, If it is 
 doubtful whether there is, or ever was or will be, any R, 
 what is the meaning of talking about R at all, and what can 
 we be entitled to affirm or deny of R ? (And unless the S and 
 P are symbols of something other than themselves, we could 
 not even say, All R is Q.) If the doubt refers to some 
 particular time, then it refers not to mere existence, but to a 
 certain determination of existence. If this is expressed, it 
 will occur as part of the attribution of S or P. If not so 
 occurring, it can only be supposed to refer to the present 
 moment, since the copula certainly contains no reference to 
 1 Cf. post, Section on Quantification and Conversion.
 
 PREDICATION AND EXISTENCE. 93 
 
 past or future time. On this view, if we take, e.g., the pro- 
 position 
 
 All Albinos have pink eyes, 
 
 our assertion must contain (a) A declaration of an universal 
 connection (namely that between being an Albino and having 
 pink eyes). (&) A doubt whether there are any Albinos 
 living at the present moment. It seems to me not only 
 that any one making the assertion would not be naturally 
 conscious of (&), but also that the presence of (Z>) to the 
 mind is not even apparent on reflection that, in fact, it is 
 quite irrelevant. 
 Or take 
 
 All cases of shooting through the heart are cases of 
 death. 
 
 Or 
 
 If a man is shot through the heart he dies immediately. 
 
 Is there any implication of doubt about the existence of 
 present cases of shooting through the heart ? 
 
 As regards the general question, Do people when they use 
 terms mean to imply that those terms apply to things having 
 all the determination usually signified by the terms or term- 
 constituents ?, I should be inclined to say in answer to it 
 that any proposition detached from context and tone of 
 assertion must inevitably be understood to have such an 
 implication. (Context or tone may, of course, so affect a pro- 
 position as to make us aware in any particular case that 
 S is P is meant to convey S is-not P. 1 ) A remark of Mr. 
 Bosanquet's (Logic, i. p. 78), though directed to another point, 
 seems confirmatory of this view. He says, " In every judg- 
 ment, as Mill incisively contends, we profess* to speak about 
 the real world and real things." That we do always so speak, 
 cannot, of course, be maintained. But I think that we do so 
 in more cases than are at first apparent. For instance, we 
 
 1 E.g. if one says to a very unpunctual person,' " You are always in time." 
 
 2 The italics are mine.
 
 94 IMPORT OF PROPOSITIONS. 
 
 not uncommonly assert a proposition from knowledge (real or 
 supposed) of the relation of the negatives of the terms which 
 we use as is no doubt the case in such sayings as, An 
 honest miller has a black thumb inferred from, and meant 
 to express, the supposed truth that All white-thumbed millers 
 are not-honest. All the wheels that go to Croyland are 
 wheels shod with silver, is another instance of the sort. 
 
 It is possible (though not common except when we are 
 using symbols) to combine a plurality of Subjects to form a 
 fresh Subject, and a plurality of Predicates to form a fresh 
 Predicate, or, in other modes, to construct complex Subjects 
 and Predicates. We may, of course, in this way construct 
 terms which determine attributes that never have been, and 
 never will be, and even never can be, conjoined in a single 
 Subject e.g. we may combine 
 
 A is b 
 and 
 
 B is a 
 
 and get the proposition 
 
 Aa is Bb 
 or 
 
 AB is ab. 
 
 Here not only denomination, but also determination, pro- 
 position, and term would vanish altogether if we could refer 
 the contradictory determinations to one and the same Subject. 
 
 But if the determinations remain as separate as the term- 
 constituents which express them, denomination lasts as much 
 as determination ; but it is a mere collocation of denomina- 
 tions (as well as of determinations) in the case of each 
 " term." 
 
 A further objection to the view under discussion is that 
 it does not afford an ultimate analysis. For let it be admitted 
 that 
 
 All K is Q 
 means
 
 PREDICATION AND EXISTENCE. 95 
 
 then what does Eq = O mean ? It must be read off as 
 either 
 
 (1) E-not-Q (is) nought (= Something is nothing], 
 or 
 
 (2) E-not-Q (is-equal-to) nought. 
 
 But (1) is in the form S is P, and (2) is reducible to that 
 form, unless we hold the complexity introduced into the 
 copula to be a step in analysis. So we seem brought back 
 to the point from which we started. 
 
 Nor does the above interpretation of Categorical Proposi- 
 tions furnish a general analysis ; for, giving a widely different 
 interpretation of Universals and Particulars (according to 
 which Particulars involve " existence " while Universals do 
 not), it does not and cannot say what S is P means where 
 8 and P may stand for any term (e.g. Some E, All E, this E, 
 one E, etc.). If the copula is unvarying, must not the con- 
 nection between S and P in all propositions be the same ? 
 And how could we interpret 
 
 All E is Q (1) 
 into 
 
 Eq = (2) 
 
 unless we had first understood (1) in its ordinarily accepted 
 (or some other) affirmative sense ? We have in (2) two 
 elements the Predicate and a constituent of the Subject 
 which do not appear at all in (1). Whence do we obtain 
 (E)q and ? and what are our data for the assertion of '(2) 
 unless we have first understood (1) to assert concerning All 11 
 that it is Q ? If a distinction is to be drawn between pro- 
 positions which do, and those which do not, make explicit 
 reference to the actual existence, definitely determined in time, 
 of what is indicated by S and P, I think the line should be 
 between those having Proper Names and Singular and Par- 
 ticular Definites e.g. This E, Those E's, etc. for S, on the 
 one hand, and all other propositions on the other. 
 
 Again, treating our propositions as Coincidentals (which
 
 96 IMPORT OF PROPOSITIONS. 
 
 for symbolic purposes, and indeed wherever we use uninter- 
 preted symbols, we are bound to do), if (1) 
 
 All E is Q 
 is expansible to 
 
 All E is some Q ; 
 
 if (2) what affirmative Categoricals express is identity of 
 denomination of S and P (in diversity of determination) ; and 
 if (3) some implies " existence ; " must not the " existence " of 
 All R be implied in 
 
 All K is Q ? 
 
 If not, some as qualifying the Predicate-name differs in the 
 most extreme way from some as qualifying the Subject-name. 
 And I do not know on what grounds such a divergence of 
 meaning can be justified. 
 
 Some exponents of the view which I am disputing, how- 
 ever, hold a different form of the doctrine. They hold 
 that the " existence " here in question is not bare or mere 
 existence, but a particular kind of existence existence in 
 (= membership of) some region to which we are referring, 
 and which is our Universe of Discourse. We must, it is 
 said, know in all cases what our Universe of Discourse is. 
 But how are we to know this in dealing with uninterpreted 
 symbols e.g. K's and Q's ? In such cases we must (1) 
 define our Universe by reference to our terms, or (2) take 
 the Universe as all-embracing. Or (3) we must admit that we 
 do not know how to describe or indicate our Universe. If 
 it is asked why we do not admit a fourth alternative, and 
 call our Universe, e.g. X, or Y, or Z, without defining X, Y, 
 or Z by reference to E or Q, I reply that since our symbols 
 are uninterpreted, we are not justified in referring E and Q 
 to any one such Universe symbolically indicated rather than 
 to any other, if X, Y, Z have any distinctive force at all. 
 And if it is said that they have not, and that taking, e.g., 
 X, as our Universe-term in reference to All E is Q, simply 
 changes All E is Q (1) into All EX is QX (2), then on
 
 PREDICATION AND EXISTENCE. 97 
 
 the proposed interpretation of (1) (since X=l and = x), 
 we et 
 
 which is a contradiction in terms. (And must not RX and 
 QX have a Universe Y, and so on ?) 
 
 On supposition (3) we must be unable to say whether 
 anything belongs, or does not belong, to the Universe of 
 Discourse, and in this case the Universe cannot affect our 
 assertions in any way. 
 
 On supposition (1) our Universe is a region containing (a) 
 E, T, Q, q, or (6) some selection from these. If (&), we are 
 forced to transcend the Universe (cf. post} ; and case (a) re- 
 solves itself into (2) where the Universe is all-embracing. 
 Here, too, we are involved in difficulties. For let the Universe- 
 Term (indicating the region which includes E, r, Q, q) be X ; 
 then we can say, 
 
 Everything is an X. 
 
 But this is no more than to say, 
 
 Nothing is x ; 
 
 and here we have transcended our Universe, and need some 
 term which will include X and x. In mentioning our Uni- 
 verse we always make it possible to transcend it. And when 
 we do transcend it, is it any longer our Universe of Discourse ! 
 What is it that entitles X rather than x to that appellation ? 
 I do not see how, here, the so-called Universe-Term differs 
 from a mere Class-Term. 
 
 And in working with limited and indicated Universes, we 
 encounter similar difficulties. If we take any limited Uni- 
 verse X, calling any member of it an X, we are immediately 
 liable to transcend X, and in the interpretation of 
 
 All E is Q, 
 (referred to the Universe X) as 
 
 we must transcend it. Here X seems obviously nothing more 
 
 G
 
 98 IMPORT OF PROPOSITIONS. 
 
 than a Class-term. I do not see that in affirming or denying 
 it one does anything more than affirm or deny membership 
 of a class; or that when one has affirmed x, one is any 
 longer entitled to speak of X as one's Universe of Discourse. 1 
 Again, let us take as our Universe the region of Animal 
 life, and referring to this, say, e.g. 
 
 All lions are tawny (1). 
 According to the interpretation I have been disputing 
 
 <l) = (Lt = 0)(2) 
 = (Lt = a) (3). 
 
 But we were supposed to be referring to the region of A, and 
 the Lions spoken of were A (stone lions, marble lions, etc. 
 need not be tawny), 
 
 .-. (3) = (LtA a) (4). 
 
 But this is a contradiction in terms, not to mention that 
 again the Universe A is transcended. 
 
 If we adopt (2) as the interpretation of (1), and refer Lt 
 to the region A, our " Universe," I do not see how we can 
 avoid arriving at (4) ; for, unless we interpret as meaning 
 unqualifiedly " nothing " or " non-existent," we must interpret 
 it as meaning " not occurring in the region A ; " but " not 
 occurring in A " means " occurring outside A," and therefore 
 being a (unless (1) A is all-embracing, which by supposition 
 it is not, and (2) " not occurring in A " indicates what is 
 absolutely non-existent ; and I have, I think, given sufficient 
 reason for refusing to admit this interpretation). The fact 
 seems to me to be that in 
 
 Lt = 
 
 both our terms refer to the region a, not to the region A. If 
 we say that we start with the Universe A in 
 
 All lions are tawny, 
 
 1 The objections to the expression Rq = as an interpretation of All 
 R is Q, are not altered if we explain Rq = to mean, not Rq = x, but Rq = 
 some x.
 
 PREDICATION AND EXISTENCE. 99 
 
 we have certainly in 
 
 Lt = 
 
 transferred ourselves to the region a, and here, as long as we 
 equate to we remain. But only has meaning with refer- 
 ence to A, therefore we have to take both A and a into our 
 Universe, and it is not merely reference to the class A, but 
 reference to that class and to its contradictory that enables us 
 to interpret 
 
 All lions are tawny 
 into 
 
 Lt = O. 
 
 Thus reference to the Class A as Universe of Discourse 
 seems necessarily to allow both inclusion in that class and 
 exclusion from it, involving free use of the terms A and a, 
 and free movement in the regions indicated by those terms. 
 But I have never understood logicians who advocate the use 
 of Universes of Discourse to mean that the Universe A 
 includes also a ; and, moreover, A and a embrace the whole 
 Universe taken in the widest sense. 
 
 Thus, as it appears to me, the attempt to use restricted 
 Universes breaks down. 
 
 Even supposing that we could use them, I do not think it 
 would be convenient in ordinary life and thought. I think 
 that in any ordinary conversation, or book, or newspaper, 
 what happens is that we constantly refer in the same para- 
 graph, if not in the same sentence, to more than one restricted 
 " Universe." If I say, " I had a strange dream last night ; it 
 reminded me of a scene in Romola" I refer to the Universes of 
 spiritual and material fact, of illusion and fiction. If I read, 
 " In the beginning God created the heavens and the earth . . . 
 and the Spirit of God moved upon the face of the waters," I 
 again find many Universes (in the narrow sense) referred to. 
 And it is the same everywhere ; no one keeps, or feels any 
 need of keeping, consistently to one Universe. But notwith- 
 standing this, we do not generally fear, nor perhaps risk, con- 
 fusion. What saves us from this (in as far as we are saved) is
 
 100 IMPORT OF PROPOSITIONS. 
 
 not, I think, the apparatus of Universes which seems awkward 
 and inadequate, but that presupposition of thought which 
 the so-called Law of Identity is sometimes interpreted to 
 mean. 1 This is perfectly simple, and fully adequate to the 
 purpose. There is no fear of confusion or mistake in the use 
 of terms as long as we give always the same value to our terms ; 
 though what our terms are can generally only be settled by 
 some reference to context. No doubt we often use implicitly 
 qualifications of terms which are indispensable to understand- 
 ing, and in this danger may lurk. But the risk must be run ; 
 and these implicit qualifications must always be capable of being 
 made explicit on demand. It seems to have been with a view 
 to such implicit qualifications that the idea of Universes of 
 Discourse has been introduced. The case for Universes seems 
 most plausible when we are concerned with Technical, etc., 
 Terms. We do, of course, have dictionaries of Technical 
 Terms, and treatises bristling with Technical Terms, and 
 something is gained by the information given us to start 
 with, that we are going to be specially concerned with a 
 particular class of objects. But in no such case are we 
 really confined to the limited region indicated ; multitudes of 
 Common Terms must be used, explanations must refer to a 
 variety of outside objects, illustrations may be taken (without 
 formal notice) from almost any region. 
 The interpretation of 
 
 (a) All R is Q, 
 (6) No R is Q, 
 to mean 
 
 Rq = O, 
 RQ = 0, 
 
 involves, it is said, the admission that (a) and (6) may both 
 be true together in the case, that is, where there is no R. 2 
 But if this is so, then if our Universe is all-embracing, Every- 
 thing is r, which seems inadmissible ; and if our Universe is 
 
 1 Cf. ante, p. 3, and post, Section on the Laws of Thought. 
 3 Cf. Symbolic Logic, p. 145.
 
 PREDICATION AND EXISTENCE. 101 
 
 restricted, let it be X. Then it is with reference to X that 
 we say that 
 
 All R is Q, 
 
 No E is Q 
 in other words, that 
 
 E is Q and q. 
 
 But if all X is destitute of E's, if the whole of it is r, what 
 is meant by saying that X is our Universe of Discourse when 
 we assert 
 
 All E is Q, 
 
 No E is Q 
 
 (meaning that there is no E within the region X) ? How can 
 we call that our Universe of Discourse which is absolutely 
 destitute of the things to which our terms apply ? 
 Suppose I say 
 
 All green lions are African, 
 No green lions are African, 
 
 and assert that my Universe of Discourse is the Zoological 
 Gardens, and that the meaning of my two propositions is to 
 deny the " existence " of green lions (that is, their presence in 
 the Zoological Gardens). Is there not force in the objection 
 that, since what I am talking of is not in the Zoological 
 Gardens, that region is not my Universe of Discourse ? Must 
 not my Universe of Discourse in this case be some region 
 where there are green lions, i.e. a region of imagination ; and 
 in this region contradictions are excluded as well as in 
 regions of material existence. If I imagine green lions, I 
 cannot imagine them as being both African and not African. 
 Mr. Bradley (Principles of Logic, p. 154) objects to allow 
 that A and E may be asserted together, and says that the 
 view that they may be so asserted is due to a confusion be- 
 tween possibility and existence. I should rather say that it 
 is due to a confusion between different kinds of existence (or 
 existence in different regions). In as far as it is not this, 
 but an actual contradiction (or contrariety) within a specified
 
 102 IMPORT OF PROPOSITIONS. 
 
 region, it involves a breach of the Law of Contradiction, which 
 (besides being, as it seems to me, a pillar of Logic) is 
 as self-evident as any principle in the world can be, and is 
 accepted because of its self-evidence, because its truth is 
 " clear and distinct." And no proposition whatever can be 
 supported by better evidence than this ; hence to question 
 the Law of Contradiction is to question the very foundations 
 of Logic, the very possibility of truth, and to open the door 
 to limitless doubt. 
 
 One further point in connection with the subject recurs 
 to me forcibly here. Logicians who hold that since all does 
 not imply existence while some does, Particulars cannot be 
 deduced from Universals, hold also that some does not exclude 
 all. The point here is, I suppose, that some is taken to 
 apply to matter of finite experience, while the Universal all 
 is not. If this is so, how is it possible that some could ever 
 be admitted to apply to all ? It appears to me that the 
 Universal all both includes and transcends experience, so 
 that some may legitimately be deduced from it, but can never 
 be intended to have, though, as a matter of fact, it may have 
 the same application. Nor even if all means merely a com- 
 pleted quantity or number, can some ever be intended to be 
 equivalent to it though it may turn out to have an identical 
 application as if, having taken apples out of a basket of 
 apples and pears in the dark, I say, " Some apples are de- 
 cayed," meaning all that I have taken out, and find on further 
 investigation that, as a matter of fact, there are no apples 
 left. 
 
 But taking either sense of all, and regarding some as 
 possibly equivalent to it (in application), how can we deny the 
 inferribility of some from all ? The truth seems to be that 
 some and all have diverse determinations, but may in any 
 given case happen to have an identical application.
 
 INFERENTIAL PROPOSITIONS. 103 
 
 SECTION" XII. 
 
 (B.) INFERENTIAL PROPOSITIONS. 
 
 PROPOSITIONS of the form 
 
 If E is F, E is H, 
 If E is F, G is H, 
 If any E is F, that E is H, etc., 
 
 are commonly called Hypothetical or Conditional (E is F, 
 any E is F, are Antecedents ; E is H, G is H, that E is H, 
 are Consequents). 
 
 My reason for wishing to adopt the name Inferential is 
 twofold. In the first place, it seems to me that the differentia 
 of such propositions is to be found in a relation between A 
 (Antecedent) and C (Consequent), such that C is inferred 
 from A. In the second place, I accept the differentiation of 
 " Hypothetical " from " Conditional " Propositions (cf. Keynes, 
 Formal Logic, pp. 64, 65, 2nd ed.) suggested by Mr. W. K 
 Johnson and accepted by Mr. Keynes, and it seems desirable 
 to have a generic term for these two species. This distinc- 
 tion itself seems to me of great value, corresponding to a 
 fundamental difference, and allaying, at the same time that it 
 explains, the dispute as to whether Hypotheticals and Con- 
 ditionals are, or are not, reducible to Categoricals having S 
 and P corresponding to the A and C of the original pro- 
 positions. 
 
 I propose to define as follows : 
 
 An Inferential Proposition is a proposition expressing a 
 relation between Antecedent and Consequent, such that an 
 identity (or identities) expressed or indicated by the Conse- 
 quent is an inference from an identity (or identities) expressed 
 or indicated by the Antecedent. (Cf. Keynes, Formal Logic, 
 p. 164, 2nd ed.; also post, Mixed Inferential Syllogisms, Table 
 XXXVIII.) 
 
 As I have mentioned above, I accept the view according
 
 104 IMPORT OF PROPOSITIONS. 
 
 to which the propositions which I wish to call Inferential 
 may be divided into two distinct species, called respectively 
 
 (1) Hypothetical. 
 
 (2) Conditional. 
 
 (Cf. Keynes, Formal Logic, pp. 64, 65, 67, etc., 2nd ed.) 
 
 (1) Differ from (2) in this, that both A and C express or 
 indicate a complete Categorical Proposition, capable of being 
 asserted in isolation (cf. op. cit. p. 65), e.g., 
 
 If you are right, he is a good man ; 
 If E were F, G would be H. 
 
 Hence the A and C of Hypothetical might be called absolute 
 assertions ; whilst the A and C of Conditionals might be dis- 
 tinguished as relative assertions ; for each refers to the other 
 and is in itself incomplete. Take, e.g., 
 
 If any flower is scarlet, it (= that flower) is scentless. 
 
 Any flower is scarlet, the A of this Conditional, if asserted in 
 isolation, is equivalent to all ftowers are scarlet ; but this is not 
 the meaning which it has as Antecedent. And that flower 
 is scentless the Consequent has obvious reference to that 
 which has gone before, and is obviously incomplete in itself. 
 A Conditional Proposition may be defined as 
 
 A Proposition which asserts that any object which is 
 indicated by a given class - name and distinguished 
 in some particular way, may be inferred to have also 
 some further distinction. (Cf. post, p. 111.) 
 
 A Hypothetical Proposition may be defined as 
 
 A Proposition in which two (expressed or indicated) 
 Categoricals (or combinations of Categoricals) are 
 combined in such a way as to express that one 
 (Consequent) is an inference from the other (Ante- 
 cedent). Cf. Keynes, Formal Logic, p. 164. 
 
 It may be observed that this inferential relation can only 
 obtain between propositions that differ from each other, but 
 are not incompatible.
 
 INFERENTIAL PROPOSITIONS. 105 
 
 The import of an Inferential may, I think, be nearly 
 expressed in a Dependent (or Systemic) Categorical e.g., 
 
 If E is F, G is H 
 
 is expressible as 
 
 G is H is an inference from E is F (1). 
 This proposition may be compared to such a proposition as 
 E is larger than F (2). 
 
 In both cases there are two non-identical elements (G is H 
 E is F, E F) having a certain relation to each other ; and 
 from both certain fresh propositions may be inferred in addition 
 to those inferrible from all Categoricals (cf. ante, Section IX.). 
 The following are examples of equivalent Inferential and 
 Categoricals : 
 
 ( 1 ) If you are disappointed, I am sorry. 
 
 (2) If all men were perfect, all men would be infallible. 
 
 (3) If any bird is a thrush, it is speckled. 
 
 (1) = That I am sorry is an inference from your being dis- 
 appointed. 
 
 (2) = That all men are infallible is an inference from all 
 men's being perfect (perfect creatures being infallible). 
 
 (3) = That any bird is speckled is an inference from its 
 being a thrush. 
 
 (2) May be regarded as enthymematic. (Cf. post, pp. 
 106, 107.) 
 
 Hypothetical Propositions may be divided as follows : 
 
 (1) Hypotheticals in which the Consequent is an inference 
 from the Antecedent alone (e.g. If all H's are Q's, some R's 
 are Q's) these I call Self-contained Hypotheticals. They 
 are further divided into Independent and Dependent. 
 
 (2) Propositions in which C is inferred not from A alone, 
 but from A taken in conjunction with some other unexpressed 
 proposition or propositions. These I call Referential Pro- 
 positions. They may refer to either (a) only one unexpressed 
 proposition, as in 
 
 If M is P, S is P [ . S is M] ;
 
 106 IMPORT OF PROPOSITIONS. 
 
 and these I have called Enthymematic ; or they may refer 
 (b) to more than one unexpressed proposition, as in 
 
 If that rope did not break, the knot must have come 
 undone. 
 
 These I call Elliptical. Both (a) and (b) may be Inde- 
 pendent or Dependent. This account of Hypothetical Pro- 
 positions involves the view that the terms contained in any 
 Hypothetical are all to be identified in application, either 
 directly as in (1), or indirectly as in (2). In the latter case 
 the identification is effected by means of Middle Terms ; this 
 indirect identification may perhaps be called Integration. 
 
 My use here of the terms Inferential, Enthymematic, and 
 Elliptical perhaps needs some further justification and expla- 
 nation. As regards Hypotheticals, I think that Mr. Keynes' 
 definition is in support of the view that these propositions 
 assert a relation between A and C, such that C is inferrible 
 from A. For he explains the import of a Hypothetical 
 proposition to be " that the truth of C follows from that of 
 A" 1 (Formal Logic, p. 164, 2nd ed.). That C follows from 
 A seems to me equivalent to saying that C is an inference 
 from A. And reference to the Hypothetico - Categorical 
 Syllogism affords further confirmation ; for, having asserted 
 
 If A, C ; 
 
 we ask no more than the Categorical assertion of A, in order 
 to go on to the Categorical assertion of C. And in a Con- 
 ditional of the form 
 
 If any D is E, that D is F, 
 
 what is asserted seems to be, that the presence of E with D 
 is sufficient ground for expecting the further presence of F 
 that is, that wherever we find DE, we may infer F. (Cf. 
 Mill's Axiom of Syllogism. Whatever has any mark (DE), 
 has that (F) which it (DE) is a mark of.) I admit that 
 frequently in Hypotheticals the A does not express the whole 
 justification for C which it implies. In 
 If M is P, S is P, 
 
 1 I have substituted A and C for P and Q.
 
 INFERENTIAL PllOPOSITIONS. 107 
 
 one unexpressed proposition (namely, S is M) is necessary in 
 order to give the whole ground. (It is because of the exact 
 correspondence between this inference and the Categorical 
 Enthymeme that I have called Hypothetical of this kind 
 Enthymematic.) And in such a Hypothetical as, 
 
 If X is Y, S is P, 
 
 it is clear that more than one Categorical proposition is 
 necessary to justify the assertion of S is P on the strength of 
 X is Y. And since these other Categoricals are unexpressed, 
 the Hypothetical as a whole is elliptical. 
 
 If the application of the term Inferential to these Hypo- 
 theticals is objected to on account of the incomplete expres- 
 sion in A of the ground of C, then on this view we ought, I 
 think, to deny that there is an inference in such assertions 
 as : This is iron, and therefore liable to rust ; or, This is a 
 square on that side of a right-angled triangle which subtends 
 the right angle, and therefore it is equal to the squares on 
 the other two sides. 
 
 Conditional Propositions may be divided into (1) Divisional 
 Propositions, in which it is asserted that if any member of 
 a specified class belongs to a subdivision indicated by the 
 P-name of A, it may be inferred to belong to one indicated 
 by the P-name of C ; e.g., 
 
 If any goose is not grey, it is white. 
 
 If any peer is not a duke, he must be a marquis, or an 
 
 earl, or a viscount, or a baron. 
 If any Briton is not English, Welsh, or Irish, he is Scotch. 
 
 These correspond to, and are derivable from, Divisional Alter- 
 natives to which also they may be reduced. 
 
 (2) Quasi -Divisional Conditionals. In these the class 
 indicated by the S-name of the A is not (as in Divisionals) 
 exhaustively subdivided by the negative of the P-name (or 
 names) of A, and the P-name (or names) of C ; but the 
 species got by combining the Term-names of the S and P of 
 the A is referred to the class indicated by the P of C, and 
 the division indicated by the P-name of A is coincident with,
 
 108 IMPORT OF PROPOSITIONS. 
 
 or included in (not co-ordinate with), that indicated by the 
 P-name of C. 
 
 The following are examples of (2) : 
 
 If any violet is white, it is fragrant ; 
 If any fowl is a Spangled Hamburgh, it is Silver or Golden; 
 If any fowl is a Plymouth Eock or a Spangled Ham- 
 burgh, it is a handsome bird. 
 
 The distinction between Hypothetical and Conditional 
 Inferentials becomes very marked when a proposition of 
 either kind is taken as major premiss in a syllogism which 
 has a Categorical minor and conclusion. 
 
 With a Hypothetical we get 
 
 If A, C; 
 
 A (or not C} ; 
 C (or not A). 
 
