l.^ LIBRARY • ■< ^ ^ UNIVERSITY OF CALIFORNIA, SAN DIEGO 3 1822 01875 0000 h- Social Sciences & Humanities Library University of California, San Diego Please Note: This item is subject to recall. Date Due u:>n 0, ) mw CI 39 (5/97) UCSD Lib. LECTURES METAPHYSICS AND LOGIC ON EARTH, THERE IS XOTHIXG GREAT BUT MAN ; IN MAN. THERE IS NOTHING GREAT BUT MIND. LECTURES METAPHYSICS AND LOGIC SIR WILLIAM HAMILTON, BART. PROFESSOR OF LOGIC AND METAPHYSICS IN THE UNIVERSITY OF EDINBURGH AitTOC.itc, A.M. (Oxon.) &c. ; Corresponding Member of the Institute of France; Honorai-y Member of the American Academy of Arts and Sciences ; and of the Latin Society of Jena, &c. EDITED BY THE REV. H. L. MANSEL, B.D., LL.D. AVNFLETn PnOFBSSOh OP MOEAI, AND METAPHYSICAL PHII.OSOPHV, OXFORD AND JOHN VEITCH, M.A., LL.D. PROKESSOB OK I.OfJlC AND BHRTORIC iN THR UNIVERSITY OF OI.A900W IN FOUR VOLUMES VOL. III. WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON MDCCCLXXIV The Right of Translatimi w reserved LECTURES LOGIC SIB WILLIAM HAMILTON, BAET, EDITED BY THE REV. H. L. MANSEL, B.D., LL.D. VNFI.BTB PBOFRSSOn IIF MOnAI, AND METAPIIVSICAI. PHILC )BOPnV, OXFORD AND JOHN VEITCH, M.A., LL.D. PROPRSSOR OK LOOIG AND RHETORIC IN THE I'NIV'KRSITV OF 0J,ASO0V%' VOL. L THIKD EDITION, REVISED WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON MDCCCLXXIV The Uifjld of Translaiiun la reserved PREFACE. The Lectures comprised in the present Volumes form the second and concluding portion of the Biennial Course on Metaphysics and Logic, which was commenced by Sir William Hamilton on his election to the Professorial Chair in 1836, and repeated, with but slight alterations, till his decease in 1856. The Appendix contains various papers, composed for the most part during this period, which, though portions of their contents were publicly taught at least as early as 1840, were only to a very small extent incorporated into the text of the Lectures. The Lectures on Logic, like those on Metaphysics, were chiefly composed during the session in which they were first delivered (1837-8) ; and the statements made in the preface to the previous volumes, as regards the cir- cumstances and manner of their composition, are equally applicable to the present course. In this, as in the preceding series, the Author has largely availed himself of the labours of previous writers, many of whom are but little known in this country. To the works of the German logicians of the present century, particularly to those of Krug and Esser, these Lectures are under espe- cial obligations. viu ri:i:iArK. Ill the compilation of the Ai^pciulix, some responsi- bility resti^ with the l^ilitors ; ami a l\'\v words of explan- ation may be necessary as re!];arils the manner in which they have attempt eil to perform this jwrtion of their task. In publishing the jiapers of a deceased writer, composed at various intervals during a long period of years, and treating of diflicult and controverted questions, there arc two opposite dangers to be guarded against. On the one hand, there is the danger of compromising the Author's reputation by the publication of documents which his maturcr judgment might not have sanctioned ; and, on the other hand, there is the danger of commit- ting an opposite injury to him and to the public, by withholding writings of interest and value. Had Sir William Hamilton, at any period of his life, published a systematic treatise on Logic, or had his projected Neiu Analytic of Logical Forms been left in a state at all approaching to completeness, the Editors might probably have obtained a criterion by which to distinguish between those speculations which would have received the final impyiymUur of their Author, and those which would not. In the absence of any such criterion, they have thought it better to run the risk of giving too much than too little ; to publish whatever appeared to have any philo- sophical or historical interest, without being influenced by its coincidence with their own opinions, or by its coherence with other parts of the Author's writings. It is possible that, among the papers thus published, may be found some which are to be considered rather as experimental exercises than as approved results ; but no PREFACE. IX papers have been intentionally omitted, except such as were either too fragmentary to be intelligible, or mani- festly imperfect sketches of what has been published here or elsewhere in a more matured form. The Notes, in these as in the previous volumes, are divided into three classes. Those printed from the manuscript of the Lectures appear without any dis- tinctive mark ; those supplied from the Author's Com- monplace-Book and other papers are enclosed within square brackets without signature ; and those added by the Editors are marked by the signature " Ed." These last, as in the Lectures on Metaphysics, are chiefly con- fined to occasional explanations of the text and verifica- tions of references. In conclusion, the Editors desire to express their ac- knowledgments to those friends from whom they have received assistance in tracing the numerous quotations and allusions scattered through these and the preceding volumes. In particular, their thanks are due to Hubert Hamilton, Esq., whose researches among his father's books and papers have supplied them with many valu- able materials ; and to H. W. Chandler, Esq., Fellow of Pembroke CoUege, Oxford, who has aided them from the resources of a philosophical learning cognate in many respects to that of Sir William Hamilton himself. CONTENTS OF VOL. I. LECTURE I. INTRODUCTION. Page LOGIC. — I. ITS DEFINITION, 1 LECTURE IL LOGIC. — I. ITS DEFINITION — HISTORICAL NOTICES OF OPINIONS REGARDING ITS OBJECT AND DOMAIN. — IL ITS UTILITY, 19 LECTURE IIL LOGIC. — IL ITS UTILITY. — III. ITS DIVISIONS— SUBJECTIVE AND OBJECTIVE — GENERAL AND SPECIAL, ... 38 LECTURE IV. LOGIC. — in. ITS DIVISIONS — PURE AND MODIFIED, . . 57 LECTURE V. PURE LOGIC. PART I. STOICHEIOLOGY. — SECTION I. NOETIC. — ON THE FUNDAMENTAL LAWS OF THOUGHT — THEIR CONTENTS AND HISTORY, 72 XI 1 CONTENTS. LKCTUIIE VI. I'AdE TllK FUN'P.VMENT.\L L.VWS OF TIIOUCillT — TIIEIT5 CLASSIKI- TATION .\Nn IMlMliT 9G LECTURE VII. SECTION 11. OF THE PRODUCTS OF THOUGHT. — I. ENNOE- MATIC— OF CONCEPTS OR NOTIONS — A. OF CONCEPTS IN GENER.VL, 110 LECTURE VIIL ENNOEMATIC — A. OF CONCEPTS IN GENERAL ; B. IN SPE- CIAL. — I. THEIR OBJECTIVE RELATION — QUANTITY, . 130 LECTURE IX. ENTfOEMATIC. — B. OF CONCEPTS IN SPECIAL. — II. THEIR SUBJECTIVE RELATION — QUALITY, . . . .157 LECTURE X. ENNOEMATIC. — IMPERFECTION OF CONCEPTS, . , . 171 LECTURE XL ENNOEMATIC. — III. RECIPROCAL RELATIONS OF CONCEPTS. — A. QUANTITY OF EXTENSION — SUBORDINATION AND CO- ORDINATION, 187 LECTURE XIL ENNOEMATIC. — III. RECIPROCAL RELATIONS OF CONCEPTS. — B. QUANTITY' OF COMPREHENSION, . . . .212 CONTENTS. XIU LECTURE XIII. Page II. APOPHANTIC, OR THE DOCTRINE OF JUDGMENTS. — JUDG- MENTS — THEIR NATURE AND DIVISIONS, . . . 225 LECTURE XIV. APOPHANTIC. — JUDGMENTS — THEIR QUALITY, OPPOSITION, AND CONVERSION, 249 LECTURE XV. III. DOCTRINE OF REASONINGS. — REASONING IN GENERAL. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO IN- TERNAL FORM, 268 LECTURE XVL DOCTRINE OF REASONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO INTERNAL FORM. — A. SIMPLE — CATEGO- RICAL. — I. DEDUCTIVE IN EXTENSION, . . . 293 LECTURE XVIL DOCTRINE OF REASONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO INTERNAL FORM. — A. SIMPLE — CATEGO- RICAL. — II. DEDUCTIVE IN COMPREHENSION. — IIL IN- DUCTIVE IN EXTENSION AND COMPREHENSION. — B. CON- DITIONAL — DISJUNCTIVE, 313 LECTURE XVIIL DOCTRINE OF REASONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO INTERNAL FORM. — B. CONDITIONAL — HYPOTHETICAL AND HYPOTIIETICO-DTSJUNCTIVE, . . 337 XIV OOXTEXTS. LECTURE XIX. Paof DOCTRIN'E OF REASOKINOS. — SYLLOGISMS — TIIKIR DIVISIONS ACCOUniNG TO KXTKUNAL FOUM. — A. COMrLKX — Kri- CHKlltF.>LV ANH SORITES, 302 LECTURE XX. DOCTRINE OF RE.VSONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO EXTERNAL FORM. — B. DEFECTIVE — EN- TIIYMEME. — C. REGUL^Ul AND IRREGULAR — FIGURE AND MOOD — FIRST AND SECOND FIGURES, . . . . 38G LECTURE XXL DOCTRINE OF RE^VSONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO EXTERNAL FORM. — THIRD AND FOURTH FIGURES, 412 LECTURE XXIL DOCTRINE OF REASONINGS. — SYLLOGISMS — THEHl DIVISIONS ACCORDING TO EXTERNAL FORM. — C. REGULAR AND IRREGULAR. — FIGLTIE — REDUCTION, . . . . 429 LECTURE XXIIL DOCTRINE OF REASONINGS. — SYLLOGISMS — THEIR DIVISIONS ACCORDING TO VALIDITY. — FALLACIES, . .449 LECTURES ON LOGIC. L E C T U E E I." INTEODUCTION". LOGIC. — I. ITS DEFINITION. Gentlemen, — We are now about to enter on the con- lect. sideration of one of tlie most important branches of mental philosophy, — the science which is conversant p^rf-mode about the Laws of Thought.^ But, before commencing conTidera- ' the discussion, I would premise a word in regard to iHe^cIn* the mode in which it ought to be conducted, with a '^'^'^ " view to your information and improvement. The End of , , . , . 1 , J iustruction. great end which every instructor ought to propose in the communication of a science, is, to afford the student clear and distinct notions of its several parts, of their relations to each other, and to the whole of which they are the constituents. For unless he ac- complish this, it is of comparatively little moment that his information be in itself either new or impor- tant ; for of what consccjuence are all the qualities of a doctrine, if that doctrine be not communicated ? — and communicated it is not, if it be not understood. o The first seven Lectures of the of Logic proper. — Ed. Metaphysical Course, (Lectures on For some remarks on the char- Metaphyaics, vol. i. p. 1-128), were acter and comiirehensiou of Logic, delivered by Sir W. Hamilton as a see Appendix I. — Ed. General Introduction to the Course VOL. I. A •2 KEOTURKS ON l.iUMO. i.Ki'i. liut in the comniuiiii-atiou of a cloctiine, the me- 1. . • thotls to be followed by an instructor who writes, Mrlhoilaof i i • i l 1 wr.tuu*ua ana bv an instructor who speaks, are not the same. oral luslruc- ' . « -i t±' tiouditTcr- 1 hev are, in fact, to a certain extent, necessarily clit- fereut : for, wliile the reader of the one can always be referred back or forward, can always compare one part of a book witli anotlier, and can always meditate at leisure on each step of the evolution ; the hearer of the other, on the contrary, must at every moment be prepared, by what has preceded, to comprehend at once what is to ensue. The oral instructor has thus a much more arduous problem to solve, in accom- plishing the end which he proposes. For if, on the one hand, he avoid obscurity by communicating only what can easily be understood as isolated fragments, he is intelligible only because he communicates no- thing worth learning ; and if, on the other, he be unintelligible in proportion as his doctrine is concate- nated and systematic, he equally fails in his attempt ; for as, in the one case, there is nothing to teach, so, in the other, there is nothing taught. It is, therefore, evident, that the oral instructor must accommodate his mode of teaching to the circumstances under which he acts. He must endeavour to make his audience fully understand each step of his movement, before another is attempted ; and he must prepare them for details by a previous survey of generals. In short, what follows should always be seen to evolve itself Use of Text- out of wliat prcccdcs. It is in consequence of this systematic condition of Oral instruction, that, where the develop- L^ct'ures. mcnt of a systematic doctrine is attempted in a course of Lectures, it is usual for the lecturer to facilitate the labour to his pupils and himself, by exhibiting in a Manual or Textbook the order of his doctrine and a LECTURES ON LOGIC. summary of its contents. As I have not been able to lect. . . . ^ prepare this useful subsidiary, I shall endeavour, as far as possible, to supply its want. I shall, in the first method of 1 -, , • 1 1 Prelection. place, endeavour always to present you with a general statement of every doctrine to be explained, before descending to the details of explanation ; and in order that you may be insured in distincter and more com- prehensive notions, I shall, where it is possible, com- prise the general statements in Propositions or Para- graphs, which I shall slowly dictate to you, in order that they may be fully taken down in writing. This being done, I shall proceed to analyse these proposi- tions or paragraphs, and to explain their clauses in detail. This, I may observe, is the method followed in those countries w^here instruction by prelection is turned to the best account ; — it is the one prevalent on the Continent, more especially in the universities of Germany and Holland. In pursuance of this plan, I at once commence by giving you, as the first proposition or paragraph, the following. I may notice, however, by parenthesis, that, as we may have sometimes occasion to refer articulately to these propositions, it would be proper for you to distinguish them by sign and number. The first paragraph, then, is this : — H I. A System of Logical Instruction consists Par. l of Two Parts, — 1°, Of an Introduction to the system of science ; 2°, Of a Body of Doctrine constituting sis°tT.'' """ the Science itself. These, of course, are to be considered in their order. Par. II. H II. The Introduction to Logic should afford The intVo- , „ ,, . . . ^TTi • Auction to answers to the following questions; — i. What is Logic. 4 l.Ki TIIJKS OX LOGIC. i.F.cT. Logic? ii. W'hixi is its Value? iii. AVliat are '■ — its Divisions? iv, Wliat is its History? and, V. AVliat is its Jiibliograpliy, that is, what arc the best books upon the subject ? In regard to the first of these questions, it is evi- dent that the answer to it is given in a definition of Logic. I, therefore, dictate to you the third paragraph. Tar. HI. ^ IIL What is Loo-ic ? Answer — Loojic is the tion of" Science of tlie Laws of Thought as Thought. F.xpiica- This definition, however, cannot be understood without an articuhate exposition of its several parts. I, therefore, proceed to this analysis and explanation, and shall consider it under the three following heads. In the first, I shall consider the meaning, and history, and synonyms of the word Logic, In the second, I shall consider the Genus of Logic, that is, explain why it is defined as a Science. In the third, I shall consider the Object-matter of Logic, that is, explain to you what is meant by saying, that it is conversant about the Laws of Thought as Thought. 1. The word First, then, in regard to the signification of the itTHisto'ry. word. Logic, you are aware, is a Greek word, XoytAoJ ; and XoyiKTi], like ypaixfJiaTLKij, prjTopLKTJ, Trovr^TLKirj, 8ta- XeKTLKt], I need hardly tell you, is an adjective, one or other of the substantives iincrTTJfxr), science, re^(inq, art, or Trpayjxareia, study, or rather matter of study, being understood. The term XoytKif. in this special signification, and as distinctly marking out a parti- cular science, is not so old as the constitution of that Aristotle, sciencc itscLf. Aristotle did not designate by the term XoyLKij, the science w^hose doctrine he first fully LECTURES ON LOGIC. 5 developed. He uses, indeed, the adjective Xo'yiKorc8selioil l)y Cicero." So niutli lor the history of \\\c woril Lot/ic, in so tar as regards its introduction and earlier oni}»loyment. We have now t(^ consider its derivation and meaning. It is derived from X6yo<;, and it had primarily the same latitude and variety of signification as its origi- nal. What then did Xoyo? signify ■? In Greek this word had a twofold meaning. It denoted both thought and its expression ; it was equivalent both to the o'atio and to the oratio of the Latins. The Greeks, in order to obviate the ambiguity thus arising from the con- fusion of two different things under one expression, were compelled to add a difi"erential epithet to the common term. Aristotle, to contradistinguish \oyos, meaning thought, from \6yo<;, meaning speech, calls the former tov ecrco, — tov eV tyj ^v-)(y, — that ivitlun, — that in the mind ; and the latter, tov e^o), — that ivith- out.^ The same distinction came subsequently to be expressed by the \6yo<; ej^Sta^eros, for thought, the verhum mentis; and by Xoyos 7rpoti>tlo'» oini.u.vimiii With liini, Dialectic is not ii term for the pure science, '*' " "' or the science in general, but for a particular and an applied part. It means merely the Logic of Probable Matter, and is thus convertible with what he other- wise denominates Topics {TOTTiKrj.Y This, I may ob- serve, has been very generally misunderstood, and it is commonly supposed that Aristotle uses the term Dialectic in two meanings, in one meaning for the science of Logic in general, in another for the Logic of Probabilities. This is, however, a mistake. There is, in fact, only a single passage in his writings, on the ground of which it can possibly be maintained that he ever employs Dialectic in the more exten- sive meaning. This is in his Rhetoric i. \,^ but the passage is not stringent, and Dialectic may there be plausibly interpreted in the more limited signification. But at any rate it is of no authority, for it is an evi- dent interpolation, — a mere gloss which has crept in from the margin into the text."^ Thus it appears that Aristotle possessed no single term by which to desig- nate the general science of which he was the principal o{ Ana- author and finisher. Analytic, and Aj^odeictic with dei^'ir, To- Topic, (equivalent to Dialectic, and including Sophis- tic), were so many special names by which he denoted particular parts or particular applications of Logic. I say nothing of the vacillating and various employ- ment of the terms Logic and Dialectic by the Stoics, a Topica, i. 1 : Aia\eKTtKhs Se (7v\- y See Balforeus [R. Balforei Com,' Xoyianhs i e| ivSu^uv avWoyi^S/xeuos. Tnentariusin Organum LogkiunArh- — Ed. totelis, Burdigalae, 1618. Qu. II. §3, /3 Ilepl 8e ffvWoyiiTiiov 6/xoiws airauros p. 12. iluretus in his version omits. iTls^ia\fKTiKT\siut if tlu' woids (liemselvcs 1. cannot valiillv i>e cUscriminatoil, it would he absurd to attempt to discriminate anything by them. When 1, therefore, define Logic by the genus science, I do not nttem})! to give it more tlian the general deno- mination of a branch of knowledge ; for I reserve the discrimination of its peculiar character to the diiFeren- tial quality attbrded by its object-matter. You will find, when we have discussed the third head of the definition, that Logic is not ouly a science, but a demonstrative or apodictic science ; but so to have defined it, would have been tautological, for a science conversant about laws is conversant about necessary matter, and a science conversant about necessary matter is demonstrative. 3. Logic,— I proceed, therefore, to the third and last head of its object- 1 T /-» • • 1 • 1 . matter, tlic definition, — to explain what is meant by the object-matter of Logic, — viz. the Laws of Thought as Thought. The consideration of this head naturally divides itself into three questions, — 1, What is Thought? 2, What is Thought as Thought ? 3, What are the Laws of ThouQ-ht as Thouo-ht 1 a. Thought, In the first place, then, in saying that Logic is conversant about Thought, we mean to say that it is conversant about thought strictly so called. The term thought is used in two significations of diflerent extent. In its wider In the wider meaning, it denotes every cognitive act er meaning, whatcvcr ; by somc philosophers, as Descartes and his disciples, it is even used for every mental modification of which we are conscious, and thus includes the Feel- ings, the Volitions, and the Desires." In the more a Descartes, PrindjJia, pars i. § 9 : scientia est. Atquc ita non modo " Cogitatiouis nomine intelligo ilia intelligere, velle,imaginari,sedetiam omnia qute nobis consciis in nobis sentire, idem est Lie quod cogitare. " Hunt, qiiatenus eorum in nobis con- ^Ed. LECTURES ON LOGIC. 13 limited meaning, it denotes only the acts of the Under- lect. standing properly so called, that is, of the Faculty of Comparison, or that which I distinguished as the Ela- borative or Discursive Faculty." It is in this more restricted signification that thought is said to be the object-matter of Logic. Thus Logic does not consider objects that the laws which regulate the other powers of mind. It the sphere takes no immediate account of the faculties by which we acquire the rude materials of knowledge ; it sup- poses these materials in possession, and considers only the manner of their elaboration. It takes no account, at least in the department of Pure Logic, of Memory and Imagination, or of the blind laws of Association, but confines its attention to connections regulated by the laws of intelligence. Finally, it does not consider the laws themselves of Intelligence as given in the Regulative Faculty, — Intelligence, — Common Sense ; for in that faculty these laws are data, facts, ultimate and, consequently, inconceivable ; but whatever tran- scends the sphere of the conceivable transcends the sphere of Logic. Such are the functions about which Logic is not con- versant, and such, in the limited signification of the word, are the acts which are not denominated Thought. "We have hitherto found what thought is not, we must now endeavour to determine generally what it is. The contemplation of the world presents to our sub- Thought proper, sidiary faculties a multitude of objects. These objects are the rude materials submitted to elaboration by a higher and self-active faculty, which operates upon them in obedience to certain laws and in conformity to certain ends. The operation of this faculty is Thought. All thought is a comparison, a recognition o See Lectures on Metaphysics, Lect. xxxiv., vol. ii. p. 277. — Ed. 14 LErTURKS ON Lt)t;IO. LKiT. of simihiritv or cUllei'ciice ; a conjimctiou or disjuiic- tion, ill other words, a synthesis or analysis of its ob- jects. In Conception, that is, in the formation of con- cepts (or general notions), it compares, disjoins or conjoins attributes ; in an act of Judgment, it com- jtares, disjoins or conjoins concepts ; in Reasoning, it compares, disjoins or conjoins judgments. In each step of this process there is one essential element ; to think, to compare, to conjoin or disjoin, it is necessary to recognise one thing through or under another, and, therefore, in defining Thought proper, we may either define it as an act of comparison, or as a recognition of one notion as in or under another. It is in per- forminor this act of thinkino^ a thinfj under a ofeneral notion, that we are said to understand or comprehend it. For example : An object is presented, say a book ; this object determines an impression, and I am even conscious of the impression, but without recognising to myself what the thing is ; in that case, there is only a perception, and not properly a thought. But sup- - pose I do recognise it for what it is, in other words, compare it with and reduce it under a certain concept, class, or complement of attributes, which I call hook ; in that case, there is more than a perception, — there is a thought. All this will, however, be fuUy explained in the sequel ; at present I only attempt to give you a rude notion of what thinking is, to the end that you may be able vaguely to comprehend the limitation of Logic to a certain department of our cognitive functions, and what is meant by saying that Logic is a science of thought, b. Thoueht But Thought simply is still too undetermined ; the —what. ' proper object of Logic is something still more definite ; LECTURES ON LOGIC. 