 If, e.g., A = Honesty is not the best policy, 
 C = Life is not worth having, 
 
 our syllogism runs 
 
 If Honesty is not the best policy, life is not worth having ; 
 Honesty is not the best policy (or Life is worth having); 
 Life is not worth having (or Honesty is the best policy). 
 
 But, taking a Conditional Proposition as major premiss, we 
 do not for minor simply affirm the A or deny the C, nor for 
 conclusion simply affirm the C or deny the A. A significant 
 syllogism having a Conditional major and a Categorical minor 
 and conclusion is always reducible (though the reduction may 
 be troublesome) to the form 
 
 If any D is E, that D is F ; 
 XD is E (or XD is not F) ; 
 XD is F (or XD is not E). 
 
 The S of the A of any Conditional is always indefinite 
 the S-name of the minor and conclusion generally has either 
 a definite Term-indicator, or is distinguished from the S-name
 
 INFERENTIAL PROPOSITIONS. 109 
 
 of the A by some distinctive attribute. We may have a 
 syllogism of the form 
 
 If any D is E, that D is F ; 
 Some D is E ; 
 Some D is F ; 
 
 but it is unusual. 
 
 If we allow Inferential of the form 
 
 If M is F, N is H 
 
 to represent both Hypothetical and Conditionals, then 
 we cannot, if we are absolutely precise, use propositions of 
 this form in Immediate Inference. For the only distinctive 
 Immediate Inference that can be drawn from an Inferential 
 is what is called the Contrapositive (cf. post, Section XIX.) ; 
 and given that 
 
 If M is F, N is H (1) 
 
 is a Conditional, and therefore (cf. post, p. Ill) reducible to 
 the form 
 
 If any E is F, that E is, H (2), 
 
 the denial of the C will not give us precisely what is wanted 
 for the A of the Contrapositive, nor will the denial of the A 
 give us precisely what is wanted for the C of the Contra- 
 positive. For the Contrapositive would be 
 
 If any E is not H, that E is not F. 
 And, similarly, if it is allowed that 
 If A, C (3) 
 
 represents indifferently Conditionals and Hypothetical, then 
 
 If A, C 
 
 cannot furnish the precise Contrapositive of the Inferential, 
 any more than an Attributive Categorical symbolized as 
 
 S is P 
 
 can directly furnish a Converse. 
 
 Also if (1) and (3) may symbolize both Hypothetical and 
 Conditionals, they cannot be used (without further informa-
 
 110 IMPORT OF PROPOSITIONS. 
 
 tion) as Major Premiss in Inferentio-Categorical Syllogisms ; 
 for in the case in which they stand for Conditionals, the A 
 cannot be simply affirmed nor the C simply denied. This 
 obviously follows from the reciprocal dependence of the A 
 and C in a Conditional proposition. 
 
 We can, however, and constantly do, use the above forms 
 as representative of both species of Inferential ; and no doubt 
 we are substantially justified in doing so. 
 
 A proposition of the form 
 
 If any E is F, that E is H (4) 
 
 is unmistakeably Conditional ; as unmistakeably Hypothetical 
 is one of the form 
 
 If E is F, E is H (5) 
 
 (containing, that is, two absolute assertions, having three, and 
 only three, terms between them ; cf. Table XXXII. " Eefer- 
 ential Hypothetical "). 
 
 We might perhaps consider (4) as the best symbolic form 
 for Conditionals, accepting (5) and (1) as representing 
 varieties of Hypotheticals, and (3) as representative of both 
 (5) and (1). 
 
 The Categorical, I think, that best expresses a Conditional 
 is of this form 
 
 Any E that is F is H ; 
 
 which is apparently equivalent to 
 
 If any E is F, that E is H. 
 
 Mr. Keynes and Mr. W. E. Johnson hold that, while Hypo- 
 thetical Propositions are not equivalent to Categoricals nor 
 reducible to them, Conditional Propositions are both reducible 
 to and precisely equivalent to Categoricals that the relation 
 between A and C in a Conditional, and the relation between 
 S and P in a Categorical, are exactly similar (cf. Keynes, 
 Formal Logic, pp. 162, 163, 2nd ed.). With this I agree to 
 a great extent, but not entirely. I think that Hypotheticals 
 are not reducible to Categoricals in the sense in which Con-
 
 INFERENTIAL PROPOSITIONS. Ill 
 
 ditionals are; 1 but that Conditionals lose something of their 
 force in reduction to a Categorical of the form, Any DE is 
 F, and that such a Categorical gains some addition of meaning 
 by reduction to a Conditional that thus Conditionals and 
 such Categoricals are not precisely equivalent, and that certain 
 Categoricals are not reducible to Conditionals at all. On 
 analysis, a Conditional Proposition resolves itself, I think 
 (though not in all cases very readily ; cf. cases where we 
 refer directly to events), into the assertion that if anything 
 called by a class-name has a distinctive given attribute, that 
 member of the class has, it is to be inferred (and inferred 
 from the combination of the distinctive attribute with the 
 attribute determined by the class-name), also another attribute. 
 In 
 
 If a child is just recovering from measles, he ought not 
 to be at school, 
 
 we have the assertion simply and directly made. In 
 If you pull the trigger of a gun, it will go off, 
 
 we may resolve into 
 
 If a gun has its trigger pulled by you, that gun will 
 go off. 
 
 If he told you anything, it is true, 
 
 resolves into 
 
 If anything was told you by him, that thing is true. 
 
 In all these cases the P of C is obviously inferred from 
 the qualification of the S of A by the P of A. And I do 
 not see that this is obvious in a Categorical of the form All 
 (or Any) DE is F. No doubt all Conditionals can be reduced 
 to Universal Categoricals of this form ; and such Cate- 
 goricals may, if significant, be reduced with the greatest ease 
 to Conditionals ; but if we are given such a Categorical 
 
 1 Of course, any statement or statements whatever may be expressed in 
 Categorical form ; but the point is that when Conditionals are reduced, the S 
 and P of the resulting Categorical correspond substantially to the A and C of 
 the given Conditional, while this is not the case with Hypotheticals.
 
 112 IMPORT OF PROPOSITIONS. 
 
 expressed in symbols, we cannot be sure of getting a valid 
 result when we reduce it to a Conditional. The order of 
 Constituents in a complex term is indifferent, and it would 
 be quite possible to take the proposition, Any BT is S, to 
 transform it to If any T is B, it is S ; and to find on inter- 
 pretation that our Conditional means 
 
 If any thrush is a bird, it is speckled. 
 
 If we take any Categoricals with a simple S-name, and 
 any Particular Categoricals, it will appear that they cannot 
 be expressed as Conditionals. Take, e.g., 
 
 (1) All lions are quadrupeds. 
 
 (2) Some birds are speckled. 
 
 It may be said that 
 
 (1) = If any creatures are lions, they are quadrupeds (3). 
 But turn this into a Categorical again and we get, not (1) but 
 
 All creatures that are lions are quadrupeds (4). 
 And supposing it is said that 
 
 (1) = If lions, then quadrupeds (5), 
 
 I remark that this reduction is not satisfactory, since (5) is 
 either unmeaning, or elliptical and obscure. 
 
 (2) Might perhaps be said to be equivalent to 
 Sometimes when a thing is a bird, it is speckled. 
 
 or, 
 
 Some things that are birds are speckled ; 
 
 but such propositions seem purely Categorical, incapable of 
 transformation to any Conditional, and compatible with the 
 corresponding propositions (cf. Some rational animals are 
 engineers, Some rational animals are not engineers). 
 If, however, 
 
 Some K is Q 
 may be expressed as 
 
 XR is Q (i.e. All XR is Q), 
 
 then particulars need not be differently treated from Universals 
 with complex S-names. But as we cannot get a Conditional
 
 INFERENTIAL PROPOSITIONS. 113 
 
 out of a Categorical unless it has a complex S-name, nor 
 reduce any but such a Categorical to a Conditional, we must 
 either admit some point of difference between Categoricals and 
 Conditionals, or divide Categoricals into two classes, distin- 
 guished from each other by certain differences. 
 What any Conditional Proposition 
 
 If any D is E, that D is E (1) 
 
 seems to me to assert is, that the E-ness of any D is an 
 inference from its being an E. Thus any Conditional would 
 be universal and affirmative. I think also that (1) implies 
 the existence of some D's that are not E. 
 
 I may, of course, assert something to be an inference, 
 either in a Hypothetical or a Conditional, when as a matter 
 of fact it is not so ; just as in a Categorical I may affirm 
 identity of the objects indicated by S and by P, when such 
 identity does not exist ; but what we are interested in, in 
 discussing the formal import of propositions, is what the 
 proposition asserts, not what is actually true. 
 
 The distinctions between Enthymematic and Elliptical 
 Propositions, and between Divisionals and Quasi-Divisionals, 
 cannot be regarded as properly formal. 
 
 [TABLES.
 
 114 
 
 IMPOKT OF PROPOSITIONS. 
 
 IS, i 
 
 O o 
 
 ** (.L 
 
 3 _ll 
 
 'C rfl 
 
 "* '8 
 
 -_, O 
 
 
 (4-1 
 
 o A 
 
 a o 
 
 w* 
 
 " a 
 
 2. 
 
 Q 
 
 00 a 
 
 
 
 o 
 g 2 
 
 
 
 X O 
 
 1 
 
 
 S s 
 
 o 
 
 c 
 
 
 PH 
 
 23 
 
 ftn 
 * 5 
 
 
 *? 
 
 .1 
 
 rf 
 
 X 
 
 <s 
 
 -1 
 
 o 
 g 
 
 
 o 
 E 
 
 fe I 1 
 
 3 ^2 s 
 j-tS'-S N 
 
 o 
 
 M 
 
 Oi 
 
 
 
 J 
 
 * tj 
 
 
 g 
 
 3gg 
 
 
 H 
 
 ||| s 
 
 
 H 
 
 
 J-^, 
 
 M 
 
 * O w ^-t. *"** 
 
 O 
 
 B 
 
 
 "" 2'g.2 "! 
 
 1 
 
 M 
 
 2-^I.J 
 
 Ti 
 
 O 
 O 
 
 
 2 a) c 
 
 c0 - j3,c o 
 
 K 65 
 
 2 & "> 
 
 O 
 
 PH 
 
 
 2 -2 _ 
 
 
 I-H 
 
 ""K-g'-S^" 
 
 
 5 
 
 
 
 O 
 
 P-i 8.2 
 
 
 
 i 
 
 S -J3 
 
 ^ . 
 
 E 
 
 IffS'S 
 
 _il 
 
 o 
 
 x -2 $ S 
 
 
 PH 
 
 W5< , 2 
 
 P 
 
 H 
 
 Sfl^g 1 - 
 
 KSSS 1 
 
 -^^g"S-MO fl ^ 
 
 A K 03 O Pn+3 , . .rH M 
 
 ,* O fli fl 
 
 *> o._ ^ 
 
 
 y 
 
 S-2'So 
 
 ~ cr.2 a & 
 
 Qo n 
 H l-H ^ 
 
 H 
 
 1*1 
 
 I 1 -S 
 
 v. SP 
 
 o 
 
 s~-^ 
 
 g 
 
 r^ w 
 
 B 
 
 S 
 
 2 
 
 
 o 
 
 M 
 
 v'S 
 
 &H 
 
 q 
 
 lalig^ 
 
 -Afi s 1 
 
 a ^ 
 
 O'? HH 
 
 
 
 g M 
 
 "*'< 
 
 111 * s l2-'82 e; 
 
 S A C -- S -2 cc c .2
 
 ALTERNATIVE PROPOSITIONS. 
 
 115 
 
 TABLE XXXIII. CONDITIONAL PROPOSITIONS. 
 
 DIVISIONAL PROPOSITIONS. 
 
 QUASI-DIVISIONAL PROPOSITIONS. 
 
 
 
 
 Independent 
 
 Dependent 
 
 Independent 
 
 Dependent 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 Propositions. 
 
 e.g. If any 
 
 e.g. If any 
 
 e.g. If any 
 
 e.g. If any 
 
 goose is not grey, 
 
 native of the 
 
 flower is scarlet, 
 
 argument is a 
 
 it is white ; if 
 
 British Islands is 
 
 it is scentless ; 
 
 syllogism in the 
 
 any Member of 
 
 not Scotch, he 
 
 if any fowl is a 
 
 3rd figure, it has 
 
 Parliament is not 
 
 is Welsh, or 
 
 spangled Ham- 
 
 a conclusion in I 
 
 a Peer, he is a 
 
 English, or Irish ; 
 
 burgh, it is either 
 
 or 0. 
 
 Member of the 
 
 if any parrot from 
 
 silver or golden. 
 
 
 House of Com- 
 
 the West Indies 
 
 
 
 mons ; if any 
 
 is not grey, it is 
 
 
 
 Peer is not a 
 
 green ; if any day 
 
 
 
 Duke, he is a 
 
 of the week is not 
 
 
 
 Marquis, or an 
 
 Sunday, Monday, 
 
 
 
 Earl, or, etc. 
 
 or Tuesday, it 
 
 
 
 
 must be Wednes- 
 
 
 
 
 day, Thursday, 
 
 
 
 
 Friday, or Satur- 
 
 
 
 
 day. 
 
 
 
 SECTION XIII. 
 
 (C.) ALTERNATIVE PROPOSITIONS. 
 
 I should like to call propositions of the form 
 S is Q or R 
 
 Alternative rather than Disjunctive, because the differentia of 
 these propositions is that they consist of elements connected 
 alternatively, and because the name disjunctive, in its untech- 
 nical sense, seems as applicable to propositions of the form 
 
 D is neither E nor F 
 
 as to those of the form 
 
 D is E or F. 
 
 The one question which has been considered of importance here
 
 116 IMPORT OF PROPOSITIONS. 
 
 is whether the members of an alternation are exclusive or 
 unexclusive. 
 
 There has never, I think, been any dispute or difficulty 
 about Alternative (Disjunctive) Propositions that has not 
 arisen out of this question concerning the force of or. 
 
 There may apparently be alternation I. between terms; 
 II. between propositions. I. may occur in the S as well as in 
 the P of a proposition ; but propositions having an alternative 
 S and not an alternative P have not been commonly called 
 Disjunctive. Such a form as 
 
 D is E, or F is G, 
 
 is clearly an alternative combination of propositions, but it is 
 generally reckoned as a " Disjunctive " Proposition, as well as 
 propositions of the form 
 
 S is Q or E. 
 
 Alternative Propositions may be divided into 
 
 I. Classificatory Alternatives, which may be (a) Subsump- 
 tional (S referred to P as Species to alternative Genera) ; e.g. 
 All men are spiritual beings or mere animals, (b) Divisional 
 (reducible to Divisional Conditionals S referred to P as Genus 
 to alternative (constituent) Species) ; e.g. Any parrot is green 
 or grey. In Divisional and Quasi-Divisional Alternatives, 
 and in them alone, the disjunction is not a disjunction of 
 ignorance or indetermination. 
 
 II. "What may be called Quasi - Divisional Alternatives 
 (reducible to Quasi-Divisional Conditionals) ; e.g. Any flower 
 is scentless or it is not scarlet. 
 
 III. A class which, for want of a better word, I call Con- 
 tingent Alternatives (corresponding to Elliptical Hypothetical) ; 
 e.g. The author of those plays is Bacon or Shakespeare, A is B 
 or C is D. 
 
 It may be said that what A or B means is simply not [a 
 and b] (using Jevons' notation, according to which a = not- A}. 
 But even supposing that we admit this to be true in all cases 
 without exception, it is still possible that it may be as insuffi- 
 cient an account of the meaning of alternation as Hobbes'
 
 ALTERNATIVE PROPOSITIONS. 117 
 
 account of a Categorical Proposition, according to which what 
 the proposition asserts is " [the belief of the speaker] that the 
 predicate is a name of the same thing of which the subject is 
 a name." This is true in all cases without exception, but it 
 is not the ivhole of what is true in each and every case, and 
 it would admit propositions (so called) of the form A is A. 
 And so it may be with the above interpretation of A or B. 
 Though A or B be granted to mean at least not (a and H), the 
 question may yet remain, Is or to be taken exclusively or 
 unexclusively ? 
 
 Various reasons may be adduced in support of the view 
 that where we have two (or more) Alternatives separated by 
 or e.g. A or B these alternatives ought to be understood as 
 mutually exclusive (as well as together exhaustive). 
 
 The view of educated persons as to the usual meaning 
 of or ought to be of some weight here. To take first 
 experts. There are a large number of distinguished logicians 
 who hold that or is exclusive. 1 Kant, Hamilton, Thom- 
 son, Boole, Bain, and Fowler take this view (cf. Keynes, 
 Formal Logic, 2nd ed. p. 167, note 2). Examples brought 
 forward in support of the unexclusiveness of or by other 
 logicians do not seem to afford very powerful confirmation. 
 Take, for instance, Jevons' well-known example (Pure Logic, 
 pp. 76, 77), "A peer is either a duke, or a marquis, or an earl, 
 or a viscount, or a baron." This instance, it is said, disproves 
 the exclusiveness of or, because a peer may have any com- 
 bination of the alternative titles. But I think that what the 
 proposition really means is, Any person, in order to be a peer, 
 must be a duke or a marquis, etc. A peer may indeed, as a 
 matter of fact, have every one of the five titles enumerated ; 
 but if he is a peer in virtue of one title, he is not a peer in 
 virtue of any other. One title gives all the privileges of 
 peerage, and all the titles in Burke can do no more. Or take 
 the proposition (which occurs in a " Previous " examination 
 paper), " Every ragged person either is poor or wishes to be 
 thought poor." This seems to me an extremely ingenious 
 1 The authorities on the other side will be mentioned later.
 
 118 IMPORT OF PROPOSITIONS. 
 
 example, and at first sight very telling on the side of unexclu- 
 siveness ; but if its full meaning were expressed, would it not 
 run as follows : Every ragged person is ragged either because 
 he is poor, or because he wishes to be thought poor ? and in this 
 case the alternation is clearly exclusive. 
 
 In legal documents, as I am informed, or is understood as 
 exclusive, e.g. " A. B. is entitled to a sheep or cow," would be 
 taken to mean that A. B. is entitled to only a sheep or only a 
 cow. (My authority here is a Chancery lawyer of much 
 learning and experience.) 
 
 I have asked a number of persons (not experts) whom I 
 know, whether they think that in using or they mean it to be 
 exclusive or unexclusive ; and to the best of my remembrance, 
 not one understood it as unexclusive. When I turn to my own 
 experience, it seems to me that this is my own case too, and 
 that when I use or I always think of it as having an exclusive 
 force. Where the terms used are not, in fact, exclusive, it 
 might perhaps be said that the alternation is elliptical, the 
 current form of speech being an abbreviated one, due to the 
 desire for conciseness, or to the fact that the full expression of 
 the meaning would be intolerably awkward, or to the circum- 
 stance that the particular case in question occurs so seldom 
 that the exact expression for it has not got minted, as happens 
 with the adjectival forms of names not often needed except in 
 the substantive form. It might, in fact, be said that in such 
 cases the alternation is taken to mean more than it actually 
 expresses, as the form A is A does in, e.g., "A man's a man," 
 " Cards are cards " (Sarah Battle) ; or as Indesignate Proposi- 
 tions do, e.g. Birds sing. 
 
 But all this, though it has some weight, needs confirma- 
 tion by the results of reflection. The confirmation which it 
 seems to me to receive from reflection is as follows : 
 
 In as far as the members of any alternation (if terms} are 
 
 taken in determination and are similar in determination, are 
 
 taken in denomination and are identical in denomination, or 
 
 (in the case of propositions) have the same signification, 
 
 (1.) The formal alternation has no alternative force. It
 
 ALTERNATIVE PROPOSITIONS. 119 
 
 may be said, in fact, that there is no alternation in the matter 
 except an alternation of words or symbols merely. A or A 
 has no more title to be called an alternation than A is A has 
 to be called a categorical proposition. A is A tells us nothing, 
 and A or A tells us no more than A. Or 
 
 (2.) The affirmation of one member involves the affirmation 
 of the other, and the denial of one member involves the 
 denial of the other, which is incompatible with interpreting 
 A or A to mean not (a and a). Or 
 
 (3.) The denial (or affirmation) of a term or proposition 
 justifies us in proceeding to its affirmation (or denial). This 
 involves a contradiction. Or 
 
 (4.) Neither member of the alternation can be denied (nor 
 affirmed, if affirmation of one member involves the denial of 
 the other). In this case an Alternative proposition cannot be 
 the major premiss of a syllogism having categorical minor 
 and conclusion. 
 
 I am bound to admit that an answer to (2) and (3) has 
 been suggested to me by which (4) is obviated, the case in 
 which neither member can be denied being seen to be merely 
 a case of the general rule that not loth can be denied. But 
 if it is only in virtue of the alternation that we can assert 
 that not both can be denied, while at the same time the 
 " alternation " A or A is said to be equivalent to A that is, 
 to have no alternative force we seem to fall upon a fresh 
 difficulty. 
 
 The reasoning of (1) remains in force, but it may be said 
 that it does not entitle us to deny that alternatives are 
 unexclusive, for their being unexclusive means no more than 
 this, that we are not in all cases entitled to pass from the 
 affirmation of one alternative to the denial of the other 
 all that A or B means is, that we cannot deny both A and B. 
 (And we cannot deny both, because the denial of either member 
 entitles us to affirm the other member.) 
 
 This is obvious, and admitted by every one when such a 
 case is proposed, as, Some parishes in the east of London are 
 peopled by paupers or criminals ; Fruit is unwholesome unless
 
 120 IMPORT OF PROPOSITIONS. 
 
 it is ripe or cooked. No one can say that in these and 
 similar instances it is impossible for the determination of 
 both alternatives to coexist in one individual subject. And 
 that these cases are comparatively infrequent is not to the 
 point. It may, however, be said that even here there is an 
 exclusiveness of determination, though not of denomination. 
 And if we admit alternation in which the members are 
 wholly unexclusive, e.g., 
 
 A is B or A is B (1), 
 
 we must, it seems to me, give up the equivalence between 
 Hypotheticals and Disjunctives, for the Hypothetical answer- 
 ing to (1) is 
 
 If A is not B, A is B (2), 
 
 which is self-contradictory, and has therefore no assertive 
 force ; whereas if (1) is equivalent to A is B, and (2) is 
 equivalent to (1), (2) means A is B. 
 
 I cannot therefore help concluding that although alter- 
 native terms may sometimes be identical in denomination 
 and it is perhaps in view of such cases that Whately, Mansel, 
 Mill, and Jevons (cf. Keynes, Formal Logic, 2nd ed. p. 167, 
 note 2) insist upon the non-exclusiveness of alternation yet 
 alternatives must always have some element of exclusiveness, that 
 otherwise they have no logical value whatever. There is no 
 escaping the admission that in as far as any form of words 
 has alternative force, the alternatives are rigidly exclusive ; 
 also that in as far as any alternation cannot be reduced to a 
 strictly exclusive form, the alternation vanishes just as in 
 S is P, the proposition would vanish if P turned out to be 
 not S. For the members, in as far as not exclusive, are one 
 a denial of either involves denial of the other, contrary 
 or contradictory. E.g. in 
 
 All R is Q (1), or this R is Q (2), 
 
 contrary denial of (1) involves denial of (2), and denial of (2) 
 involves contradictory denial of (1). Cf. post. pp. 151, 152. 
 So, if by alternatives being unexclusive is meant only that
 
 ALTERNATIVE PROPOSITIONS. 121 
 
 the affirmation of one member (or members) does not justify 
 the denial of the rest, then alternatives are unexclusive ; if 
 by alternatives being unexclusive it is meant that they may 
 be without any element of exclusiveness, then they are not 
 unexclusive. 
 
 An Alternative Proposition then may, I think, be defined 
 as 
 
 A proposition in which a plurality of differing elements 
 (connected by or, and called the alternatives) are so 
 related that not all of them can be denied, because 
 the denial of some justifies the assertion of the rest. 
 
 Hence from (1) the denial of some elements we can pro- 
 ceed to (2), the affirmation (categorical or alternative) of the 
 rest (2) is inferrible from (1). Thus all Alternations are 
 reducible to Inferential Propositions (cf. Keynes, Formal 
 Logic, p. 170, 2nd ed.), and, conversely, all Inferential Pro- 
 positions are reducible to Alternations. Divisional and Quasi- 
 Divisional Alternatives reduce to Divisional and Quasi-Divi- 
 sional Conditionals, e.g. Any goose is grey or white, reduces 
 to, If any goose is not white it is grey. Any flower is scent- 
 less or it is not scarlet, reduces to, If any flower is scarlet 
 it is scentless. 
 
 Subsumptional and Contingent Alternatives reduce to 
 Hypotheticals, e.g. All parts of space are infinitely divisible, 
 or they are not continuous quantity; That bird is a Guillemot 
 or a Razorbill ; S is P or P is not S ; reduce to, If all parts 
 of space are continuous quantity, they are infinitely divisible ; 
 If that bird is not a Razorbill it is a Guillemot; If P is S, 
 Sis P. 
 
 [TABLE.
 
 122 
 
 IMPORT OF PROPOSITIONS. 
 
 PH 
 
 K 
 
 W 
 
 E 
 
 Js 53 1 
 
 H 
 
 *O tC 
 
 3 
 
 03 t< "^ 
 
 W 
 
 cS O 'XJ o> 
 
 55 
 
 11 HI 
 
 _1-1 ElK 
 
 & a. ' g.s= c 
 
 00 
 
 fe 
 
 
 
 Sgjj 
 
 > 
 
 H 
 i i 
 03 
 
 3 H 2 
 
 > 2 
 
 
 
 Q B! o 
 
 PH 
 
 
 
 g H 
 
 M 
 
 ^j (5 
 
 PH 
 
 i~& 
 
 O 
 
 d 
 
 
 
 , 
 
 . 
 
 1 s 
 
 "S - 
 
 - ^J 30 
 
 5,3 
 
 < S 03' S 
 
 - 
 
 o P<W S ^ o3 as 
 
 <5 Tt a 
 
 ? .2 
 
 " 2 "a o 
 
 
 e'-S 
 
 s -s 
 
 57 o 
 < 
 
 O o 
 
 03 : *3 3 
 
 Mi 
 
 o
 
 NOTE ON CLASSIFICATION AND DIVISION. 123 
 
 SECTION XIV. 
 
 NOTE ON CLASSIFICATION AND DIVISION. 
 
 A convenient way of expressing a Classification or Division 
 briefly and clearly in words is by a combination of Divisional 
 Propositions (Inferential or Alternative) and Quantified 
 Enumerative Propositions ; e.g. If any triangle is not equi- 
 angular, it is isosceles or scalene (or, Any triangle is isosceles 
 or scalene, or not equiangular) ; and, Equiangular triangles, 
 isosceles triangles, and scalene triangles are all triangles. 
 The Enumerative Propositions would hardly be sufficient 
 taken alone, because of a possible confusion between Dis- 
 tributive and Collective Propositions ; and Divisional Pro- 
 positions, though they often are used alone to express 
 Division or Classification, are not of themselves formally 
 sufficient, because they are not distinguishable in form from 
 Quasi-Divisionals. 
 
 Division and Classification are the same thing looked at 
 from different points of view ; any table presenting a Division 
 presents also a Classification. A Division starts with unity 
 and differentiates it; a Classification starts with multiplicity, 
 and reduces it to unity, or at least to system. If the 
 Classification stops short of unity, it presents not one 
 Division, but a plurality of Divisions. A Table is generally 
 most convenient which starts from unity, that is, which is 
 primarily a Division. Some Tables in Whewell's Novum 
 Organon Renovatum are an example of the reverse arrange- 
 ment, which is that which naturally occurs in a synthetic 
 procedure ; while Division is as naturally the appropriate 
 form in cases where the procedure is analytical. 
 
 From a Division or Classification, a Definition of any 
 Constituent class (not, of course, the Summum Genus) may be 
 framed. It is not the business of a Definition to indicate 
 the place of the thing defined in any except a very simple 
 Classification ; to do so where the Classification is at all
 
 124 IMPORT OF PROPOSITIONS. 
 
 complex, would make the Definition intolerably cumbersome. 
 It is desirable, I think, to distinguish (1) the collection into a 
 group, of things which are quantitively different but qualitively 
 similar ; (2) the arrangement of such groups in their relations 
 to one another ; l (3) the arrangement of differing parts, which 
 do not consist of groups of homogeneous members, in their 
 relations to each other and to the whole which they con- 
 stitute. (1) might be conveniently distinguished from (2) as 
 Classification from Classing; (3) might be perhaps distinguished 
 from the other two as Systematization. This term seems 
 more applicable than Classification to the arrangement of 
 the Sciences in relation to one another, or the arrangement of 
 the parts of an organic whole, e.g. the human body, etc. 
 
 SECTION XV. 
 
 QUANTIFICATION AND CONVERSION. 
 
 Quantification of the Predicate in Categorical Propositions 
 seems to me to occupy an impregnable position in Logic, a 
 position, however, very different from that assigned to it by Sir 
 William Hamilton, Dr. Thomson, Professor Baynes, and others. 
 My opinion is that while the traditional form of A, E, I, 
 Propositions is to be retained, Quantification is an indispens- 
 able instrument of Conversion, and therefore of Reduction. 
 The place of Quantification in Logic is very curious, its func- 
 tion being often as completely hidden from those whose pro- 
 cesses of Conversion, etc., involve it, as the subterranean 
 course of a train in one of the loop-tunnels of the Swiss 
 Alps would be to an observer who only saw it rush into one 
 opening, and emerge again in a few minutes from another, 
 just above or just below. My meaning will be . best eluci- 
 dated by taking an ordinary proposition and tracing the 
 
 1 Cf. The Logic of Classification, by Rev. W. L. Davidson, Mind, vol. xii. 
 p. 233.
 
 QUANTIFICATION AND CONVERSION. 125 
 
 changes which it undergoes in Conversion. Let the pro- 
 position be 
 
 All human beings are rational (1). 
 The ordinary converse of this is 
 
 Some rational creatures are human beings (2), 
 or 
 
 Some rational creatures are human (3). 
 
 (3) is perhaps the more perfect converse, because (1) and (3) 
 resemble each other in having an Adjectival Term for P, 
 while (2) has a Substantive Term for P. (1) and (3) are 
 Adjectival Propositions, (2) a Coincidental Proposition. 
 Adjectival Propositions cannot be converted. If I alter 
 the relative position of S and P in (1) as it stands, and 
 say 
 
 Rational are all human beings, 
 
 it is clear that Conversion in the logical sense has not taken 
 place ; for Rational is still the Predicate, and all human 
 beings is still the Subject. The proposition has been merely 
 turned round. No Conversion of (1) while it is (1), that is, 
 while it retains the Adjectival form, is possible. But it may 
 be transformed to the equivalent Coincidental Proposition 
 
 All human beings are rational creatures (4) ; 
 
 and with this we can deal. It is not, however, any more 
 than the Adjectival (1), simply convertible. If altered into 
 
 Eational creatures are all human beings, 
 
 the proposition thus obtained, besides being awkward, is am- 
 biguous it is by no means clear which term is to be taken 
 as Subject, and the all might even be understood to qualify 
 (or quantify) Eational creatures. 
 
 The first step towards real Conversion is taken when we 
 pass from the unquantificated Coincidental (4) to the quanti- 
 ticated proposition 
 
 All human beiugs are some rational creatures (5) ;
 
 126 IMPORT OF PROPOSITIONS. 
 
 from this we go on to the quantificated converse 
 
 Some rational creatures are all human beings (6) ; 
 
 and from (6) to the unquantificated converse of (5) 
 Some rational creatures are human beings (7). 
 
 From (7) we can pass to the equivalent Adjectival Pro- 
 position 
 
 Some rational creatures are human (8). 
 
 It is to be observed that in going from (4) to (7), we have 
 not only inserted a sign of quantity before the new Subject- 
 name (rational creatures) which, as the old Predicate, had not 
 any to start with ; we have also dropped the sign of quantity 
 which the new Predicate (human beings) had when it was 
 the old Subject-name. Thus, as we began with an unquanti- 
 ficated proposition, so we end with an unquantificated pro- 
 position. The propositions which logicians (on the whole) 
 have recognised and dealt with are unquantificated proposi- 
 tions ; it is for enabling us to pass (by an elliptical procedure) 
 from uiiquantificated to un-quantificated propositions that the 
 ordinary rules of Conversion and Reduction are framed ; it 
 is of unquantificated propositions that the " nineteen valid 
 moods " of the traditional Categorical Syllogism are composed. 
 And it is hardly necessary to remark that in ordinary speech 
 it is almost always unquantificated propositions that are used 
 (that is, when we are dealing with Unrestricted Names ; cf. 
 Table III.). 
 
 In converting an E proposition, we should, I think, pro- 
 ceed as follows : Let the proposition to be converted be, No 
 E is Q (1). (1) = (2) Any E is not Q (by mere equival- 
 ence). Quantificating (2) we get, Any E is not any Q (3). 
 (3) Converts to, Any Q is not any E (4). By disquantifi- 
 cating (4) we reach (5), Any Q is not E And (5) = No Q 
 is E (by equivalence). 
 
 The usage of Logic and of ordinary speech can be justified, 1 
 
 1 It is this usage of both Logic and ordinary speech, I think, which explains 
 the common failure to distinguish between terms and term-names. Taking, e.fj., 
 the proposition All R's are Q' (1), our terms, so far as expressed, are (a) All
 
 QUANTIFICATION AND CONVEKSION. 127 
 
 and also the validity and necessity (in a subordinate office) 
 of Quantification can be shown, I think, by reference to the 
 Import of Categorical Propositions. What a significant Cate- 
 gorical Proposition affirms or denies is, it seems, identity of 
 denomination of the S and the P in diversity of determination. 
 Denomination (and application) of S and of P in an affirma- 
 tive Categorical Proposition are the same ; determination of 
 the S and P being, of course, always diverse, unless we admit 
 propositions of the form A is A, and being in any case 
 diverse in all propositions of the form A is B. And 
 denomination is sufficiently indicated by the S ; identity 
 or non-identity is indicated by the copula ; while diversity 
 of determination comes into view only when the Predicate 
 is enunciated. In regard to any assertion, we want to 
 know in the first place what it is of which something is 
 affirmed or denied ; this knowledge is given with the enuncia- 
 tion of the Subject, which indicates the thing or things spoken 
 of. We want, in the second place, to know what it is that is 
 affirmed or denied of the thing or things indicated by the Sub- 
 ject. This information is supplied by the Predicate that 
 is, by its determination since it is evident that in affirmative 
 propositions the denomination of the Predicate is identical with, 
 in negative propositions is altogether distinct from, that of the 
 Subject. Hence it seems clear that in the Predicate of any pro- 
 position, it is naturally and inevitably determination and not 
 denomination which is prominent. 1 This is confirmed by the 
 
 R's, (6) Q's. Converting (1) we get (2), Some Q's are R's, and here our expressed 
 terms are (a) Some Q's, (b) R's hence All R's and R's, Some Q's and Q's, aie 
 indiscriminately called terms. And a further point which throws light upon 
 this, and also upon the appropriateness of the Canon and Rules of Categorical 
 Syllogism to clashes rather than to terms, is that we have a practical interest in 
 the relations of classes (which are indicated by term-names), and we are con- 
 tinually comparing propositions which have the same term-names but not the 
 same terms. 
 
 1 This interpretation seems to me to be very forcibly illustrated by Mill in 
 chap. xxii. of his Examination of Hamilton. E.g. "when, for example, I say, 
 The sky is blue, my meaning, and my whole meaning, is that the sky has 
 that particular colour. I am not thinking of the class blue, as regards extension, 
 at all. I am not caring, nor necessarily knowing, what blue things there are, or 
 if there is any blue thing except the sky. I am thinking only of the sensation 
 of blue, and am judging that the sky produces this sensation in my sensitive
 
 128 IMPORT OF PROPOSITIONS. 
 
 consideration that we commonly use Adjectival rather than 
 Coincidental Propositions, if appropriate Adjectival Terms are 
 available ; and that such terms in English cannot take the sign 
 of the plural (cf. ante, p. 13), though the Substantive Terms 
 which they qualify can, and though no one doubts that the 
 denomination of an Adjectival Term is the same as that of the 
 Substantive Term which it qualifies. It is also to be remembered 
 that an Adjectival Term cannot be Subject in a proposition. 
 Now if it is the primary function of the S in any Categorical 
 Proposition to indicate denomination, while it is the primary 
 function of the P to indicate determination, 1 it seems obvious 
 that quantification is appropriate, and may be necessary in 
 the case of S, but not in the case of P, under ordinary circum- 
 stances. And a further reason against admitting Quantifica- 
 tion of the Predicate (except as a transformation - stage) in 
 most propositions, is deducible from the consideration that 
 what propositions assert or wholly deny is the identity of 
 denomination (in diversity of determination) of S and P ; for 
 in a quantificated affirmative, though indeed denominational 
 identity of the terms is still asserted (as it is bound to be), the 
 fact that the denomination of both terms is made prominent 
 tends to obscure this especially where difference of denomina- 
 
 faculty ; or (to express the meaning in technical language), that the quality 
 answering to the sensation of blue, or the power of exciting the sensation of blue, 
 is an attribute of the sky. When again I say, All oxen ruminate, I have nothing 
 to do with the predicate, considered in extension. . . . The Comprehension of the 
 predicate the attribute or set of attributes signified by it are all that I have iu 
 my mind ; and the relation of thin attribute or these attributes to the subject is 
 the entire matter of the judgment" (pp. 497, 498, 4th ed.). 
 
 "... When we say, Philip is a man, or a herring is a fish, do the words 
 man and fish signify anything to us but the bundles of attributes connoted by 
 them ? Do the propositions mean anything except that Philip has the human 
 attributes, and a herring the piscine ones ? Assuredly not. Any notion of a 
 multitude of other men, among whom Philip is ranked, or a variety of fishes 
 besides herrings, is foreign to the proposition " (p. 498). 
 
 Cf. also Dr. Venn (Empirical Logic, p. 219): "I have little doubt that, 
 speaking generally, the subject is by comparison contemplated as a class, i.e. in 
 its extension, and the predicate as an attribute, i.e. in its intension." (The 
 italics in both quotations are mine.) Cf. also Keynes, Formal Logic, p. 92. 
 
 1 If both terms are taken in denomination, S is P=S is S, since S and P have 
 identical denomination, and hence apply to the very same objects. If both 
 terms are taken in determination, again all propositions must be of the form S 
 is S, since of any determination S, we cannot affirm a different determination P.
 
 QUANTIFICATION AND CONVERSION. 129 
 
 tion of the classes referred to is suggested. And, moreover, 
 quantificated affirmatives are all collective. It might indeed be 
 asserted that where both terms of our propositions are taken in 
 denomination, quautificated propositions are most appropriate, 
 and are the form of proposition which makes the denomina- 
 tion of both S and P most prominent. But I should maintain 
 that both Terms cannot be taken purely in denomination. If, 
 e.g., in S is P, both S and P are taken in denomination only, 
 then to say S is P is exactly equivalent to saying S is S, for 
 the denomination of P is the very same as that of S. But 
 S is S is not entitled to be called a significant assertion (cf. 
 ante, p. 52, also note 1, p. 128). On the other hand, the view 
 here advocated of the Import of Categorical Propositions 
 justifies the recognition of Quantification as a phase of pro- 
 positions. For the Predicates of propositions have denomina- 
 tion as well as the Subjects, 1 and (in affirmative propositions) 
 a denomination which is identical with that of the Subjects. 
 It is therefore (in a Coincidental proposition) possible, and 
 under certain conditions allowable and necessary, to make 
 this prominent by quantification. And the Subjects of pro- 
 positions have determination ; and this may be allowed to 
 come into prominence by dropping the sign of quantity 
 (Term-Indicator) which inevitably fixes attention rather upon 
 the denominational than the determinational aspect of a 
 term. 
 
 The above view of Quantification is, I think, confirmed and 
 illustrated by a consideration of the traditional logical treat- 
 ment of propositions. Of the four categorical propositions, 
 A E I 0, the first three have always been regarded as 
 capable, the fourth as incapable, of Conversion. 
 
 We have seen that propositions on their way to Conversion 
 have to undergo the process of Quantification. But the 
 reason why is pronounced inconvertible is not because there 
 is any more difficulty in quantificating it than in quantificat- 
 ing the other propositions, but because, when the quantificated 
 
 1 Cf. that in many languages (Greek, Latin, French, Italian, etc.) adjectives 
 that qualify a plural term always take the sign of the plural. 
 
 I
 
 130 IMPORT OF PROPOSITIONS. 
 
 converse of has been reached, the quantification of its pre- 
 dicate cannot be dropped without an illegitimate alteration 
 of signification. For the commonly accepted signification of 
 the dis-quantificated converse of involves a quantification 
 different from that which has been dropped the dropped 
 P-indicator being some, the P-indicator understood as involved 
 in the unquantificated proposition reached by dropping it being 
 any. And as, at the same time, ordinary thought and speech 
 will not admit the explicitly quantificated form, it is inevitable 
 that a Logic which deals with the forms of ordinary thought 
 and speech should regard as inconvertible. To take an 
 instance The proposition, Some blackbirds are not black birds 
 (1), becomes by quantification (2) Some blackbirds are not 
 any black birds. This converts to (3) Any black birds are 
 not some blackbirds. Dropping the quantification of (3) we 
 get (4) Any black birds are not blackbirds, and this would 
 be understood to mean (5) Any black birds are not any 
 blackbirds (= No black birds are blackbirds). 
 
 SECTION XVI. 
 
 THE MEANING OF SOME. 
 
 If Quantification of ordinary propositions is recognised as 
 being admissible and necessary in processes of Conversion, 
 but to be discarded as soon as the process has been gone 
 through, it seems desirable to inquire a little more particularly 
 into the force and meaning of propositions while in the 
 quantified stage. This depends principally upon the significa- 
 tion given to Some. Some, it is said, may mean (1) "Some 
 but not all ; " (2) " Some at least, it may be all " (cf. e.g. 
 Jevons, Elementary Lessons in Logic, 7th ed. p. 67). But 
 when the above are offered as interpretations or explanations 
 of Some, the question obviously arises, What exactly does the 
 Some in Some at least, Some at most, mean ? Must not the
 
 THE MEANING OF SOME. 131 
 
 meaning which it has as constituent of these expressions be its 
 real minimum of meaning ? 
 
 Again, Some has been defined to mean not none (cf. e.g. 
 Bain, Logic, i. p. 81, 2nd ed. ; Venn, Empirical Logic, p. 
 223). This definition is more satisfactory than (1) or 
 (2), since it is wide enough to cover the meaning intended 
 by each (while (1) excludes (2), and is evidently not 
 applicable in all cases), and also it does not present a 
 direct and explicit circulus in definiendo. But I am afraid 
 it is still open to the reproach of being circular ; for how 
 is none to be defined except as not some ? And if Some 
 means merely not none, and none means merely not some, 
 what do we know about either except that it is the negative 
 of the other ? Some is not-none contraposits (contraverts) to 
 None is not-some, and if we have nothing else to say about the 
 meaning of None and Some, we are simply revolving in a 
 circle which is closed against all connection with other 
 meanings. 
 
 If we ask, What is intended by, e.g., Some R, in common 
 speech, it must be admitted (and is recognised by logicians) 
 that the almost invariable intention of the speaker, in any 
 particular case, is to indicate some modification of E quanti- 
 tively different from All R (this must be the case, for 
 instance, whenever it is got by Sub-alternation Subversion 
 from All R) ; or some modification of R qualitively diverse 
 from mere R. Therefore it may be said that what is intended 
 is part (not all) of R, or certain (somehow distinguished) R. If 
 All R were intended, then in order that the intended meaning 
 might be unequivocally conveyed, All R would be used. 
 Similarly, if R unmodified were intended, R unmodified would 
 be used. 
 
 But it must be admitted that Some R may happen to have 
 the same extension (application) as All R ; e.g. I may say, 
 Some scarlet flowers are scentless ; and it may be true, though 
 I did not know it, that All scarlet flowers are scentless. 
 
 Or I may say, Some (= certain somehow distinguished) 
 cloven-hoofed animals are ruminants ; and it may turn out
 
 132 IMPORT OF PROPOSITIONS. 
 
 that I might with equal truth (whether or not I was aware 
 of it) have asserted simply that Cloven-hoofed animals are 
 ruminants. 
 
 The recognition of such cases as these, and of other cases 
 where one is fully conscious that one's knowledge is indeter- 
 minate, makes it clear that any definition of Some which 
 restricts it to (1) Less-than-all, or (2) Certain-somehow-dis- 
 distinguished (and (1) and (2) involve each other), cannot be 
 valid. 
 
 I should propose to define Some R as meaning An indefinite 
 quantity or number of R. Such a definition, it is clear, in- 
 volves no implication either (a) of there being or not being 
 other E, or (6) of what may be asserted concerning those other 
 E, if there are any. And the definition will be found 
 to give all the meaning that is common to Some in all cases, 
 and that justifies its use that is, it gives the whole deter- 
 mination of the word. 
 
 This account of the meaning of Some makes the question 
 (which is sometimes asked), Does Some mean One at least, or 
 Two at least ? appear irrelevant. 
 
 If Some means merely an indefinite quantity, Quantifica- 
 tion by Some makes our terms explicitly indeterminate ; for 
 it excludes (1) explicit universality, and (2) definite limitation. 
 And it affords no definite determination of the relations of the 
 classes involved. 
 
 The reason why it can be used where All cannot (as in the 
 Conversion per Accidens (Intraversion) of an A proposition), 
 is that it does not explicitly claim Universality. 
 
 The results of quantifying with Some when Some means 
 not-all, and what is asserted of part is denied of the rest, are 
 fully discussed in Mr. Keynes' Formal Logic, Part iii. ch. ix. 
 2nd ed. 
 
 The function of Quantification on the whole seems to be 
 simply to bring into prominence the quantitive aspect of the 
 Predicate.
 
 PART II. 
 EELATIONS OF PROPOSITIONS. 
 
 SECTION XVII. 
 
 GENERAL REMARKS ON THE RELATIONS OF PROPOSITIONS. 
 
 UNDER the head Relations of Propositions, we may consider 
 I. Relations of two Propositions to each other ; II. Relations 
 of two Propositions taken together to a third. 
 I. subdivides into Relations between 
 
 (i.) Incompatible ^ 
 
 / \ r< i"ui f (1) Unattached 
 
 (n.) Compatible | ^ Mtg ^ ed (a} Cone j ative j- Proposition,. 
 
 ( (b) Premissal ) 
 
 (i.) are propositions which are inconsistent, i.e. cannot both 
 be true. 
 
 (S is P ( All Q is R / All Q is K 
 
 ' "JS is not P ( Some Q is not R \ No Q is R 
 f A is B or C 
 ( A is neither B nor C. 
 
 The Propositions under this head may be distinguished 
 into 
 
 (a) Those which can ) 
 
 )IA m, T^- i <- f 
 
 (b) Ihose which cannot J 
 
 . J All men are trustworthy ) 
 "( No men are trustworthy. ) 
 . f No scarlet flowers are fragrant ( S i 
 " ( S i 
 
 f No scarlet flowers are fragrant ( S is P 
 ^ Some scarlet flowers are fragrant ( S is not P 
 
 In categoricals, this distinction depends upon the distinction
 
 134 RELATIONS OF PROPOSITIONS. 
 
 between Terra and Term-name any Proposition expressed 
 as S is P has only one negative, namely, S is not P. Any 
 one of a pair of Incompatibles and the negative of the other are 
 either Correlative or Identical. 
 
 (ii.) (1) are propositions which are consistent with each 
 other, but neither of them is inferrible from the other, and 
 the two, when taken together, do not constitute the premisses 
 of an argument. 
 
 Some Q is E ^ 
 
 S is P ) Some Q is not E ) Some N is E \ 
 Q is E / Some N is Q ( 
 
 A relation of consistency between one proposition and 
 another is reciprocal. A relation of independence need not be 
 so e.g. Some Q is E (1) may be independent of All Q is E 
 (2) i.e. in the case where (1) is not got by Sub-alternation 
 from (2); for (2) is not inferrible from (I), and (1) may be 
 true while (2) is false. But (2) can never be independent of 
 (1), for it cannot be true unless (1) is true, and (1) is always 
 inferrible from it. No doubt any proposition of the form 
 Some E is Q might be expressed as an Universal e.g. All 
 XQ is E, but the relation of All XQ is E to (2) is the 
 same as that of (1) to (2). 1 The relation between Unattached 
 Propositions is altogether undetermined. They must of course 
 he, really, Incompatible or Attached, but the relation is not 
 apparent. 
 
 (ii.) (2) subdivides into (a) Correlative Propositions (propo- 
 sitions related" as inference and inferend), e.g., 
 
 All Q is E ) No Q is E ) 
 
 [Therefore] Some Q is E ) [Therefore] No E is Q ) 
 
 If E is F, K is H ) 
 
 [Therefore] If K is not H, E is not F. J 
 
 1 It may be remarked also that any Universal Proposition, All H is Q (I) may 
 be expressed as a Particular (if the R is definable, that is, is not a Genus 
 Generalissimum). For R is resolvable into [the determination of] Genus -+- 
 Difference e.g. into X and Y ; and when thus resolved, (1) may be expressed as 
 
 Some X (i.e. the X that is Y) is Q. 
 
 Where we take a strictly formal view, and consider the terms of propositions 
 and not the term-names, the logical difference between (1) Universal or 
 General, and (2) Particular Categoricals, disappears.
 
 GENERAL REMARKS ON THE RELATIONS OF PROPOSITIONS. 135 
 
 Under this head come the relations betweeen all pairs of 
 propositions of which either one is immediately inferrible 
 (educible) from the other. 
 
 (b) Premissal Propositions are two propositions having 
 some element in common, and from which, taken together, a 
 third proposition may be inferred. These are interesting and 
 important only when we come to II., but they are mentioned 
 here for the sake of formal completeness. Examples of (b) 
 are 
 
 All M is P ) If E is F, K is H 
 
 All S is M j If K is H, L is M. 
 
 II. Here we consider the relation of any two Premissal 
 Propositions to a third proposition. This relation may be 
 one of 
 
 (i.) Inferribility 
 
 (ii.) Non-Inferribility ; 
 
 (i.) gives us valid syllogisms (or what, by some Immediate 
 Inference, may be reduced to valid syllogisms), (ii.) gives us 
 invalid syllogisms. Examples are 
 
 (i.) M is P (ii.) All M is P 
 
 S is M Some R is M 
 
 S is P. All R is P. 
 
 If E is F, K is H All M is P 
 
 E is F No S is M 
 
 K is H. All S is P. 
 
 A is B or C 
 A is not B 
 A is C. 
 
 Under this head we are principally concerned with (i.), 
 and it is of (i.) only that I have given examples in the 
 Table of Inferences. But we may, of course, consider the 
 relation (of Compatibility, etc.) between any two (or more) 
 propositions, and another which is not an inference from 
 them.
 
 136 
 
 KKLATIONS OF PKOl'OSITIONS. 
 
 BISH 
 
 w g a H 
 
 -<! WO 
 
 H 
 
 .2 .2 - 
 
 H^5 W 
 
 j X -S <u 
 
 = 2-ge 
 
 H ^ ^ 
 
 -^ss^- 
 
 ?*|5 
 
 <s^ 
 
 OH 
 
 .2 .2 -2 .2 S S -2 - 
 
 S 
 
 n 
 
 fc- 7 -^ , 
 
 m " *t - 
 
 _, O -J3 " M ffi 
 
 ^B ^J J* 
 
 ~ a< oj 2 jj ^ c 
 
 1 1|| 3 
 
 > , O Q *^- ^M
 
 INFERENCE. 137 
 
 SECTION XVIII. 
 
 INFERENCE. 
 
 Before going on to consider briefly Categorical, Inferential 
 and Alternative Syllogisms, I desire to offer a few remarks on 
 what are commonly called Induction and Deduction, and 
 Immediate and Mediate Inference. 
 
 An Induction, unless it is formal, does not seem to be 
 logical at all. There is, of course, a broad and important 
 difference between (1) arguing from two universal statements, 
 or applying an universal to a particular case ; and (2) arguing 
 from one universal in conjunction with some fact or facts, and 
 reaching therefrom a fresh universal. But if a deductive 
 inference means simply an argument (or Mediate Inference), 
 the conclusion of which is justified by the premisses, (2) is a 
 deductive inference as much as (1); and the conclusion of 
 (2) is as much " contained " in the premisses as (1) is. 1 If 
 we pass from 
 
 These X's are Y's (a) 
 
 to All X's are Y's (6) 
 
 or to Those X's are Y's. (c) 
 
 there is nothing cogent in the process it is wholly unlogical. 
 (6) or (c) cannot follow from, or be justified by, or contained 
 in, (a) taken alone. If we take any case of the application 
 of one of Mill's " Four Methods of Experimental Inquiry " 
 (Inductive Methods)? and set out at length the reasoning 
 
 1 On the other hand, if deductive is taken in a narrower sense and restricted 
 to (1), we cannot describe an "inductive" Inference as deductive. It seems 
 convenient to use deductive in the narrower sense, as contrasted with inductive 
 and traductive, using Syllogism instead of Deduction in the wider sense. 
 
 The employment of the name Eduction instead of Immediate Inference would 
 make the terminology here more symmetrical and convenient, I think. 
 
 3 Mill's "Methods" seem to he methods for determining in what cases we 
 are justified in assuming connection (not mere conjunction) between phenomena.
 
 138 RELATIONS OF PROPOSITIONS. 
 
 involved, what we get is a plurality of Syllogisms. 1 No 
 doubt we often do think that All X's are Y's, because we 
 have met with some X's that are Y's ; but our thought here 
 is not logical thought, and the premiss merely suggests, it 
 does not really justify, the conclusion. It can only justify it 
 in so far as this, that the actual occurrence, in some cases, of 
 X's that are Y's proves that the attributes connoted by X and 
 Y respectively are not incompatible ; so that the experience 
 of some X's that are Y's is ground for asserting that possibly 
 all X's may be Y's (as long, that is, as we have no experience 
 of X's that are not Y's). 
 