15 it is not thought in general, but thought considered lect. merely as thought, of which this science takes cognis ance. This expression requires explanation ; we come therefore to the second question, — What is meant by Thought as Thoughf? To answer this question, let us remember what has just been said of the act constitutive of thought, — viz. that it is the recognition of a thing as coming under a concept; in other words, the marking an object by an attribute or attributes previously known as common to sundry objects, and to which we have accordingly given a general name. " In this process we are able, by abstraction, to distinguish from each other, — 1°, The Matter and object thought of; and, 2°, The kind and manner of Thought, thinking it. Let us, employing the old and established technical expressions, call the first of these the matter, the second the/or»i, of the thought. For example, when I think that the book before me is a folio, the matter of this thought is book and folio, the form of it is a judg- ment. Now it is abundantly evident, that this analy- sis of thought into two phases or sides is only the work of a scientific discrimination and contrast ; for as, on the one hand, the matter of wliich we think is only cogitable through a certain form, so, on the other, the form under which we think cannot be realised in con- sciousness, unless in actual application to an object." " Now, when I said that Logic was conversant about Logic pro- thought considered merely as thought, I meant simply versant only to say, that Logic is conversant with the form of Form of thought to the exclusion of the matter. This being '*'"^'' understood, I now proceed to show how Logic only proposes, — how Logic only can propose, the form of thought for its object of consideration. It is indeed o Esser, Livjih, § .3, p. 4, 2a edit. Munster, 18:50. —Ed. IG LECTUKKS ON LOCIC. LKiT. truo. tliat tills limitation of Lou^ic to the form of tliou<^lit I. "... . . — '■ — lui;^ not ahsays W-vw kv\A st» adily in virw by logicians, that it is only grailually that iii-ojkt views of the soionc'o havo been sju'i-ulatively acU>})te(l, and still more "gradually that tlu-y have been carried ])ra('tically into effect, insomuch that to the pivscDt hour, as 1 shall hereafter show }'ou, tlierc are sundry doctrines still taught as logical, which, as relative to the matter of thought, are in fact foreign to the science of its form. Thi. shown " 15ut although it is impossible to show by the history l>v a i-onsi »i?r^iio'u of of the science, that Logic is conversant with the form, the naturo .udcoiX- to the exclusion of the matter, of thought ; this can, th'inVit"^ however, be satisfactorily done by a consideration of the nature and conditions of the thing itself. For, if it be maintained that Logic takes not merely the form but the matter of thought into account, (the matter, you will recollect, is a collective expression for the several objects about which thought is conversant), in that case, Logic must either consider all those objects without distinction, or make a selection of some alone. Now the former of these alternatives is manifestly impossible ; for if it were rec^uired that Logic should comprise a full discussion of all cogitable objects, in other words, if Logic must draw within its sphere all other sciences, and thus constitute itself in fact the one universal science, every one at once perceives the absurdity of the requisition and the impossibility of its fulfilment. But is the second alternative more reasonable "? Can it be proposed to Logic to take cognisance of certain objects of thought to the exclu- sion of others "? On this supposition, it must be shown why Logic should consider this particular object and not also that ; but as none but an arbitrary answer, that is no answer at all, can be given to this interro- LECTURES ON LOGIC. 17 gation, the absurdity of this alternative is no less lect. manifest than that of the other. The particular ob jects, or the matter of thought, being thus excluded, the form of human thought alone remains as the ob- ject-matter of our science ; in other words, Logic has only to do with thinking as thinking, and has no, at least no immediate, concernment with that which is thought about. Logic thus obtains, in common par- lance, the appellation of a formal science, not indeed in the sense as if Logic had only a form and not an object, but simply because the form of human thought is the object of logic ; so that the title fo7^7nal science is properly only an abbreviated expression." " I proceed now to the third question under this c The Laws head, — viz. What is meant by the Laws of Thought ab Thought, as Thought '? in other words, Wliat is meant by the Formal Laws of Thought 1 We have already limited the object of Logic to the form of thought. But there is still required a last and final limitation ; for this form contains more than Logic can legitimately consider. " Human thought, regarded merely in its formal relation, may be con- sidered in a twofold point of view ; for, on the one hand, it is either known to us merely from experience or observation, — we are merely aware of its phseno- mena historically or empirically, or, on the other, by a reflective speculation, — by analysis and abstraction, we seek out and discriminate in the manifestations of thought what is contained of necessary and universal. The empirical or historical consideration of our think- ing faculty does not belong to Logic, but to the Phae- nomenology of Mind, — to Psychology. The empirical a Esser, Logik, § .3, pp. 5, G. Cf. 17 et seq. 2d edit. 1819.— En. Krug, Dcnhlehre oder Logik, § 8, p. VOL. L B IS LECTURES ON LOOIO. LEiT. observation oi' the plKunomeiia necessarily, indeed, — ^ — preeodes tluir speculative analysis. But notwith- standing this. Logic possesses a })eculiar province of its own, and constitutes an independent and exclusive science. For where our empirical consideration of the mind terminates, there our speculative consideration commences ; the necessary elements which the latter secures from the contingent materials of observation, — these are what constitute the laws of thouirht as thought. a Cf. Esser, Logik, § 4, pji. 0, 7.— Ed. LECTURES ON LOGIC. 19 LECTURE II. INTRODUCTION. LOGIC L ITS DEFINITION. — HISTORICAL NOTICES OF OPINIONS REGARDING ITS OBJECT AND DOMAIN. II. ITS UTILITY. In my last Lecture I commenced the consideration of lect. Logic, — of Logic properly so denominated, — a science "' for the cultivation of which every European university uo^n!"'"'"'^ has provided a special chair, but which, in this countr}-^, in consequence of the misconceptions which have lat- terly arisen in regard to its nature and its end, has been very generally superseded : insomuch that, for a considerable period, the chairs of Logic in our Scottish universities have in fact taught almost everything except the doctrine which they were established to teach. After some precursory observations in regard to the mode of communication which I should follow in my lectures On this subject, I entered on the treat- ment of the science itself, and stated to you that a systematic view of Logic would consist of two parts, the one being an Introduction to the doctrine, the other a body of the Doctrine itself. In the introduc- tion were considered certain preparatory points, neces- sary to be understood before entering on the discus- sion of the science itself; and I stated that these preparatory points were, in relation to our science, exhausted in five questions and their answers — 1°, 20 MXTi'iiKs ON i.onic. LECT. Wliat is Loiric? 2\ What is its value ? 3", How is it tlistribiitoil i 4\ AVbat is its history 1 5°, What are its subsiiliaries ? I then proceei,led to the consideration of the first of these questions ; and, as the answer to the question, — what is r.ogic ? — is given in its definition, I defined Logic to be the science conversant about the laws of tliought considered merely as thought; warning you, however, that this definition could only be understood after an articulate explanation of its contents. Now this definition, I showed you, naturally fell into three parts, and each of these parts it behoved to consider and illustrate by itself. The first was the word sig- nificant of the thing defined, — Logic. The second was the genus by which Logic was defined, — science. The third was the object-matter constituting the differen- tial quality of Logic, — the laws of thought as thought. Each of these I considered in its order. I, first of all, explained the original meaning of the term Logic, and gave you a brief history of its application. I then stated what was necessary in regard to the genus, — science ; and, lastly, what is of principal importance, I endeavoured to make you vaguely aware of that which you cannot as yet be supposed competent dis- tinctly to comprehend, I mean the peculiar character of the object, — object-matter, — about which Logic is conversant. The object of Logic, as stated in the definition, is the laws of thought as thought. This required an articulate explanation ; and such an ex- planation I endeavoured to afford you under three distinct heads ; expounding, 1°, What was meant by thought ; 2°, What was meant by thought as thought ; 3°, What was meant by the laws of thought as thought. In reference to the first head, I stated that Logic is LECTURES ON LOGIC. 21 conversant about thouglit taken in its stricter signifi- lect, . *^ II. cation, that is, about thought considered as the opera tion of the Understanding Proper, or of that faculty which I distinguished as the Elaborative or Discur- sive, — the Faculty of Relations, or Comparison. I at- tempted to make you vaguely apprehend what is the essential characteristic of thought, — viz. the compre- hension of a thing under a general notion or attribute. For such a comprehension enters into every act of the discursive faculty, in its different gradations of Con- ception, Judgment, and Reasoning. But by saying that Logic is conversant about thought proper. Logic is not yet discriminated as a peculiar science, for there are many sciences, likewise, intei' alia, conversant about the operations and objects of the Elaborative Faculty. There is required a further determination of its object-matter. This is done by the limitation, that Logic is conversant not merely about thought, but about thought as thought. The explanation of this constituted the second head of our exposition of the object-matter. Thought, I showed, could be viewed, by an analytic abstraction, on two sides or phases. We could either consider the object thought, or the manner of thinking it; in other words, we could scientifically distinguish from each other the matter and the form of thought. Not that the matter and form have any separate existence ; no object being cogitable except under some form of thought, and no form of thought having any existence in consciousness except some object be thought under it. This, how- ever, formed no impediment to our analysis of these elements, through a mental abstraction. This is in fact only one of a thousand similar abstractions we are in the habit of making ; and if such were impos- 22 LEOTl'KKS ON I.OCIK'. LEix siblo, all liuinaii sciiiui' would be impossible. For 11. Ill oxaniplo, oxtonsioii is pivsented to souse only iinacr some modifieation of colour, and even imagination eaniiot represent extension except as coloured. We may view it in phantasy as black or white, as trans- lucent or opaque ; but represent it we cannot, except either under some positive variety of light, or under the negation of light, which is darkness. But, psycho- logically considered, darkness or blackness is as much a colour, that is, a })ositive sensation, as whiteness or redness; and thus we cannot image to ourselves aught extended, not even space itself, out of relation to colour. But is this inability even to imagine exten- sion, apart from some colour, any hindrance to our considering it scientifically apart from all colour? Not in the smallest ; nor do Mathematics and the other sciences find any difficulty in treating of extension, without even a sinole reference to this condition of its actual manifestation. The case of Logic is precisely the same. Logic considers the form apart from the matter of thought ; and it is able to do this without any trouble, for though the form is only an actual phenomenon when applied to some matter, — object, — yet, as it is not necessarily astricted to any object, we can alw^ays consider it abstract from all objects, — in other w^ords, from all matter. For as the mathemati- cian, w^ho cannot construct his diagrams, either to sense or to imagination, apart from some j)articular coloui", is still able to consider the properties of exten- sion apart from all colour ; so the logician, though he cannot concretely represent the forms of thought except in examples of some particular matter, is still able to consider the properties of these forms apart from all matter. The possibility being thus apparent of a con- LECTURES ON LOGIC. 23 sideration of the form abstractly from the matter of lect. thought, I showed you that such an abstraction was '■ — necessary. The objects (the matter) of thought are infinite ; no one science can embrace them all, and, therefore, to suppose Logic conversant about the mat- ter of thought in general, is to say that Logic is another name for the encyclopaedia, — the omne scihile, — of human knowledge. The absurdity of this sup- position is apparent. But if it be impossible for Logic to treat of all the objects of thought, it cannot be supposed that it treats of any ; for no reason can be given why it should limit its consideration to some, to the exclusion of others. As Logic cannot, therefore, possibly include all objects, and as it cannot possibly be shown why it should include only some, it follows that it must exclude from its domain the consideration of the matter of thought altogether ; and as, apart from the matter of thought, there only remains the form, it follows that Logic, as a special science of thought, must be viewed as conversant exclusively about the form of thought. But the limitation of the object-matter of Logic to c. The Laws the form of thought, (and the expression /orm o/"as Thoufht. thought is convertible with the expression thought as thought), is not yet enough to discriminate its province from that of other sciences ; for Psychology, or the Empirical Science of Mind, is, likewise, among the other mental phaenomena, conversant about the phse- nomena of formal thought. A still further limitation is, therefore, requisite ; and this is given in saying, that Logic is the science not merely of Thought as Thought, but of the Laws of Thought as Thought. It is this determination which affords the proximate and peculiar difference of Logic, in contradistinction from 24 LECTURES ON LOGIC. LECT. all other sl•il•lu•o^^; aiul tlio oxiilaiiation of its njcaning _i!: constitutes tlie tliiril head of illustration demanded by ohjeet-niatter in the dt'finition. Theph.no- The phaMioniena of the formal or subjective phases "onxlf of thought are of two kinds. They arc cither such as I,te''ki!^» are contingent, that is, such as may or may not appear; ^w"«mV or they are such as arc necessary, that is, such as can- nece=s*ary. ^^^^ ^^^^ appear. Tlicsc two classes of pha^nomcna are, however, only manifested in conjunction ; they arc not discriminated in the actual operations of thought; and it requires a speculative analysis to separate them into their several classes. In so far as these phteno- mena are considered merely as pha3nomena, that is, in so fiir as philosophy is observant of them merely as manifestations in general, they belong to the science of Empirical or Historical Psychology. But when philosophy, by a reflective abstraction, analyses the necessary from the contingent forms of thought, there results a science, which is distinguished from all others by taking for its object-matter the former of these classes ; and this science is Logic. Logic, therefore, is at last fully and finally defined as the science of the necessary forms of thought. Here terminated our last Lecture. But though full and final, this defini- tion is not explicit ; and it still remains to evolve it into a more precise expression. Now when we say that Logic is the science of the necessary forms of thought, what does the quality of necessity here imply? Form of " lu the first place, it is evident that in so far as a Fw cinT form of thought is necessary, this form must be deter- iuM^ity. mined or necessitated by the nature of the thinking min^?by subjcct itsclf ; for if it were determined by anything the nature pj^^-gj-^^j^j |-q i]^q miud, thcn would it not be a necessary LECTURES ON LOGIC. 25 but a merely contingent determination. The first con- lect. dition, therefore, of the necessity of a form of thought is, that it is subjectively, not objectively, determined, subject ft- self. " In the second place, if a form of thouojht be subiec- „ ,, . . , -•- ' _ _ C / 2. Original. tively necessary, it must be original and not acquired. For if it were acquired, there must have been a time when it did not exist ; but if it did ever actually not exist, we must be able at least to conceive the possi- bility of its not existing now. But if we are so able, then is the form not necessary ; for the criterion of a contingent cognition is, that we can represent to our- selves the possibility of its non-existence. The second condition, therefore, of the necessity of a form of thought is, that it is original, and not acquired. " In the third place, if a form of thought be neces- 3. Universal, sary and original, it must be universal ; that is, it cannot be that it necessitates on some occasions, and does not necessitate on others. For if it did not ne- cessitate universally, then would its necessitation be contingent, and it would consequently not be an ori- ginal and necessary principle of mind. The third condition, therefore, of the necessity of a form of thought is, that it is universal. " In the fourth place, if a form of thought be neces- 4. a law. sary and universal, it must be a law ; for a law is that which applies to all cases without exception, and from which a deviation is ever, and everywhere, im- possible, or, at least, unallowed. The fourth and last condition, therefore, of the necessity of a form of thought is, that it is a law."" This last condition, like- wise, enables us to give the most explicit enunciation The object- of the object-matter of Logic, in saying that Logic is Logic cx- the science of the Laws of Thought as Thought, or the enounced. a Esser, Loyik, § G, i>[h 9, 10, with a few original interpolations.— Ed. 26 LECTURES ON LOGIC. I. FAT. soionco o( the l-'onnal Laws of Tlionolit or the science IL , of the Laws of the Form of Thought; for all these are merely various exi)ressions of the same thing, (nnerai liefore procceiliug further, it may be proper to take rvtn«i»ect a vcry general retrospect oi the views that have pre- rt'garti to vaikxl iu rcgaTcl to the object and domain of Logic, and domain froui tlic cia wlicu tlic scicncc rcccivcd its first grand and distinctive development from the genius of Aris- totle to the present time. Morii of ihc I may say, in general, that the view which I have view of now presented to you of the object and domain of Logic, is the one which concentrates, corrects, and completes the views which have been generally held by logicians of the peculiar province of their science. It is the one towards which they all gravitate. Aristotle, It is unfortuuatc, that by far the greater number of the logical "writings of Aristotle have perished, and that those which remain to us exhibit only his view^s of the science considered in its parts, or in certain special relations. None of the treatises which are now collected in the Organon,"' considers the science from a central point ; and w^e do not even possess a general definition of Logic by its illustrious founder. It w^ould, therefore, be unjust to the mighty master, if, as has usually been done, we estimated his conception of the science only by the partial views contained in the fragmentary or special treatises which have chanced to float ashore from the general wreck of his logical writings. These by themselves are certainly enough to place the Stagirite high above comparison with any subsequent logician ; but still if he has done so much in the half-dozen treatises that still remain, wdiat may w^e not conceive him to have accomplished in the a See below, p. 34. — Ed. LECTURES ON LOGIC. 