 If we could conclude directly from (1) Some X's are 
 Y's to (2) All X's are Y's, or (3) Some other X's are Y's, (2) 
 and (3) must be called Immediate Inferences from (1) 
 (according to the usual de6nition of an Immediate Inference). 
 But we never find that Inductions are treated under the head 
 of Immediate Inferences ; if they were, it would be apparent 
 at once that such " Immediate Inferences " are not illative. 
 The qualification immediate indicates, of course, that we know 
 directly or intuitively, that, e.g., if S is P, then P is S. But do 
 we not know just as intuitively or directly that if M is P and 
 S is M, then S is P? And is not any argument, however 
 long and complex, reducible to just a series of intuitions ? 
 
 1 E.g. an "Induction" by the Method of Difference might be obtained 
 thus : 
 
 (i.) (Anything, the introduction of which has on one occasion been followed 
 
 by Y), is (on one occasion the cause of Y). 
 (X) is (a thing, the introduction of which, etc.) 
 
 (X) is (on one occasion the cause of Y). 
 
 (Deductive Syllogism.) 
 
 (ii.) (Anything that has on one occasion been cause of Y) is (always cause 
 
 ofY). 
 (X) is (a thing that has on one occasion, etc.) 
 
 (X) is (always cause of Y). (= All X is cause of Y.) 
 
 (Inductive Syllogism.) 
 
 For the answer which I should suggest to the question, What justification can 
 be given for the assertion of such a proposition as the Major Premiss of (ii. ) ? 
 cf. post, Section on the Ground of Induction. I call (ii. ) an Inductive Syllo- 
 gism on account of the content of its Major Premiss, which makes it possible 
 to pass, with the help of a single instance, to a new law or generalization.
 
 INFERENCE. 139 
 
 And when we have fully grasped all the connections, and have 
 the whole argument before the mind at once, must it not be 
 regarded as really only one highly complex intuition ? It 
 one takes the proof of some theorem in Euclid, e.g. the 
 47th Proposition of the 1st Book, and goes through it step 
 by step, one sees (or may see) the connection between every 
 two contiguous steps before grasping the whole reasoning, 
 and therefore one cannot avoid believing, even at this stage, 
 that the Q.E.D. follows from the data. Here one has, 
 strictly speaking, just a series of intuitions. But when the 
 proposition has been so grasped that the whole reasoning is 
 before the mind simultaneously, then I think that it must 
 be said that one has not a series of intuitions, but just 
 one complex intuition, and one sees that the final conclusion 
 follows from the data. It seems to me, therefore, that an 
 " Inductive " Inference must be allowed to be formal, as well as 
 the Inferences commonly distinguished as " Deductive " (cf. 
 Table XXXVI.), and that a "Mediate" Inference only differs 
 from an Immediate Inference in being more complex. 
 
 I would suggest the following definitions I. of Inference 
 in general ; II. Of Immediate Inference ; III. Of Mediate 
 Inference : 
 
 I. One proposition is an inference from another, or 
 others, when the assertion of the former is justi- 
 fied by the latter, and the latter is, in some 
 respect, different from the former. 
 
 II. An Immediate Inference is a proposition inferred 
 from one other proposition (the Inferend). 
 
 III. A Mediate Inference is a proposition (the Conclusion) 
 inferred from two other propositions (the Pre- 
 misses). 
 
 I should like to define Equivalent as follows : 
 
 Any two Categorematic words (or phrases) are equi- 
 valent when they have identical denomination and 
 diverse determination ; and any two Syncategore-
 
 140 RELATIONS OF PROPOSITIONS. 
 
 matic words are equivalent when they have the 
 
 same meaning ; l 
 and to suggest the following as Canons of 
 
 ( Conversion. 
 
 | Conversion per Accidens (Intra version). 
 
 (2) Obversion. 
 
 Complex Conception ) 
 
 AJJ j -Tk * r (Extraversion). 
 
 Added Determinants ) 
 
 (4) Substitution generally. (This seems to me to include 
 a brief Canon of Syllogism, and might perhaps be 
 offered as an amended form of Jevons' " Substitu- 
 tion of Similars.") 
 
 Taking any two equivalent terms, of either one the other 
 (1) may be affirmed, and (2) its negative denied : 
 and taking any two terms which are non-coincident, 
 of either one the other (1) may be denied, and (2) 
 its negative affirmed provided, in each case, that 
 the change does not result in tautology. 
 
 (3) If any qualification or determination is attached to a 
 
 name, the same qualification or determination may 
 be attached to its equivalent ; and 
 
 (4) Any equivalent of a word can be substituted for it, 
 
 provided the substitution does not produce tau- 
 tology. 
 
 The Dictum de omni et nullo supplies a Canon of Sub- 
 alternation (Subversion). 
 
 As regards terminology, I think the following restrictions 
 and additions would be convenient : 
 
 (1) Inference (in narrow sense) proposition inferred to 
 
 (cf. above). 
 
 (2) Inferend = proposition or propositions inferred from. 
 
 1 E.g. also, likewise are equivalent Syncategorematic words. Any two 
 differing propositions are equivalent which are reciprocally inferrible.
 
 INFERENCE. 141 
 
 (3) Inference (in wider sense) = (1) and (2) taken together. 
 
 (4) To infer = to pass from (2) to (1), (2) being the justi- 
 
 fication for (1), and (1) and (2) being in some 
 respect different from one another. 
 
 (5) P]duct = An inference (1) from one proposition. 
 
 (6) Educend = The one proposition inferred from. 
 
 (7) Eduction = (5) together with (6). 
 
 (8) Educe = to pass from (6) to (5). 
 
 (9) Conclusion = An inference (1) from two (or more) pro- 
 
 positions taken together. 
 
 (10) Premisses = The two (or more) propositions from 
 which a conclusion is drawn. 
 
 [TABLE.
 
 142 
 
 RELATIONS OF PROPOSITIONS. 
 
 s ~' 
 
 K OX 
 
 
 35 
 9:2 
 
 1 * 
 
 
 
 o^ 
 
 <! ^2 M 
 
 I 
 
 
 
 s 3 
 
 
 
 
 
 ii s 
 
 
 s 
 
 
 
 
 Hrtl 1 
 
 H . s 
 
 8 
 
 
 
 
 
 '? 
 
 ^5*' 
 
 
 
 
 a ,K j$> 
 
 
 ^ 
 
 
 
 
 S ^^ 
 
 
 * .^J 
 
 
 
 
 N 
 
 o: "o 
 
 S ^ 
 
 
 
 
 
 S . <D 
 
 *"" 
 
 
 
 
 
 3 "H 2 
 
 . <&f^ 
 
 |M 
 
 
 
 
 -3h> -1 <B r* 
 
 K 'S'C- C 
 
 ** 
 
 
 
 
 1 
 
 :RENTIAL SY 
 f. Table XX 
 
 J? 5 "3 
 
 % g 
 
 ^ s 3 
 
 f5 S 
 jog 
 
 the cause of 
 
 once coheres 
 be always c< 
 coherent wii 
 
 11 
 
 c -*j i> 
 
 S ,*.; 
 
 o C 
 
 - & 
 o o 
 
 o .i ^i. 
 
 
 
 
 go 
 
 "1 o 
 
 P^j ^ T 1 O 
 
 ^. "S I 
 
 
 
 
 55 
 
 ***^ ^ S c 
 
 fc * 1 
 
 S 'g <r' 
 
 
 
 
 HH 
 
 = o 
 
 
 ^ H tog S 
 
 
 
 
 
 -sgg 
 
 "* oo B 
 
 1 ais, | 
 
 
 
 
 
 >^^ 
 
 <C ^ g 
 
 -^ ^ o ^ 
 
 
 
 
 
 * 3 co 
 
 ^ -M f on 
 
 j2 
 
 S X - U 
 
 
 
 
 
 m C3 
 
 
 ' 
 
 
 u 
 
 
 
 
 ^^X !xj ^ IX 
 
 H 
 
 J 1 i o -8"* 
 
 a 
 
 od 
 
 
 
 3 j ; 
 
 
 "Sj'el) c3 ^" 
 
 ^ 
 
 B 
 
 
 
 
 C/} 1 g g oj 
 
 0> 
 
 o 
 
 
 
 
 S _O * t-, 
 
 H 
 
 
 
 93 
 
 
 
 
 Oi 
 ^ 
 
 
 a 
 S 
 
 3 
 
 a 1 "S 
 
 J'S o S 
 "c'CPn iO 
 
 ^O 
 
 ^ 
 
 
 d 
 
 JS 
 
 s 
 
 
 
 
 BD 
 
 M 
 
 
 
 
 3 
 
 s 
 
 6^" 2 
 
 
 
 
 
 i 
 
 1 
 
 PH 
 
 o 
 
 
 o 
 
 
 
 
 
 1 
 
 q 
 
 ll 
 
 s, 
 
 c 
 
 
 -< 
 
 
 g " 
 
 
 
 
 
 5 a" 
 
 ^ 
 
 
 ^^ J" 
 
 s 
 
 
 
 "3 * 
 
 S 
 
 
 ill " 
 
 6b 
 
 e3 B 
 
 
 
 ? "S 
 
 a) 
 
 
 Q OJ V 
 
 - t3 !>> 
 
 ^J 
 
 
 
 .S 
 
 j 
 
 
 * o cS 
 oJ 3 r$ 
 
 0> 
 
 OJ CO 
 
 
 
 
 
 
 J3 t.-a 
 
 ^ s 
 
 
 8^ . 
 
 S.s 
 
 3 
 
 ^.^c 
 
 03 O 
 
 ! XXX VI. J 
 
 FROM ONE PROPOSITION' 
 ANOTHER = Immedi 
 Inferences (Eductions) 
 Cf. Table XXXVII. 
 
 Traductive Syllogisms. 
 
 wdon is the highest mount 
 has the most extensive ' 
 
 IS. 
 
 est mountain in Wales 1 
 ews. 
 
 n are statesmen, 
 n are authors. 
 
 ;esmen are authors. 
 ante, p. 60.) 
 
 Limited Sylloyigm 
 position for mi 
 called " Perfect 
 
 e.g. Sunday, ] 
 days of the week. 
 All the days of t 
 which are each 24 
 
 W c ,3 
 
 -C ' ^ rt <44 
 
 
 
 
 
 ^T=^ 
 
 ^5 ^ 
 
 80 >^* 
 
 
 < . la 
 
 a,"* S S 
 -c s J3J: 
 
 
 S 
 
 
 \>'tfl 
 
 EH -2 HH en 
 
 
 3 
 
 H i 
 
 

 
 IMMEDIATE INFERENCES (EDUCTIONS). 143 
 
 SECTION XIX. 
 
 IMMEDIATE INFERENCES (EDUCTIONS). 
 
 WHEN we pass from one proposition to another, and the 
 latter is justified by the former, and differs from it in some 
 respect, the latter is an Immediate Inference (Eduction) from 
 the former. 
 
 Eductions may have I. Categoricals (a), or Inferential 
 (&), or Alternatives (c) for both educt and educend ; these 
 may be called Pure Eductiotis or Aversions. Or II. they may 
 have a Categorical with an Inferential (a), or a Categorical with 
 an Alternative (b), or an Inferential with an Alternative (c). 
 These may be called Mixed Eductions, or Transversions. 
 
 Five principal subdivisions of Categorical Eversions are 
 recognised, to which the names Subalternation, Obversion, 
 Simple Conversion, Conversion per Accidens (the two latter 
 being frequently included under the one name of Conversion 
 or Ordinary Conversion), and Contraposition have been given. 
 It would be convenient, I think, to make the terminology 
 here more uniform, using Subversion for Subalternation, Rever- 
 sion for Simple Conversion, Intraversion for Conversion per 
 Accidens. and Contraversion for Contraposition. This ter- 
 minology, besides its uniformity, would have the further 
 advantage of allowing of convenient distinctive terms (framed 
 on the model of the current Converse and Convertend) for the 
 educt and educend in each of these particular cases. Perhaps 
 to these five Eductions there may be added the Inverse and 
 the Obverted Converse, both of which have been recognised 
 by some recent writers. The latter seems to stand on pre- 
 cisely the same footing as the Converted Obverse, to which, 
 however, a distinctive name has been already appropriated. 
 For the sake of symmetry and convenience I would propose 
 to assign one to the Obverted Converse also, and to call it the 
 Retroverse. 
 
 Two other kinds of Eversion are mentioned by some
 
 144 RELATIONS- OF PROPOSITIONS. 
 
 logicians, called respectively Inference by Added Determinants 
 and Inference by Complex Conception 1 (they might, I think, 
 be conveniently classed together as Extr -aversions). However, 
 where significant terms are used, the force of words becomes 
 so variously and subtilely altered by combination with others, 
 that in inferences of this kind (constant and indispensable as 
 they are) there is a liability to Fallacies of Accident which 
 can only be guarded against by reference to the special cir- 
 cumstances of each case. 
 
 In Subversion we pass from a Complete or Total Proposi- 
 tion to a Partial Proposition, having the same Subject-name, 
 the same Predicate, and the same Quality. E.g., from 
 
 Every wind is ill to a broken ship 
 to 
 
 Some winds are ill to a broken ship. 
 
 In Obversion, the passage is from an affirmative (or nega- 
 tive) proposition (1) Total, or (2) Partial, to a negative (or 
 affirmative), (1) Total, or (2) Partial. The obverse has the 
 same Subject-name and the same Quantity as the obvertend, 
 but different Quality ; and the Predicate-name of the obverse 
 is the negative of the Predicate-name of the obvertend. E.g., 
 
 All is fine that is fit 
 obverts to 
 
 Nothing is not fine that is fit. 
 
 The principle of obverting is, that the affirmation (or 
 denial) of any Predicate justifies the denial (or affirmation) of 
 its negative (cf. Law of Contradiction, note, p. 177). Every 
 categorical proposition can be obverted. 
 
 In a Reversion, the educt has the P-name of the educend 
 for its S-name, and the S-name of the educend for its P-name. 
 Reverse and revertend do not differ in Quantity or Quality. 
 Of the four propositions, A, E, I, 0, it is only E and I that 
 can be reverted ; for if A and propositions are treated in 
 this way, the propositions which result are not justified by 
 1 Cf. ante, Section XVIII. p. 140.
 
 IMMEDIATE INFERENCES (EDUCTIONS). 145 
 
 those from which we started. All affirmative Partial Pro- 
 positions can be reverted (cf. Tables XXVII. XXXI.). 
 To take two simple examples 
 
 Those plants are biennials 
 reverts to 
 
 Some biennials are those plants. 
 
 No man is a free agent who cannot command himself 
 reverts to 
 
 No free agent is a man who cannot command himself. 
 In what I have called Intraversion, we infer from an 
 Affirmative Proposition which is Complete or Total to a 
 Partial Proposition of the same Quality, and having the 
 P-name of the educend for its S-name, and the S-name of 
 the educend for its P-name. E.g., 
 
 An honest miller has a black thumb 
 intraverts to 
 
 Some persons having a black thumb are honest millers. 
 In Contraversion the educt differs from the educend in 
 the following respects : 
 
 (1) The Subject-name of the educt is the negative of the 
 Predicate-name of the educend. 
 
 (2) The Predicate-name of the educt is the Subject-name 
 of the educend. 
 
 (3) Educt and educend differ in Quality. 
 
 (4) Every Contraverse but that of E has the same Quantity 
 as the Contravertend ; the contraverse of E has different 
 Quantity. E.g., 
 
 IF is stiff 
 contraverts to 
 
 Not-stiff is-not IF. 
 
 There is no contraverse of I, because its obverse is O, 
 which cannot be converted ; and to reach the contraverse of 
 any proposition, it has to be obverted, and then the obverse 
 thus obtained has to be converted. 1 Hence every proposition 
 of which the obverse can be converted is capable of being 
 contraverted. 
 
 1 Cf. Keynes, Formal Logic, 2nd ed. p. 100.
 
 146 RELATIONS OF PROPOSITIONS. 
 
 lu Eetroversion (which applies to all Categorical Proposi- 
 tions except 0) the educt differs from the educend in Quality, 
 the Predicate-name of the educend is the Subject-name of the 
 educt, and the negative of the Subject-name of the educend 
 is the Predicate-name of the educt. In the case of A, educt 
 and educend differ in Quantity ; in other cases the Quantity 
 is the same. 
 
 To take examples 
 
 All who love me keep my commandments 
 retroverts to 
 
 Some who keep my commandments are not those who 
 do not love me. 
 
 Some true doctrines are universally accepted 
 retroverts to 
 
 Some things universally accepted are not doctrines which 
 are not true. 
 
 Some believers in Spiritualism are these well-known writers 
 retroverts to 
 These well-known writers are not disbelievers in Spiritualism. 
 
 These E's are Q's 
 retroverts to 
 
 Some Q's are-not not-these R's. 
 
 In an Inversion " we obtain from a given proposition a 
 new proposition having the contradictory of the original 
 subject [name] for its subject [name], and the original 
 predicate for its predicate" (Keynes, Formal Logic, 2nd ed. 
 p. 107). 1 
 
 Also the Inverse of any proposition differs from the 
 invertend in both Quantity and Quality. A and E are the 
 only propositions which can be inverted. 
 
 1 The whole subject of Categorical Immediate Inferences lias been admirably 
 worked out and systematized by Mr. Keynes in Part ii. of the second edition 
 of his Formal Logic.
 
 IMMEDIATE INFERENCES (EDUCTIONS). 147 
 
 The following are examples : 
 
 No sunshine is without shadow 
 inverts to 
 
 Some things that are not sunshine are without shadow. 
 
 A friend in need is a friend indeed 
 inverts to 
 
 Some who are not friends in need are not friends indeed. 
 
 Only Coincidental propositions can be converted, contra- 
 verted, retroverted, or inverted. Only A Propositions can 
 be intraverted. Adjectivals as well as Coincidentals may be 
 subverted, obverted, and extraverted. 
 
 With Inferential there seems to be only one kind of 
 Eversion, which corresponds pretty nearly to Contraversion. 
 E.g. from any Hypothetical 
 
 If A, then C, 
 another Hypothetical 
 
 If not C, then not A, 
 
 may be educed. The reason why this is the only kind of 
 Eduction in which the Inferential form is retained is that 
 from its very form an Inferential must be affirmative and 
 Whole (cf. Table XXXVIII.). 
 
 Apparently the only Alternative Eversion is the unim- 
 portant one (which may perhaps be called a Converse) in 
 which from A or B we pass to B or A. 
 
 It is, in my opinion, only Complex Categoricals (cf. Jevons, 
 Elementary Lessons in Logic, 7th ed., p. 91) which are 
 Universals or Generals, that are formally reducible to an 
 Inferential or an Alternative (cf. ante, Section XII.). A 
 Categorical of the form 
 
 Any D that is not E is F (1) 
 is reducible to the Conditional 
 
 If any D is not E, that D is F (2), 
 and to the Alternative 
 
 Any D is F or E.
 
 148 RELATIONS OF PROPOSITIONS. 
 
 (This latter proposition is reducible indifferently to (1) or 
 its contraverse, and to (2) or its contraverse.) 
 Again (2) is equivalent to 
 
 If all D's are not E, all D's are F. 
 
 This proposition is Hypothetical (cf. the distinction between 
 Hypothetical and Conditionals referred to above, Section XII.), 
 and it is reducible to Conditional and to Categorical form if 
 we know that the Subject of A and C is to be taken distri- 
 butively. Of an Inferential which is in the form 
 
 If D is E, F is G, 
 or 
 
 If A, then C, 
 
 it is impossible to say, on inspection, whether it is Hypotheti- 
 cal or Conditional. If we know that it is Hypothetical, then, 
 without still further information, we cannot say whether or not 
 it is equivalent to a Conditional of the form 
 
 If any K is E, that K is G, 
 
 just as it is impossible to say, from mere inspection, whether 
 a Categorical expressed as 
 
 All R is Q 
 
 is an Adjectival or a Coincidental Proposition. 
 
 Table XXXVII. contains illustrations in symbols of all the 
 above-mentioned kinds of Eversions. 
 
 In Transversion, the most interesting points are that all 
 Inferentials and Alternatives may (as I think) be fully and 
 accurately expressed in Categorical form ; that Conditionals 
 and Categoricals, of which S and P in the one correspond to 
 A and C in the other, are reciprocally educible ; that Infer- 
 entials are educible from Alternatives and Alternatives from 
 Inferentials, and thus the Alternative answering to any 
 Inferential has a corresponding Categorical, educible from the 
 Categorical which answers to the Inferential.
 
 IMMEDIATE INFERENCES (EDUCTIONS). 149 
 
 For instance, the Conditional 
 
 If any flower is a Datura, that flower is fragrant (1) 
 is equivalent to the Categorical 
 
 (2) Any flower that is a Datura is fragrant (is a flower 
 that is fragrant) ; 
 
 (1) is also equivalent to the Categorical 
 
 That any flower is fragrant is an inference from its 
 being a Datura (3) ; 
 
 but (2) is the most natural and characteristic Categorical 
 equivalent of (1). 
 The Hypothetical 
 
 If Honesty is not the best policy, life is not worth living, 
 may be expressed as 
 
 Life is not worth living is an inference from Honesty is 
 not the lest policy (4). 
 
 The meaning of (4) is expressed in the Alternative, 
 
 Life is not worth living or Honesty is the best policy ; 
 and this has its meaning conveyed by the Categorical 
 
 Life is not worth living is alternative with Honesty is the 
 best policy (5). 
 
 We feel the Categorical expression here (as the Inferential 
 form in (3)) to be somewhat awkward and inappropriate ; 
 but this being admitted, it appears to me to be adequate. 
 And (5) is equivalent to (4), not formally, but in virtue of a 
 knowledge of what is involved in the relations of inference 
 and alternation between propositions, (4) and (5) being 
 Systemic or Dependent Propositions. (Cf. ante, Section IX.) 
 
 [TABLE.
 
 150 
 
 RELATIONS OF PKOPOSITIONS. 
 
 , 
 
 <"" 
 - <! 
 
 >. 2 
 
 OS S5 
 
 a o 
 W 
 
 w 
 
 .J 
 
 pa 
 
 ~ 
 
 o ^ 
 
 
 .3 e 
 
 :Q - 2 s 
 
 Q -2 C3 -2 
 
 02.2 
 
 W .2 SW 
 
 O 4 
 
 2 
 
 si 
 
 O 1 
 
 .2 
 
 M 
 
 ".C?
 
 INCOMPATIBLE PROPOSITIONS. 151 
 
 SECTION XX. 
 
 INCOMPATIBLE PROPOSITIONS. 
 
 Propositions are Incompatible when they cannot both be 
 true ; and while of Propositions related as educt and educend, 
 the first is true if the second is true, of propositions related 
 as Incompatibles, either is false if the other is true. 
 
 Propositions are generally said to be contrarily opposed 
 when they cannot both be true but may both be false e.g. 
 All R is Q, No R is Q ; contradictorily opposed when they 
 cannot both be true and cannot both be false e.g. All R is 
 Q, Some R is not Q. With simple Categoricals, it is only 
 where we are concerned with class-names that Propositions 
 can be contrarily opposed. All R is Q and No R is Q are, I 
 think, the only contraries ordinarily recognised. We may 
 indeed have opposition between such propositions as 
 
 ( These R's are Q (1) 
 
 | Some of these R's are not Q (3). 
 
 ( These R's are not Q (2) 
 ( One of these R's is Q (4); 
 
 but the relation between (1) and (2), (1) and (3), (2) and (4) 
 respectively, exactly corresponds to that between A and E, 
 A and 0, E and I. For These R's as contrasted with Some of 
 these R's is equivalent to All tlwse R's. 
 
 In all other cases, each Categorical that is not compound (cf. 
 Jevons, Elementary Lessons in Logic, p. 90) has but one formal 
 categorical Incompatible, and that one is its Contradictory. 
 
 E.g. ( S is P 
 
 { S is not P. 
 
 (Charles I. was a saint 
 (Charles I. was not a saint. 
 
 {His set are to be trusted 
 His set are not to be trusted.
 
 152 RELATIONS OF PROPOSITIONS. 
 
 {X's children are my cousins. 
 X's children are not my cousins. 
 
 In such a proposition as 
 
 Billy and Colin are at school, 
 
 we have what Jevons calls a Compound proposition, which is 
 really an abbreviated expression of a plurality of single pro- 
 positions. And here, as in the case of A and E, we may have 
 two Categorical Incompatibles but here both of them are 
 contrary e.g. 
 
 Neither Billy nor Colin is at school (1) 
 One only of the two is not at school (2). 
 
 The contradictory is obtained by a combination of (1) and 
 (2). It must be true either that 
 
 (a) Billy and Colin are at school, 
 or that 
 
 (b) One only is at school, or neither is. 
 
 Billy is at school and in the first class, 
 may be treated in the same way. 
 A Conditional Proposition 
 
 If any D is E, that D is F (1) 
 is certainly incompatible with 
 
 If any D is E, that D is not F (2). 
 But if the import of (1) can be expressed by saying 
 That any D is F is an inference from its being an E (3), 
 
 then (1) and (2) do not exhaust all possibilities : for it may 
 be that neither D is F nor D is not F is an inference from 
 J)'s being E ; it may be that no connection is known between 
 Ifs being E and Us being F. No doubt between any two 
 identifications there must be a connection if we only knew it ; 
 but unless we do know it, we cannot make any inference 
 from the one to the other. Just in the same way, Any A
 
 INCOMPATIBLE PROPOSITIONS. 153 
 
 must be B or not B ; but we may not be in a position to 
 affirm either the one Predicate or the other. 
 Again 
 
 This D is E and this I) is not F, 
 
 though it is certainly incompatible with (1), does not seem to 
 me to be properly called its contradictory. For if I take such 
 a proposition as the following : 
 
 If any figure has 1000 equal sides, it has 1001 equal 
 angles, 
 
 am I not to be allowed to deny it, unless I can say, indicating 
 some figure, 
 
 This figure has 1000 equal sides, and it has not 1001 
 equal angles ? 
 
 But taking what seems to be the more natural and cha- 
 racteristic interpretation of (1), namely, 
 
 Any D that is E is F, 
 we get a perfectly simple and satisfactory contradictory in 
 
 Some D's that are E are not F. 
 The contrary of (1) as thus interpreted would be 
 
 No D that is E is F 
 ( = If any D is E, that D is not F). 
 
 (3) can, however, be simply and fully negatived by 
 
 That any D is F is not an inference from its being an E. 
 
 And all Hypotheticals without exception may, I think, be 
 contradicted in the same way e.g., 
 
 (1) If S is P, P is S 
 
 (2) If M is P, S is P, 
 
 are contradicted by 
 
 (!') P is S is not an inference from S is P. 
 S is P is not an inference from M is P.
 
 154 RELATIONS OF PROPOSITIONS. 
 
 If we take such propositions as 
 
 If black is white, he is a person to be trusted ; 
 
 If I pain you, I pain myself more ; 
 
 If this bill becomes law, it will be to the advantage 
 
 of tenant-farmers ; 
 If the earth were only 6000 miles in diameter, it would 
 
 be less than 24,000 miles in circumference; 
 If ye love me, ye will keep my commandments ; 
 If it is six o'clock, Mary will soon be here 
 
 in each case the full import can, I think, be expressed in a 
 Categorical of the form 
 
 C is an inference from A. 
 
 (Perhaps the exact form, in the case of the proposition about 
 the earth's diameter, would be 
 
 C would be an inference from A.) 
 And 
 
 C is an inference from A 
 
 is contradictorily opposed by 
 
 C is not an inference from A. 
 Neither 
 
 If A, not C 
 nor 
 
 A and not C 
 
 seem possible contradictories in the concrete cases given above. 
 And this seems strikingly the case too, if we take such an 
 absurd Inferential as 
 
 If Middlemarch is a fine book, Sarah Battle was devoted 
 to whist. 
 
 An Alternation of the form 
 
 (1) A is B or C is D (or, A is B or A is D) 
 is said to be contradicted by 
 
 (2) A is not B and C is not D (or, and A is not D).
 
 INCOMPATIBLE PROPOSITIONS. 155 
 
 But here again, as in the case of Inferential, I think a third 
 possibility remains. The import of (1) is that the elements 
 of the alternation are so related as that the denial of either 
 justifies the affirmation of the other. The import of (2) is 
 that the denial of either member is bound up with the denial 
 of the other. But it may be that not only is there not the 
 relation between A is B, C is D, which is indicated by (1), 
 but also that in addition there is not the (incompatible) 
 relation indicated by (2); and since (1) and (2) exhaust the 
 possible relations of inference between A is B, C is D, and 
 their negatives, the only possibility that remains is, that A is 
 B, C is D, are entirely unconnected. 
 
 To take an example : 
 The " Alternative " 
 
 Sarah Battle was devoted to whist, or Middlemarch is 
 not a fine book, 
 
 does not seem to be effectively denied by 
 
 Sarah Battle was not devoted to whist, and Middlemarch 
 is a fine book. 
 
 Sarah Battle was devoted to whist is not alternative with 
 Middlemarch is not a fine look, 
 
 appears to me a more satisfactory contradictory. And this 
 form of denial (C is not alternative with not-A) seems to be 
 applicable in every case. 
 
 In Inferentials where A cannot be simply affirmed, nor C 
 simply denied as in, e.g., 
 
 If Charles I. had not deserted Strafford, he would have 
 
 been more deserving of sympathy ; 
 If this bill passes, the dock labourers will benefit ; 
 If any violet were scarlet, it would be scentless ; 
 If I finish my paper this morning, I shall be at liberty 
 
 this afternoon 
 
 we cannot use the Inferential as it stands as the Major 
 Premiss of an Inferentio-Categorical Syllogism. We can, of
 
 156 RELATIONS OF PROPOSITIONS. 
 
 course, affirm that a negation of the identity indicated by A, 
 and an affirmation of the identity indicated by C, cannot be 
 asserted together ; but this will not enable us to go on to any 
 syllogistic Inference as long as we are unable in each case to 
 affirm the identity indicated by A because of its falsity or 
 uncertainty this falsity or uncertainty being shown by the 
 peculiar phrasing of the proposition. 
 
 Inferential like some of the above are exceedingly frequent. 
 They express forecasts of consequences which we are con- 
 tinually making and acting upon. How often one thinks, If I 
 buy those books, I shall be inconveniently short of money ; 
 If I undertook this work, it would interfere with more 
 important business ; If I go to Switzerland for July and 
 August, I must put off these visits in England and so on. 
 Prevision or estimation of the probable effects of action must 
 constantly be expressed, or expressible, in such propositions 
 as these. 
 
 MEDIATE INFERENCES (SYLLOGISMS}. 
 
 SECTION XXI. 
 
 (A.) CATEGORICAL SYLLOGISMS. 
 
 IT seems to me that Mill's criticism of the Dictum de omni 
 et nullo is well founded, and that that Canon merely amounts 
 to saying that what is predicated of every member or every 
 portion of a class, may be predicated of any member or any 
 portion of that class. For when we say, " Whatever is pre- 
 dicated of a term distributed may be predicated in like manner 
 of everything contained under it," it seems clear that by term
 
 CATEGORICAL SYLLOGISMS. 157 
 
 is meant the term-name for in, e.g., Some men are mortals, 
 the S (i.e. Some men) is as much (or as little) " distributed " 
 as in All men are mortals i.e. some class-name ; and what 
 is predicated of a class-name distributed is, ex m termini, 
 predicated of each member of the class the Dictum is not 
 a Canon of Syllogism (if Syllogism means Formal Mediate 
 Inference), nor even a statement of relations between different 
 classes, but merely a formulation of the truth that if any 
 object or objects belong to a class, what can be said about 
 the class (distributively) can be said about it or them. It 
 seems to apply only in cases in which we are dealing with 
 A, E, I, or propositions. 1 But a Canon of Syllogism ought 
 to apply, whatever terms and term-names we are dealing with, 
 and whatever admissible arrangement of these we are con- 
 sidering. It ought to apply to Syllogisms in the 2nd, 3rd, 
 and 4th figures, and to arguments in which all the terms are 
 Partial or Single, as well as to Syllogisms in Fig. 1, which 
 have a class-name " distributed " for the S-name in the major 
 premiss. When Jevons says (Principles of Science, p. 9, 3rd 
 ed.) that " the great rule of inference " is that " so far as there 
 exists sameness, identity, or likeness, what is true of one 
 thing will be true of another," I do not think he helps us 
 much. For in any purely formal (affirmative) inference by 
 Categorical Syllogism, it is not " two things " that are named 
 by the terms in each proposition, but one thing (or group) ; 
 and in a whole syllogism, not two things, or three things, or 
 six things, but one thing, or one thing and part of that same 
 " thing." The denomination (and the application) of the 
 two terms in any affirmative proposition must be absolutely 
 identical, and where there are more than three terms in an 
 affirmative syllogism, the extra ones must be identical in 
 
 i Somewhat similar remarks seem to be applicable to the ordinary rules 01 
 Conversion and the traditional rules of the Categorical Syllogism. They are all 
 framed for application to certain class propositions propositions of the A, E, 
 I, type. Indeed the rules of the Syllogism seem to be just a kind of rule of 
 thumb for facilitating the application of the Dictum to propositions of this 
 kind. The traditional Formal Logic is rather a Logic of Classes than a Logic 
 of Proposition*.
 
 158 RELATIONS OF PROPOSITIONS. 
 
 denomination with part of the denomination of some one of 
 the three. E.g. in 
 
 All N's are Q's, 
 Some R's are N's, 
 Some R's are Q's, 
 
 we have four terms, viz. : (1) all N's, (2) some Q's, (3) some 
 N's, (4) some H's ; but we have not three (or more) things, 
 but one group of things, viz. : the Q's that are N's, and a 
 group that is all or a part of this, the R's that are N's. And 
 in negative propositions and syllogisms we have only two 
 " things," or two things and a part of one of them. Jevons' 
 rule has the further fault of being reducible to tautology, for 
 " So far as there exists sameness, identity, or likeness, what 
 is true of one thing will be true also of another," can only 
 mean, " two things are like in as far as they are like " (two 
 things cannot be identical or the same). In this " rule " some 
 of the important terms are in themselves ambiguous, and they 
 are very loosely used. In employing likeness, identity, same- 
 ness, what is true, as he does in this Canon, Jevons errs, it 
 seems to me, in two ways (1) he confuses things that differ 
 (qualitive likeness and quantitive identity this confusion 
 runs through his whole account of inference) ; (2) his phrase- 
 ology implies a distinction where there is no difference, and 
 thus a real tautology wears the guise of significant assertion. 
 When (pp. cit. p. 10) he says, in speaking of measuring ex- 
 tended objects, that " we obviously employ the axiom that 
 whatever is true of a thing as regards its length is true of 
 its equal " [in length], the absolute uselessness of the "axiom" 
 seems clear it amounts to no more than this, " What is true 
 of a given length in one case, is true of that length in another 
 case ; " but this is only equivalent to saying that a given 
 length is a given length a form of words which has no pre- 
 dicative force. The matter is not mended by the further 
 discussion (op. cit. p. 17, and following pages) of logical 
 inference, which appears to me to be spoiled all through by 
 the ever-recurring confusion (1) between quantitive identity
 
 CATEGORICAL SYLLOGISMS. 159 
 
 (what Jevons would perhaps call numerical sameness or 
 identity) and qualitive likeness ; (2) between what I have 
 called Independent and Dependent Propositions (to which 
 latter class all Mathematical Equations belong). There is 
 perhaps also some confusion between terms and application 
 (Denotation) of terms. The implication that two things can 
 be so similar, point for point, as to be capable of being 
 logically substituted one for another (cf. p. 20, etc.), seems 
 due to (1). It appears to me that Jevons was constantly 
 on the very verge of escaping from the first of the confusions 
 indicated above, but that somehow he always just missed 
 doing so. 
 
 I should propose to define Categorical Syllogism as 
 follows : 
 
 A Categorical Syllogism is a combination of three cate- 
 gorical propositions, one of which (the Conclusion) is inferred 
 from the other two taken together these two being called 
 the Premisses, and having in common one term-name which 
 does not occur in the conclusion. The conclusion has its 
 S-name in common with one premiss, and its P-name in 
 common with the other premiss. 
 
 Taking Term as meaning Term-name -f indicator, it is clear 
 that in a Syllogism as thus defined, though there can be only 
 three term-names there may be Jive terms (when we are dealing 
 with class-names). 
 
 E.g. in 
 
 All N is Q, 
 All E is N, 
 Some E is Q ; 
 
 the Terms are, All N, [Some] N, All E, Some E, [some] Q. 
 
 If I may still use the names Middle Term, Major Term, and 
 Minor Term, All N and [some] N are Middle Terms, All E and 
 Some E are Minors, and [some] Q is Major both in premisses 
 and conclusion. [Some] N of course coincides, ex m termini, 
 with part of All N, and it is this part of All N that is the 
 real medium of connection between Major and Minor just as
 
 160 RELATIONS OF PROPOSITIONS. 
 
 when we call N the Middle Term in the above Syllogism, it 
 is tliat part of N which is coincident with loth R and Q that is 
 the real medium between them. 
 
 The Middle Term in either premiss of a Syllogism is that 
 which has the Term-name common to both premisses. 
 
 The Major Term in the premisses of a Syllogism is that which 
 has its term-name in common with the P of the conclusion. 
 
 The Minor Term in the premisses of a Syllogism is that which 
 has its term-name in common with the S of the conclusion. 
 
 The Major Premiss is that which contains the Major Term. 
 The Minor Premiss is that which contains the Minor Term. 
 
 I think the Canon of Categorical Syllogism may be 
 amended as follows : 
 
 If the denomination of two terms is identical (or non- 
 identical), any third term which has a different term-name 
 and is denominationally identical with the whole (or part) of 
 one of those two. is also identical (or non-identical), in whole 
 or part, with the denomination of the other. 
 To take examples of application, in 
 No N is Q, 
 All K is N, 
 No E is Q ; 
 
 the denomination of (1) All N is non-identical (absolutely 
 uncoincident) with the denomination of (2) [all] Q ; and the 
 denomination of (3) All E is identical with some of the 
 denomination of All N; hence All E is non-identical with 
 [all] Q. 
 In 
 
 All Q is N, 
 
 No E is N, 
 
 No E is Q ; 
 
 the denomination of (1) All E is non-identical with that of (2) 
 [all] N ; the denomination of (3) All Q is identical with some 
 of the denomination of [all] N ; hence the denomination of 
 All E is non-identical with the denomination of [all] Q.
 
 CATEGORICAL SYLLOGISMS. 161 
 
 In 
 
 All N is Q, 
 All N is E, 
 Some E is Q ; 
 
 denomination of (1) All N is identical with that of (2) 
 [some] Q ; denomination of (3) [some] E is identical with 
 that of All N ; therefore the denomination of Some E is 
 identical with that of [some] Q. 
 In 
 
 All Q is N, 
 
 All N is E, 
 
 Some E is Q ; 
 
 (1) All N is identical in denomination with (2) [some] E ; 
 the denomination of (3) All Q is identical with some of the 
 denomination of All N ; hence the denomination of Some E 
 is identical with some of the denomination of All Q (namely 
 [some] Q). 
 
 In considering the ordinarily accepted rules of Syllogism, 
 the distinction between term and term-name again becomes 
 important. 1 For if, in, e.g., the syllogism 
 
 All N's are Q's, 
 Some E's are N's, 
 Some E's are Q's, 
 
 we call (1) all N's, (2) some Q's, (3) some E's, (4) some N's, 
 Terms, then the rule that in a valid syllogism we must have 
 only three terms, excludes all syllogisms except those in Fig. 
 3, which have the middle " term " distributed twice. In the 
 instance above taken we have four terms. 
 
 But if we call E, Q, and N " Terms," then, if Syllogism is 
 defined as having only three Terms, to have three Terms is no 
 differentia of valid (no rule for valid) Syllogism. (In any 
 case the rule is superfluous, the condition which it lays 
 
 1 Of. ante, pp. 4, 5. 
 L
 
 162 RELATIONS OF PROPOSITIONS. 
 
 down being secured by the other ordinarily received rules of 
 Syllogism.) 
 
 Again, if Syllogism is not defined as having only three 
 Terms, then the other rules of Syllogism exclude valid argu- 
 ments admitted by the definition, such as 
 
 A is greater than B, 
 B is greater than C, 
 C is not less than A, 
 
 and (still taking Term to mean Term-name} Eule 3 excludes 
 such an argument as 
 
 These men are my brothers, 
 These men are under 7 foot, 
 My brothers are under 7 foot, 
 
 and Eule 4 does not exclude Illicit process of the Major and 
 Minor Terms, e.g., 
 
 All N's are Q's, 
 Four R's are N's, 
 Five E's are Q's ; 
 
 All N's are some Q's, 
 All E's are some N's, 
 Some E's are most Q's. 
 
 I would suggest the following as substitutes for the old 
 syllogistic rules : 
 
 (1) In every syllogism the denomination of the middle 
 term in one premiss must be identical with the whole, or a 
 part, of the denomination of the middle term in the other 
 premiss ; x and the denomination of the major term and minor 
 term in the conclusion must be identical with the whole, or 
 a part, of the denomination of the major and minor terms 
 respectively in the premisses. 2 
 
 1 By Ob version of either premiss, these corresponding terms in the two pre- 
 misses may, of course, be made absolutely non-identical. 
 
 - By Obversion of the conclusion, the denomination of the major and minor 
 terms in the conclusion may be made absolutely non-identical with the denomi- 
 nation of the corresponding terms in the premisses.
 
 CATEGORICAL SYLLOGISMS. 163 
 
 This liule (or Rules) will replace Rules 1, 2, 3, 4, 7, 8, and 
 it provides against Tautological Fallacy, which they do not. 
 
 (2) Identity of denomination of the terms in the conclu- 
 sion requires identity of terms in both premisses ; and non- 
 identity of terms in the conclusion requires non-identity of 
 terms in one, and only one, premiss. 
 
 This will replace Rules 5 and 6. 
 
 Breach of (2) involves breach of (1) cf. Section XXVI. ; 
 hence any invalid Categorical Syllogism involves the Fallacy 
 of more or less than three Terms, directly or indirectly. There 
 are many valid arguments which are not expressed in strict 
 syllogistic form ; but every such argument is, I think, reducible 
 to formally valid inferences Syllogisms (Categorical, Infer- 
 ential, or Alternative), and Eductions. Such a syllogism as 
 
 A is greater than B, 
 B is greater than C, 
 A is greater than C, 
 
 I do not consider formal in the strictest sense, though its 
 cogency would be immediately evident to most persons. 
 
 A is not-B, 
 C is B, 
 
 C is not A, 
 
 is a cogent form of argument to which, by means of Obver- 
 sion of one premiss, valid syllogisms may be reduced, and a 
 form which itself, by Obversion of one premiss, reduces to 
 valid syllogism. (Cf. post, Section XXVI.) 
 
 SECTION XXII. 
 
 (B.) INFERENTIAL SYLLOGISMS. 
 
 I would define Inferential Syllogism as 
 
 A Syllogism having an Inferential premiss ;
 
 1()4 RELATIONS OF PROPOSITIONS. 
 
 Pure Inferential Syllogism as 
 
 A Syllogism of which the conclusion and both the 
 premisses are Inferential Propositions ; 
 
 Mixed Inferential Syllogism as 
 
 A Syllogism of which the major premiss is an Inferen- 
 tial Proposition, the minor premiss and the con- 
 clusion being Categorical Propositions. 
 
 I propose to classify Inferential Syllogisms as follows : 
 What Mr. Keynes calls (1) Conditional and (2) Hypothetical 
 Syllogisms (cf. Formal Logic, 2nd ed. pp. 264, 265). I would 
 propose to group together as " Pure Inferentials," subdividing 
 into 
 
 (1) Pure Hypotheticals, 
 
 (2) Pure Conditionals ; 
 
 (1) are what Mr. Keynes calls Hypothetical Syllogisms; 
 
 (2) are what he calls Conditional Syllogisms. 
 
 The other two kinds of Inferentials I would call " Mixed 
 Inferentials," and what Mr. Keynes calls Hypothetico-Cate- 
 gorical, e.g., 
 
 If E is F, G is H 
 
 G is not H (1) 
 
 E is not F, 
 
 1 would call by the same name giving the name Conditio- 
 Categorical Syllogisms to Syllogisms of the form 
 
 If any D is E, that D is F 
 
 XD is E ' (2) 
 
 XD is F. 
 
 (1) is Modus Tollend, (2) is Modus Ponend. 
 
 The only further subdivision of Inferential Syllogisms which 
 seems to me to be of consequence on a formal view, is that 
 into Dependent and Independent, which may be carried out 
 under each head. By a Dependent Syllogism, I mean a 
 Syllogism that contains at least one Dependent Term. 
 
 I would suggest the following as Canons of (1) Hypothetico-
 
 INFERENTIAL SYLLOGISMS. 165 
 
 Categorical, (2) Conditio-Categorical, (3) Hypothetical, (4) 
 Conditional Syllogisms. 
 
 (1) If one Categorical Proposition, C, is inferrible from 
 another Categorical Proposition, A ; then the assertion of A 
 justifies the assertion of C, and the denial of C justifies the 
 denial of A. 
 
 (2) If from some distinguishing mark, D, in any member 
 of a given class, K, some further mark, M, is to be inferred ; 
 then the assertion that any K is I), justifies the assertion that 
 that K is also M ; and the assertion that any K is not M, 
 justifies the further assertion that that K is also not D. 
 
 (3) If from one Categorical Proposition, A, another propo- 
 sition, C, is inferrible, and from C there is inferrible a third 
 proposition, D ; then I) is inferrible from A. 1 
 
 (4) If from the presence in any member of a class, K, of a 
 distinctive mark, D, a second mark, M, may be inferred ; and if 
 from the presence of M in any K, the presence (or absence) of 
 a further mark, M 2 , may be inferred ; then from the presence of 
 D in any K, the presence (or absence) of M 2 may be inferred. 1 
 
 1 A valid Inferential reasoning may need to have some of its propositions 
 obverted before this Canon will apply directly. 
 
 [TABLE.
 
 166 
 
 DELATIONS OF PROPOSITIONS. 
 
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 ALTERNATIVE SYLLOGISMS. 167 
 
 SECTION XXIII. 
 
 (C.) ALTERNATIVE SYLLOGISMS. 
 
 AN Alternative Syllogism may be defined as 
 
 A syllogism of which one premiss is an Alternative 
 Proposition or a combination of Alternative Pro- 
 positions, and of which one premiss and the conclusion, 
 or both premisses, or both premisses and the con- 
 clusion, may be alternative. 
 
 Alternative Syllogisms may be divided into I. Pure 
 Alternative Syllogisms ; II. Mixed Alternative Syllo- 
 gisms. 
 
 I. In a Pure Alternative Syllogism, both of the premisses 
 and the conclusion are alternative, e.g., 
 
 C is D, or A is not B ; 
 E is F, or C is not D ; 
 E is F, or A is not B. 
 
 II. Mixed Alternative Syllogisms may be distinguished as 
 (1) Categorico-Alternative Syllogisms, in which either con- 
 stituent (major or minor premiss, or conclusion) of the syl- 
 logism that is not alternative is categorical ; and (2) Inferentio- 
 Alternative Syllogisms, in which the major premiss is always 
 inferential in form, and the other premiss and the conclusion 
 are either (a) one alternative and the other categorical, or (b) 
 both alternative. 
 
 Inferentio - Alternative Syllogisms, which include what 
 are commonly called Disjunctive Syllogisms and Dilemmas, 
 may be divided into (i.) Hypothetico - Alternative, and 
 (ii.) Conditio - Alternative ; and each of these again into 
 1'onend Syllogisms and Tollend Syllogisms (corresponding 
 to the two ordinarily recognised forms of Inferential 
 Syllogisms).
 
 168 RELATIONS OF PROPOSITIONS. 
 
 The following may be suggested as Canons of 
 
 (1) Pure Alternative \ 
 
 (2) Categorico-Alternative 
 
 /-.x TT /" Syllogisms. 
 
 (3) Hypothetico- Alternative I 
 
 (4) Conditio-Alternative / 
 
 (1) From two alternative propositions, of which one has 
 an alternative that is the negative of an alternative in 
 the other, a third alternative proposition may be inferred, 
 having for its members the remaining alternatives of the 
 premisses. 
 
 (2) The denial of one member (or more) of any alternation 
 (or combination of alternations) justifies the affirmation of the 
 other member or members. 
 
 (3) Of two Hypothetical Propositions determinately com- 
 bined, if (Modus Ponend) A be alternatively affirmed, then 
 C may be alternatively affirmed (when not diverse, cate- 
 gorically affirmed) ; and if (Modus Tollend) C be alternatively 
 denied, then A may be categorically denied (when diverse, 
 alternatively denied). 
 
 (4) Modus Ponend. 
 
 Of any two Conditional Propositions determinately com- 
 bined, if the P's of the A's are alternatively affirmed of any 
 member (or members) of the class (or classes) indicated by 
 the S-name (or S-names) of the A's ; then of that member (or 
 those members) the P of C may be affirmed categorically if 
 the C's are indistinguishable, alternatively if the C's are 
 diverse. 
 
 Modus Tollend. 
 
 Of any two Conditional Propositions determinately com- 
 bined, if the P's of the C's are alternatively denied of 
 any member (or members) of the class (or classes) indicated 
 by the S-name (or S-names) of the A's ; then of that member 
 (or those members) the P of A may be denied categorically 
 if the A's are indistinguishable, alternatively if the A's are 
 diverse.
 
 ALTERNATIVE SYLLOGISMS. 
 
 169 
 
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 170 
 
 RELATIONS OF PROPOSITIONS. 
 
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 NOTE ON THE GROUND OF INDUCTION. 171 
 
 SECTION XXIV. 
 
 NOTE ON THE GROUND OF INDUCTION. 
 
 Mill tells us (Logic, Bk. iii. ch. iii.) that the fundamental 
 axiom or ground of Induction is the axiom which asserts 
 " that the course of nature is uniform ; that the universe is 
 governed by general laws." This axiom or principle is itself 
 a generalization from particulars, " an instance of induction, 
 and induction by no means of the most obvious kind." It 
 seems, when we inquire closely, to reduce itself to the Law of 
 Causation, for Mill (Bk. iii. ch. iii. 1, p. 358 of vol. i. in the 
 9th ed.) refers to ch. xxi., " Of the evidence of the Law of 
 Universal Causation," as concerned with the " fundamental 
 axiom of induction ; " and in ch. v. of the same book " Of the 
 Law of Universal Causation " he says that " the notion of 
 Cause" is " the root of the whole theory of Induction" (vol. ii. 
 p. 376); that "of all truths relating to phenomena, the most 
 valuable to us are those which relate to the order of their 
 succession" (vol. i. p. 374); that "there is no general axiom 
 standing in the same relation to the uniformities of co-exist- 
 ence as the law of causation does to those of succession " 
 (vol. ii. p. 117); and that this "great deficiency . . . precludes 
 the application to the ultimate uniformities of coexistence, of 
 a system of rigorous scientific induction, such as the unifor- 
 mities in the succession of phenomena have been found to 
 admit of" (vol. ii. p. 117); that Bacon's great error lay in 
 thinking (vol. ii. p. 118) "that as every event has a cause, or 
 invariable antecedent, so every property of an object has an 
 invariable coexistent, which he called its Form," Mill hold- 
 ing, on the contrary, that objects which are, e.g., soft or moist, 
 etc., " agree in the one point inquired into, and in nothing 
 else" (vol. ii. p. 118), so that when dealing with coexistences 
 we are thrown back upon Induction by Simple Enumeration. 
 What the Law of Causation asserts is that every event has a 
 cause ("change can only be produced by change," vol. i. 407),
 
 172 DELATIONS OF PROPOSITIONS. 
 
 and that [unconditional] "invariability of succession is found 
 by observation to obtain between every fact in nature and some 
 other fact which has preceded it" (cf. pp. 377 and 392 of 
 vol. i.) the cause of anything is " the antecedent which it 
 invariably [and unconditionally] follows" (vol. i. p. 390). 
 
 Cause as thus defined seems a contradictory notion ; for 
 let ABC be any antecedent, and let DEF be its consequent, 
 that which unconditionally and invariably follows If ABC 
 be the sole antecedent, it cannot be followed by DEF ; because, 
 since ABC alone is sufficient cause, the moment ABC, the 
 all-sufficient cause, is present, that same moment the effect of 
 which it is the sufficient cause must be there too ; therefore 
 DEF must be simultaneous with ABC. The Law of Causa- 
 tion as formulated by Mill is not workable. And if for 
 Antecedent we put Concomitant we get a law, not of succession, 
 but of coexistence. 1 
 
 If we consider that event means change in subjects of 
 attributes, it would seem that our power of predicting that 
 one event A, will be followed by another event B, must 
 depend wholly upon coexistence of attributes in the subjects 
 concerned. If we have seen one animal dosed with arsenic 
 and subsequently die, and hence conclude that another animal, 
 called by the same name, and dosed with an equal amount of 
 arsenic, will die, is not our inference based upon the assumption 
 of a certain constant coinherence of attributes, both in the 
 animal and in the poison a coinherence of such a kind 
 that when the two subjects are so collocated as to act upon 
 each other, a result similar to that produced in the first case 
 will be produced in the second also ? If the properties of 
 this arsenic are different from the other, or if the second 
 animal, though looking like the first, has a different internal 
 constitution, there is no reason why death should result. 
 This sort of uniformity an uniformity primarily of coexist- 
 ence is the only sort that we look for or find in terrestrial 
 
 1 The difficulty raised here does not seem to me to be met by what Mill says 
 at the end of 7 of the chapter on the Law of Causation (Logic, i. 397) ; 
 especially when this is taken in connection with what he says elsewhere iu 
 that chapter, and in various other places.
 