27 forty wLicli are recorded and seem to have been lost ? lect. It is, therefore, not to be attributed to Aristotle, that sub- '— sequent logicians, mistaking his surviving treatises of a logical nature, — few in number and written, in general, not in exposition of the pure science, but only of the sci- ence in certain modified applications, — for a systematic body of logical doctrine, should have allowed his views of its partial relations to influence their conceptions of the science absolutely and as a whole. By this influence of the Aristotelic treatises, Ave may explain the sin- gular circumstance, that, Avhile many, indeed most, of the subsequent logicians speculatively held the sound- est views in regard to the proper object and end of Logic, few or none of them have attempted by these views to purify the science of those extraneous doc- trines, to which the authority of Aristotle seemed to have given a right of occupancy within its domain. I Greek ahs- shall not attempt to show you, in extenso, how correct, and Lwin in general, were the notions entertained by the Greek Aristotelians, and even by the Latin schoolmen, for this would require an explanation of the signification of the terms in which their opinions were embodied, which would lead me into details which the import- ance of the matter would hardly warrant. I shall only say, in general, that, in their multifarious contro- versies under this head, the diversity of their opinions on subordinate points is not more remarkable than their unanimity on principal. Logic they all discri- minated as a science of the form and not of the matter of thought." Those of the schoolmen who held the a ' ' Logicus solas considerat f ormas iii. ; Zabarella, De Natura Logicce, intentionum communes." Albertus lib. i. cap. 19; Smiglecius, Logica, Magnus, In Dc Anima, L. I. tract, i. Disp. ii. qu. 1 ; Camerarius, Disjmta- c. 8. For various scholastic theories tiones Philosophicce, Pars i. qu. 1, on the object- matter of Logic, see j). 2 et seq. Compare Discussions, Scotus, Suiicr Univ. Porphyrii, Qu. p. 138.— Ed. 28 I.KCTrKKS ON I.OOIC. i.Krr. object of Logic to be tilings in general, licld this, how- '■ — ovor, luuler tlio (|iialitication that things in general wore not inmicHliately and in themselves considered by the logician, but only as they stood under the general forms imposed on them by the intellect, (" qua- tenus secimdis intentionibus substabant "), — a mode of speaking which is only a periphrasis of our assertion, that Locfie is conversant about the forms of thouoht.* The other schoolmen, again, who maintained that the object of Logic was thought in its processes of simple apprehension, judgment, and reasoning, (three, tw^o, or one,) carefully explained that these operations were not in their own nature proposed to the logician, for as such they belonged to Animastic, as they called it, or Psychology, but only in so far as they "were diri- gible or subject to laws, — a statement which is only a less simple expression of the fact, that Logic is the science of the laws of thought.^ Finally, those school- men who held that the object-matter of Logic w^as found in second notions as applied to first, only meant to say that Logic was conversant with conceptions, judgments and reasonings, not in themselves, but only as regulators of thought,'^ — a statement which merely varies and perplexes the expression, that the object of Logic is the formal laws of thought. The same views, various in appearance, but, when a [G. J. Vossins, Be Nat. Artium qu. 1, p. 3. Schuler, PhilosopMa, sit;cZ>e Zo;/iV«, c.iv.] [Compare Alex. p. 307, [L. v., Lofjka, Exerc. i., diG A\gs, IiiArist. Metaph.ylj. iv.t.5: ed. Hagae Comitis, 1763. — Ed.] "Dialectica est inventa ad regiilan- D'Abra de Raconis, [Tractatio To- dumdiscursumintellectusetrationis; this Philosophia, Praeludia Logica, ideo qujedam secundfc intentiones in- Post., c. i. p. 48, ed. Parisiis, 1640. — ventae sunt ad regulandum discursum, Ed. ] de quibua proprie est Logica." See y See Zabarella and Camerarius, also Zabarella and Camerarius, as as above. — Ed. [Compare Poncius, above. — Ed. ] CursusPhiloso^Mcus, Disp. i. qu. ult. , /3 Camerarius, Disp. Phil, P. i. p. 48, 2d ed. Pari.s, 1649.] LECTURES ON LOGIC. 29 analysed, essentially the same, and essentially correct, lect, may be traced through the Leibnitio-Wolfian school into the Kantian ; so that, while it must be owned woifiantnd that they were never adequately carried out into sXoX practical application, it cannot be denied that they were theoretically not unsound. The country in which, perhaps, the nature of Logic Bacon,— has been most completely and generally misunder- stood, is Great Britain. Bacon wholly misconceived its character in certain resj)ects ; but his errors are insignificant, when compared with the total misap- prehension of its nature by Locke. The character of these mistakes I shall have occasion to illustrate in the sequel ; at present I need only say, that, while those who, till lately, attempted to write on Logic in the English language, were otherwise wholly incompe- tent to the task, they, at the same time, either shared the misconceptions of its nature with Locke, or only contributed, by their own hapless attempts, to justify the prejudices prevalent against the science which they professed to cultivate and improve. It would be unjust to confound with other attempts whateiy,— of our countrymen in logical science the work of Dr character of Whateiy. The author, if not endowed with any high mints!' talent for philosophical speculation, possesses at least a sound and vigorous understanding. He unfortunately, however, wrote his Elements of Logic in singular unacquaintance with all that had been written on the science in ancient and in modern times, with the exception apparently of the works of two Oxford logicians — the Institutio of Wallis, and the Compen- waiiis. diiim of Aldrich, — both written above a century ago, Auirici.. neither of them rising above a humble mediocrity, even at the date of its composition ; and Aldrich, whom so LECTURES ON LOGIC. LECT. Whatoly unfortunately regards as a safe and learned '■ — i^uide, had himself written his book in ignorance of Aristotle and of all the principal authors on the science, — an ignorance manifested by the grossest errors in the most elementary parts of the science. It is not therefore to be wondered at, that the Ele- ments of Whately, though the production of an able man, are so far behind the advancement of the science of which they treat; that they are deformed with numerous and serious errors ; and that the only re- commendation they possess is that of being the best book on the subject in a language which has abso- lutely no other deserving of notice ! °' \yhatci>'s I have now, therefore, to call your attention to Dr object-mat- Whatcly's account of the object-matter and domain of main of' Logic. " The treatise of Dr Whately," says his Vice- and criti- Principal and epitomator Dr Hinds,^ "displays, and it is the only one that has clearly done so, the true nature and use of Logic; so that it may be approached, no longer as a dark, curious, and merely speculative study, such as one is apt in fancy to class with astrology and alchemy." Let us try whether this eulogy ])e as merited as it is unmeasured. Whately Now Dr Whatcly cannot truly be said clearly to lSc dfffe" display the nature of Logic, because in different pas- contrad'ict- sagcs hc proposcs to it different and contradictory ^tter.^*^ objects ; and he cannot be said to display the true nature of Logic, for of these different objects there is not one which is the true. In several passages,"^ he says that " the process or operation of reasoning is alone the appropriate pro- o See Discussions, p. 128, second p. viiL, Oxford, 1827. — Ed. edition, foot-note. 7 See pp. 1, 13, 140, third edi- /3 Introdtidion to Logic, Preface, tion. LECTURES ON LOGIC. 31 vince of Looic." Now this statement is incorrect in lect. ... II two respects. In the first place, it is incorrect, inas- much as it limits the object-matter of Logic to that part of the Discursive Faculty which is especially de- nominated Reasoning. In this view Logic is made con- vertible with Syllogistic. This is an old error, which has been frequently refuted, and into which Whately seems to have been led by his guide Dr Wallis. In the second place, this statement is incorrect, in- The opera- asmuch as it makes the process, or, as he also calls it, sonlng^mr the operation, of reasoning the object-matter of Logic. mattS'o''f' Now, a definition which merely affirms that Logic is mlteiy^ the science which has the process of reasoning for its ^^™'* object, is not a definition of this science at all ; it does not contain the differential quality by which Logic is discriminated from other sciences; and it does not prevent the most erroneous opinions, (it even suggests them,) from being taken up in regard to its nature. Other sciences, as Psychology and Metaphysic, propose for their object, (among the other faculties,) the operation of reasoning, but this con- sidered in its real nature : Logic, on the contrary, has the same for its object, but only in its formal capacity ; in fact, it has in propriety of speech nothing to do with the process or operation, but is conversant only with its laws. Dr Whately's definition is, therefore, not only incompetent, but delusive ; it would confound Logic and Psychology and Metaphysic, and tend to perpetuate the misconceptions in regard to the nature of Logic which have been so long prevalent in this country. But Dr Whately is not only wrong as measured by wi.ateiy P • 1 1 1 1 • 1 1 -1 • erroneously a loreign standard, he is wrong as measured by his and coutra- own ; he is himself contradictory. You have just seen make" Ln- that, in some places, he makes the operation of reason- adefuate" 32 LECTITRES ON LOGIC. LK.rr. inn- not oiilv the priiu-ipal l»iit tlie aclcquate object of Logic. \\ ell, ill others he makes this total or adequate TorrfL^Kio. object to be hmguage. But as there cannot be two adequate objects, and as hmguage and the operation of reasoning are not the same, there is, therefore, a contradiction. " In introducing," he says, " the men- tion of language previously to the definition of logic, I have departed from established practice, in order tliat it may be clearly understood that logic is entirely conversant about lans^uaoe : a truth which most writers on the subject, if indeed they were fully aware of it themselves, have certainly not taken due care to im- press on their readers." " And again : " Logic is wholly concerned in the use of lansjuasje."'^ In our last Lecture, I called your attention to the ambiguity of the term Xoyo?, in Greek, meaning am- biguously either thought or its expression ; and this ambiguity favoured the rise of two counter-opinions in regard to the object of logic; for while it was generally and correctly held to be immediately conver- sant about the internal Xoyos, thought, some, however, on the contrary, maintained that it was immediately conversant about the external Xoyog, language. Now, bysome unaccountable illusion, Dr Whately,in different places, adopts these opposite opinions, and enunciates them without a word of explanation, or without even a suspicion that they are contradictory of each other."^ The true From what I have now^ said, you may, in some i^'^^more dcgrcc, be able to judge how far credit is to be ac- undeStLd corded to the assertion, that Dr Whately is the only scholastic logician who ever clearly displayed the true nature thfn by* and use of Logic. In fact, so far is this assertion from ANhateiy. ^^^^ truth, that thc object-matter and scope of Logic a Page 56. /3 Page 74. y Besides most vague. — Jotting. LECTURES ON LOGIC. 33 were far more correctly understood even by the scho- lect. lastic logicians than by Dr Whately ; and I may cau — tion you, by the way, that what you may find stated in the Elements of the views of the schoolmen touch- ing the nature and end of Logic, is in general wrong ; in particular, I may notice one most erroneous allega- tion, that the schoolmen " attempted to employ logic for the purpose of physical discovery." But if, compared only with the older logicians, the assertion of Dr Hinds is found untenable, what will it be found, if we compare Whately with the logicians of the Kantian and Leibnitian schools, of whose writings neither the Archbishop nor his abbre- viator seems ever to have heard 'i And here I may observe, that Great Britain is, I believe, the only country of Europe in which books are written by respectable authors upon sciences, of the progress of which, for above a century, they have never taken the trouble to inform themselves. The second question, to which in the Introduction to ii. The Logic an answer is required, is, — What is the Value or Logic? " Utility of this science ? Before proceeding to a special consideration of this question, it may be proper to observe in general, that the real utility of Logic has been obscured and disparaged by the false utilities which have too frequently been arrogated to it ; for when Logic was found unable to accomplish what its unwise encomiasts had promised, the recoil was natural, and as it failed in performing everything, it was lightly inferred that it could perform nothing. Both of these extremes are equally erroneous. There is that which Logic can, and there is that which Logic cannot, per- form ; and, therefore, before attempting to show what it is that we ought to expect from the study of this VOL. I. c ;U LECTURES ON LOGIC. LKCT. scieiico, it will bo proper to show what it is. that '■ — we ought not. 1 shall, therefore, iu the first place, eousitler its false utilities, and, in the second, its true. I'uiuus The attribution of every false utility to Logic has imuxV w '" arisen from erroneous opinions held in regard to the *'"^'"" object of the science. So long as it was supposed that logic took any cognisance of the matter of thought, — so loner as it was not distinctly understood that the form of thought was the exclusive object of this science, and so long as it was not disencumbered of its extraneous lumber ; so long must erroneous opin- ions have been prevalent as to the nature and com- prehension of its end. As an in- It was accordiugly, in the first place, frequently sSS " supposed that Logic was, in a certain sort, an instru- ciiscoverj-. ^^^^ q£ scleutific discovcry. The title of Organon, — instrument, — bestowed on the collection we possess of the logical treatises of Aristotle, contributed to this error. These treatises, as I observed, are but a few of the many writings of the Stagirite on Logic, and to him we owe neither the order in w^hich they stand arranged, nor the general name under which they are now comprehended." In later times, these treatises were supposed to contain a complete system of Logic, and Logic was viewed as the organ not only of Philo- sophy but of the sciences in general. Thus it was that Logic obtained not only the name of instrument, or instrumental philosophy, but many other high-sound- ing titles. It was long generally styled the Art of arts and Science of sciences. — " Logica," says Scotus, "est ars artium et scientia scientiarum, qua aperta, a See Brandis, Aristoteles, seine delenburg, Elementa Log. Aristot., akademischcH Zeitgenosseti und ndch- p. 38. — Ed. sten Nachfolfje-r, P. i. p. 140. Tren- LECTURES ON LOGIC. 35 omnes aliae aperiuntur ; et qua clausa, omnes alise lect. clauduntur ; cum qua quselibet, sine qua nulla." " In '■ — modern times, we have systems of this science under the titles of Via ad Veritatem^ — Cynosura Veritatis^ — Caput et Apex Pliilosophice ^ — Hewnstica, sive In- ti'oductio ad Artem Inveniendi,^ &c. But it was not as the cm-- rector of only viewed as an instrument of discovery, it was intellectual likewise held to be the infallible corrector of our intellectual vices, the invigorator of our intellectual imbecility. Hence some entitled their Logics, — The Medicine of the Mind,^ The Art of ThinhingJ' The Lighthouse of the Intellect,^ The Science Teaching the Right Use of Reason,' &c. &c. Now in all this there is a mixture of truth and error. To a certain extent, and in certain points of view, Logic is the organ of philosophy, the criterion of truth, and the corrector of error, and in others it is not. In reference to the dispute whether logic may with in what re- propriety be called the instrument, the organon of ifan ins^tm^- the other sciences, the question may be at once solved sde'liccs. ' by a distinction. One science may be styled the instrument of another, either in a material or in a a Mauritii Ex2Wsitio Qucestionum were probably taken. — Ed. Doctoris Suhtilis in quinque Univer- e Guuuer, Ars Hcurlstica Intdlec- ftalia Porphyrii, Qusest. i. {Scoti tualis, Lipsise, 1756. Trattato dl Opera, Lugd., 1639, torn. i. p. 434). Messer Scbastiano Eriz%o, deW Istni- Mauritius refers to St Augustin as mcnto et Via Inventrice de gli antichi his authoi-ity for the above quotation, nelle scientie, Venice, 1554. — Ed. It slightly resembles a jiassage in the ( Tschirnhausen, Medicina Mentis, Dc Ordine, L. ii. c. 13. — Ed. slve Artls Inveniendi Pracepta Gcnc- /3 Gundling, Via ad VerUatem 3Io- ralia, Amst., 1687. Lange, Medicina ralem, Hah-e, 1713. Darjes, Via ad Mentis, Hal;e, 1703. — Ed. Vtritatem, Jenae, 1764 (2d edit.) — t) UArt de Pcnser, commonly Ed. known as the Port Royal Logic. 7 P. Laurembergius, Cynosura Several other works have apjieared Bonce mentis s. Lofjica, Rostoch, under the same title. — Ed. 16.33. 11. Ijoenua, Cynosura Pationis, OGvosacrwa, Phar us I ntellcctus, sive Arnhem, 1667. — Ed. Lorjica Electiva, Lips., 1697. — Ed. 5 See Krug, Jjorjik, § 9, p. 23, from i Watts, Logic, or the Rvjhl Use of whom several of tlieabove definitions Ptasou. — Ed. 36 LECTURES ON LOOIC. i.F.rr. fonujil i>(>iiit of \ii'\\. lii llic loniu'r point ot" view, II. . . '■ — one scioiu'o is the origan oi' aiiotlier when one science determines for anotlier its contents or objects. Thus IMatlieniaties may l>o ealled the material instru- ment of the various branches of physical science ; Philology, — or study of the languages, Latin, Greek, Hebrew, Chaldee, &c., with a knowledge of their relative history, — constitutes a material instrument to Christian Tlieology ; and the jurist, in like manner, finds a material instrument in a knowledge of the history of the country whose laws he expounds." Thus also Physiology, in a material point of view, is the organon of Medicine ; Aristotle has indeed well said that medicine begins where the philosophy of nature leaves off.'^ In the latter point of view, one science is the organon of another, when one science determines the scientific form of another. Now, as it is gene- rally admitted that Logic stands in this relation to the other sciences, as it appertains to Logic to con- sider the general doctrine of Method and of systematic construction, in this respect Logic may be properly allowed to be to the sciences an instrument, but only a formal instrument."^ Lo^c not In regard to the other titles of honour, Logic can- properlv an . r^ .it • i ttt • ~i artofdis- not With propriety be denominated a [Heuretic orj Art of Discovery. " For discovery or invention is not to be taught by rules, but is either the free act of an original genius, or the consequence of a lucky accident, which either conducts the finder to something un- known, or gives him the impulse to seek it out. Logic can at best only analytically teach how to discover, that is, by the development and dismemberment of a See Genovesi, Elementa Artis y Krug, Logik, § 9, p. 23 ; Cf. Logico-Crilicce, L. i. c. iii. p. 41, Platner, Pldlosophische Aphorismen, /3 Dc Sensu et Sensili, c. i. Part i. p. 23, ed. 1703.— Ed. LECTURES ON LOGIC. 37 what is already discovered. By this process there lect. is nothing new evolved, and our knowledge is not amplified; all that is accomplished is a clearer and distincter comprehension of the old ; — our knowledge is purified and systematised." * It is well observed by Antonius, in Cicero : — " Nullum est prseceptum in hac arte quomodo verum inveniatur, sed tantum est,quomo- do judicetur." ^ Logic is thus not creative ; it is only plastic, only formative, in relation to our knowledge. Again, " Logic cannot with propriety be styled the in what medicine of the mind, at least without some qualify- caHe °^'° ing adjective, to show that the only remedy it can medicine of apply is to our formal errors, while our material errors lie beyond its reach. This is evident. Logic is the science of the formal laws of thought. But we can- not, in limiting our consideration to the laws of for- mal thinking, investigate the contents, — the matter, of our thought. Logic can, therefore, only propose to purge the understanding of those errors which lie in the confusion and perplexities of an inconsequent thinking. This, however, it must be confessed, is no radical cure, but merely a purification of the under- standing. In this respect, however, and to this extent, Logic may justly pretend to be the medicine of the mind, and may, therefore, in a formal relation, be styled, as by some logicians it has in fact been, Cath- articon intellectus. " By these observations the value of Logic is not depreciated ; they only prepare us to form an esti- mate of its real amount. Precisely, in fact, as too much was promised and expected from this study, did it lose in credit and esteem." "^ a Krug, Logik, § 9, p. 24.— Ed. 7 Krug, Zo^*, § 9, pp. 24-G.— En. Cf. [Richter, Logik, p. 83 e.t seq.] Cf. [Kichter, Logik, p. 85.] /8 De Oratore, ii. 38.