 NOTE ON THE GROUND OF INDUCTION. 173 
 
 nature. What subjects of attributes will be collocated, and 
 when and where, we cannot say beforehand ; all that we can 
 say is, that if subjects having certain attributes are collocated, 
 certain changes in them will take place. Hence laws of 
 succession in events seem to depend upon laws of coexistence 
 of attributes in subjects, and proof of Causation (in another 
 sense than that which Mill professedly adopts) is perhaps 
 chiefly valuable as an indirect proof of connection of 
 attributes. And I think not only that every attribute is 
 invariably accompanied by some other attribute, as Bacon 
 surmised, but also that every kind of attribute is one of an 
 unique group with which it is invariably and inseparably 
 connected. We certainly act as if we believed this ; from the 
 perception of a mere odour, we infer unhesitatingly the 
 neighbourhood of roses or jessamine or lavender, of coffee or 
 tea, hay, ripening corn, freshly fallen snow, or a bean-field ; 
 from a mere vocal sound, we infer the neighbourhood of a 
 man, or woman, or child, or bird or dog or even of a 
 particular individual in a particular mood. A mere touch or 
 taste will enable us fully to describe objects of a familiar 
 kind ; the mere view of a thing will enable us to say what 
 it is called, how it will act on various sense - organs, what 
 effect it will have under a great variety of circumstances. 
 Perhaps the principle which we proceed on in these cases 
 might be formulated as follows : 
 
 Any subject of attributes that is like another in one 
 respect, is like it in a plurality of respects. 
 
 And where mere coexistence is in question, the same thing 
 holds. If I see an object looking like what I am accustomed 
 to call a squirrel, sitting on the top bar of a stile, or on a 
 branch, I infer unhesitatingly that if I startle it, it will 
 escape with the kind of movement common to squirrels ; that 
 if I shoot it and examine its structure, I shall find it to have a 
 backbone, a brain, etc. No two things are alike only in visual 
 appearance, or only in smell, or only in taste, etc. From one 
 ))one a whole skeleton may be made out ; from one specially
 
 174 RELATIONS OF PROPOSITIONS. 
 
 modified symptom the whole diagnosis of a disease. We may, 
 I think, say that any intensive attribute can occur only with 
 special modifications of all the other intensive attributes of 
 its subject and similarly of extensive and adventitious 
 (temporal, circumstantial, etc.) attributes respectively. (I 
 believe this is substantially Lotze's view.) What particular 
 modifications of attributes are connected, can, of course, be 
 known only from special experience one kind of experience 
 establishes the connection in the case of classes, and a 
 different kind in the case of individuals. If we believe 
 that in any case certain attributes are really connected as 
 coexistent, and not merely collocated, as stones may be in a 
 heap, we infer at once (as in the case of cause and effect) 
 that they are invariably connected. Why should they be 
 connected in that one case, unless there were ground for 
 formulating a law of their connection ? We need the 
 Universal to justify the Particular. 
 
 The principle above suggested may perhaps be called the 
 Principle of Similarity. 
 
 We may add to it as a kind of converse the rule that, No 
 subject of attributes is unlike another (or its former self) 
 in one respect only. This may be called the Principle of 
 Dissimilarity. If we observe two objects unlike in one 
 respect, we always infer further unlikeness ; if we observe a 
 person or thing to be changed in one point, we always infer 
 some further change. In such inferences we proceed upon 
 this Principle of Dis-similarity. We see here the close con- 
 nection there is between Induction (so called) and Analogy 
 both may proceed upon the principles here suggested. There 
 seem to be two other principles which are complementary to 
 these one (similar to Leibnitz's " Identity of Indiscernibles ") 
 that, No two objects are alike in all respects (two classes 
 alike in all respects would be the same) this may be called 
 the Principle of Differentiation ; the other that, No two 
 objects or classes are unlike in all respects this may 
 perhaps be called the Principle of Community. 
 
 The maxim by which we are guided in practice might
 
 NOTE ON THE LAWS OF THOUGHT. 175 
 
 perhaps be said to be this, Apparent likeness, unlikeness, or 
 alteration is accompanied by non-apparent likeness, unlikeness, 
 or alteration. 
 
 SECTION XXV. 
 
 NOTE ON THE LAWS OF THOUGHT. 
 
 Logic has frequenfly been defined as the Science of the Laws 
 of Thought, and the Laws of Thought as commonly enumerated 
 are the laws 
 
 (1) Of Identity. 
 
 (2) Of Contradiction. 
 
 (3) Of Excluded Middle. 
 
 (1) and (2) are generally represented by the formula) 
 
 A is A, A is-not not-A 
 respectively; (3) is expressed as 
 
 A is B or not B. 
 
 What I wish to do in this Section is to inquire what the 
 force and meaning of these Laws is, and what seems the 
 most appropriate expression for them. 
 
 If (1) and (2) have meaning, that meaning cannot, I think, 
 be adequately conveyed by A is A, A is-not not-A, because 
 (for reasons which I have already given at length, cf. ante, 
 p. 52) those forms of words appear to me to have absolutely 
 no predicative force whatever that is, if they are taken 
 literally as they stand. They are, however, as Mr. Bosanquet 
 says (Mind, vol. xiii. p. 356), "susceptible of many interpre- 
 tations " interpretation meaning that they are understood to 
 carry implications which go beyond the strict signification of 
 the terms used. We have instances of this sort of implica- 
 tion in such phrases as " Cards are Cards " (Sarah Battle), 
 " A man's a man (for a' that)," " Man is man (and master of 
 his fate)," " Love is love (in the humblest cottage) " (cf. also 
 " There are books and books," etc.). In such " propositions,"
 
 176 RELATIONS OF PROPOSITIONS. 
 
 I think that, as a matter of fact, we generally take the 
 Subject-term in its Denomination, and the Predicate-term in 
 Determination ; and probably the currency of such formally 
 tautological locutions, into which we thus read a real meaning, 
 helps to make the form A is A seem plausible. 
 
 If A is A and A is-not not- A mean that every A is nothing 
 whatever besides A, i.e. if they entirely exclude difference 
 (cf. op. cit. p. 357), all propositions of the form A is are 
 prohibited. But we can and do constantly use propositions 
 of the form A is B ; no one disputes their propriety and 
 value. Therefore, propositions of this form being admitted, 
 the above interpretation must be rejected. 
 
 Again, A is A may be explained to signify that terms 
 have an uniform meaning that A, wherever occurring, has 
 the same Determination (hence also the same Denomination), 
 i.e. that This A is (e.g.) X, That A is X, etc. ; i.e. All As are 
 X. We regard the various A's the actually recurring words 
 or symbols as members of a class, and of them, as such, we 
 assert exact similarity of Determination. But it seems hardly 
 fair to express this Universal as A is A ; and its expression 
 as All A's are X presupposes a general uniformity in refer- 
 ence and significance of symbols. The presupposition is, of 
 course, capable of expression in language, but only in language 
 every word of which itself involves the presupposition. This 
 law of the use of language is indeed a law of Identity in 
 Diversity ; for it affirms that the reference of A, under what- 
 ever diversity of occurrence, is to some thing or things 
 quantitively identical and qualitively similar. But it is a 
 rule of language made possible and necessary by a Law of 
 Identity in things, rather than the Law of Identity itself. 
 What I regard as this Law, is a necessary condition of there 
 being anything at all which can be named, much more there- 
 fore of there being names of those things. But I cannot 
 regard it as meaning, as even Lotze says that it does (Logic, 
 p. 60, English translation), "What is contradictory is contra- 
 dictory, What is, is," etc., and this for the reasons which I 
 have given for holding that A is A has not really any pre-
 
 NOTE ON THE LAWS OF THOUGHT. 177 
 
 dicative force. The Law of Identity seems to me to be an 
 expression of the principle of the permanence of things their 
 existence in time. Whatever exists in time at all has some 
 permanence ; whatever has permanence at all has existence in 
 time ; and since time is infinitely divisible, what exists in time 
 is necessarily an identity in diversity, the diversity, namely, of 
 change (succession) in time. This seems to me to be the root 
 of identity. One cannot conceive anything which does not to 
 some extent perdure, and thus exist as a unity in diversity. 
 If this is so, it must be possible to assert of the simplest 
 thing A that it is B (or not B). And I should agree with 
 Mr. Bosanquet (op. cit. p. 357) that "Every A is B, would be 
 much better than Every A is A " as a schematic expression 
 of the Law of Identity. I should differ from him, however, in 
 being disposed to accept this formula, which he is not. 
 
 A is-not non-A, as an expression of the Law of Contradic- 
 tion, is open to objections similar to those brought against 
 the answering form A is A as representative of the Law of 
 Identity. 
 
 If A is B, A is-not non-B? 
 or 
 
 Two contradictory propositions cannot both be affirmed, 
 
 seem preferable ; and in this form the Law of Contradiction 
 precisely corresponds to the Law of Excluded Middle, which is 
 seen to be complementary to it, and may be thus expressed 
 
 A is either B or not B, 
 or 
 
 Two contradictory propositions cannot both be denied. 
 
 1 There is a distinction of the last importance between 
 
 If A is B, A is not not-B (1), 
 anil 
 
 If A is B, A is B (2) ; 
 
 for in (1) the Consequent and Antecedent are obverses of each other, either is 
 inferrible from the other ; while in (2) the Consequent is simply a repetition of 
 the Antecedent ; there is no relation of inference between them, and the whole 
 Hypothetical has no assertive force. 
 
 II
 
 IT 8 RELATIONS OF PROPOSITIONS. 
 
 If this formulation is adopted, it appears that the Law 
 of Identity is the principle of the possibility of significant 
 assertion, while the Law of Contradiction is the principle 
 of consistency, and the Law of Excluded Middle may be 
 regarded as a principle of inter-relation or reciprocity. 1 
 The three might, I think, be appropriately called the Axioms 
 of Logic. 
 
 SECTION XXVI. 
 
 FALLACIES. 
 
 I should prefer not to speak of Fallacies of Confusion, but 
 to reckon Confusion as a source of Fallacy. Any Fallacy itself, 
 however caused, will be reducible to one of the heads which 
 follow (cf. pp. 182-193). 
 
 Where there is confusion, we cannot say what our proposi- 
 tions really are or mean. This may be (a) because of the 
 ambiguity of some Term or Term-Constituent (Term-name or 
 Term-indicator). Fallacy produced by the use of Question- 
 begging Epithets seems to come under this head. Or (b) 
 
 1 As I have referred to Mr. Bosanquet's interesting article on "The Import- 
 ance of a True Theory of Identity," in Mind, vol. xiii., I ought perhaps to 
 mention that I cannot accept the sense which he sometimes seems to give to 
 Identity, identical. E.g. when he says, "The element of identity between two 
 outlines can be accurately pointed out and limited, but the moment they cease 
 to be two, it ceases to be an identity" (p. 359). "If Identity is atomic or 
 abstract, i.e. excludes difference, then you cannot speak of your present impres- 
 sion as being identical, or having identical elements with a former impression 
 which, qud former, is by the hypothesis different" (p. 360). "If there is no 
 identity, we cannot revive a former impression, but only one like it" (p. 361). 
 In these passages identity seems to mean exact similarity, not sameness of 
 individuality (cf. ante, Section VI. note, p. 46). The meaning to which I 
 should wish to restrict Identity, and the meaning which the whole theory of 
 Identity seems to me to require, is what I should call guantitive (not qualitive) 
 samenesit what Jevons would perhaps call numerical sameness the same- 
 ness that I mean when I say, This pencil is the identical pencil which I lost 
 last week.
 
 FALLACIES. 179 
 
 because of the ambiguity of construction. Or (c) because of the 
 ambiguity of context or implication. I think it is allowable 
 to take (c) as a third head here. What is called the Fallacy 
 of Continuous Questioning may be referrible to confusion of 
 this sort. (In this case, however, it seems to me that the 
 confusion is of a kind which rather brings one to a standstill 
 altogether than gives rise to Fallacy.) E.g. if I ask, " Is what 
 you are thinking of, over 1 Ib. in weight ? " the difficulty to 
 the person questioned of framing an answer, if his " object " is 
 without weight, is due to what may be called ambiguity of 
 implication or reference, for there is no ambiguity in the 
 terms or construction of iny question. " Why does a dead 
 fish weigh more than a living one ? " is another and familiar 
 instance of a fallacious question. In these cases it is assumed 
 that the conditions exist which are necessary in order to 
 make the question such as is capable of receiving a truthful 
 answer, without necessarily referring to some other question, 
 when, as a matter of fact, this may not be the case. Fallacy 
 of Accent (as explained in recent Text-books of Logic) seems 
 to come also under the head (c). 
 
 In other instances of Fallacious Questioning, the fallacy, 
 in as far as there is fallacy, may be due to ambiguity of con- 
 struction ; e.g. Are you ready and willing ? Have you read 
 Robert Elsmere and John Ward, Preacher ? Are Billy and 
 Colin at school ? 
 
 What are called Fallacies of Equivocation (a), Amphibology 
 (I), and Figure of Speech, are due to confusion. Composition, 
 Division, Accident (arguing from a general rule to a special 
 case), Converse Fallacy of Accident (arguing from a special 
 case to a general rule), and arguing from one special case to 
 another special case, are instances of Equivocation. When 
 the confusion to which such fallacies are due has been 
 pointed out, they generally appear at once as Eductive 
 Fallacies of three or more Terms, or as Syllogistic Fallacies 
 of more than three distinct Terms. The Fallacy of the Con- 
 sequent (or Non-Sequitur) reduces to a Syllogistic Fallacy of 
 more than three distinct terms
 
 180 RELATIONS OF PEOPOSITIONS. 
 
 The sea was the place where the incidents of 
 
 my story occurred ; 
 There is the sea ; 
 Therefore ray story is true. 1 
 
 The Fallacy of the False Cause (Non Causa pro Causa, 
 Post hoc ergo propter hoc) reduces to an Eductive Fallacy of 
 three Terms (" Simple Conversion of an A Proposition " ). 
 E.g. 
 
 Whatever is cause of X precedes X ; 
 . '. Whatever precedes X is cause of X. 
 
 The Fallacy of Irrelevant Conclusion is reducible to an 
 Eductive Fallacy of four, or of three Terms. (A perfectly 
 valid Eductive Inference may, of course, have three Terms. 
 taking Term in the sense indicated at the beginning of 
 Section II. (cf. ante, pp. 4, 5), as distinct from Term-name. 
 Kg. 
 
 All E is Q, 
 . . Some E is Q ; 
 
 or four terms e.g. 
 
 All E is Q, 
 . ' . All not-Q is not-E. 
 
 To all such cases the rules of Immediate Inference (Educ 
 tion) in Section XIX. are applicable, and the proposition 
 educed must contain no Term-names except those occurring 
 in the original proposition, or the precise negatives of these.) 
 A person who, wishing to prove that S is Q, argues as 
 follows : 
 
 M is P, 
 
 SisM. 
 
 SisP, 
 
 and offers this argument in support of the assertion S is Q, 
 commits the fallacy of Irrelevant Conclusion (Ignoratio 
 Elenchi). He proves a conclusion other than that required 
 
 1 This " argument " was actually used by a beggar in my hearing.
 
 FALLACIES. 181 
 
 to be proved. What is implied in this procedure is, that 
 because S is P, therefore S is Q. When thus barely stated, 
 the illicit nature of the inference is at once apparent. To 
 such a case the rules of Eduction referred to above will not 
 apply. 
 
 Since all Fallacy consists in identifying what is different 
 or differencing what is identical, we get a primary sub- 
 division of Fallacies into (a) those of professed Difference, 
 which may be called Fallacies of Tautology ; (b) those of 
 professed Identification, which may be called Fallacies of 
 Discontinuity. 
 
 (a) Embrace all such Fallacies as Circulus in Definiendo, 
 Petitio Principii, Arguing in a Circle. 
 
 Fallacy in the broadest sense may perhaps be defined as, 
 The assertion or assumption of some relation between (i.) 
 Terms, or (ii.) Propositions which does not hold between them, 
 (i.) are not generally treated among logical Fallacies, though 
 they are included by Mansel (Hansel's Aldrich, Note M) as 
 Fallacies of Judgment. It would, I think, be convenient to 
 call them Elemental Fallacies. All combinations of words 
 having the form of a proposition, which either (a) cannot be 
 significant, or (/3) cannot be true, would come under this 
 head. A is A would be a case of (a) the case where 
 compatibility between the terms merges into complete tauto- 
 logy ; A is not- A would be a case of (/3) the case where 
 diversity merges into absolute incompatibility (or discon- 
 tinuity). 
 
 If Fallacy is understood in a narrower sense, as being con- 
 cerned only with relations between Propositions, it may be 
 defined as follows : 
 
 There is Fallacy whenever we conclude from one or more 
 propositions to another, the conclusion not being justified by 
 the premiss or premisses. 
 
 This must be understood to include the cases (Tautological) 
 in which a proposition which professes to be a conclusion 
 simply repeats the datum or a part of it, or claims to be 
 proved by the help of an assertion which the professed con-
 
 182 RELATIONS OF PROPOSITIONS. 
 
 elusion has itself contributed to prove for clearly a proposi- 
 tion can be no justification for itself. 
 
 Where fallacious Inference is from one proposition to 
 another, there is a Fallacy of Immediate Inference (or Educ- 
 tion) ; where it is from two propositions taken together to a 
 third, there is a Fallacy of Mediate Inference (or Syllogism). 
 There are, besides, certain Tautologous Fallacies which involve 
 relations between a plurality of Syllogisms. 
 
 FALLACIES OF IMMEDIATE INFERENCE OR EDUCTION. 
 
 These may be divided into Eversive and Tmnsversive 
 Fallacies. Eversive Fallacies may be I. Categorical ; II. 
 Inferential ; III. Alternative. 
 
 I. Here we may (1) pass from one proposition to another 
 when the two propositions have no Term or Term-name in 
 common e.g. from M is N to Q 'is R. This is not a common 
 form of Fallacy. It may be called an Eductive Fallacy of 
 Four Terms. 
 
 (2) Or we may pass from one proposition to a second pro- 
 position which contains one Term or Term-name not contained 
 in the first proposition. Here there are two cases (a) when 
 the second proposition contains a Term-name not contained 
 in the first, nor formally equivalent to any contained in it ; 
 e.g. when from All R is Q it is inferred that Some X is Q ; 
 or from Some R is not-Q that Some Q is R. 
 
 This, again, is not perhaps a common Fallacy. 
 
 (b) When one of the terms of the second proposition has a 
 wider Term - indicator than the corresponding Term in the 
 first proposition, e.g. \vhen from 
 
 Some II is Q 
 it is inferred that 
 
 All E is Q, or All Q is E, 
 
 (2) may be called Eductive Fallacies of Three Terms. 
 
 (3) Or we may profess to educe a Proposition from itself 
 to infer S is P from S is P.
 
 FALLACIES. 183 
 
 II. Inferential Fallacies of Eduction. Here, beside Tauto- 
 logous Fallacies, in which it is professed to educe a proposition 
 from itself, there are two Fallacies which, from their corre- 
 spondence with the Syllogistic Inferential Fallacies, it seems 
 best to call the Fallacy (a) of the Antecedent, (&) of the 
 Consequent. 
 
 Kg. (a) If E is F, G is H ; 
 
 . . If E is not F, G is not H. 
 
 (6) If E is F, G is H ; 
 . . If G is H, E is F. 
 
 III. Alternative Fallacies of Eduction. Here, besides Tauto- 
 logous Fallacies, we may enumerate the four following Fallacies 
 of Discontinuity : 
 
 (1) Fallacy of Denial. 
 
 Kg. All E is Q or T ; 
 
 . . No E is Q and T. 
 
 (2) Fallacy of Conversion. 
 
 Kg. Any E is Q or T ; 
 
 . ' . Any Q or T is E. 
 
 (3) Fallacy of Enlargement. 
 
 Ky. Some E is Q or T ; 
 
 . ' . Any E is Q or T. 
 
 (4) Fallacy of Analogy. 
 
 Kg. E 1 is Q or T ; 
 
 ;.".. E 2 is Q or T. 
 
 or 
 
 E 1 is Q 1 or T 1 ; 
 . . E 2 is Q 2 or T 2 . 
 
 Transversive Fallacies occur in passing from Categorical to 
 Inferential or Alternative Propositions, from Inferential to 
 Categorical s or Alternatives, and from Alternatives to Cate- 
 goricals or Inferential. All Transversive Fallacies are 
 Fallacies of Discontinuity.
 
 184 KELATIONS OF PROPOSITIONS. 
 
 SYLLOGISTIC FALLACIES. 
 
 Syllogistic Fallacies likewise fall into the three subdivisions 
 of I. Categorical ; II. Inferential ; III. Alternative. 
 
 I. In I. we have either (i.) the case where no conclusion is 
 inferrible ; or (ii.) the case where the proposition, which is 
 professedly inferred, is not inferrible, though some conclusion 
 is inferrible including the cases (tautological) where the 
 proposition professedly inferred is simply a repetition of one 
 of the premisses, or asserts part of what is asserted by one of 
 the premisses. 
 
 (i.) All cases here are reducible to cases (1) of Tautology, 
 or (2) of four terms and two non-identities in the pre- 
 misses. 
 
 In (1), one premiss repeats the other, (a) wholly, or (&) 
 partly. E.g. 
 
 (a) M is P, (&) All E is Q, 
 
 M is P. Some E is Q. 
 
 In (2) there is (a) the case of four Term-names. Then (b) 
 if the Term-name of the Middle Term is a class-name and 
 not distributed, the Some N of one premiss is, for all we 
 know, quite different in Denomination from the Some N of 
 the other premiss. 
 
 (Some N is ambiguous on account of the indeterminateness 
 of Some.) 
 
 (c) If the Term-name of the Middle Term is ambiguous, 
 again, for all we know, it is a different term in both premisses. 
 And the only case where from two negative premisses it is 
 impossible to infer some conclusion, is the case where these 
 premisses cannot be reduced to affirmative premisses having 
 three terms ; or four terms, one of which is included in one of 
 the others, so that though there are apparently four Terms, 
 there are not really four distinct Terms. 
 
 E.g. No N is Q, 
 
 No E is N,
 
 FALLACIES. 185 
 
 reduces to 
 
 All N is not-Q, 
 All N is not-E, 
 
 formally justifying the conclusion 
 
 Some not-E is not-Q. 
 But from 
 
 Some N" is not Q, (1) 
 Some E is not N, 
 
 which will not reduce to less than four distinct Terms, no 
 conclusion can be obtained. 
 Again, from 
 
 Some N is not Q, (2) 
 
 Some N is not E, 
 from 
 
 Some N is not Q, (3) 
 
 Some N is E, 
 and from 
 
 Some N is Q, (4) 
 
 Some N is not-E, 
 
 we can draw no conclusion because Some N is ambiguous, 
 and thus we have what is equivalent to four distinct 
 Terms. 
 
 From two particular affirmative premisses, for the same 
 reason, we can draw no conclusion. 
 
 From a particular major and a negative minor we can get 
 a conclusion e.g. 
 
 Some N is Q, 
 No E is N, 
 reduces to 
 
 Some N is Q, 
 All N is not-E, 
 
 which gives the formally valid conclusion 
 Some not-E is Q.
 
 186 RELATIONS OF PROPOSITIONS. 
 
 And with a negative minor in Fig. 1 we can get a conclu- 
 sion, by reducing to Fig. 3 e.g. 
 
 Alt N is Q, 
 
 No E is N, 
 reduces to 
 
 All N is Q, 
 
 All N is not-E, 
 
 and gives the formally valid conclusion 
 Some not-E is Q. 
 
 (ii.) Where the third proposition which is inferred is not 
 inferrible, though some conclusion is inferrible. 
 Under this head come the fallacies of 
 (a) Tautology eg. 
 
 M is P, (5) 
 
 S is M, 
 Mis P. 
 
 (&) The Consequent (or Non-Sequitur) e.g., 
 
 All N is Q, (6) 
 
 Some E is N", 
 No E is Q 
 (or, All X is Y, etc.). 
 
 (In all cases of (ii.), except (a), the whole syllogism contains 
 more than three distinct Terms by which I mean that it 
 contains more than three term-names, or that some term in 
 the conclusion is wider than the corresponding term in the 
 premisses.) 
 
 (c) Illicit major and minor, (d) negative conclusion from 
 affirmative premisses, and (e) affirmative conclusion from a 
 negative premiss. E.g. 
 
 (c) All N is Q, (7) 
 
 Some E is N, 
 All E is Q.
 
 FALLACIES. 187 
 
 Some Q is not N, (8) 
 All E is N, 
 
 All E is not Q. 
 
 (The conclusion Some Q is not R is valid.) 
 
 In these two cases we conclude to a fourth Term not 
 coincident with the whole or a part of any term in the 
 premisses. 
 
 (d) All N is Q, 
 All E is N, 
 
 No E is Q. 
 
 (A fourth Term (Q minus some-Q), not known to be 
 coincident with any term in the premisses, is inferred to in 
 the conclusion.) 
 
 (e) No N is Q, 
 All E is N, 
 
 All E is Q. 
 This reduces to 
 
 All N is not-Q, 
 All E is N, 
 
 All E is Q (four distinct Terms). 
 
 All the Categorical Fallacies of Syllogism pointed out 
 above are excluded by the Canon of Syllogism suggested in 
 Section XXI. ("If the denomination of two terms is identical 
 (or non - identical), any third term which has a different 
 term-name and is denominationally identical with the whole 
 (or a part) of one of those two, is also identical (or non- 
 identical), in whole or part, with the denomination of the 
 other." 1 Cf. ante, p. 160.) For instance, (1) and (2) are 
 incompatible with that part of it which indicates that there 
 must be identity of denomination between two of the terms. 
 
 1 I talce identical to mean completely coincident, and non-identical to mean 
 altogether uncoincident.
 
 188 KELATIOXS OF PROPOSITIONS. 
 
 For in (1) 
 
 Some N is-not Q, 
 Some E is-not N, 
 
 if we take either Q or Some E as a third term, we cannot 
 say that it is denominationally identical with the whole (or 
 a part) of any other term in the two premisses. 
 Similar objections apply to (2) 
 
 Some N is-not Q, 
 Some N is-not E. 
 
 And again, in (3), of neither of the premisses can it be 
 said that one of its terms is identical (in whole or part) with 
 either term of the other premiss, since Some N is ambiguous. 
 And the same holds of (4). 
 
 (5) is not in accordance with the condition indicated by 
 the last clause of the Canon (and referring to the conclusion), 
 that " the denomination of any third term ... is also 
 identical (or non - identical) in whole (or part) with the 
 denomination of the other" (i.e. with that other which is 
 not a Middle Term). 
 
 In (6), (7), (8), etc., a term is introduced in the conclusion, 
 of which it cannot be said that its whole denomination is 
 either identical with, or a part of, the denomination of any 
 term in the premisses. 
 
 II. Fallacies of Inferential Syllogism. These fall under 
 four heads, corresponding to the division of Inferential 
 Syllogisms, into 
 
 (i.) Pure Hypothetical \ 
 
 (ii.) Pure Conditional 
 
 } Syllogisms. 
 (111.) Hypothetico-Categorical 
 
 (iv.) Conditio-Categorical J 
 
 Besides Tautological Fallacy, which occurs under each 
 head, the Fallacies incident to (i.) appear to be of two 
 kinds. (1) Where the premisses are such that no conclu-
 
 FALLACIES. 189 
 
 sion can be drawn. When this is the case, there is no such 
 connection between the two premisses that a third proposi- 
 tion (having elements in common with both the premisses) 
 can be inferred from them. This may arise from the fact 
 either (a) that the elements of the propositions consist of 
 four distinct Categoricals, or (&) that the element which is 
 common occurs as Antecedent in both premisses, or as Con- 
 sequent in both premisses. 
 