— Ed. 3S LECTURES ON LOOI(\ Rciapitula- tiuu. LECTURE 111. INTRODUCTION. LOGIC — II. IT8 ITILITY. — IIL ITS DIVISIONS — SUBJEC- TIVE AND OBJECTIVE — GENERAL AND SPECIAL. LEc-r. The last Lecture was occupied with the consideration HI . of the latter part of the introductory question, — What is Logic ? and with that of the first part of the second, — What is its LTtility ? — In tlie Lecture preceding the last, I had given the definition of Logic, as the science of the laws of thought as thought, and, taking the several parts of this definition, had articulately ex- plained, 1°, What was the meaning and history of the ■word Logic ; 2°, What was the import of the term science, the genus of Logic ; and, 3°, What was signi- fied by laws of thought as thought, the object-matter of Logic. This last I had considered under three heads, explaining, 1°, What is meant by thought ; 2°, What is meant by thought as thought ; and, 3°, What is meant by laivs of thought a^ thought. It was under the last of these heads that the last Lecture commenced. I had, in the preceding, shown that the form of thought comprises two kinds of phsenonena, given always in conjunction, but that we are able by abstraction and analysis to discriminate them from each other. The one of these classes comprehends what is contingent, the other what is necessary, in the manifestations of thought. The necessary element is the peculiar and III. LECTURES ON LOGIC. 39 exclusive object of Logic ; whereas the phsenomena of lect thought and of mind in general are indiscriminately proposed to Psychology. Logic, therefore, I said, is distinguished from the other philosophical sciences by its definition, as the science of the necessary form of thought. This, however, though a full and final de- finition, is capable of a still more explicit enunciation ; and I showed how we are entitled to convert the term necessary into the term laws, and, in doing so, I took the opportunity of explaining how, the necessity of a mental element being given, there is also implicitly given the four conditions, 1°, That it is subjective ; 2°, That it is original ; 3°, That it is universal ; and, 4°, That it is a law. The full and explicit definition of Logic, therefore, is, — the science of the Laws of Thought as Thought ; or, the science of the Laws of the Form of Thought ; or, the science of the Formal Laws of Thought : — these being only three various expressions of what is really the same. Logic being thus defined, I gave a brief and gene- ral retrospect of the history of opinion in regard to the proper object and domain of Logic, and showed how, though most logicians had taken speculatively, and in general, a very correct view of the nature of their science, they had not carried this view out into application, by excluding from the sphere of Pure or Abstract Logic all not strictly relative to the form of thought, but had allowed many doctrines relative merely to the matter of thought to complicate and to deform the science. I then called attention to the opinions of the author whom I recommend to your attention, and showed that Dr AVhately, in his statements relative to the object-matter of Logic, is vague and obscure, errone- 40 L1-:CTUHKS ON I,0(!1C. LF.rr. c)us ;uul self-contradictory ; unci that, so far from being entitled to tlie praise of having been the only logician who has clearly displayed the true nature of the science, on the contrary, in the exposition of this nature, he is far inferior, not only in perspicuity and precision, but in truth, to the logicians of almost every age and country except our own. ouorvn- And here, taking a view of what we have already tious lutcr- j>ose.iR-ia- established, I would interpolate some observations questi,.!.,— which I ought, in my last Lecture, to have made. Logic? before leaving the consideration of the first cpaestion, — viz. What is Logic 1 Logic, we have seen, is ex- clusively conversant about thought, — about thought considered strictly as the operation of Comparison or the faculty of Eelations ; and thought, in this re- stricted signification, is the cognition of any mental object by another in which it is considered as in- cluded, — in other words, thought is the knowledge of The terms thiuffs undei conceptions. By the way, I would here CoHceptioti ^ \ . '' /' ^ and Con- pause to make an observation upon the word concep- tion, and to prepare you for the employment of a term which I mean hereafter to adopt. You are aware, from what I have already said, that I do not use conception in the signification in which it is applied by Mr Stewart. He usurps it in a very limited meaning, in a meaning which is peculiar to himself, — viz. for the simple and unmodified repre- sentation of an object presented in Perception." Reid, again, vacillates in the signification he attaches to this term, — using it sometimes as a synon5nn for Imagination, sometimes as comprehending not only Imagination, but Understanding and the object of Understanding.'^ It is in the latter relation alone that a See Lectures on Metaphysics, Lect. xxxiii., vol. ii. p. 261. — Ed. /3 Ihid. LECTURES ON LOGIC. 41 I ever employ it, and this is its correct and genuine lect. siornifi cation, whether we regard the derivation of the , . r^ • Author's word, or its general use by philosophers. Conceptio7i, employment in English, is equivalent to conceptio and conceptus terms. in Latin, and these terms, by the best philosophers and the most extensive schools, have been employed as synonyms for notion (notio), the act or object of the Understanding Proper or Faculty of Eelations. So far, therefore, you are sufficiently prepared not to attribute to the word conception, when you hear it from me, the meaning which it bears in the philoso- phical writings with which you are most likely to be familiar. What is the precise meaning of the term will be soon fully explained in its proper place, when we commence the treatment of Logic itself. But what I principally pause at present to say is, — that, for the sake of perspicuity, I think it necessary, in reference to this word, to make the following distinction. The term conception, like perception, imagi7iation, &c., means two things, or rather the same thing in two different relations, — relations, however, which it is of great importance to distinguish, and to mark the dis- tinction by the employment of distinct words. Con- ception means both the act of conceiving, and the object conceived; as perceptio7i, both the act of per- ceiving and the thing perceived ; imagination, both the act of imagining and what is imagined. Now this is a source of great vagueness in our philoso- phical discussions ; have we no means of avoiding this inconvenience ? I think wc have ; and that too with- out committing any violence upon language. I would propose the following distinction. For the act of conceiving, the term conception should be employed, and that exclusively ; while for the object of conccp- 42 LECTURES ON l,0(iU'. LK<.T. tion, or that wliit-h is conceived, the term concept III. . . -^ sluniKl be iiseih" (.V>iicept is tlie English of the Latin concrpttim, — id quod coucc2->fi(m est, — and had it no vested riirht as an actual denizen of the lanouajxe, it has good warrant lor its naturalisation. There arc a thousand words in English formed on precisely the same analog}'", as 'precept, digest, &c. &c. But wc have no occasion to appeal to analog}''. The term concept was in common use among the older philoso- phical writers in English,'^ though, like many other valuable expressions of these authors, it has been over- looked by our English lexicographers. I may add that nearly the same fortune has befallen the term in French. Concep)t was in ordinary use by the old French philosophers, but had latterly waxed obsolete. It has, however, I see, been reinstated in its rights since the reawakening of philosophy in France ; and, in particular, it is now employed in that lang-uage in translating from the German the term Begriff. I shall, therefore, make no scruple in using the expres- sion concept for the object of conception, and con- ception I shall exclusively employ to designate the act of conceiving. "Whether it might not, in like manner, be proper to introduce the term ^^ercep^ for the object of perception, I shall not at present inquire. But to return from this digression. Logic, we have seen, is exclusively conversant about thought strictly a See Biel [In Sent., lib. i. tlist. Gideon Harvey, Archdogia Philo.to- 2, qu. 8 ; lib. ii. dist. .3, qu. 2. By ^jAica Nova, or Nev} Princi-ple-'i of Occam and most others, conceptii^ is Philosophy, Lond., 1GG3, P. i., b. used as " id quod terminat actum in- ii., c. 4, p. 22. For several authori- tellif^endi." See Occam, In Sent., ties for the use of this term among lib. i. dist. 2, q. 8 ; and Biel, lib. i. the older English logicians, see dist. 3, q. 5.] Baynes, New Analytic of Loffical a See Zac]i3,Ty Coke, Art of Lofjicl; Forms, pp. 5, G, note.— En. London 1654, ])p. 11, 101, ct alibi; LECTURES ON LOaiC. 43 SO denominated, and thought proper, we have seen, lect, is the cognition of one object of thought by another, in or under which it is mentally included, — in other between words, thought is the knowledge of a thing through a Mathe- concept or general notion, or oi one notion through another. In thought, all that we think about is con- sidered either as something containing, or as something contained, — in other words, every process of thought is only a cognition of the necessary relations of our concepts. This being the case, it need not move our wonder, that Logic, within its proper sphere, is of such irrefragable certainty, that, in the midst of all the revolutions of philosophical doctrines, it has stood not only unshattered but unshaken. In this respect, Logic and Mathematics stand alone among the sciences, and their peculiar certainty flows from the same source. Both are conversant about the relations of certain a priori forms of intelligence : — Mathematics about the necessary forms of Imagination ; Logic about the necessary forms of Understanding ; Mathematics about the relations of our representations of objects, as out of each other in space and time ; Logic about the relations of our concepts of objects, as in or under each other, that is, as, in different relations, respectively containing and contained. Both are thus demonstra- tive or absolutely certain sciences only as each de- velops what is given, — what is given as necessary, in the mind itself. The laws of Logic are grounded on the mere possibility of a knowledge through the con- cepts of the Understanding, and through these we know only by comprehending the many under the one. Concerning the nature of the objects delivered by the Subsidiary Faculties to the Elaborative, Logic pronounces nothing, but restricts its consideration to 44 LECTURES ON LOOIC. LEiT. till' laws according" to w liuli tlioir ai^recment or dis- 111 . . " '. airivenient is affirnu'il." ix^pif i» tiio It is of itself manifest, that every science must obey "ou'aitun. the laws of Logic, If it does not, such pretended science is not founded on reflection, and is only an irrational absurdity. All inference, evolution, con- catenation, is conducted on logical principles, — prin- ciples which are ever valid, ever imperative, over the same. But an extension of any science through Logic is absolutely impossible ; for by conforming to logical canons we acquire no knowledge, — receive nothing new, but are only enal)led to render what is already oljtained more intelligible, by analysis and arrangement. Logic is only the negative condition of truth. '^ To attempt by a mere logical knowledge to amplify a science, is an absurdity as great as if we should attempt by a knowdedge of the grammatical laws of a lanojuasre to discover what was written in this language, without a perusal of the several wait- ings themselves. But though Logic cannot extend, cannot amplify a science by the discovery of new facts, it is not to be supposed that it does not contri- bute to the progress of science. The progress of the sciences consists not merely in the accumulation of new matter, but likewdse in the detection of the rela- tions subsisting among the materials accumulated ; and the reflective abstraction by which this is effected must not only follow the law^s of Logic, but is most powerfully cultivated by the habits of logical study. In these intercalary observations I have, however, in- sensibly encroached upon the second question, — What is the Utility of Logic ? On this question I now dic- tate the following paragraph : — a Cf. Bachmann, Loglk, Einleitimg, fi [Aiicillon, Essais Phihsophiques, § 20, edit. 1 828.— Ed. t. ii. p. 291.] LECTURES ON LOGIC. 45 11 IV. As the rules of Logic do not regard the lect, matter but only the form of thought, the Utility of Par. IV. Logic must, in like manner, be viewed as limited utility of to its influence on our manner of thinking, and not sought for in any effect it can exert upon what we think about. It is, therefore, in the first place, not to be considered useful as a Material Instrument, that is, as a mean of extend- ing our knowledge by the discovery of new truths ; but merely as a Formal Instrument, that is, as a mean by which knowledge, already ac- quired, may be methodised into the form accom- modated to the conditions of our understandino;. In the second place, it is not to be regarded as a Medicine of the mind to the extent of remedying the various errors which originate in the nature of the objects of our knowledge, but merely to the extent of purging the mind of those errors which arise from inconsequence and confusion in thinking." Logic, however, is still of eminent utility, not only as presenting to us the most in- teresting object of contemplation in the mechan- ism of human thought, but as teaching how, iu many relations, to discriminate truth from error, and how to methodise our knowledge into system ; while, at the same time, in turning the mind upon itself, it affords to our higher faculties one of their most invigorating exercises. Another utility is, that Logic alone affords us the means requisite to accomplish a rational criticism, and to com- municate its results. What is now summarily stated in the preceding paragraph, I illustrated, in my last Lecture, in detail, — a Cf. Knig, iMifik, § 9.— Ed. 46 LECTUKES ON LOGIC. LECT. ill SO far as it was requisite to disencumber the real 111. YiUue of our science from those false utilities which, in })laee of enhancing its worth in the opinion of the workl, have, in fact, mainly contributed to reduce the common estimate of its importance far beneath the truth. I no\v proceed to terminate what I have to say under this head by a few words, in exposition of what renders the cultivation of Logic, — of genuine logic, one of the most important and profitable of our studies. Lopic gives " Admitting, therefore, that this science teaches no- tain extent, thing new, — that it neither extends the boundaries of over our knowlcdgc, uor uniolds the mysteries which lie be- yond the compass of the reflective intellect, — and that it only investigates the immutable laws to which the mind in thinking is subjected, still, inasmuch as it develops the application of these laws, it bestows on us, to a certain extent, a dominion over our thoughts themselves. And is it nothing to w'atch the secret workshop in which nature fabricates cognitions and thoughts, and to penetrate into the sanctuary of self- consciousness, to the end that, having learnt to know ourselves, we may be qualified rightly to understand all else ? Is it nothing to seize the helm of thought, and to be able to turn it at our will 1 For, through a research into the laws of thinking, Logic gives us, in a certain sort, a possession of the thoughts themselves. It is true, indeed, that the mind of man is, like the universe of matter, governed by eternal laws, and foUows, even without consciousness, the invariable canons of its nature. But to know and understand itself, and out of the boundless chaos of phgenomena presented to the senses to form concepts, through con- cepts to reduce that chaos to harmony and arrange- LECTURES ON LOGIC. 47 mcnt, and tlius to establish the dominion of intelli- lect. gence over the universe of existence, — it is this alone '— error. which constitutes man's grand and distinctive pre- eminence."" " Man," says the great Pascal, " is but a reed, — the very frailest in nature ; but he is a reed that thinks. It needs not that the whole universe should arm to crush him. He dies from an exhala- tion, from a drop of water. But should the universe conspire to crush him, man would still be nobler than that by which he falls ; for he knows that he dies ; and of the victory which the universe has over him, the universe knows nothing. Thus our whole dignity consists in thought Let us labour, then, to think aright ; this is the foundation of morality."^ In the world of sense, illusive appearances hover supplies in around us like evil spirits; unreal dreams mingle Si oV" themselves with real knowledge ; the accustomed «'" ' "^""^ assumes the character of certainty ; and the associa- tions of thought are mistaken for the connections of existence. We thus require a criterion to discriminate truth from error ; and this criterion is, in part at least, supplied to us by Logic. Logic teaches us to analyse the concrete masses of our knowledge into its elements, and thus gives us a clear and distinct apprehension of its parts, it teaches us to think consistently and with method, and it teaches us how to build up our accu- mulated knowledge into a firm and harmonious edifice.^ " The study of logic is as necessary for correct thinking, as the study of grammar is for correct speaking ; were it not otherwise and in itself an interesting study to o [Heinricli Richter], [Uber den ii. p. 84, eel. Faug5re). Compare Geyenstaiul und den Uiiif((ng der Discussions, p. SIL — Ed. Lngik, pp. 3, 4, Leipsic, 1825.— Ed.] y Cf. Richter, Lo(jik, pp. 5, G, 12. /3 Pensies, P. i. art. iv. § G, (vol. —Ed. 48 LECTURE;^ ON LOGIC. KKrr. investi<;ate the iiiocluuiism of the humuii intellect in '■ — tlie niarveHous processes of thought. Tlicy, at least, who are familiar with this mechanism, arc less exposed to the covert fallacies which so easily delude those unaccustomed to an analysis of these processes." " iuvi-,.ratos ])ut it is uot ouly by atfording knowledge and skill staiidiug' that Logic is thus useful ; it is perhaps equally condu- cive to the same end by bestowing power. The retor- sion of thought upon itself, — the thinking of thought, — is a vigorous etlbrt, and, consequently, an invigorat- ing exercise of the Understanding, and as the under- standing is the instrument of all scientific, of all philosophical, speculation. Logic, by pre-eminently cul- tivating the understanding, in this respect likewise vindicates its ancient title to be viewed as the best preparatory discipline for Philosophy and the sciences at large. There is, however, one utility which, though of a subordinate kind, I must not omit, though I do not remember to have seen it insisted on by any logical writer. In reference to this, I give you the following paragraph : — Par. V. 1" V. But Logic is further useful as affording a Logic,— Nomenclature of the laws by which legitimate a scie°ntific thinking is governed, and of the violation of these ture. laws, through which thought becomes vicious or null. Illustration. It is Said, in Hudibras,^ — " That all a Rhetorician's rules Serve only but to name his tools ; " and it may be safely confessed that this is one of the principal utilities of Rhetoric. A mere knowledge of o Krug, Loyik, § 9, p. 2G.— Ed, )3 P. i. Cant, i. 89,— Ed. LECTURES ON LOGIC. 49 the rules of Ehetoric can no more enable us to com- lect. pose well, than a mere knowledge of the rules of Logic '— can enable us to think well. There is required from nature in both the faculty; but this faculty must, in both departments, be cultivated by an assiduous and also a well-directed exercise, that is, in the one, the powers of Comparison must be exercised according to the rules of a sound Ehetoric, in the other, according to the rules of a sound Logic. In so far, therefore, the utility of either science is something more than a mere naming of their tools. But the naming of their importance tools, though in itself of little value, is valuable as the fie nomen-'' condition of an important function, which, without this, could not be performed. Words do not give thoughts, but without words thoughts could not be fixed, limited, and expressed. They are, therefore, in general, the essential condition of all thinking worthy of the name. Now, what is true of human thought in general, is true of Logic and Rhetoric in particular. The nomenclature in these sciences is the nomencla- ture of certain general analyses and distinctions, which express to the initiated, in a single word, what the uninitiated could (supposing, — what is not probable, — that he could perform the relative processes) neither understand nor express without a tedious and vague periphrasis ; while, in his hands, it would assume only the appearance of a particular observation, instead of a particular instance of a general and acknowledged rule. To take a very simple example, there is in Example. Logic a certain sophism, or act of illegal inference, by which two things are, perhaps in a very concealed and circuitous manner, made to prove each other. Now, the man unacquainted with Logic may perhaps detect and be convinced of the fallacy ; but how will he VOL. I. I) 50 LECTURES ON LOGIC. LF.CT. expose it '^ lie must enter ii])oii a Kmg statement •*— ami explanation, and after much lalnnir to himself and others, he [)robably does not make his objection clear and demonstrative after all. But between those aci.[uainted with Logic, the whole matter would Ijo settled in two words. It would be enough to say and show, that the inference in question involved a circidus in cojichnlendo, and the refutation is at once under- stood and admitted. It is in like manner that one lawyer will express to another the ratio decidendi of a case in a single technical expression ; while their clients will only perplex themselves and others in theii' attempts to set forth the merits of their cause. Now, if Loojic did nothin<2f more than establish a certain number of decided and decisive rules in reasoning, and afford us brief and precise expressions by which to bring particular cases under these general rules, it would confer on all who in any way employ their intellect, that is, on the cultivators of every human science, the most important obligation. For it is only in the possession of such established rules, and of such a technical nomenclature, that w^e can accomplish, with facility, and to an adequate extent, a criticism of any work of reasoning. Logical language is thus to the general reasoner, wdiat the notation of Arith- metic, and still more of Algebra, is to the mathema- tician. Both enable us to comprehend and express, in a few significant symbols, what would otherwise overpower us by their complexity; and thus it is that nothini? would contribute more to facilitate and extend the faculty of reasoning, than a general acquaintance with the rules and language of Logic, — an advantage extending indeed to every department of knowledge, but more especially of importance to those professions LECTURES ON LOGIC. 