 The following are examples : 
 
 (a) If K is L, F is G ; 
 If D is E, M is N. 
 
 (&) If F is G, K is L ; 
 If F is G, D is E. 
 
 If K is L, F is G ; 
 If D is E, F is G. 
 
 If K is L, F is G ; 
 If F is not G, D is E. 
 
 If F is G, K is L ; 
 If D is E, F is not G. 
 
 (2) Where the conclusion drawn is not deducible from the 
 premisses, though some conclusion is deducible. Here, unless 
 the Fallacy consists (a) in asserting as Conclusion an entirely 
 fresh Inferential, it consists either (b) in denying the Ante- 
 cedent, or (c) in affirming the Consequent. 
 
 S.g. 
 
 (1) If K is L, F is G ; 
 
 If D is E, F is not G ; 
 If K is not L, D is E. 
 
 (If K is L, D is not E may be deduced.) 
 
 (c) If K is L, F is G ; 
 If F is G. D is E ; 
 If D is E, K is L. 
 
 (The consequence, If D is not E, K is not L, is deducible.)
 
 190 RELATIONS OF PROPOSITIONS. 
 
 (ii.) Fallacies of Pure Conditional Syllogism. 
 
 In as far as Conditional Propositions are similar to Hypo- 
 theticals, the Fallacies under this head correspond precisely 
 with those under the preceding head. In as far as they are 
 similar to Categoricals, Conditional Fallacies are the same as 
 Categorical ; but Conditional Propositions on my view differ 
 in some respects from Categoricals. 
 
 (iii.) and (iv.) Fallacies of Hypothetico-Categorical Syllogism, 
 and of Conditio-Categorical Syllogism have corresponding 
 subdivisions. They include Tautological Fallacies and 
 Fallacies of Discontinuity. The chief Fallacies of Discon- 
 tinuity are two namely (1) the Fallacy of the Antecedent, 
 (2) the Fallacy of the Consequent. E.g. 
 
 (1) If D is E, F is G ; If any D is E, that D is F ; 
 D is not E ; This D is not E ; 
 
 F is not G. This D is not F. 
 
 (2) If D is E, F is G ; If any D is E, that D is F ; 
 F is G ; This D is F ; 
 
 D is E. This D is E. 
 
 Fallacy here may be due also (3) to the presence in the 
 Minor Premiss of a constituent not contained in the Major 
 Premiss, thus rendering it impossible to draw any conclusion. 
 (4) to the presence in the Conclusion of a constituent not 
 contained in the Premisses the Conclusion thus being 
 invalid. 
 
 III. Fallacies of Alternative Syllogism. In Pure Alterna- 
 tive Syllogisms we have Fallacies of Tautology (1) in the 
 premisses alone (a) when one premiss repeats the other; (b) 
 when an alternative in one premiss is wholly the same as 
 one in the other ; (c) when an alternative in one premiss is 
 partly the same as one in the other. 
 
 E.g. (a) A is B or C is D, 
 
 C is D or A is B.
 
 FALLACIES. 191 
 
 All A is B or C is D, 
 All A is B or E is F. 
 
 (c) All A is B or C is D, 
 
 Some A is B or K is L, etc. 
 
 (2) In concluding from valid premisses when (a) the Con- 
 clusion is the same as a premiss. 
 
 E.g. (a) A is B or C is D, 
 
 E is F or A is not B, 
 A is B or C is D. 
 
 (l>) The Conclusion asserts part of a premiss. 
 
 E.g. (b) C is not D or E is F, 
 
 Any A is B or C is D, 
 Some A is B or C is D. 
 
 We may have Fallacies of Discontinuity (1) in the pre- 
 misses, when the premisses are not connected by means of 
 an alternative of which the affirmative occurs in one premiss 
 and the negative in the other. 
 
 E.g. A is B or C is D, 
 
 E is F or G is H. 
 
 A is B or C is D, 
 C is D or G is H. 
 
 (2) In passing from premisses to conclusion, where the 
 alternatives of the conclusion are not the extremes of the 
 premisses. 
 
 E.g. C is D or A is not B, 
 
 E is F or C is not D, 
 K is H or L is M. 
 
 The Fallacies of Discontinuity which are most obviously 
 possible in what I have called Categorico-Alternative Syl- 
 logisms are, (1) the introduction into the Minor Premiss of 
 an element distinct from those contained in the Major Pre-
 
 192 RELATIONS OF PROPOSITIONS. 
 
 miss in which case no inference is possible. (2) The in- 
 troduction into the Conclusion of an element not contained 
 in the Premisses in which case the Conclusion is unjustifi- 
 able. (3) The Fallacy of Denial, corresponding to the Infer- 
 ential Fallacies of Antecedent and Consequent. 
 
 Again, in Fallacies of Inferentio-Alternative Syllogism there 
 may be Fallacy due to the unwarrantable introduction of a 
 fresh element (a) into the Minor Premiss, (b) into the con- 
 clusion, but the chief Fallacies are those of the Antecedent 
 and Consequent (as in the case of Inferentio - Categorical 
 Fallacies). With both kinds of Alternative Syllogism, Tauto- 
 logical Fallacies may occur. 
 
 CIRCULAR FALLACIES. 
 
 Besides Elemental, Eductive, and Syllogistic Fallacies, 
 there are the Fallacies that occur when, in the attempt 
 to prove an assertion, recourse is had to some proposition 
 which that assertion itself has contributed to prove which 
 Fallacies involve relations between a plurality of Syllogisms. 
 
 The name Circular fallacies may, I think, be conveniently 
 appropriated to these. They occur in the simplest form 
 when there are only two Syllogisms concerned, but may 
 (and often do) involve relations between several Syllogisms. 
 
 The following are examples. Taking the Syllogism 
 
 Q is P, 
 M is Q, 
 
 M is P, 
 
 it may be required to prove M is Q. If this is clone by 
 means of the Syllogism 
 
 Pis Q, 
 MisP, 
 
 M is Q. 
 
 we have a case of circular reasoning.
 
 FALLACIES. 193 
 
 Or if we have the Hypothetical Syllogism 
 
 If G is H, K is L, 
 If E is F, G is H, 
 If E is F, K is L, 
 
 and proceed to prove the Minor Premiss by the following 
 argument : 
 
 If K is L, G is H, 
 If E is F, K is L, 
 If E is F, G is H, 
 
 we have again a case of arguing in a circle. 
 Again, taking the Syllogism 
 
 If Jack is a good boy, he will do what he is told ; 
 
 He is a good boy ; 
 
 He will do what he is told 
 
 if we go on to prove the Minor Premiss by the following 
 Syllogism : 
 
 If Jack will do what he is told, he is a good boy ; 
 Jack will do what he is told ; 
 He is a good boy, 
 
 we have committed a Circular Fallacy. 
 
 [TABLES.
 
 194 
 
 EELATIONS OF PROPOSITIONS.
 
 FALLACIES. 
 
 195 
 
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 c-3.2 
 
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 w - C 
 
 Hi 
 
 III 
 
 P4 1 
 
 Si 
 
 3(2 
 
 PnSQ 
 
 O 5 
 
 O c- 
 
 g 5 
 
 
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 ..fc 
 
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 196 SUPPLEMENT. 
 
 SUPPLEMENT. 
 
 SECTION XXVII. 
 
 RECAPITULATORY. 
 
 WHAT I wish to do in this concluding Section is to reca- 
 pitulate some points which seem to me specially important, 
 and to repair as far as I can any omission or want of clear- 
 ness in previous Sections of which I have become aware. 
 
 In what precedes I have, I hope, been working towards a 
 unification and generalization of Logic. On my view, there 
 can be no chasm between " Formal " and " Material " Logic. 
 All Logic is (more or less strictly) Formal, and Material Logic 
 almost a contradiction in terms. Logic may be defined as 
 The Science of Propositions a definition which is obviously 
 all-embracing as far as knowledge is concerned, and which 
 will be found to apply with great appropriateness to the actual 
 treatment of logicians who set out by defining Logic as a 
 psychological or semi-psychological science as the Science of 
 Reasoning, of The Laws of Thought, or of Inference. It may 
 be observed that the " mental processes " of Reasoning and In- 
 ference are not expressly treated by all Psychologists. And it 
 is evident that however Logic may be defined, our only means 
 of arriving at truth or exhibiting inconsistency is by a con- 
 sideration of propositions and their relations to one another. 
 This being so, the question which first arises is, What do pro- 
 positions mean ? And as a preliminary to answering this 
 question, it is necessary to inquire into the character of Terms, 
 which are the constituents of categorical propositions. Terms 
 have a reference beyond themselves, and the reference is, I 
 think, always to some thing or things which, besides being 
 existent in some fashion (as seems to be implied in the word 
 thing), have characteristics. In every term, therefore, two 
 momenta may be distinguished (1) Denomination, correspond-
 
 RECAPITULATORY. 197 
 
 ing to the existence of the thing named ; (2) Determination, 
 corresponding to the character of the thing named. Whether 
 in any case Denomination or Determination is most promi- 
 nent depends upon two considerations (i.) the character of the 
 term itself, considered as a name, and not with reference to 
 its place in the proposition in which it occurs; and (ii.) the 
 position which it has as actually used in predication. Taking 
 (i.), it appears that names may be primarily divided into 
 (a) Substantival Names ; (6) Attribute Names ; and (c) Adjec- 
 tival names () being Names of Subjects of Attributes, (b) 
 Names of Attributes, and (c) Names which are added (adjected) 
 to (a) or (b), and help to characterize further the Subjects of 
 Attributes, or Attributes, to which (a) and (b) apply. This 
 being their essential character and office, it is clear that De- 
 termination is naturally prominent in adjectives. And since 
 they are never used by themselves as Subjects of propositions, 
 but only as Predicates, this prominence is never obscured. 
 At least this is my view, for I hold that it is inevitably Deno- 
 mination which is prominent in the Subject of a categorical 
 proposition, while, as inevitably, Determination is felt to be 
 the most important aspect in the Predicate of a proposition. 
 And the use which we make of adjectives in modern English 
 justifies this view (cf. ante, pp. 13, 128); for where we have 
 an adjective for Predicate, qualifying a plural Subject, the 
 Predicate does not take the sign of the plural, whereas a Sub- 
 stantive Term in the same position does. It may be said that 
 this is no proof, for that we never inflect adjectives. This 
 latter fact, however, seems to me in itself a very strong proof 
 that characterization, involving, of course, prominence of 
 Determination, has been felt to be the essential function 
 of adjectives. In German this feeling has so far operated, 
 that an adjective occurring by itself as Predicate is not 
 inflected. 
 
 In Substantive Names, Denomination appears naturally 
 prominent ; in Attribute Names, Determination. 
 
 But in predication, if an Attribute Name is Subject, this 
 prominence becomes relatively subordinate; and if a Sub-
 
 198 SUPPLEMENT. 
 
 stantive Name is Predicate, we inevitably become most 
 interested in its Determination. For the Denomination of 
 what we are talking about is settled by the Subject ; and 
 what we say of it must in affirmative propositions hare 
 precisely the same Denomination (though it may not be 
 prominent), and in negative propositions a totally different 
 Denomination. This Denomination which the Predicate 
 has, may be made prominent ; and this is done to some extent 
 when the Predicate is inflected, so that a plural Subject has 
 a plural Predicate (cf. ante, pp. 128, 129). It is done 
 more decidedly when the Predicate is quantified. And 
 the Determination, which the Subject always has, is made 
 prominent when in conversion it becomes Predicate, and drops 
 any sign of quantity which it had as Subject. 
 
 Any categorical proposition may, I think, be analysed into 
 three parts namely, two Terms (Subject and Predicate) and 
 the Copula, I take the copula to be always is or is not, 
 are or are not. The whole of the rest of the proposition goes 
 to make up the Subject and the Predicate. This use of Term 
 necessitates a distinction between Term and Term-name (cf. 
 ante, pp. 3-5, and pp. 161, 162), and the admission of all 
 categorical propositions, and not merely the class propositions, 
 A E I 0, to logical treatment. 
 
 "What a categorical proposition imports is complete Identity, 
 or complete Difference (Non-Identity) of Denomination in 
 Diversity of Determination that is, what the Predicate 
 applies to in affirmative propositions is the same thing as what 
 the Subject applies to, but the Attributes by which the Subject 
 refers to it are diverse from the Attributes by which the 
 Predicate refers to it. The affirmative copula imports 
 identity, and identity can only be identity of existence. This 
 identity can only be expressed or apprehended in diversity 
 that is, in difference of attributes or characteristics. The 
 pencil with which I am now writing may be the identical 
 pencil with which I wrote yesterday, but if I could refer to it 
 for only one indivisible moment, it would be absurd to talk of 
 its identity. I am the identical person I was twenty years
 
 KECAPITULATORY. 199 
 
 ago, or last week. If I say, That pretty child is my 
 cousin's heir, S and P apply to one identical thing, a being 
 having continued existence throughout some appreciable 
 extent of time ; but it is referred to by diverse attributes, 
 by Subject and Predicate respectively ; if it were not, there 
 could be no statement or apprehension of identity. Identity 
 (which is quantitive) can only be apprehended or expressed 
 as an identity in qualitive diversity (cf. ante, pp. 46-49, 51, 
 52, 127, 128 (note 1), 129, 176, 177). And exact similarity 
 (which is qualitive) can only be apprehended as qualitive 
 oneness in a quantitive manifold i.e. in a variety of manifesta- 
 tions, whether of the same identical one or of different identicals 
 (cf. ante, p. 46, note). 
 
 In negative categorical propositions what is asserted is, 
 that the Denomination of the Subject is absolutely different from 
 (non-identical with) the Denomination of the Predicate the 
 identity of the things denoted by the Subject is different from 
 the identity of the things denoted by the Predicate. In other 
 words, the things to which the Subject applies are not the 
 things to which the Predicate applies. And the determination 
 of Subject and Predicate is diverse otherwise all negative 
 propositions would be of the form, A is-not A. 
 
 I have in Section VI. tried to test and illustrate the above 
 account of the import of categoricals by applying it to various 
 propositions ; but as I have reason to think that the illustra- 
 tions which I gave in that Section were insufficient, I will 
 add a few more here. 
 
 In 
 
 Some violets are white, 
 
 certain objects are indicated by the Subject (Some violets), 
 and the Denomination (and hence the application) of the term 
 Some violets is identical with that of the Predicate. For if it 
 is not, the application of the Predicate is different from that 
 of the Subject, and we are declaring Some violets to be some- 
 thing different from themselves. But while Denomination, 
 and hence application, of Subject and Predicate are identical
 
 200 SUPPLEMENT. 
 
 the Determination of the two terms is diverse. Certain 
 objects having more or less continued existence and distinc- 
 tive characteristics are referred to by the term, Some violets, 
 and it is the very same objects that are referred to by the term 
 white. The quantitiveness of the things referred to by the two 
 terms, and hence the Denomination of those terms, is identi- 
 cal the Denomination of the Predicate necessarily follows 
 that of the Subject. But the characteristics indicated by Some 
 violets are diverse from the characteristic indicated by white. 
 In 
 
 Kemeys is my cousin, 
 
 the Denomination (and hence the application) of Kemeys is 
 identical with that of my cousin only one existent being is 
 referred to but the Determination of Kemeys would not be 
 the Determination of my cousin. 
 In 
 
 240 pennies are equal to 1, 
 
 the Subject (240 pennies) has the same Denomination, and 
 hence the same application, as the Predicate (equal to 1). 
 An object is indicated, and to that object the term Equal 
 to 1 applies, just as much as the term &40 pennies applies. 
 If not, Equal to 1 applies to something different from 240 
 pennies, and there is no positive connection between Subject 
 and Predicate, for the characteristics signified by %4O pennies 
 are diverse from those signified by equal to 1. 
 This proposition may also be written 
 
 240 pennies = 1, (1) 
 
 i.e. (Any 240 pennies) is (some equal to 1). 
 
 But the last two propositions differ from the first example 
 given in this, that they are what I have called Dependent or 
 Systemic Propositions (cf. ante, Section III. p. 20, and Section 
 IX.), and from them, besides the eductions common to all 
 categoricals, a large number of other eductions may be 
 derived by any one who knows the systems to which in the
 
 RECAPITULATORY. 201 
 
 different cases reference is made. E.g. from (1) it may be 
 inferred that 
 
 1 = 240 pennies 
 (i.e. 1 is equal to 240 pennies) 
 
 (of. ante, Section X.). But taking any proposition which has 
 numbers for the terms, and = for the copula, what Indicator 
 is to be given to the terms ? E.g. does 
 
 2 + 2 = 4 
 mean 
 
 All(2 + 2)'s = all 4's? 
 
 And if so, are the terms to be taken collectively ? Mr. 
 Monck (Introduction to Logic, p. 19) says, "In Algebra the 
 terms are always used collectively. . . . All armies = all 
 soldiers, is a perfectly correct algebraic equation ; but as no 
 army is a soldier, it is inadmissible in Logic, except, indeed, 
 as a singular proposition of the same kind as, Hyde was 
 Clarendon." 
 
 If in the example 
 
 All armies = all soldiers, 
 
 we replace armies by (e.g.) 2 + 2, and soldiers by 4, it 
 appears that this is not a satisfactory account of mathematical 
 propositions, whether the 2's and the 4 are understood as 
 having the most abstract possible application i.e. as applying 
 to numbers merely or as having a more concrete application 
 as applying to some assigned unit. And if we took 1, 2, 
 etc., collectively, to mean all 1's, all 2's, etc. (cf. ante,'p. 85), we 
 might have 
 
 l + l + l+etc. = l, 
 
 1 + 1 + 1 + etc. = 1 + 2 + 3 + etc., 
 
 and so on. For if we have taken all 1's, whether of an 
 assigned unit or of abstract numbers, we have taken the 
 whole sum and there is no way of increasing it; and it 
 includes, of course, all groups composed of and analyzable
 
 202 SUPPLEMENT. 
 
 into units. We must then, it would seem, quantify either 
 with a distributive all, or with a Partial Term-indicator (This, 
 These, Some, etc.). But 
 
 2+ 2 = 4 
 assuredly means more than 
 
 This 2 + 2 = that 4, 
 or than 
 
 Some (2 + 2)'s = Some 4's. 
 
 It must therefore mean 
 
 Any 2 + 2 = Any 4. 
 
 And the numbers used must be understood in the most 
 abstract sense (cf. ante, Section X. p. 86). 
 In the concrete example 
 
 1 = 240 pennies, 
 
 we can also quantify with all (distributive) or any, because 
 the pounds and the pence referred to are, ex m terminorum, 
 different objects. 
 But in, e.g. 
 
 (24 x 10) pence = 240 pence, (2) 
 
 we cannot do so, because a thing cannot be equal to itself 
 (cf. ante, pp. 85, 86). 
 
 We must say that (2) means 
 
 Any (24 x 10) pence = Some 240 pence, 
 
 i.e. Any (24 x 10) pence is something equal to some 
 240 pence. 
 
 I have said in the Section on Quantification (p. 129) that 
 all quantificated affirmative propositions are collective, but it 
 appears to me now that that statement requires qualification. 
 For a proposition of the form 
 
 (3) Any E is some Q,
 
 RECAPITULATORY. 203 
 
 which is quantificated, is by the very force of the S-indicator 
 a Distributive Proposition. (3) is equivalent to 
 
 An R is a Q, 
 
 and this may have its import analysed in the same way as the 
 Singular Proposition, Kemeys is my cousin, given on p. 100 
 (cf. also pp. 47, 48). The difference between these two 
 propositions is, that (3) having a Subject determined only 
 as being an R, has the force of an Universal (cf. ante, 
 p. 61). 
 
 Substituting different from for identical with, the same 
 analysis applies to the Universal Negative E (Any R is-not 
 any Q ; An R is-not a Q). 
 
 I think, however, that a plural affirmative categorical that 
 is quantificated, may always be put in a form in which it 
 may be understood as Collective ; and I do not see how 
 a quantificated Indefinite Particular or Indefinite Plurative 
 Proposition (cf. Tables XXVII.-XXXL) is to be taken other- 
 wise than as Collective. 
 
 It is, I think, only the recognition of Existence and 
 Character (Quantitiveness and Qualitiveness) in the Things 
 to which Terms refer, and of Denomination and Deter- 
 mination of Terms (corresponding to these momenta in the 
 Things), together with the possibility of making either 
 aspect of the Term prominent, which enables us to frame 
 and manipulate significant assertions. And it seems to me 
 to be some statement concerning the possibility of signi- 
 ficant assertion that is needed, in place of the unmeaning 
 formula A is A, which is offered to us under the name 
 of the Law of Identity (cf. ante, Section XXV.). 
 
 All Inferential Propositions may, as I think, be reduced, 
 more or less naturally and more or less immediately, to Cate- 
 goricals related as Inference and Inferend (cf. Sections XII., 
 XIX., XX., and Tables XXXII, XXXIIL, XXXVII.). And 
 Alternatives are likewise reducible to Categoricals, either 
 directly or through Inferentials (cf. Sections XIX., XX., and
 
 204 SUPPLEMENT. 
 
 Table XXXVIL). But it is obvious that the meanings of 
 Inferential and Alternatives are likely to be best and 
 most naturally expressed in Inferential and Alternatives 
 respectively. 
 
 Unless A is C or B is an Eduction from A is B or C and 
 I think that it is one, and the only one absolutely formal 
 (cf. pp. 121, 147, 148) the Alternative got by Transversion 
 from an Inferential states more than the Transvertend ; while 
 similarly in the Inferential got by Transversion from an 
 Alternative, the Transverse states less than the Transvertend. 
 To take an example 
 
 If A is B, A is-not not-B, (1) 
 
 transverts to 
 
 A is-not not-B, or A is-not B, (2) 
 
 and the meaning of (2) would be explicitly stated in Hypo- 
 thetical form only by giving both (1) and its Contrapositive, 
 thus 
 
 (If A is B, A is-not not-B, 
 If A is not-B, A is-not B 
 
 just as, for instance, S is P and P is 8 would state more than 
 Sis P. 
 
 My treatment of Alternatives perhaps requires some 
 explanation, possibly some apology also. The question 
 whether alternatives are to be regarded as exclusive or un- 
 exclusive has been one of extreme difficulty to me. And the 
 fact that the most distinguished names in Logic are about 
 equally divided on this matter, and that neither side, as far 
 as I know, seems to see any reason in the view of the other, 
 and neither attempts to give any explanation of the diver- 
 gence, makes one feel that, in the first place, there must be 
 some reason on both sides, and that it is very desirable to 
 get at it if possible ; and, in the second place, that the reason, 
 though sure to be there, is probably somewhat difficult to 
 find. My own experience has been, that after having long
 
 KECAPITULATORY. 205 
 
 believed in the exclusiveness of or, I became converted to 
 the view that it is unexclusive ; but eventually found that 
 also unsatisfactory, and have now reached the opinion that 
 Alternatives may have some element of unexclusiveness, but 
 must also have some element of exclusiveness, that otherwise 
 there is no true alternation ; that so far as alternatives are 
 absolutely unexclusive, our " alternation " is of the form A or 
 A, which means neither more nor less than A simply. Where 
 the alternatives are propositions, there must be some difference 
 of meaning in the propositions or there is no alternation, and 
 so far there is exclusiveness ; but alternatives may be true 
 together, and so far there is unexclusiveness. E.g. in 
 
 XY is a knave or XY is a fool, 
 
 there is the element of exclusiveness which seems to me 
 indispensable there is also an undoubted possibility of un- 
 exclusiveness (in the sense above assigned). Where the 
 alternatives are (or appear to be) terms, there may be un- 
 exclusiveness of denomination, but there must be some 
 exclusiveness of determination. E.g. in 
 
 Any voter is a householder or a ratepayer, 
 
 the denomination (and therefore the application) of householders 
 and ratepayers is to some extent coincident ; but in determina- 
 tion the two terms are exclusive that is, they would be 
 differently defined. Perhaps it may be said that all this is 
 so obvious that it is superfluous to state it ; but I do not 
 remember to have seen it either expressed or implied, and it 
 appears to me to provide some solution of what many have 
 felt to be a serious difficulty. 
 
 My treatment of Categorical Syllogisms (Section XXI.) 
 results entirely from the view which I take of the import 
 and analysis of Categorical Propositions. 
 
 The Relations of Propositions with which Logic is pre- 
 eminently concerned are relations of Inference. This may 
 be inference from the truth of some propositions to the truth 
 of others, as in Eductions, Syllogisms, and Hypothetical
 
 206 SUPPLEMENT. 
 
 Propositions. Or it may be inference from the truth of 
 some propositions to the falsehood of others, or from the 
 falsehood of some to the truth of others as with Incom- 
 patible Propositions. Or from the falseness of some we may 
 conclude to the falseness of others. E.g, from the falseness 
 of an I proposition we may conclude to the falseness of the 
 corresponding A, or from the denial of the Consequent of 
 any Hypothetical to the denial of its Antecedent. 
 
 The validity of these inferences in particular instances, 
 and of the Canons of the different kinds of inference is, in 
 most cases, self-evident ; and the infringement of any of the 
 Canons involves breach of the Laws of Contradiction and 
 Excluded Middle (which I have proposed, in Section XXV., 
 to regard as the axioms of Consistency and Pteciprocity). 
 
 What the Law of Identity conveys is, that since any 
 name applies to something which is an identity in diversity, 
 of that name, as Subject of a proposition, some Predicate 
 other than itself may be asserted. It also involves, I think, 
 that no term can be predicated of itself or denied of itself. 
 What the Law of Excluded Middle conveys is, that if of 
 any term, A, some other term, B, is denied, then of A, not-B 
 is to be affirmed ; and if of that term A, not-B is denied, 
 then of A, B is to be affirmed. What the Law of Contra- 
 diction conveys is, that if of any term, A, some other term, 
 B, is affirmed, then of that term A, B cannot be denied. 
 
 In an Induction there is a characteristic element which 
 essentially differentiates it from all the other relations of 
 propositions with which Logic deals, namely, an element of 
 discovery. In an Induction the starting-point is perception 
 or recognition of the Universal in the Particular. Of this 
 there seem to be two aspects or stages. First, a perception 
 of some connection between things (whether Subjects of 
 Attributes or Attributes) in some particular case or cases. 
 Second, an extension from this known case to unknown cases 
 a recognition that the particular connection involves a con- 
 nection holding universally. In Mill's and Whewell's treat- 
 ment of Induction, Mill lays most stress upon the second
 
 RECAPITULATORY. 207 
 
 point, Whewell upon the first ; and Mill is concerned chiefly 
 with the connections of attributes in some given subject. 
 The first stage is the sphere of Hypothesis; and here the 
 business of Logic is to require the fulfilment of certain con- 
 ditions on the part of any Hypothesis before it is regarded as 
 admissible. These conditions seem to me to be two: (1) that 
 the Hypothesis should be in harmony with accepted know- 
 ledge, (2) that it should explain and connect the facts to 
 which it is applied. (1) involves an application of the 
 Laws of Contradiction and Excluded Middle to the relation 
 between the facts under consideration and other facts ; 
 (2) applies the same laws to the inter-relation of those facts 
 themselves. 
 