51 which arc occupied in inference and conversant with lect abstract matter, — such as Theology and Law. L I now proceed to the third of the preliminary ques- in. Divi- tions — viz. How is Logic divided 1 Now, it is mani- LogL" fest that this question may be viewed in two relations ; for in asking how is Logic divided, we either mean how many kinds are there of Logic, or into how many constituent parts is it distributed ? " We may consider Logic either as a universal, or as an integrate, whole. It is necessary to consider the former question first; i. The for before proceeding to show what are the parts ofLogi^c!^" which a logic is made up, it is requisite previously to determine what the logic is of which these parts are the components. Under the former head, I, therefore, give you the following : — H VL Logic, considered as a Genus or Class, Par. vi. may, in different relations, be divided into differ- rektwn L ent Species. And, in the first place, considered by iso^ctVve relation to the mind or thinking subject, Logic uvc. " ''^'^ is divided into Objective and Subjective, or, in the language of some older authors, into Logica systematica and Logica hdbitualisf By Objective or Systematic Logic is meant that ExpiiVa- complement of doctrines of which the science of Logic o Division of Logic into Natural authore M. Clemente Timplcro, Han- ,ind Artificial, inept. ovire, 1012. Vossius, Dc Natura Artium, L. iv., Sive De Logica, c. " ""^ min?'^ ^''''"* ""'''' "''"'''' *"''''° "^ '''■ ^^^"''' ^'' Por-phyrii Imgocjen, 1171-1 i. ' 1 1 T • . 1(1 p. 2, ed. Francof., 1697. — Ed.1 On Whilst puzzled Logic struggles fur be- * .' ,. . . . -, • m- j^jjjjj „ various divisions of Logic, see 1 im- pler, Logicm Systema, L. i. c. 1, q. Cf. Krug, Lo(jik, p. 29. Troxler, 13-20, p. 40-50; Gisbert ab Isen- Lofjik, i. 48. doom, Effata, Philosophica, [Cent. i. j8 Sec Timpler, p. 877 ; Vossius, § 51-03, p. 95 ct seq., ed. Davcntria^, p. 217; Pacius. [Logkw Sydema, 1043. — Ed.] 52 LECTURES ON LOGIC. LECT. is made up ; by Subjective or Habitual Logic is meaut '■ — the speculative knowledge of these doctrines whicli aiiv individual, (as Socrates, Plato, Aristotle), may possess, and the practical dexterity with which he is able to apply them. Both these Now, it is cvldcnt that both these Logics, or, rather, Loi;icsou:;ht . .- ^ . .. pii i • ^ lokj.rx). Logic considered in this twoiold relation, ought to cnTofu.gi- be proposed to himself by an academical instructor, tion. We must, therefore, neglect neither. Logic con- sidered as a system of rules, is only valuable as a mean towards logic considered as a habit of the mind ; and, therefore, a logical instructor ought not to think that he fulfils his duty, — that he accom- plishes all that he is called on to perform, if he limit himself to the mere enouncement of a code of doc- trine, leaving his pupils to turn his instructions to their own account as best they may. On the con- trary, he is bound to recollect that he should be something more than a book ; that he ought not only himself to deliver the one Logic, but to take care that his pupils acquire the other. The former, indeed, he must do as a condition of the latter ; but if he considers the systematic logic which he pronounces, as of any value, except in so far as his pupils convert it into an habitual logic, he under- stands nothino- of the character of the function which he attempts to perform. It is, therefore, incumbent on an academical instructor, to do what in him lies to induce his pupils, by logical exercise, to digest w^hat is presented to them as an objective system into a subjective habit. Logic, therefore, in both these relations belongs to us, and neither can be ne- glected without compromising the utility of a course like the present. . LECTURES ON LOGIC. 53 H VIL In the second place, by relation to its lect ^ "^ III. application or non-application to objects, Logic is divided into Abstract or General, and Con- Logic, by Crete or Special. The former of these is called objects, is by the Greek Aristotelians, StaXe/cTi/ci) x<^P^5 General, TTpay[xdTO)p, and by the Arabian and Latin crate or schoolmen, Logica docens ; while the latter is ^^"* ' denominated by the Greeks, hiakeKriKX) iv )(^prjpears multiform." So far Alex- ander. This appearance of multiformity I may, how- ever, add, is not real ; for the mind has truly only one mode of thinking, one mode of reasoning, one mode of conducting itself in the investigation of truth, whatever may be the object on which it exer- cises itself. Logic may, therefore, be again well com- pared to the authority of an universal empire, — of an empire governing the world by common laws. In such a dominion there are many provinces, various regions, and different praafectures. There is one prse- fect in Asia, another in Europe, a third in Africa, and each is decorated by diflferent titles ; but each governs and is governed by the common laws of the Empire confided to his administration. The nature of Gene- ral Logic may, likewise, be illustrated by another comparison. The Thames, for instance, in passing- London, is a single river, — is one water, but is there applied to many and different uses ; it is employed a [Isendoorn Effata, Cent. i. 55 ; Crellius, Imcjoffc Logica, p. 12.] [The illustration is fully given by Balfo- reus, Commentarius in Orjanum, p. 23, q. V. § 2. "Alexander Aphro- disiensis Logicam illain abjunctam similem esse ait figurte geometricje, utpote triangulo, diun in se et per se spectatur ; Logicam vero cum re- bus conjunctam similem eidem trian- gulo huic aut illi materitu impresso. Xam trianguli in se una est et eadem ratio ; at [iru varietate materiae, varia. Aliud enim est argenteum, aliud aureum, aliud ligneum, lapideiim aut pliunbeum. " The passage referred to is probably one in the Commen- tary on the Prior Analytics, p. 2, ed. Aid. The distinction itself, though not the illustration, is given more exactly in the language of the text by some of the later commentators. See the Introductions of Ammonius to the Cakf/ories, and of I'hiloponus to the Prior Analytics. — Ed.] LECTURES ON LOGIC. 55 for drinking, for cooking, for brewing, for washing, lect. for irrigation, for navigation, &c. In like manner, — Logic in itself is one : — as a science or an art, it is single ; but, in its applications, it is of various and multiform use in the various branches of knowledge, conversant be it with necessary, or be it with con- tingent matter. Or further, to take the example of a cognate science, if any one were to lay down different grammars of a tongue, as that may be applied to the different purposes of life, he would be justly derided by all grammarians, indeed by all men ; for who is there so ignorant as not to know that there is but one grammar of the same language in all its various applications ? " Thus, likewise, there is only one General method of reasoning, which all the sciences indiffer- aione one ; ently employ ; and although men are severally oc- Logic is cupied in different pursuits, and although one is, ami part of therefore, entitled a Theologian, another a Jurist, ainwhlchTt third a Physician, and so on, each employs the same " ^^'^ '^ ' processes, and is governed by the same laws, of thought. Logic itself is, therefore, widely different from the use, — the application of Logic. For Logic is astricted to no determinate matter, but is extended to all that is the object of reason and intelligence. The use of Logic on the contrary, although potentially applicable to every matter, is always actually mani- fested by special reference to some one. In point of fact, Logic, in its particular applications, no longer o See Kami Sch. , p. 350, [P. Jia^ni babili, captiosa ; ars tamen una. Si ScholcB in Liberules Artts. Basilea-, Grammaticas tres aliquis ineptus no- 1578: " Unus est Lutetiiu Secpiana, bis instituat, unam civilem, alteram ad multos tamen usus et varios ac- agrestem, tertiam do vitis ambornm, commodatus, lavandnm, acpiandum, merito rideatur a Grammaticis omni- vehendum> irrigandum, coquendiim: bus, qui unam Grammaticam noruiit sic una est Logica, varii et multiplicis omnium ejusdcm linguae hominunj usus, in proposition e necessaria, ]>ro- oommunem." — Eu. ] 56 LECTURES ON LOGIC. Lv.cv. roinaiiis loi>ii.', but bocoiuos paiL and ])arccl of the iirt 111. r> ' J. -I — '■ — or science in wliich it is applied. Thus Logic, applied to the objects of geometry, is nothing else than Geo- metry, — Logic applied to the objects of physics, nothing else than Natural Philosophy. AVe have, indeed, certain treatises of Logic in reference to dif- ferent sciences, which may be viewed as something more than these sciences themselves. For example, we have treatises on Legal Logic, &c. But such treatises are only introductions, — only methodologies of the art or science to which they relate. For such special logics only exhibit the mode in which a deter- minate matter or object of science, the knowledge of which is presupposed, must be treated, the conditions which regulate the certainty of inferences in that matter, and the methods by which our knowledge of it may be constructed into a scientific whole. Special Logic is thus not a single discipline, not the science of the universal laws of thought, but a con- geries of disciplines, as numerous as there are special sciences in which it may be applied. Abstract or General Logic, on the contrary, in virtue of its uni- versal character, can only and alone be one ; and can exclusively pretend to the dignity of an independent science. This, therefore, likewise exclusively con- cerns us. LECTURES ON LOGIC. 57 LECTURE IV. lE^TEODUCTIOK LOGIC — III. ITS DIVISIONS — PURE AND MODIFIED. In my last Lecture, after terminating the considera- lect, tion of the second introductory question, touching the Utilities of Logic, I proceeded to the third introduc- tion!^' tory question, — What are the Divisions of Logic ? and stated to you the two most general classifications of this science. Of these, the first is the division of Logic into Objective and Subjective, or Systematic and Habitual ; the second is its division into General and Special, or Abstract and Concrete. To speak only of the latter : — Abstract or General Logic is logic viewed as treating of the formal laws of thought, without respect to any particular matter. Concrete or Special Logic is logic viewed as treating of these laws in relation to a certain matter, and in subordination to the end of some determinate science. The former of these is one, and belongs alone to philo- sophy, that is, to the science of the universal principles of knowledge ; the latter is as manifold as the sciences to which it is subservient, and of which it, in fact, constitutes a part, — viz. their Methodology. This division of logic is given, but in difierent terms, by the Greek Aristotelians and by the Latin schoolmen. The Greek division does not remount to Aristotle, but it is found in his earliest expositor, Alexander 58 LEcrruKs on locic. i.Krr. of Aphrotlisias, ;iiul he was probably iu)t the lirst liy whom it was enounced. It is into Sta\e/crt/cry \'L;i(', a'^ain, cxhiMls those laws as moilil'uMl in '. — ■ tlioir actual applications by certain general cii- ciinistances oxtcnial ami internal, contingent in themselves, hut hywiiich human thought is always more or less inilueuccd in its manifestations.* Pure Logir. Ture Logic considers Thought Proper simply and in itself, and apart from the various circnmstances by which it may be effected in its actual application. Human thought, it is evident, is not exerted except by men and individual men. By men, thought is not exerted out of connection with the other constituents of their intellectual and moral character, and, in each individual, this character is variously modified by various contingent conditions of different original genius, and of different circumstances contributing Mollified to develop different faculties and habits. Now there may be conceived a science, which considers thought not merely as determined by its necessary and universal laws, but as contingently affected by the empirical conditions under which thought is actually exerted ; — which shows what these conditions are, how they impede, and, in general, modify, the act of thinking, and how, in fine, their influence may be counteracted. Logic. Nomencia- TMs scicncc is Modified or Concrete Loo;ic. What I Modified have called Modified Logic is identical with what ^'*^' Kant and other philosophers have denominated Ap- plied Logic (angeivandte Logik, Logica applicata.Y a For distinction of reason in ab- Schriften wclche den logischen Calcul stracto aMArediSon in concreto, gronrxdi- Herrn Prof. Ploucqi'xts hetreffcn, ing the tlistiuctiou of au Abstract (or Tubingen, 1773. — Ed.] Pure) and a Concrete (or Modified) /3 Kant, Logik, Einleitung ii. ; Logic, see Boyle's Works, iv.\>. 164. 'ilofiha,\ier,Anfangsf/rundc der Logik, See also Lambert, Xeuc-i Organon, i. §§ 17, 406 ; Kruj,', Logik, Einleitung, § 444, who says that the sciences in § 11 ; Fries, Sijstcm dcr Logik, § 2. — general are only apijlied logics. Cf. Ed. Ploucquet^ p. 236 [Sammhmg da- LECTURES ON LOGIC. 61 This expression I think improper. For the term lect. Applied Logic can only with propriety be used to '— denote Special or Concrete Logic ; and is, in fact, a Applied brief and excellent translation of the terms by which "' ' Special Logic was designated by the Greeks, as that ev )(py](T€i Koi yvfxvacrta irpayyidToyv. And SO, in fact, by the Latin Logicians was the Greek expression rendered. Let us consider the meaning of the term app>lied. Logic, as applied, must be applied to some- thing, and that something can only be an object or matter. Now, Special Logic is necessarily an applied logic ; therefore the term applied, if given to what I would call Modified Logic, would not distinguish Modified from Special Logic. But further, the term applied as given to Modified Logic, considered in itself, is wrong ; for in Modified Logic thought is no more considered as actually applied to any particular matter than in Pure Logic. Modified Logic only considers the necessary in conjunction with the con- tingent conditions under which thought is actually exertible ; but it does not consider it as applied to one class of objects more than to another ; that is, it does not consider it as actually applied to any, but as potentially applicable to all. In every point of view, Howpro- therefore, the term applied, as given to Modified p%ed."' Logic, is improper ; whereas, if used at all, it ought to be used as a synonym for special; which I would positively have done, were it not that, having been unfortunately bestowed by high authority on what I have called Modified Logic, the employment of it to designate a totally different distinction might generate confusion. I have, therefore, refrained from making use of the term. I find, indeed, that all logicians who, ])cfore Kant, ever employed the expression Ap)- 02 LECTURES ON LOGIC. LKiT. plicil Logic, oini>loyo(l it as convcrtibk' with ISpeeial — ^ — or Concrete Loij-ic." in line, it is to be observed tlmt the terms pun- and applied, as usually employed in opi>(Ksilion in the Kantian pliiloso})hy, and in that of Germany in general, are not properly relative and eorrelative to each other. For |;?t?'c has its proper correlative in modified ov mixed; applied it^ '^yo\)Q,v relative in iinapplied, that is, divorced from things, that is, abstract. MiMiitied iiut passing from words to things, I may observe i.n.i.oriyan tliat it cau bc qucstioucd whether Modified or Con- i.ari of Crete Logic be entitled to the dignity of an essential part of Logic in general, far less of a co-ordinate species as opposed to Pure or Abstract Logic. You are aware, from what I have previously stated under the first introductory question, that Logic, as conver- sant about a certain class of mental phsenomena, is only a part of the general philosophy of mind ; but that, as exclusively conversant about what is neces- sary in the phsenomena of thought, that is, the laws of thinking, it is contradistinguished from Empirical Psychology, or that philosophy of mind which is merely observant and inductive of the mental phseno- mena as facts. But if Modified or Concrete Logic be considered either as a part or as a species of General Logic, this discrimination of Logic, as the Nomology of thought, from Psychology, as the Phsenomcnology of mind, will not hold. For Modified Logic, pre- supposing a knowledge of the general and the con- tingent phsenomena of mind, will thus either comprise Psychology withm its sphere, or be itself comprised a See Balforeus, [R. Bal/orei Logicam abjunctam et a rebus se- Commentaritis in Orfjanum, q. v. § 2, paratam ; aliam rebus applicatam et p. 22: "Grreci . . . aliam dicunt cum iis conjunctam. " — Ed.] LECTURES ON LOGIC. 63 within the sphere of Psychology. But whichever lect. alternative may be preferred, the two sciences are no longer distinct. It is on this ground that I hold, that, in reality. Modified Logic is neither an essential part nor an independent species of General Logic, but that it is a mere mixture of Logic and Psychology, and may, therefore, be called, either Logical Psycho- logy or Psychological Logic." There is thus in truth only one Logic, that is, Pure or Abstract Logic. But while this, I think, must be admitted in speculative rigour, still, as all sciences are only organised for human ends, and as a general consideration of the modifying circumstances which aftect the abstract law^s of thought in their actual manifestations, is of great practical utility, I trust that I shall not be regarded as deforming the simplicity of the science, if I follow the example of most modern logicians, and add (be it under protest) to Pure or Abstract Logic a part, or an appendix, under the name of Modified Logic. In distributing the science, therefore, into these two principal heads, you will always, I request, keep steadily in mind, that, in strict propriety. Pure Logic is the only science of Logic, Modified Logic being only a scientific accident, ambiguously belonging either to Logic or to Psychology. This being understood, I now proceed to state to ConspcctuR you the distribution of the general science into its Course of parts ; and as it is of high importance that you now "^"'' obtain a comprehensive view of the relation of these parts to each other and to the w^hole which they con- stitute, in order that you may clearly understand the point towards which we travel and every stage in our a [See Kichter, \>. G7] [Ubcr den Logik, § 17, Loipsic, 1825.— Ed.] 0<'p 1 • 1 • 1 parts. FiED. Of thcsc lu tlicir ordcp. -Pure Logic may, I think, best be distributed upon the following principles. We may think; and we may think w^ell. On the one hand, the conditions of thinking do not involve the conditions of thinking well ; but the conditions of thinking well involve the conditions of thinking. Logic, therefore, as the science of thought, must neces- sarily consider the conditions of the possibility of thought. On the other hand, the end of thought is not merely to think, but to think well ; there- fore, as the end of a science must be conformed to the end of its object-matter. Logic, as the science of thought, must display not only the laws of possible, but the laws of perfect, thinking. Logic, therefore, naturally falls into two parts, the one of which investio-ates the formal condi- tions of mere thinking ; the other, the formal conditions of thinking well. i. — In regard to the former : — The conditions LECTURES ON LOGIC. of mere thinking are given in certain elemen- lect, tary requisites ; and that part of Logic which analyses and considers these may be called its Stoicheiology, or Doctrine of Elements. These elements are either Laws or Products. ii. — In regard to the latter, as perfect thinking is an end, and as, the elementary means being supposed, the conditions of an end are the ways or methods by which it may be accomplished, that part of Logic which analyses and considers the methods of perfect thinking, may be called its Methodology, or Doctrine of Method. Thus Pure Logic is divided into two parts, — Stoicheiology, or the Doctrine of Elements, and Methodology, or the Doctrine of Method. Of these in their order. Logical Stoicheiology, or the doctrine conver- sant about the elementary requisites of mere thought, I shall divide into two parts. The first of these treats of the fundamental laws of think- ing, in other words, of the universal conditions of the thinkable, — Noetic, — Nomology. The second treats of the laws of thinking, as governing the special functions, faculties, or products of thought, in its three gradations of Conception, — or, as it is otherwise called. Simple Apprehension, — Judg- ment, and Keasoning, — Dianoetic — Dynamic. This second part of Stoicheiology will, there- fore, fall into three subordinate divisions corre- sponding to these several degrees of Conception, Judgment, and Reasoning. — So much for the Doctrine of Elements. Logical Methodology, or the doctrine conver- sant about the regulated ways or methods in VOL. I. E IV. IV. 66 LECTURES ON LOCK'. i.KiT. which the moans of thiiikiiig iiro CDiidiK'ted to thoir eml of thinking well, is divided into as many parts as there are methods, and there arc as many methods as there are diflereut qualities in the end to Ik? differently accomplished. Now the perfection of tliouglit consists of three vir- tues — Clear Thinking, Distinct Thinking, and Connected Thinking ; each of these virtues is accomplished by a distinct method ; and the three methods will consequently afford the divi- sion of Logical Methodology into three parts. The first part comprises the Method of Clear Thinking, or the Doctrine of Illustration or Defi- nition, Tlie second part comprises the Method of Dis- tinct Thinking, or the doctrine of Division. The third part comprises the Method of Con- catenated or Connected Thinking, or the doctrine of Proof. These three parts are only, however, three par- ticular applications of method ; they, therefore, constitute each only a Special Methodology. But such special methodology, or union of methodo- logies, supposes a previous consideration of Me- thod in general, in its notion, its species, and its conditions. Logical Methodology will, therefore, consist of tw^o parts, of a General and of a Spe- cial, — the Special being subdivided, as above stated. So much for the distribution of Pure Logic. II. — Modified Logic falls naturally into three parts. The First Part treats of the nature of Truth and Error, and of the highest laws for their dis- crimination, — Alethiology. LECTURES ON LOGIC. 67 The second treats of the Impediments to think- lect. ing, with the means of their removal. These im- _ pediments arise, 1°, From the Mind ; 2°, From the Body ; or, 3°, From External Circumstances. In relation to the Mind, these impediments originate in the Senses, in Self-consciousness, in Memory, in Association, in Imagination, in Kea- son, in the faculty of Language, in the Feelings, in the Desires, in the Will. In relation to the Body, they originate in Temperament, or in the state of Health. In relation to External Circum- stances, they originate in the diversities of Edu- cation, of Rank, of Age, of Climate, of Social In- tercourse, &c. The Third Part treats of the Aids or Subsidi- aries of thinking ; and thinking is aided either, 1°, Through the Acquisition, or, 2°, Through the Communication, of Knowledge. The former of these subsidiaries, (the acquisi- tion of knowledge,) consists, 1°, Of Experience, (and that either by ourselves or by others) ; 2°, Of Generalisation, (and this through Induction and Analogy) ; and, 3°, Of Testimony, (and this either Oral or Written). Under this last head falls to be considered the Credibility of Witnesses, the Authenticity and Integrity of Writings, the Rules of Criticism, and of Intei-pretation. The latter of these subsidiaries, the Commu- nication of Knowledge, is either One - sided or Reciprocal. The former consists of Instruction, either Oral or Written ; the latter of Conversa- tion, Conference, Disputation. So much for the distribution of Modified Logic. 08 l.KcTrr.KS ON LOGIC. LECT. The l\>llo\viiig is a n^onoral tabular view of tlic Divi- sions of IjOi^ic " now iiiven : — Tubular MOW of tlio nivisiotu of TV. The History of Lopic. This (jues- tion post- poned. 1. rure. ^i. Stoii'heiology /l. Noetic, I Nomo lology. 2. Dianoetic,- Dyuaiuic. a. Confe]ilioii. 6. Jmlj^iiieut. c. Reasoning. Geskral or Abstkact\ Loaio. /Clear Thinking. - 1. I Illustration. ii. Methodology. ,) Distinct TImiking.-2 Dellnition or Division. Connected Tliinking. — 3. Proba- tion or Proving. II. Modified. '. Truth and Error — Certainty and Illusion. /'. ii. Inijiediments to Thinking, with^ f,' Remedies. These Inipedi ments arise from iii. Aids or Subsidiaries to Thinking,— tlirouffh ' The Mind. ' _. The Body, j 3. Kxternal Cir- ^ cum stances. 1. The Acquisition of Knowledge. 2. The Comnmnication of Knowledge, &c. The fourth and fifth questions of the Introduction would now fall to be considered, — viz. What is the His- tory, and what is the Bibliography, of Logic 1 Were I writing a book, and not gi^^g a course of Lectures upon Logic, I would certainly consider these questions in the introduction to the science, but I would do this with the admonition that beginners should pass these over, and make themselves first of all familiar with the doctrines of which the science is itself the comple- ment. For why 1 The history of a science is a narra- tive of the order in which its several parts have been developed, and of the contributions which have been made to it by different cultivators ; but such a narra- tive necessarily supposes a previous knowledge of the contents of the science, — a knowledge which is iden- It is, a See further Appendix III. — Ed. tical with a knowledge of the science itself. LECTURES ON LOGIC. 69 therefore, evident that a history of Logic can only be lect, IV. proposed with advantage to those who are already in some degree familiar with Logic itself; and as, in a course like the present, I am bound to presume that you are not as yet conversant with the science, it follows that such a history cannot with any propriety be attempted in the commencement, but only towards the conclusion, of the Lectures. In regard to the fifth question, — What is the Biblio- v. The grajDhy or Literature of Logic ? — the same is true, in graphy of so far as a knowledge of the books written upon a ''^"'' science is correlative to a knowledge of its history. At the same time nothing could be more unprofitable, than for me to recite to you a long series of works to which you have not access, by authors of whom you probably never heard, often in languages which few of you understand. In the present stage of your studies, it is not requisite that you should know of many books, but that you should read attentively a few ; — non multa sed multum. — I shall, therefore, ad- journ, at least, the consideration of the question, — What in general are the principal books on the science of Logic 1 — simply recommending to you a few not absolutely the best, but such as you can most easily procure, such as are in languages which most of you can read, and which are of such a character as may be studied with most general advantage. Of works in our own language, as those most acces- General sible and most intelligible to all, there are unfortu- worC on nately hardly any which I can recommend to you as "^"'' exhibiting the doctrines of Logic, either in purity or completeness. The Logics of Watts, of Duncan, and others, are worth reading as books, but not as books upon Logic. The Elements of Logic by Dr Whately IV. rO LECTURES OX LOOIC. LEcr. is, upon tho wlioK', the one best entitled to your atten- tion, thougli it is erroneous in various respects, and imperfect in more. The abridgment of tliis work by Hinds contains wliat of the original is most worthy of study, in the commencement of a logical education. In French, there arc sundry works deserving of your attention, (Damiron," Delarivitjre) ; ^ but the only one which I would at present earnestly recommend to your study, is the celebrated Port Royal Art of Think- ing, — L'Art de Pcnser, — an anonymous work, but the authors of which were the two distinguished Jan- senists, Arnauld and Nicole. It has been frequently reprinted ; and there is a recent stereotyped edition, by Hachette of Paris, which can easily be procured. There are more than one translation of the w^ork into Latin, and at least two English versions, both bad.*^ In Latin there is a very elegant compend of Logic by the late illustrious Daniel Wyttenbach of Leyden. Besides the Dutch editions, which are handsome, there is a cheap reprint published by Professor Maass of Halle, who has, however, ventured on the unwarrant- able liberty of silently altering the text, besides omit- ting what he did not consider as absolutely indispen- sable for a text-book. This work can be easily procured. There is also in Latin a system of Logic by Genovesi, under the title, Genuensis Ars Logico-cr^itica. This work is, however, extremely rare even in Italy, and it was many years before I w^as able to procure a copy. There was an edition of this work published in Ger- o Cours dc Philosophic, t. iv. ; Lo- Mr Baynes, Edinburgh, 1850 ; 2d f/ique, Paris, 1837. — Ed. edition, 1851. In the Introduction j3 Logiquc Classique, Paris, 1829. — to this version will be found an ac- Ed. count of the various editions and y A third and far sujjerior trans- translations of the work. — Ed. lation has subsequently appeared by LECTURES ON LOGIC. 7l many in 1760 at Augsburg, but the impression seems lect. to have been small, for it also is out of print. The - Italian Logic of Genovesi has, however, been repeat- edly reprinted, and this, with the valuable additions of Romagnosi, is easily obtained. Of the older writers on Logic in Latin, the one I would principally recom- mend to you is Burgersdyk, — Burgersdicius. His InstitiUio7ies Logicce is not a rare work, though, as there are no recent editions, it is not always without trouble to be obtained." o. See Appendix IV. foi- note of the Author to his class. — Ed. treatises on Logic, recommended by LECTUKKS ON LOdlC. LECTUIIE V. PURE LOGIC. TART I.— STOICIIEIOLOGY. SECTION I. NOETIC. — ON THE FUNDAMENTAL LAWS OP THOUGHT THEIR CONTENTS AND HISTORY. LECT. Having terminated our consideration of the various '- — questions of wJiich the Introduction to Logic is com- ro^^'""*^ posed, we proceed to the doctrines which make up the science itself, and commence the first great division of Pure Logic — that which treats of its elementary or constituent processes, — Stoicheiology. But Stoicheio- logy was again divided into two parts, — into a part which considered the Fundamental Laws of Thought in general, and into a part which considered these laws as applied to and regulating the special function of Thought in its various gradations of Conception, Judg- ment, and Reasoning. The title, therefore, of the part of Logic on which we are about to enter is, — Pure Logic — Part I. Stoiclieiology — Section I. Noetic — On the Fundamental Laivs of Thought. Tiic charac- Bcforc, liowcvcr, dcsccuding to the consideration of ter of . . Thought in these laws, it is necessary to make one or two pre- liminary statements touching the character of that thought of which they are the necessary conditions ; and, on this point, I give, in the first place, the follow- ing paragraph : — LECTURES ON LOGIC. 73 H X, Logic considers Thought, not as the oper- lect. ation of thinking, but as its product ; it does not '- — treat of Conception, Judgment, and Reasoning, but of Concepts, Judgments, and Reasonings. I have already endeavoured to ffive you a general Tiiought as 1 11 PI- 177^? the object knowledge oi what is meant by tliouglit. You are of Logic. aware that this term is, in relation to Logic, employed in its strictest and most limited signification, — viz. as the act or product of the Discursive Faculty, or Fa- culty of Relations ; but it is now proper to consider, somewhat more closely, the determinate nature of this process, and the special point of view in which it is regarded by the logician. In an act of thinking, there are three things which The subject, 1 . . . . . o rni • 1 form, and we can discrimmate m consciousness, — 1 , Ihere is the matter of thinking subject, that is, the mind or ego, which exerts or manifests the thought; 2°, There is the object about which we think, which is called the matter of thought ; and, 3°, There is a relation be- tween subject and object of which we are conscious, — a relation always manifested in some determinate mode or manner, — this is th^form of thought. Now Thought as of these three. Logic does not consider either the first respectively or the second. It takes no account, at least no direct logy andof account, of the real subject, or of the real object, of thought, but is limited exclusively to the form of thought. This has been already stated. But, again, this form of thought is considered by Logic only in a certain aspect. The form of thought may be viewed on two sides or in two relations. It holds, as has been said, a relation both to its subject and to its object, and it may accordingly be viewed either in the one of these relations or in the other. In so far as the form 74 1. Kerr RES on Looir. i.KcT. ,){" thouixht is considoriMl in reference to the tliiukino; V. miiul, to the mind by wliicli it is exerted, it is considered as an act, or operation, or energy ; and in this relation it belongs to riuxMiomenal Psychology. Whereas, in so far as this form is considered in refer- ence to what thought is about, it is considered as the })roduct of such an act, and, in this relation, it be- longs to Logic. Thus Phronomenal Psychology treats of thought proper as conception, judgment, reasoning; Logic, or the Nomology of the Understanding, treats of thought proper as a concept, as a judgment, as a reasoning. Whately, I have already shown you, among other errors in his determination of the object- matter of Logic, confounds or reverses this ; for he proposes to Logic, not thought considered as a product, but reasoning alone ; and that, too, considered as a producing operation. He thus confounds Logic with Phsenomenal Psychology. Be it, therefore, observed, that Logic, in treating of the formal laws of thought, treats of these in refer- ence to thought considered as a product, that is, as a concept, a judgment, a reasoning ; whereas Psy- chology, as the Phsenomenology of mind, considers thought as the producing act, that is, as conception, judgment, reasoning. (You here see, by the way, the utility of distinguishing concept and conception. It is unfortunate that we cannot also distinguish more precisely judgment and reasoning as pro- ducing acts, from a judgment and a reasoning as products.) Par. XL H XL Thought, as the knowledge of one thing mediate and in rclation to auothcr, is a mediate and complex complex . . cognition. COgUltlOn. LECTURES ON LOGIC. 75 The distinctive peculiarity of thinking in general lect. is, that it involves the cognition of one thing by the cognition of another. All thinking is, therefore, a tion. mediate cognition; and is thus distinguished from our knowledge in perception, external and internal, and imagination ; in both of which acts we are immediately cognitive of the object, external or in- ternal, presented in the one, and of the object, external or internal, represented in the other. In the Presenta- tive and Eepresentative Faculties, our knowledge is of something considered directly and in itself; in thought, on the contrary, we know one object only through the knowledge of another. Thus in perception, of either kind, and in imagination, the object known is always a single determinate object ; whereas in thought, — in thought proper, as one object is only known through another, there must always be a plurality of objects in every single thought. Let us take an example of this, in regard to the simplest act of thought. When I see an individual, — say Bucephalus or Highflyer, or when I represent him in imagination, I have a direct and immediate apprehension of a certain object in and through itself, without reference to aught else. But when I pronounce the term Horse, I am unable either to perceive in nature, or to repre- sent in imagination, any one determinate object cor- responding to the word. I obtain the notion corre- sponding to this word, only as the result of a com- parison of many perceptions or imaginations of Bucephalus, Highflyer, Dobbin, and other indivi- dual horses ; it, therefore, contains many represen- tations under it, has reference to many objects, out of relation to which it cannot possibly be realised in thought ; and it is in consequence of this necessity of 70 LECTUKKS ON LOGIC. LErr. ivj>ivsontin<]j (potent iall\ at least) a plurality of in- iliviilual olijt'i'ts uikKt {\\c notion //<*/>•(•, that it obtains till' (Icnoniination concept, that is, something taken up or ap}»relKMuleil in connection with something else. This, however, requires ;i further explication. When we j)orforni an act of thought, of positive thought, this is done by thinking something, and we can think anything only by thinking it as existing ; while, again, we cannot think a thing to exist except in certain determinate modes of existence. On the other hand, when we perform an act of negative thought, this is done by thinking something as not existing in this or that determinate mode, and when we think it as existing in no determinate mode, we cease to think it at all ; it becomes a nothing, a logical nonentity, {non-ens logicuni). It being thus understood, that thought can only be realised by thinking something ; it being further understood that this something, as it is thought, must be thought as existing ; and it being still further understood, that we can think a thing as existing only by thinking it as existing in this, that, and the other determinate manner of existence, and that whenever we cease to think something, something existing, some- thinor existino: in a determinate manner of existence, we cease to think at all ; this, I say, being under- stood, it is here proper to make you, once for all, acquainted with the various terms by which logicians designate the modes or manners of cogitable existence. I shall, therefore, comprise these in the following para- graph : — Par. XII. IF XII. When we think a thing, this is done by The various ... i ^ • i terms by coucciving it as ptosscsscd of certam modes of LECTURES ON LOGIC. 77 being, or qualities, and the sum of tliese qualities lect. constitutes its concept or notion, {vo-qfia, euvoia, eVtVota, conceptum, conceptiis, notio). As these modeViT qualities or modes, [TTOLOTiqreq, qualitates, modi), exfSe are only identified with the thing by a mental nlted?'^" attribution, they are called attributes, {Karyjyo- povixeva, attrihuta) ; as it is only in or through them that we say or enounce aught of a thing, they are called predicates, 2^^'^dicables, and predicaments, or categories, these words being here used in their more extensive signification, (Xeyo/xe^'a Trepi, KaTiqyopiai, Kariqyoprjixara, Karr)- yopo-ufxeua, prwdicata, p>rcedicabilia, prcedica- menta) ; as it is only in and through them that we recognise a thing for what it is, they are called notes, signs, marks, characters, {notes, signa, characteres, discrimina) ; finally, as it is only in and through them that we become aware that a thing is possessed of a peculiar and determinate existence, they are called properties, differences, determiyiations, {prop^ietates, determinationes). As consequent on, or resulting from, the exist- ence of a thing, they have likewise obtained the name of consequents, (eTrofxeva, conseque^itia, &c.) What in reality has no qualities, has no existence in thought, — it is a logical nonentity ; hence, e converse, the scholastic aphorism, — non-entis nulla sunt prcedicata. What, again, has no qualities attributed to it, though attributable, is said to be indete^^mined, {ddiopLo-Tov, indeter- minatum) ; it is only a possible object of thought." a [Schulze, Lofjlk, § 13. Rosling, Ulm, 1826. Cf. Krug, LoyiJc, § 10. 63. ] [ Die Lchren der rcincn Logik, — Ed. ] 78 l.KCTrUKS UN LOtJlC. LKAT. V. Kxplici- tiou. Wlial i.t in vol vol iu iliinkiug ail objoct. The attri- bution in- volved in thought is regulated by laws. What is meant by a law as applicable to free in- telligences. Tliis paraoTn})!!, Nvliidi 1 liavo clictalecl that you ini^lit 1)0 mailo once i'ov all iicquaintcd "with the ri'lativo terms in use amoug logicians, requires but little explanation. T may state, however, that tlie mind only thinks an object by separating it from others, that is, by marking it out or characterising it ; and iu so far as it does this, it encloses it within cer- tain fixed limits, that is, determines it. But if this discriminative act be expressed in words, I predicate the marks, notes, characters, or determinations of the thing ; and if, again, these be comprehended in one total thought, they constitute its concept or notion. If, for example, I think of Socrates as son of Sojyh- roniscus, as Athenian, as philosopher, as fug-nosed, these are only so many characters, limitations, or de- terminations, which I predicate of Socrates, which distinguish him from all other men, and together make up my notion or concept of him. But as thought, in all its gradations of conception, judgment, and reasoning, is only realised by the attri- bution of certain qualities or characters to the objects of, or about, which we think, so this attribution is regulated by laws, which render a great part of this process absolutely necessary^ But when I speak of laws and of their absolute necessity in relation to thought, you must not suppose that these laws and that necessity are the same in the world of mind as in the world of matter. For free intelligences, a law is an ideal necessity given in the form of a precept, which we ought to follow, but wliich we may also violate if we please ; whereas, for the existences which constitute the universe of nature, a law is only another name for those causes which operate blindly and uni- versally in producing certain inevitable results. By LECTURES ON LOGIC. 79 laio of thought, or by logical necessity, we do not, there- lect. fore, mean a physical law, such as the law of gravi- - — '- — tation, but a general precept which we are able cer- tainly to violate, but which if we do not obey, our whole process of thinking is suicidal or absolutely null. These laws are, consequently, the primary con- ditions of the possibility of valid thought, and as the whole of Pure Logic is only an articulate development of the various modes in which they are applied, their consideration in general constitutes the first chapter in an orderly system of the science. Now, in explain- order of ing to you this subject, the method I shall pursue istTon'oUho the following : — I shall, first of all, state in general tariawnt" the number and significance of the laws as commonly ' °"^ ^'' received ; I shall then more particularly consider each of these by itself and in relation to the others ; then detail to you their history ; and, finally, state to you my own views in regard to their deduction, number, and arrangement. H XIII. The Fundamental Laws of Thought Par. xin. or the conditions of the thinkable, as commonly tarLaws'^of received, are four : — 1. The Law of Identity ; 2. ''"^' " The Law of Contradiction ; 3. The Law of Exclu- sion or of Excluded Middle ; and, 4. The Law of Eeason and Consequent, or of Sufficient Keason.