 In the second stage the business of Logic is to justify the 
 extension from the known to the unknown. 
 
 In Section XXIV. (cf. also pp. 137, 138, and Table 
 XXXVI.) I have indicated what seem to me to be the 
 assumptions, and the connections of propositions, required for 
 such justification. 
 
 The way in which I should justify the assumptions which 
 I propose in Section XXIV. is as follows. These assumptions 
 seem to be necessarily involved in all inductions inductions 
 which we constantly make, and on the trustworthiness of 
 which we unhesitatingly depend. If we accept the inductions, 
 we must, in consistency, accept the principles which they 
 involve. And if we do not accept the inductions, we are 
 entangled in a web of hopeless inconsistencies. 
 
 I have referred (p. 174) to Analogy as explicable on the 
 same principles as Induction. One further point I should 
 like to notice, the case of Mathematical and Geometrical 
 Induction. Here the principles suggested in Section XXIV. 
 apply just as much as to the other species of Inductions, and 
 the absolutely unquestioned certainty which we have in these 
 cases, and the fact that we argue unhesitatingly from a single 
 instance to the universal, seem explicable from the considera- 
 tion that we here see at once the connection, which in other 
 cases we believe on grounds very different from a perception
 
 208 SUPPLEMENT. 
 
 of self - evident interdependence of attributes. When the 
 equality of the interior angles of any one triangle to two 
 right angles has been demonstrated to us, we infer without a 
 moment's doubt that the same relation of equality may be 
 asserted of the interior angles of every triangle, and this 
 because we have seen that with the attributes signified by 
 " the interior angles of a triangle " there is bound up the 
 attribute of " being equal to two right angles." We believe 
 that if a certain amount of arsenic has on some occasions 
 produced death, it will always produce death, on the ground 
 that the apparent likenesses are connected with un apparent 
 likenesses ; but we have not seen in this case that there is a 
 self-evident interdependence between them. This is why, in 
 the case of Mathematical Inductions, we do not need to use 
 Mill's Inductive Methods (cf. ante, p. 137, note 2). 
 
 MORRISON AND OIBB, PRINTERS, EDINBURGH.
 
 T. and T. Clark's Publications. 
 
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 TRANSLATED FROM THE FOURTH EDITION BY KATHLEEN LYTTELTON. 
 
 4 Other champions much more competent and learned than myself might have been 
 placed in the field ; I will only name one of the most recent, Dr. Eeusch, author of 
 " Nature and the Bible."' The Eight Hon. W. E. GLADSTONE. 
 
 4 The work, we need hardly say, is of profound and perennial interest, and it can 
 scarcely be too highly commended as,in many respects, a very successful attempt to settle 
 one of the most perplexing questions of the day. It is impossible to read it without 
 obtaining larger views of theology, and more accurate opinions respecting its relations 
 to science, and no one will rise from its perusal without feeling a deep sense of gratitude 
 to its author.' Scottish Review. 
 
 4 This graceful and accurate translation of Dr. Eeusch's well-known treatise on the 
 identity of the doctrines of the Bible and the revelations of Nature is a valuable addition 
 to English literature.' Whitehall Review. 
 
 ' We owe to Dr. Eeusch, a Catholic theologian, one of the most valuable treatises on 
 the relation of Eeligion and Natural Science that has appeared for many years. Its fine 
 impartial tone, its absolute freedom from passion, its glow of sympathy with all sound 
 science, and its liberality of religious views, are likely to surprise all readers who are 
 unacquainted with the fact that, whatever may be the errors of the Eomish Church, its 
 more enlightened members are, as a rule, free from that idolatry of the letter of Scrip- 
 ture which is one of the most dangerous faults of ultra-Protestantism.' Literary World.
 
 T. and T. Clark's Publications. 
 
 Just published, in post 8vo, price Is. Gd., 
 
 THE PREACHERS OF SCOTLAND FROM THE 
 SIXTH TO THE NINETEENTH CENTURY. 
 
 TWELFTH SERIES OF CUNNINGHAM LECTURES 
 
 BY W. G. BLAIKIE, D.D., 
 
 PBOFESSOB OF APOLOGETICS AND PASTORAL THEOLOGY, THE NEW COLLEGE, 
 EDINBURGH. 
 
 ' Exceedingly interesting and well worth reading both for information and pleasure. 
 ... A better review of Scottish preaching from an evangelical standpoint could not be 
 desired. 'Scotsman. 
 
 Jthst ptMished, in crown 8vo, price 3.s. Qd., 
 SECOND EDITION, REVISED 
 
 THE THEOLOGY 
 
 AND 
 
 THEOLOGIANS OF SCOTLAND, 
 
 CHIEFLY OF THE 
 
 JSeftenteentf) anti <S5icjl)teent|j Centuries, 
 
 Being one of the 'Cunningham Lectures.' 
 
 BY JAMES WALKEE, D.D., CARNWATH. 
 
 ' These pages glow with fervent and eloquent rejoinder to the cheap scorn and 
 scunilous satire poured out upon evangelical theology as it has been developed north 
 of the Tweed.' British Quarterly Review. 
 
 ' We do not wonder that in their delivery Dr. Walker's lectures excited great interest ; 
 we should have wondered far more if they had not done so.' Mr. SPURGEON in Sword 
 and Trowel. 
 
 In Two Vols., Svo, price 21s., 
 
 A SYSTEM OF BIBLICAL THEOLOGY. 
 
 BY THE LATE 
 
 W. LINDSAY ALEXANDER, D.D., LL.D.,. 
 
 PRINCIPAL OF THE THEOLOGICAL HALL OF THE CONGREGATIONAL CHURCHES 
 IN SCOTLAND. 
 
 4 A work like this is of priceless advantage. It is the testimony of a powerful and 
 accomplished mind to the supreme authority of the Scriptures, a lucid and orderly 
 exhibition of their contents, and a vindication, at once logical, scholarly, and conclusive, 
 of their absolute sufficiency and abiding truthfulness. It is a pleasure to read lectures 
 so vigorous and comprehensive in their gi'asp, so subtle in their dialect, so reverent in 
 spirit, and so severely chaste in their style. There are scores of men who would suffer 
 no loss if 'for the next couple of years they read no other book than this. To master it 
 thoroughly would be an incalculable gain.' Baptist Magazine. 
 
 ' This is probably the most interesting and scholarly system of theology on the lines 
 of orthodoxy which has seen the light.' Literary World. 
 
 1 This has been characterised as probably the most valuable contribution which our 
 country has made to theology during the present century, and we do not think this an 
 exaggerated estimate.' Scottish Congregationaliit. 
 
 ' Oh, that Scotland and Congregationalism had many worthies like Dr. Lindsay 
 Alexander! . . . The ripe man, full of rich experience and heavenly knowledge, will 
 prize each leaf, and give himself a glorious drilling as he masters chapter by chapter.' 
 Mr. SPURGEON in The Sword and Trowel.
 
 T. and T. Clark's Publications. 
 
 WORKS BY PROFESSOR I. A. DORNER. 
 
 Just published, in demy 8vo, price 14*., 
 
 SYSTEM OF CHRISTIAN ETHICS. 
 
 BY DR. I. A. DORNER, 
 
 PROFBSSOK OF THEOLOGY, BERLIN. 
 
 EDITED BY DR. A. DORNER. 
 
 TRANSLATED BY 
 
 PROFESSOR C. M. MEAD, D.D., AND REV. R. T. CUNNINGHAM, M.A. 
 
 'This noble Look is the crown of the Systematic Theology of the author. ... It is 
 a masterpiece. It is the fruit of a lifetime of profound investigation in the philo- 
 sophical, biblical, and historical sources of theology. The system of Corner is 
 comprehensive, profound, evangelical, and catholic. It rises into the clear heaven of 
 Christian thought above the strifes of Scholasticism, Rationalism, and Mysticism. It 
 is, indeed, comprehensive of all that is valuable in these three types of human thought.' 
 Professor C. A. BRIGGS, D.D. 
 
 ' There rested on his whole being a consecration such as is lent only by the nobility 
 of a thorougli sauctiticatiou of the inmost nature, and by the dignity of a matured 
 wisdom.' Professor WKISS. 
 
 ' This is the last work we shall obtain from the able pen of the late Dr. Dorner, and 
 it may be said that it fitly crowns the edifice of his manifold labours.' Spectator. 
 
 In Four Volumes, 8vo, price 2, 2s., 
 
 A SYSTEM OF CHRISTIAN DOCTRINE. 
 
 ' In all investigations the author is fair, clear, and moderate ; ... he has shown that 
 his work is one to be valued, for its real ability, as an important contribution to the litera- 
 ture of theology.' Scotsman. 
 
 ' Had it been the work of an entire lifetime, it would have been a monument of 
 marvellous industry and rare scholarship. It is a tribute alike to the genius, the learn- 
 ing, and the untiring perseverance of its author.' Baptist Magazine. 
 
 ' The work has many and great excellences, and is really indispensable to all who 
 would obtain a thorough acquaintance with the great problems of theology. It is a 
 great benefit to English students that it should be made accessible to them in their own 
 language, and in a form so elegant and convenient.' Literary Churchman. 
 
 In Five Volumes, 8vo, price 2, 12s. 6rf., 
 
 HISTORY OF THE DEVELOPMENT OF THE 
 DOCTRINE OF THE PERSON OF CHRIST. 
 
 ' So great a mass of learning and thought so ably set forth has never before been 
 presented to English readers, at least on this subject.' Journal of Sacred Literature. 
 
 In crown 8vo, price 4s. 6d., 
 
 THE BIBLE 
 
 AN OUTGROWTH OF THEOCRATIC LIFE. 
 BY D. W. SIMON, 
 
 PRINCIPAL OF THE CONGREGATIONAL COLLEGE, EDINBURGH. 
 
 'A more valuable and suggestive book has not recently come into our hands.' 
 British Quarterly Review. 
 
 ' This book will well repay perusal. It contains a great deal of learning as well as 
 ingenuity, and the style is clear.' Guardian. 
 
 ' A book of absorbing interest, and well worthy of study.' Methodist New Connexion 
 Magazine- 
 
 'Dr. Simon's little book is worthy of the most careful attention. Baptist. 
 
 ' We have read the book with much appreciation, and heartily commend it to all 
 interested in the subject with which it deals.' Scottish Congregatwnalist.
 
 T. and T, Claris Piiblications. 
 
 HISTORY OF THE CHRISTIAN CHURCH. 
 
 BY PHILIP SCHAFF, D.D., LL.D. 
 
 . New Edition, Re-written and Enlarged. 
 
 APOSTOLIC CHRISTIANITY, A.D. 1-100. Two Vols. Ex. demy 8vo, price 21s. 
 ANTE-NICENE CHRISTIANITY, A.D. 100-325. Two Vols. Ex. demy 8vo, price 21s. 
 
 NICENE and POST-NICENE CHRISTIANITY, A.D. 325-600. Two Vols. Ex. demy 
 8vo, price 21s. 
 
 MEDIAEVAL CHRISTIANITY, A.D. 590-1073. Two Vols. Ex. demy 8vo, price 21s. 
 (Completion of this Period, 1073-1517, in preparation.) 
 
 MODERN CHRISTIANITY. The German Reformation, A.D. 1517-1530. Two Vols. 
 Ex. demy 8vo, price 21s. 
 
 'Dr. Schaff's "History of the Christian Church " is the most valuable contribution to Ecclesias- 
 tical History that has ever been published in this country. When completed it will have no riual 
 in point of comprehensiveness, and in presenting the results of the most advanced scholarship 
 and the latest discoveries. Each division covers a separate and distinct epoch, and is complete in 
 itself.' 
 
 ' No student, and indeed no critic, can with fairness overlook a work like the present, 
 written with such evident candour, and, at the same time, with so thorough a knowledge 
 of the sources of early Christian history.' Scotsman. 
 
 'In no other work of its kind with which I am acquainted will students and general 
 readers find so much to instruct and interest them.' Eev. Prof. HITCHCOCK, D.D. 
 
 'A work of the freshest and most conscientious research.' Dr. JOSEPH COOK, in 
 Boston Monday Lectures. 
 
 ' Dr. Schaff presents a connected history of all the great movements of thought and 
 action in a pleasant and memorable stylo. His discrimination is keen, his courage 
 undaunted, his candour transparent, and for general readers he has produced what we 
 have no hesitation in pronouncing the History of the Church.' Freeman. 
 
 Just published in ex. 8vo, Second Edition, price 9s., 
 
 THE OLDEST CHURCH MANUAL 
 
 CALLED THB 
 
 Ueacbing of tbe Uwelve Hpostles, 
 
 The Didache and Kindred Documents in the Original, with Translations and Discussions of 
 
 Post-Apostolic Teaching, Baptism, Worship, and Discipline, and with 
 
 Illustrations and Fac-Similes of the Jerusalem Manuscript. 
 
 BY PHILIP SCHAFF, D.D., LL.D., 
 
 PROFESSOR IN UNION THEOLOGICAL SEMINARY, NEW YORK. 
 
 ' The best work on the Didache which has yet appeared.' Churchman. 
 
 'Dr. Schaff's "Oldest Church Manual" is by a long way the ablest, most complete, 
 and in every way valuable edition of the recently-discovered " Teaching of the Apostles " 
 which has been or is likely to be published. . . . Dr. Schaff's Prolegomena will hence- 
 forth be regarded as indispensable. . . . We have nothing but praise for this most 
 scholarly and valuable edition of the Didache'. We ought to add that it is enriched by 
 a striking portrait of Bryennios and many other useful illustrations.' Baptist Magazine.
 
 T. & T. CLARK, 
 
 38 GEORGE STREET, EDINBURGH. 
 LONDON: HAMILTON, ADAMS, & CO. 
 
 GRIMM'S LEXICON. 
 
 Just published, in demy 4/0, price 36s., 
 
 GREEK-ENGLISH LEXICON OF THE 
 NEW TESTAMENT, 
 
 BEING 
 
 ffin'mm's SUEtlfce's Clabfa N0fn ^Testament*. 
 
 TRANSLATED, REVISED, AND ENLARGED 
 
 BY 
 
 JOSEPH HENKY THAYER, D.D., 
 
 BUSSBY PROFESSOR OF NEW TESTAMENT CRITICISM AND INTERPRETATION IN THE 
 DIVINITY SCHOOL OF HARVARD UNIVERSITY. 
 
 EXTRACT FROM PREFACE. 
 
 the close of the year 1862, the " Arnoldische Buchhandlung " 
 I in Leipzig published the First Part of a Greek-Latin Lexicon of the 
 New Testament, prepared, upon the basis of the "Clavis Novi Testament! 
 Philologica" of C. G. Wilke (second edition, 2 vols. 1851), by Professor C. L. 
 WILIBALD GRIMM of Jena. In his Prospectus Professor Grimm announced it 
 as his purpose not only (in accordance with the improvements in classical lexico- 
 graphy embodied in the Paris edition of Stephen's Thesaurus and in the fifth 
 edition of Passow's Dictionary edited by Host and his coadjutors) to exhibit the 
 historical growth of a word's significations, and accordingly in selecting his 
 vouchers for New Testament usage to show at what time and in what class of 
 writers a given word became current, but also duly to notice the usage of the 
 Septuagint and of the Old Testament Apocrypha, and especially to produce a 
 Lexicon which should correspond to the present condition of textual criticism, 
 of exegesis, and of biblical theology. He devoted more than seven years to his 
 task. The successive Parts of his work received, as they appeared, the out- 
 spoken commendation of scholars diverging as widely in their views as Hupfeld 
 and Hengstenberg ; and since its completion in 1868 it has been generally 
 acknowledged to be by far the best Lexicon of the New Testament extant.' 
 
 ' I regard it as a work of the greatest importance. ... It seems to me a work show- 
 ing the most patient diligence, and the most carefully arranged collection of useful and 
 helpful references.' THE BISHOP OF GLOUCESTER AND BRISTOL. 
 
 ' The use of Professor Grimm's book for years has convinced me that it is not only 
 unquestionably the best among existing New Testament Lexicons, but that, apart from 
 all comparisons, it is a work of the highest intrinsic merit, and one which is admirably 
 adapted to initiate a learner into an acquaintance with the language of the New Testa- 
 ment. It ought to be regarded as one of the first and most necessary requisites for the 
 study of the New Testament, and consequently for the study of theology in general.' 
 Professor EMIL SCHCRER. 
 
 ' This is indeed a noble volume, and satisfies in these days of advancing scholarship 
 a very great want. It is certainly unequalled in its lexicography, and invaluable in its 
 literary perfectiiess. ... It should, will, must make for itself a place in the library of 
 all those students who want to be thoroughly furnished for the work of understanding, 
 expounding, and applying the Word of God.' Evangelical Magazine. 
 
 ' Undoubtedly the best of its kind. Beautifully printed and well translated, with 
 some corrections and improvements of the original, it will be prized by students of the 
 Christian Scriptures.' Athenaeum.
 
 T. and T. Clark 's Publications. 
 <^i ^ 
 
 Just published, in demy 8vo, price 16s., 
 
 HISTORY OF THE 
 CHRISTIAN PHILOSOPHY OF RELIGION, 
 
 FROM THE REFORMATION TO KANT. 
 
 BY BERNHARD PUNJEE. 
 
 TRANSLATED FROM THE GERMAN BY W. HASTIE, B.D. 
 WITH A PREFACE BY PROFESSOR FLINT, D.D., LL.D. 
 
 ' The merits of Punjer's history are not difficult to discover; on the contrary, they 
 are of the kind which, as the French say, sautent aux yeux. The language is almost 
 everywhere as plain and easy to apprehend as, considering the nature of the matter 
 conveyed, it could be made. The style is simple, natural, and direct; the only sort of 
 style appropriate to the subject. The amount of information imparted is most exten- 
 sive, and strictly relevant. Nowhere else will a student get nearly so much knowledge 
 as to what has been thought and written, within the area of Christendom, on the philo- 
 sophy of religion. He must be an excessively learned man in that department who has 
 nothing to learn from this book.' Extract from the Preface. 
 
 ' Punjer's "History of the Philosophy of Religion" is fuller of information on its 
 subject than any other book of the kind that I have either seen or heard of. The writing 
 in it is, on the whole, clear, simple, and uninvolved. The Translation appears to me 
 true to the German, and, at the same time, a piece of very satisfactory English. I should 
 think the work would prove useful, or even indispensable, as well for clergymen as for 
 professors and students.' DR. HUTCHISON STIRLING. 
 
 'A book of wide and most detailed research, showing true philosophic grasp*' 
 Professor H. CALDERWOOD. 
 
 'We consider Dr. Punjer's work the most valuable contribution to this subject which 
 has yet appeared.' Church Sells. 
 
 ' Remarkable for the extent of ground covered, for systematic arrangement, lucidity 
 of expression, and judicial impartiality.' London Quarterly Review. 
 
 Just published, in Two Vols., in demy 8vo, price 21s., 
 
 HANDBOOK OF BIBLICAL ARCHEOLOGY. 
 
 BY CAEL FEIEDEICH KEIL, 
 
 DOCTOR AND PROFESSOR OF THEOLOGY. 
 
 Third Improved and Corrected Edition. 
 
 NOTE. This third edition is virtually a new book, for the learned Author has made 
 large additions and corrections, bringing it up to the present state of knowledge. 
 
 ' This work is the standard scientific treatise on Biblical Archaeology. It is a very 
 mine of learning.' John Bull. 
 
 ' No mere dreary mass of details, but a very luminous, philosophical, and suggestive 
 treatise. Many chapters are not simply invaluable to the student, but have also very 
 direct homiletic usefulness.' Literary World. 
 
 ' A mine of biblical information, out of which the diligent student may dig precious 
 treasures.' The Rock. 
 
 Kail's Biblical Archaeology will be a standard work from the day of its appearance.' 
 Presbyterian Review. 
 
 Just published, in demy 8vo, price 10s. Qd., 
 
 THE FORM OF THE CHRISTIAN TEMPLE. 
 
 Being a Treatise on the Constitution of the 
 
 New Testament Church. 
 BY THOMAS WITHEROW, D.D, LL.D., 
 
 PROFESSOR OF CHURCH H1STOHY IN MAGEE COLLEGE, LONDONDERRY. 
 
 We welcome the appearance of another work from the scholarly pen of Dr. Witherow. 
 . . No such able discussion of the constitution of the New Testament Church has 
 appeared for a long time.' The Witness.
 
 T. and T. Clark's Publications. 
 
 In Two Vols., demy 8vo. Vol. T. now ready, pi-ice 10s. Qd., 
 
 A NEW COMMENTARY 
 
 JiA122J3JVL HAJT3L>LH_D 3.HT 
 THE BOOK OF GENESIS. 
 
 BY PROFESSOR FRANZ DELITZSCH, D.D. 
 
 ESSRS. CLARK have pleasure in intimating, that by special arrangement 
 with the author they are publishing a translation of the Fifth Edition, 
 thoroughly revised, and in large part re-written, of this standard Commentary. 
 The learned author, who has for a generation been one of the foremost biblical 
 scholars of Germany, and who is revered alike for his learning and his piety, has 
 here stated with evident care his latest and most matured opinions. 
 
 ' Thirty-five years have elapsed since Prof. Delitzsch's Commentary on Genesis first 
 appeared ; fifteen years since the fourth edition was published in 1872. Ever in the van 
 of historical and philological research, the venerable author now comes forward with 
 another fresh edition in which he incorporates what fifteen years have achieved for 
 illustration and criticism of the text of Genesis. . . . We congratulate Prof. Delitzsch 
 on this new edition, and trust that it may appear before long in an English dress. By 
 it, not less than by his other commentaries, he has earned the gratitude of every lover 
 of biblical science, and we shall be surprised if, in the future, many do not acknowledge 
 that they have found in it a welcome help and guide.' Professor S. R. DRIVER, in The 
 Academy. 
 
 Just published, in post 8vo, price 9s., 
 
 THE TEXT OF JEREMIAH: 
 
 OR, 
 
 A Critical investigation of the Greek and Hebrew, with the 
 
 Variations in the LXX. Retranslated into the 
 
 Original and Explained. 
 
 BY PROFESSOR G. C. WOKKMAN, M.A., 
 
 VICTORIA UNIVERSITY, COBURG, CANADA. 
 
 WITH AN INTRODUCTION BY PROFESSOR F. DELITZSCH, D.D. 
 
 Besides discussing the relation between the texts, this book solves the difficult 
 problem of the variations, and reveals important matter for the history, the inter- 
 pretations, the correction, and the reconstruction of the present Massoretic text. 
 ' A work of valuable and lasting service.' Professor DBLITZSCII. 
 
 Just published, in demy 8vo, price 7s. 6d., 
 
 THE BOOK OF PSALMS. 
 
 The Structural Connection of the Booh of Psalms both in single Psalms and 
 in the Psalter as an organic whole. 
 
 BY JOHN FORBES, D.D., 
 
 PROFESSOR OF ORIENTAL LANGUAGES, ABERDEEN. 
 
 'One cannot but admire the keenness of insight and deftness of handling with which 
 thought is balanced against thought, line against line, stanza against stanza, poem against 
 poem. Only long familiarity and loving research could have given such skill and ease 
 of movement. ... A more suggestive, able, and original biblical monograph has not 
 appeared recently, the contents and purport of which commend themselves more power- 
 fully to believers in the Christian revelation and the inspiration of the Scriptures.' 
 British and Foreign Evangelical Review.
 
 T. and 7\ Clark's Piiblications. 
 
 Just published, tn demy 8ro, price 10s. 6rf., 
 
 THE JEWISH 
 
 AND 
 
 THE CHRISTIAN MESSIAH. 
 
 A STUDY IN THE EARLIEST HISTORY OF CHRISTIANITY. 
 BY VINCENT HENRY STANTON, M.A., 
 
 FELLOW, TUTOR, AND DIVINITY LECTURER OF TRINITY COLLEGE, CAMBRIDGE; 
 LATE HULSEAN LECTURBR. 
 
 'Mr. Stanton's book answers a real want, and will be indispensable to students of the 
 origin of Christianity. We hope that Mr. Stanton will be able to continue his labours 
 in that most obscure and most important period, of his competency to deal with which 
 he has given such good proof in this book.' Guardian. 
 
 4 We welcome this book as a valuable addition to the literature of a most important 
 subject. . . . The book is remarkable for the clearness of its style. Mr. Stanton is never 
 obscure from beginning to end, and we think that no reader of average attainments will 
 be able to put the book down without having learnt much from his lucid and scholarly 
 exposition.' Ecclesiastical Gazette. 
 
 Now ready, Second Division, in Three Vols., 8vo, price 10s. 6d. each, 
 
 HISTORY OF THE JEWISH PEOPLE IN THE 
 TIME OF OUR LORD. 
 
 BY DR. EMIL SCHURER, 
 
 PROFESSOR OF THEOLOGY IN THE UNIVERSITY OF GIESSEN. 
 
 TRANSLATED FROM THE SECOND EDITION (REVISED THROUGHOUT, AND 
 GREATLY ENLARGED) OF 'HISTORY OF THE NEW TESTAMENT TIME: 
 The First Division, which will probably be in a single volume, is undergoing revision 
 by the Author. (The Second Division is complete in itself.) 
 
 4 Under Professor Schilrer's guidance, we are enabled to a large extent to construct a 
 social and political framework for the Gospel History, and to set it in such a light as to 
 see new evidences of the truthfulness of that history and of its contemporaneousness. . . 
 The length of our notice shows our estimate of the value of his work.' English 
 Churchman. 
 
 4 We gladly welcome the publication of this most valuable work.' Dublin Review. 
 
 4 Most heartily do we commend this work as an invaluable aid in the intelligent study 
 of the New Testament.' Nonconformist. 
 
 4 As a handbook for the study of the New Testament, the work is invaluable and 
 unique.' British Quarterly Review. 
 
 Just published, in demy 8vo, price 10*. Qd., 
 
 AN EXPLANATORY COMMENTARY ON 
 ESTHER. 
 
 TOttfj four appendices, 
 
 CONSISTING OF 
 
 THE SECOND TAROUM TRANSLATED FROM THE ARAMAIC 
 WITH NOTES, MITHRA, THE WINGED BULLS 
 
 OF PERSEPOLIS, AND ZOROASTER. 
 BY PROFESSOR PAULUS CASSEL, D.D., BERLIN. 
 
 A specially remarkable exposition, which will secure for itself a commanding 
 position in Biblical literature. It has great charms from a literary and historical point 
 of view.' Sword and Trowel. 
 
 ' A perfect mine of information.' Record. 
 
 4 It is manifestly the ready expression of a full and richly stored mind, dispensing the 
 treasures accumulated by years of labour and research. . . . No one whose fortune it is 
 to secure this commentary will rise from its study without a new and lively realization 
 of the life, trials, and triumphs of Esther and Mordecni.' Ecclesiastical Gazette.
 
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