* Of these in their order. H XIV. The principle of Identity (princiimmi Par. xiv. Identitatis) expresses the relation of total same- iduutuy. ness in which a concept stands to all, and the relation of partial sameness in which it stands o See Ajipundix V. — Ed. 80 LECTURES ON LO^IO. LKiT. to cat'li, of its constituent diameters. In other \' tion ^vo^ls, it declares tlie impossibility of thinking the concept aiul its characters as reciprocally unlike. It is expressed in the formula A is A, or A^^A ; and by A is denoted every logical thing, every product of our thinking faculty, — coucept, judgment, reasoning, &c." F.xpiica- The principle of Identity is an application of the principle of the absolute equivalence of a whole and of all its parts taken together, to the thinking of a thinf^ l)y the attribution of constituent cjualitics or characters. The concept of the thing is a whole, the characters are the parts of that whole./^ This law may, therefore, be also thus enounced, — Everything is equal to itself; for in a logical relation the thing and its concept coincide ; as, in Logic, we abstract alto- gether from the reality of the thing which the concept represents. It is, therefore, the same whether we say that the concept is equal to all its characters, or that the thing is equal to itself."^ The law has, likewise, been expressed by the for- ijiula, — In the predicate, the ivhole is contained ex- lolicitly, ivhich in the subject is contained imj)licithj. It is also involved in the axiom, — Nota notce est nota rei iiosius} Its logical The logical importance of the law of Identity lies -Theprin- iu this, — that it is the principle of all logical afhrma- lo^icauffir- tion aud definition. An example or two may be ration'!'' given to illustrate this. This iiius- 1 . In a concept, which we may call Z, the charac- trated. a [Schulze, Logik, § 17. Gerlach )3 See Schulze, Lofjilc, p. 32-3.— Ed. Lorjik, § .37.] Cf. Krug, Lorjik, § 17. y See Krug, Logik, p. 40.— Ed. Ed. S See Kant, Logik, p. 40. — Ed. LECTURES ON LOGIC. 81 ters a, h, and c are thouejht as its constituents ; con- lect, sequently, the concept, as a unity, is equal to the cha- '. — racters taken together, — Z ={a + h + c). If the former be affirmed, so also is the latter ; therefore, Z being (a + h + c) is a, is h, is c. To take a concrete example, — The concept man is a complement made up of the characters, 1°, substance, 2°, material, 3°, organised, 4°, animated, 5°, rational, 6°, of this earth ; in other words, man is substantial, is material, is organised, is animated, is rational, is of this earth. Being, as en- tering into every attribution, may be discharged as affording no distinction. 2. Again, suppose that, in the example given, the character a is made up of the characters I, m, n, it follows, by the same law of Identity, that Z = a = (l, m, n) is I, is on, is n. The concept ma7i contains in it the character animal, and the character animal contains in it the characters corporeal, oj^ganised, living, &c. The second law is the principle of Contradiction or Non-Contradiction, in relation to which I dictate the following paragraph : — H XV. When an object is determined by the Par. xy. affirmation of a certain character, this object tradiction. cannot be thought to be the same when such character is denied of it. The impossibility of this is enounced in what is called the principle of Contradiction, {prmcijnum Contradictionis seu Repugnantice) . Assertions concerning a thing are mutually contradictory, when the one asserts that the thing possesses the character which the other asserts that it does not. This law is logically expressed in the formula, — What is VOL, I. F 82 LECTURES ON LOnil". i.v.cY. contnulirtory is uiitliiukablo. yl=y/o/-/l=0, or V. "^ — .1— .1-0. Its proper Now, in the first place, in regard to the name of til is law, it may be observed that, as it enjoins the absence of contradiction as the indispensable condi- tion of thought, it ought to be called, not the Law of Contradiction, but the Law of Non-Contradiction, or of jwn-rejnignantia."- How This law has frequently been enounced in the for- mula, — It is imj^ossihle that the same thing can at once he and not he; but this is exposed to sundry objections. It is vague and, therefore, useless. It does not indicate whether a real or a notional existence is meant ; and if it mean the former, then is it not a logical but a metaphysical axiom. But even as a metaphysical axiom it is imperfect, for to the expres- sion at once {simiil) must be added, — m the same place, in the same respect, &c.^ This law has likewise been expressed by the for- mula, — Contradictory attributes cannot he united in one act of consciousness. But this also is obnoxious to objection. For a judgment expresses as good a unity of consciousness as a concept. But when I judge that round and square are contradictory attri- butes, there are found in this judgment contradictory attributes, but yet a unity of consciousness. The for- mula is, therefore, vaguely and inaccurately exj^ressed. The prin- ' The logical importance of this law lies in its being logical nega- thc principle of all logical negation and distinction. distinction. The law of Identity and the law of Contradiction are co-ordinate and reciprocally relative, and neither a Compare Krug, Logik, § 18. — Kritih d. r. V., p. 134. ed. Rosen- Ed. krauz. — Ed. )8 Compare the criticism of Kant, LECTURES ON LOGIC. 83 can be educed as second from the other as first ; for lect. V, in every such attempt at derivation, the supposed secondary law is, in fact, always necessarily presup- posed.*^ They are, in fact, one and the same law, — differing only by a positive and negative expression. In relation to the third law, take the following paragraph : — *[[ XVI. The principle of Excluded Third or Par. xvl Middle — viz. between two contradictories, {prin- Excluded cipium Exclusi Medii vel Tertii), enounces that condition of thought, which compels us, of two repugnant notions, which cannot both coexist, to think either the one or the other as existing. Hence arises the general axiom, — Of contradic- tory attributions, we can only affirm one of a thing; and if one be explicitly affirmed, the other is implicitly denied. A either is or is not. A either is or is not B.^ By the laws of Identity and Contradiction, I am Logical warranted to conclude from the truth of one contra- of this iaw. dictory proposition to the falsehood of the other, and by the law of Excluded Middle, I am warranted to conclude from the falsehood of one contradictory pro- position to the truth of the other. And in this lies the peculiar force and import of this last principle. For the logical significance of the law of Excluded Middle consists in this, that it limits or shuts in the sphere of the thinkable in relation to affirmation ; for it determines, that, of the two forms given in the laws of Identity and Contradiction, and by these laws a This is shown more in detail by § 23. — Ed. Wo^hsMcr, Anfangsgri'iTide derLo(jik, /3 See Schulze, Loglk, Jj 19. — En. 84 LKCTURES ON LOGIC. i.K.rr. V. Tlio princi- vlo of Dis- jiiui-iivo Judginouti. atlirmod as tlioso exclusively possible, the one or the other must he allirmed as necessary. The law of Excludecl IMidJle is the principle of Disjunctive Judgments, that is, of judgments in which a i^lurality of judgments arc contained, and which stand in such a reciprocal relation that the affirmation of one is the denial of the other. I now oo on to the fourth Law. Par. XVII. Law of Surticieut Reason, or of licaaou and Conse- quent. H X\'I1. The thinking of an object, as actually characterised by positive or by negative attributes, is not left to the caprice of Understanding, — the Faculty of Thought ; but that faculty must be necessitated to this or that determinate act of thinking by a knowledge of something different from, and independent of, the process of thinking itself. This condition of our understanding is expressed by the law, as it is called, of Sufficient Reason, (^principium Rationis Sujfficientis); but it is more properly denominated the law of Reason and Consequent, {jprincipium Rationis et Conse- cutionis). That knowledge by which the mind is necessitated to affirm or posit something else, is called the logical reason, ground, or antecedent; that something else which the mind is necessi- tated to affirm or posit, is called the logical con- sequent ; and the relation between the reason and consequent, is called the logical connection, or consequence. This law is expressed in the for- mula, — Infer nothing without a ground or reason." Relations Thc relations between Reason and Consequent, when Reason and comprcliended in a pure thought, are the following : — Consequent. a See Schulze, Loyik, § 19, and Krug, Logik, § 20. -Ed. LECTURES ON LOGIC. 85 1. When areason is explicitly or implicitly given, then lect. V. there must exist a consequent ; and, vice versa, when a consequent is given, there must also exist a reason. 2. Where there is no reason, there can be no conse- quent ; and, vice versa, where there is no consequent, (either implicitly or explicitly,) there can be no reason. That is, the concepts of reason and of consequent, as reciprocally relative, involve and suppose each other. The logical significance of the law of Keason and Logical sig- Consequent lies in this, — That in virtue of it, thought ulis'^iaw. " is constituted into a series of acts all indissolubly con- nected ; each necessarily inferring the other. Thus it is that the distinction and opposition of possible, actual, and necessary matter, which has been introduced into Logic, is a doctrine wholly extraneous to this science. I may observe that " Reason is something different Reason and from Cause, and Consequent something different from and Cause ' -n/Y> 11 ^ m ' p ^ '^^'^ Effect. -Ciiiect ; though cause and enect, m so lar as they are conceived in thought, stand to each other in the rela- tion of reason and consequent. Cause is thus thought of as a real object, which affords the reason of the existence of another real object, the effect; and eff'ect is thought of as a real object, which is the consequent of another real object, the cause. Accordingly, every cause is recognised in thought as a reason, and every efiect is recognised in thought as a consequent ; but the converse is not true, that every reason is really considered a cause, and every consequent really con- sidered an effect. We must, therefore, carefully dis- tinguish mere reason and mere consequent, that is, ideal or logical reason and consequent, from the reason which is a cause and the consequent which is an effect, that is, real or metaphysical reason and consequent. "The expression logical reason and consequent refers 80 LECTUKKS ON LOGIC. LECT. to the moiv synthesis of thoughts; whereas the ex - — — — prcssion mctaphijttical reason and consequent denotes Moi«i.h>TH- the reiil eonnection of existences. Hence the axiom aaau.u«.- ot (. ausality, as a metaphysical principle, is essentially ''"*^ ' Jiireront from the axiom of Reason and Consequent, as a logical principle. Both, however, are frequently confounded with each other ; and the law of Keasou and Consequent, indeed, formerly found its place in the systems of Metaphysic, while it was not, at least tTcncniiiiy explicitly, considered in those of Logic. The two ofthctcnns ^ 7- . T 7- • 7 1 -, t'ondition terms condition and conditioned happily express at .liiiontvi. once the relations both oi reason and consequent, and of cause and effect. A condition is a thing which determines, [negatively at least,] the existence of another ; the conditioned is a thing whose existence is determined in and by another. If used in an ideal or lomcal sio-nification, condition and conditioned import only the reason in conjunction with its con- sequent ; if used in a real or metaphysical sense, they express the cause in connection with its effect." * Histon- of I have now, in the prosecution of our inquiry into mentofthe thc fundamental laws of logical thinking, to say a few tai Laws of words iu regard to their History, — their history being ""^ " the narration of the order in which, and of the philo- sophers by whom, they were articulately developed. . a Kmg, Lofjik, pp. 62, 63. This work, p. 603 : " The principle of exposition of the law of Reason and Sufficient Reason should be excluded Consequent does not represent the from Logic. For, inasmuch as this Author's latest view. In a note to principle is not material, it is only a the Discussions, p. 160, (where a derivation of the three formal laws ; similar doctrine had been main- and inasmuch as it is material, it tained in the article as originally coincides with the principle of C'au- published), he says: "The Logical sality, and is extra-logical." The relation of lieoson and Consequent, Laws of Thought, properly so called, as more than a mere corollary of the are thus reduced to three, — those of law of Non-confrudiclton in its three Identity, Contradiction, and Excluded phases, is, I am confident of proving, Middle. — Ed. erroneous." And again, in the same LECTURES ON LOGIC. 87 Of the first three laws, which, from their intimate lect. V. cognation, may not unreasonably be regarded as only the three sides or phases of a single law, the law of identity ° Identity, which stands first in the order of nature, was oped fn the indeed that last developed in the order of time ; the thne^ "" axioms of Contradiction and of Excluded Middle hav- ing been long enounced, ere that of Identity had been discriminated and raised to the rank of a co-ordinate principle. I shall not, therefore, now follow the order in which I detailed to you these laws, but the order in which they were chronologically generalised. The principles of Contradiction and of Excluded The prin- Middle can both be traced back to Plato, by whom contradic- they were enounced and frequently applied ; though Excluded it was not tiU long after, that either of them obtained be traced a distinctive appellation. To take the principle ofpiato. Contradiction first. This law Plato frequently em- ploys, but the most remarkable passages are found in the Phcedo, in the Sophista, and in the fourth and seventh books of the Republic."- This law was, however, more distinctively and em- Law of phatically enounced by Aristotle. In one place, ^ he tionempha- says : "It is manifest that no one can conceive to enounced by himself that the same thing can at once be and not be, for thus he would hold repugnant opinions, and subvert the reality of truth. Wherefore, all who at- tempt to demonstrate, reduce everything to this as the ultimate doctrine ; for this is by nature the principle of all other axioms." And in several passages of his Metaj)hysics,y in his Prior Analytics,^ and in his Posterior Analytics,^ he observes that "some had a See Phcedo, p. 103 ; Sophista, p. 7 L. iii. c. A. 252 ; neimblic, iv. p. 436 ; vii. p. 5 L. ii. c. 2. 525.— Ed. e L. i. c. 2. ^ Mctaph., L. iii. (iv.) c. 3. 88 LECTURES ON LOGIC. LK.rr. attcmptoil to ilomoiistrate this principle, — an attempt ' wliii'li bt'traved an ignorance of tliose things whereof we ouujht to require a demonstration, and of those thino\«< whereof we ought not : for it is impossible to demonstrate everything; as in this case, we must regress and regress to infinity, and all demonstration would, on that supposition, be impossible." With the Following Aristotle, the Peripatetics established this ti.o hi,:hcst' law as the highest principle of knowledge. From the l^nrwk-.i£re. Greek Aristotelians it obtained the name by which it naiue from has subscqucutly been denominated, the princijyle, or Arieiotoi- JcnCjOraxiomfOf contradiction, {d^Lojfxa rrj^ di/Tt^acreaj?)- This name, at least," is found in the Commentaries of Ammonius and Philoponus, where it is said to be "the criterion which divides truth from falsehood The School- throughout the universe of existence." « The School- rez"'"^''* men, in general, taught the same doctrine ; and Suarez even says, that the law of contradiction holds the same supremacy among the principles of know- ledge which the Deity does among the principles of existence.^ Controver- Aftcr thc declinc of the Aristotelian philosophy, [ng the'''^''' many controversies arose touching the truth, and still cEL*t^?of more touching the primitive or axiomatic character, this law. ^£ ^j^^g 2^^^ Some maintained that it was indemon- a For the name, see Ammonius, Staipt? rh yf/ev5os koI ttji/ aKridfiav. In Dc Intoyret., p. 153 b, ed. Aid. In Anal. Post., L. i. c. xi. f. 30b.— Venet. 1546. Philoponus, In Anal. Ed. [Cf. Augustinus Niphus Sues- Pr., p. 13 b, 38 b, ed. Venet. 1536; sanus, In Anal. Post., p. 88, ed. In Anal. Post., p. 30 b, ed. Aid. Paris, 1540.] Venet. 1534. The language quoted ^ See [Alstedius, Artiuni Lihcra- in the text is nearly a translation of Hum Systema (8vo), p. 174 ; " Cog- Ammonius, In Categ. , p. 140a : 'H fxtv nitio a priori est principiorum ; inter ■yap Kardcpoffis Kol aTr6cpa(ris ad iirl qute agmen ducit hoc, impossihile est irdvTwv Twv uvToiv Ka.\ p.r) ofTwv Siatpt'i idem esse ct non esse. . . . Consuls Th a\v6es koI rh \pfvSos. Ammonius Mctaph. Suarezii : ' Hoc, inquam, is followed by Philoponu?, who says : tenet primatum inter principia cog- To 5e TTis a.vTinlinato dignity with (lie huv of Contradiction, but, against Aristotle, he maintains, that the jn-inciple of Identity, and not the principle of Contradiction, is the one absolutely first. The for- mula in which Andreas expressed it was, Ens est ens. Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools : thoufifh there were also found some who asserted to the law of Excluded Middle this supreme Leibnitz, rank." Leibnitz, as I have said, did not ahvays dis- tinguish the principles of Identity and of Contradic- Woif. tion. By Wolf the former was styled the principle of Certainty, {principium Certitudinis) ; ^ but he, no more than Leil^nitz himself, sufficiently discriminated betw^een it and the law of Contradiction. This was, Baum- how^ever, done by Baumgarten, another distinguished gartcu. follower of LeibnitZj'y and from him it received the name of the principle of Position, that is, of Affirma- tion or Identity, [principium Positionis sive Identi- tatis), — the name by which it is now universally known. This principle has found greater favour in the eyes of the absolutist philosophers, than those of Fichte and Coutradiction and Excluded Middle. By Fichte and ' *" '°^" Schelling it has been placed as the primary principle Hegel. of all philosophy.^ Hegel alone subjects it, along with the other laws of thought, to a rigid but fallaci- ous criticism ; and rejects it along with them as be- a [AJex. de Ales, In Arist. Me- eluded Middle, de quovis affirmatio taph., iv. t. 9.] Compare Suarez, vel nqiatio. — Ed. D'lSp. Mctnjih., Disp. iii. § 3. Alex- /3 Onlologia, §§ 55, 288.— Ed. ander professes to agree with Aris- y Metaphijsica, § 11, —Ed. totle in giving the first place to the S See Fichte, Grundlage der ge- principle of Contradiction, but, in sammten Wissenschaftslehre, § L fact, he identifies it with that of Ex- Schelling, Vom Ich, § 7. — Ed. LECTURES ON LOGIC. 93 longing to that lower sphere of knowledge, which is lect. conversant only with the relative and finite." The fourth law, that of Reason and Consequent, Law of which stands apart by itself from the other three, was, consequent. like the laws of Contradiction and Excluded Middle, recognised bv Plato. /^ He lays it down as a postu- Recognised , f. "^ ,. , . . ^ J by Plato late 01 reason, to admit nothmg without a cause ; and and aiIs- the same is frequently done by his scholar Aristotle.'^ Both, however, in reference to this principle, employ the ambiguous term cause, {air la, alnov) . Aristotle, indeed, distinguishes the law of Reason, as the ideal principle '^py\ "i? of knowledge, (apx^ ''"^5 yvwcrecu?, principium cognos- '^pxn rv-: cendi), from the real principle of production, {apx^ tV'^ yevecreo)?, principium Jiendi, principium essendi).^ By Cicero the axiom of reason and consequent was, cicero. in like manner, comprehended under the formula, nihil sine causa,^ — a formula adopted by the school- The School- men ; although they, after Aristotle, distinguished under it the ratio essendi, and the ratio cognoscendi. In modern times, the attention of philosophers was Leibnitz called to this law by Leibnitz, who, on the two prin- tion to Law • 1 /•-r» -t f /~i T • n 111°^ Sufficient ciples of Reason and of Contradiction, founded the Reason, whole edifice of his philosophy.^ Under the latter law, as I have mentioned, he comprehended, however, the principle of Identity ; and in the former he did not sufficiently discriminate, in terms, the law of Cau- sality, as a real principle, from the law of Reason, properly so called, as a formal or ideal principle. To this axiom he gave various denominations, — now call- ing it the principle of Determining Reason, now the a See above, p. 90 note a.— Ed. 5 Mctaph., iv. (v.) 1. — Ed. )3 Philcbus, p. 26.— Ed. e De Divinatioiie, ii. c. 28.— Ed. y^. g., Anal. Post., u.\&; Fhys., ^ See TlUodicee, % 4A. Monadolo- ii. .3 ; Metaph., i. 1, 3; RM., ii. 23. cjie, ^ 31, 32.— Ed. —Ed. 94 l,K»TirvK.>< ON lAlOU". i.Krr. principle of Siifticioiit Keasoii, and now the principle '■ — of Convenience or Aoreement, (convenientia) ; making it, in its real relation, the ground of all existence, in its ideal, the ground of all positive knowledge. On this subject there was a celebrated controversy be- tween Leibnitz and Dr Samuel Clarke, — a controversy on this, as on other points, eminently worthy of your study. The documents in which this controversy is contained, were published in the English edition under the title, A collection of Papers which passed hetioeen the late learned Mr Leibnitz and Dr Clarke, in the years 1715 and 1716, relating to the Principles of Natural Philosophy and Religion, London, 1717." Wolf. Wolf, the most distinguished follower of Leibnitz, employs the formula, — " Nothing is without a suffi- cient reason why it is, rather than why it is not; that is, if anything is supposed to be {ponitur esse) something also must be supposed, whence it may be understood why the same is rather than is not." ^ He blames the schoolmen for confusing reason (ratio) with cause (causa) : but his censure equally applies to his master Leibnitz as to them and Aristotle ; for all of these philosophers, though they did not confound the two principles, employed ambiguous terms to denote them. Discussion The Leibnitian doctrine of the universality of the thfLe^^ law of Sufficient Reason, both as a principle of exist- nitian doctrine of cncc and of thought, excited much discussion among suffiden" the philosophers, more particularly of Germany. In *^°' the earlier half of the last century, some controverted a Seeespecially, Leibnitz's Second Reason as the foundation of natural Letter, p. 20, in which the principle philosophy. — Ed. of Contradiction or Identity is as- $ See Fischer's Loyik, [§ 59, p. .38, sumed as the foundation of all ma- ed. 1838. Compare Wolf, Ontologia, thematics, and that of Sufficient §§ 70, 7L— Ed.] V. LECTUHES ON LOGIC. 95 the validity of the principle, others attempted to re- lect, strict it.* Among other arguments, it was alleged, by the advocates of the former opinion, if the principle be admitted, that everything must have a sufficient reason why it is, rather than why it is not, — on this hypothesis, error itself will have such a reason, and, therefore, must cease forthwith to be error. ^^ Many philosophers, as Wolf and Baumgarten, endeavoured to demonstrate this principle by the principle of Contradiction ; while others, with better success, showed that all such demonstrations were illogical.'^ In the more recent systems of philosophy, the uni- versality and necessity of the axiom of Eeason has, with other logical laws, been controverted and rejected by speculators on the absolute.^ a As Feuerlin and Darjes. See P. i. p. 57] ; compare Lectures on Bachmann, Logik, p. 56, Leipsig, Metaphysics, ii. pp. 396, 397, notes. 1828; Cf. Degerando, Hist. Comp. —Ed. des Syst. de Phil., t. ii. p. 145, ed. 5 [On principle of Double Nega- 1804. — Ed. tion as another law of Thought, see |8 See Bachmann, Logik, p. 56. Fries, Logik, § 41, p. 190 ; Calker, With the foregoing history of the Dcnklehre odcr Logik und Dialcklik, laws of Thought compare the same § 165, p. 453 ; Beneke, Lehrhuch dcr author, Logik, § 18-31.— Ed. Logik, § 64, p. 41.] 7 [Kiesewetter, Allgemeine Logik, 96 LECTURES ON LOGIC. LECTURE V I. STOIC HEIOLOGY. SECTION I.— NOETIC. THE FUNDAMENTAL LAWS OF THOUGHT — THEIR CLASSIFICATION AND IMPORT. LECT. Having concluded the Introductory Questions, we '. — entered, in our last Lecture, upon our science itself. ^jcapitu a- rpj^^ ^^^ ^^^ ^^ Purc Logic is tlic Doctriuc of Ele- ments, or that which considers the conditions of mere or possible thinking. These elements are of two kinds, — they are either the fundamental laws of thought as regulating its necessary products, or they are the pro- ducts themselves as regulated by those laws. The fundamental laws are four in number, — the law of Identity, the law of Contradiction, the law of Ex- cluded Middle, the law of Reason and Consequent." The products of thought are three, — 1°, Concepts or Notions ; 2°, Judgments ; and 3°, Reasonings. In our last Lecture, we considered the first of these two parts of the doctrine of elements, and I went through the general explanation of the contents and import of the four laws, and their history. AVithout recapitulating what was then stated, I shall now proceed to certain general observations, which may be suggested in rela- tion to the four laws. o See, however, above, p. 86, note a. — Ed. LECTURES ON LOGIC. 97 And, first of all, I may remark, that they naturally lect. fall into two classes. The first of these classes con- '— sists of the three principles of Identity, Contradiction, observations and Excluded Middle ; the second comprehends the Z lie (our principle of Keason and Consequent alone. This clas- tariaw^of sification is founded both on the difierent reciprocal xh "si 'fail connection of the laws, and on the difi'erent nature of chssS" their results. In the first place, in regard to the difference of con- This cias- nection between the laws themselves, it is at once founded, r, evident that the first three stand in a far more proxi- ference of * mate relation to each other than to the fourth. The between the first three are, indeed, so intimately connected, that selves. though it has not even been attempted to carry them up into a higher principle, and though the various and con- tradictory endeavours that have been made to elevate one or other into an antecedent, and to degrade others into consequents, have only shown, by their failure, the impossibility of reducing the three to one ; still so intimate is their connection, that each in fact sup- poses the others. They are like the three sides of a triangle ; not the same, not reducible to unity, each pretending with equal right to a prior consideration, and each, if considered first, giving in its own exist- ence the existence of the other two. This intimacy of relation does not subsist between the principle of Reason and Consequent and the three other laws ; they do not, in the same necessary manner, suggest each other in thought. The explanation of this is found in the difi'erent nature of their results; and this is the second subject of our consideration." In the second place, then, the distinction of the four o For a later development of the distinction hero indicated, see Dis- Author's philosophy as regards the cussions, p, 602 et seq. — Ed. VOL. L G 98 LECTl'UKS ON l.Oi'AC. i.F.rr. laws into [wo ihissos is not only wairantod by tlic ; ditloivnce of tlioir mutual tlepeiidence in thought, but, riitToAuo likewise, by the differeucc of the end which the two which iho classes severally accomplish. For the first three laws 'JvcratiT" "^t only stand ai)art by themselves, (forming, as it accomplish. y^.^yQ^ r^ single principle viewed in three different as- pects,) but they necessitate a result very different, both in kind and in degree, from that determined by the law of Reason and Consequent. The difference in their result consists in this, — Whatever violates the laws, whether of Identity, of Contradiction, or of Ex- cluded ]\Iiddle, we feel to be absolutely impossible, not only in thought but in existence. Thus we cannot atti'ibute even to Omnipotence the power of making a thing different from itself, of making a thing at once to be and not to be, of making a thing neither to be nor not to be. These three laws thus determine to us the sphere of possibility and of impossibility ; and this not merely in thought Ijut in reality, not only logically but metaphysically. Very different is the result of the law of Reast)n and Consequent. This principle merely excludes from the sphere of positive thought what we camiot comprehend ; for whatever we comprehend, that through which we comprehend it is its reason. What, therefore, violates the law of Reason and Consequent merely, in virtue of this law becomes a logical zero ; that is, we are compelled to think it as unthinkable, but not to think it, though actually non-existent subjectively or in thought, as therefore necessarily non-existent objectively or in reality. And why, it may be asked, does the law of Reason and Consequent not equally determine the sphere of general possibility, as the laws of Identity, Contradiction, and Excluded Middle ? Why are we LECTURES ON LOGIC. 99 to view the unthinkable in the one case not to be lect. equally impossible in reality, as the unthinkable in the other 1 Some philosophers have, on the one hand, Two counter asserted to the Deity the power of reconciling contra- regardl'ng dictions ;" while, on the other, a greater number have of oi^ective made the conceivable in human thought the gauge of ''"'" ' ''^' the possible in existence. What warrants us, it may be asked, to condemn these opposite procedures as equally unphilosophical 1 In answer to this, though the matter belongs more properly to Metaphysic than to Logic, I may say a few words, which, however, I am aware, cannot, by many of you, be as yet ade- quately understood. To deny the universal application of the first three The respcc- laws, is, in fact, to subvert the reality of thought ; o7uie uvo''^ and as this subversion is itself an act of thought, it unlaws of P , '^ '1 , •, 1 r« thought de- m tact annihilates itseli. fined au.i When, for example, I say that A is, and then say l^^^^H "jj^ that A is not, by the second assertion I sublate or take un'^?'''f'.i ' •' application away what, by the first assertion, I posited or laid ^J^.^i|f jjj^f' down ; thought, in the one case, undoing by negation jy^p^Jt*''^' what, in the other, it had by affirmation done. But "*' ^''''"g'"- when it is asserted, that A existing and A non-existing are at once true, what does this imply ? It implies that negation and affirmation correspond to nothing out of the mind, — that there is no agreement, no dis- agreement between thought and its objects ; and this is tantamount to saying that truth and falsehood are merely empty sounds. For if we only think by affir- mation and negation, and if these are only as they are exclusive of each other, it follows, that unless existence and non-existence be opposed objectively in the same manner as affirmation and negation are a Compare Le Clerc, Logica, part ii. c. 3. — Ed. 100 LECTURES OX LOGIC. LKcr. oi>pi>soil sul)joctivcly, all our tliought is a more illu- ' sioii. Thus it is, that those who would assert the possibility of contrailietories being at once true, in fact annihilate the possibility of truth itself, and the whole .siunitiitanee of thoui>;ht. Hut this \i J)Ut this is not the case when we deny the universal, iuihodo-""' the absolute, application of the law of Reason and unlvrrsar Consequcnt. When I say that a thing may be, of oFtVobw of which I cannot conceive the possibility, (that is, by cCmsiHi'uau. conceiving it as the consequent of a certain reason,) I only say that thought is limited ; but within its limits, I do not deny, I do not subvert, its truth. But how, it may be asked, is it shown that thought is thus limited ? How is it shown that the inconceivable is not an index of the impossible, and that those philo- sophers who have employed it as the criterion of the absurd, are themselves guilty of absurdity ? This is a matter w4iich will come under our consideration at This bw another time and in its proper place ; at present it general' not wlll bc sufficicnt to statc iu general, that the hypothe- moa^urc^of sis whicli makcs the thinkable the measure of the pos- Joisibiiuy. sible brings the principle of Reason and Consequent at once into collision with the three higher laws, and this hypothesis itself is thus reduced at once to contradic- tion and absurdity. For if we take a comprehensive view of the phenomena of thought, we shall find that all that Ave can positively think, that is, all that is within the jurisdiction of the law of Reason and Con- sequent, lies between two opposite poles of thought, wdiich, as exclusive of each other, cannot, on the prin- ciples of Identity and Contradiction, both be true, but of which, on the principle of Excluded Middle, the one or the other must. Let us take, for example, any of the general objects of our knowledge. Let us take LECTURES ON LOGIC. 101 body, or rather, since body as extended is included lect. under extension, let us take extension itself, or space. '■ — Now extension alone will exhibit to us two pairs of contradictory inconceivables, that is, in all, four in- comprehensibles, but of which, though all are equally unthinkable, and, on the hypothesis in question, all, therefore, equally impossible, we are compelled, by the law of Excluded Middle, to admit some two as true and necessary. Extension, then, may be viewed either as a whole By rcfer- , . jY , encc to Ex- or as a part ; and, m each aspect, it anords us two tension, \°, As a Whole, incogitable contradictories. 1°, Taking it as a whole : — space, it is evident, must either be limited, that is, have an end, a circumference ; or unlimited, that is, have no end, no circumference. These are contradic- tory suppositions ; both, therefore, cannot, but one must, be true. Now let us try positively to compre- hend, positively to conceive, the possibility of either of these two mutually exclusive alternatives. Can we represent or realise in thought extension as absolutely limited 1 in other words, can we mentally hedge round the whole of space, conceive it absolutely bounded, that is, so that beyond its boundary there is no outlying, space or no surrounding space ? This is impossible. What- absolutely* f, I 1 1 • • 1 bounded un- ever compass oi space we may enclose by any limita- thinkable, tion of thought, we shall find that we have no dif- ficulty in transcending these limits. Nay, we shall find that we cannot but transcend them ; for we are unable to think any extent of space except as within a still ulterior space, of which, let us think till the powers of thinking fail, we can never reach the cir- cumference. It is thus impossible for us to think space as a totality, that is, as absolutely bounded, but all-containing. We may, therefore, lay down this first 102 LECTUllKS ON LOOIC. LKCT. oxtrome lUi iiicouccivablc. Wc cauuot think space as VI. ,. . , liinitetl. s,.».o «n. Let us now consider its contradictory ; can wo able, comprehend the possibility of infinite or unlimited M i-iMitrn lictory. space i io supposc tliis IS a du'ect contradiction in terms ; it is to comprehend the incomprehensible. We think, we conceive, we comprehend, a thing, only as we think it as within or under something else ; but to do this of the infinite is to think the infinite as finite, which is contradictory and absurd. oi.jootion Now here it may be asked, how have we then the from tlio . . "^ , . , , . name and Word infinite f How have we the notion which this Dotiun of ''^ the inHniic word cxDresscs ? The answer to this question is con- tained in the distinction of positive and negative Distinction thought. Wc havc a positive concept of a thing, when an!inei:!«he WC think it by the qualities of which it is the comple- uotwii! ^ ment. But as the attribution of qualities is an aflSr- mation, as afiirmation and negation are relatives, and as relatives are known only in and through each other, we cannot, therefore, have a consciousness of the affir- mation of any quality, without having at the same time the correlative consciousness of its negation. Now, the one consciousness is a positive, the other consciousness is a negative notion. But, in point of fact, a negative notion is only the negation of a notion ; we think only by the attribution of certain qualities, and the negation of these qualities and of this attribution, is simply, in so far, a denial of our thinking at all. As affirmation always suggests nega- tion, every positive notion must likewise suggest a neorative notion : and as lano-ua ore is the reflex of thought, the positive and negative notions are ex- pressed by positive and negative names. Thus it is with the infinite. The finite is the only object of real LECTURES ON LOGIC. 103 or positive thought ; it is that alone which we think lect. by the attribution of determinate characters; the infinite, on the contrary, is conceived only by the expreLd' " thinking away of every character by which the finite terasr'"^" was conceived ; in other words, we conceive it only as inconceivable. This relation of the infinite to the finite is shown, indeed, in the terms by which it is expressed in every language. Thus in Latin, infinitum; in Greek, aTreipov ; in German, unendlich ; in all of which original tongues the word expressive of the infinite is only a negative expression of the finite or limited. Thus the very objection from the existence of a name and notion of the infinite, when analysed, only proves more clearly that the infinite is no object of thought ; that we conceive it, not in itself, but only in correlation and contrast to the finite. The indefinite is, however, sometimes confounded The inde- with the infinite ; though there are hardly two notions infinite,— which, without being contradictory, difier more widely, guished."" The indefinite has a subjective, the infinite an objec- tive relation. The one is merely the negation of the actual apprehension of limits, the other the negation of the possible existence of limits. But to return whence we have been carried, it is Space as manifest that we can no more realise the thought or andVacc as .• /••r»'i 1 11 T-,1 unbounded conception oi innnite, unbounded, or unlimited space, being two than we can realise the conception of a finite or ab- aurc^tra- solutely bounded space. But these two inconceivablcs the la'^of 1 j_Tj.- ^ t 11, Reason and are reciprocal contradictories, and it we are unable to Consequent comprehend the possibility of either, while, however, therefore, on the principle of Excluded Middle one or other must cHt"rion of be admitted, the hypothesis is manifestly false, that pro- JoSmy. poses the subjective or formal law of Reason and Con- sequent as the criterion of real or objective possibility. 104 LECTURES ON LOGIC. LECT. It is noedloss to sliow that the same result is given VI. by the. experiment made on extension considered as siu.wu'i.V"^ a jKirt, as divisible. Here, if wc attempt to divide KluusioD," extension in thought, we shall neither, on the one i-m.'" hand, succeed in conceiving the possibility of an absolute minimum of space, that is, a minimum ex hypothesi extended, but which cannot be conceived as divisible into parts, nor, on the other, of carrying on this division to infinity. But as these are contradic- tory opposites, they again aflbrd a similar refutation of the hypothesis in question. 3% By refer- But the samc conclusion is reached by simply con- Law of sidering the law of Reason and Consequent in itself, consequent This law cnjoins, — Think nothing without a reason why we must think it, that is, think nothing except as contained in, as evolved out of, something else which we already know. Now this reason, — this something else, — in obedience to this very law, must, as itself known, be itself a consequent of some other antecedent ; and this antecedent be again the conse- quent of some anterior or higher reason ; and so on, ad infinitum. But the human mind is not possessed of infinite powers, or of an infinite series of reasons and consequents ; on the contrary, its faculties are very limited, and its stock of knowledge is very small. To erect this law, therefore, into a standard of exist- ence, is, in fact, to bring down the infinitude of the universe to the finitude of man, — a proceeding than The laws of which uothiug can be imagined more absurd. The Co^quent, fact is, that the law of Reason and Consequent can, cibie'^to a' with the law of Cause and Efiect, the law of Sub- cipie"^"'' stance and Phsenomenon, &c., be, if I am not mis- taken, all reduced to one higher principle ; a principle which explains from the very limitation of the human LECTURES ON LOGIC. 105 mind, from the very imbecility of its powers, a great lect. variety of phsenomena, which, from the liberality of — = — '- — philosophers, have obtained for their solution a num- ber of positive and special principles. This, however, is a discussion which would here be out of place." What, however, has been said may suffice to show, summary that, while the first three laws of thought are of an the spheres absolute and universal cogency, the fourth is only of of thought. a cogency relative and particular ; that while the for- mer determine the possibility, not only of all thought but of all real knowledge, the latter only regulates the validity of mediate or reflective thought. The laws of Identity, Contradiction, and Excluded Middle are, therefore, not only logical but metaphysical principles, the law of Reason and Consequent a logical principle alone ; a doctrine which is, however, the converse of what is generally taught. I proceed, now, to say a few words on the general The general influence which these laws exert upon the operations whicrtL of thinking. These operations, however various and laws^exeH multiform they may seem, are so governed in all their operations manifestations by the preceding laws, that no thought " "" '"^' can pretend to validity and truth which is not in consonance with, which is not governed by, them. For man can recognise that alone as real and assured, which the laws of his understanding sanction ; and he cannot but regard that as false and unreal, which these laws condemn. From this, however, it by no means follows that what is thought in conformity to these laws is, therefore, true ; for the sphere of thought is far wider than the sphere of reality, and no inference is valid from the correctest thinkincf of an object to its actual existence. While these lawa^ a See Discussions, p. 609. — Ed. 106 LECTUKKS ON UHllV. LKiT. tlieivfoiv, are the higliost criterion of the non-reality ^'' of an ol)ject, they are no criterion at all of its reality; auil tlu'v thus stand to existence in a nci^ative and not in a positive relation. And what J now say of the fundamental principles of thought in general, holds equally of all their proximate and special api)li- catious, that is, of the whole of Logic. Logic, as I have already explained, considering the form alone of thought to the exclusion of its matter, can draw no conclusion from the correctness of the manner of thinking an object to the reality of the object itself. The true Yct amoug modcm, nay recent, philosophers, two lu'.sic over- opposite doctrines have sprung up, which, on opposite two'^wavs:- sldcs, liavc ovcrlookcd the true relations of Logic, crr^ll^usiy " C)ne party of philosophers defining truth in general, tSVosit^^e — ^^® absolute harmony of our thoughts and cogni- tm^h.^'^'^"^ tions, — divide truth into formal (or logical) and The division material (or metaphysical), according as that harmony formal and'" is in cousonaucc with the laws of formal thought, or, Sciled." over and above, with the laws of real knowledge." The criterion of formal truth they place in the prin- ciples of Contradiction and of sufficient Keason, enouncing that what is non-contradictory and conse- quent is formally true. This criterion, which is posi- tive and immediate of formal truth, (inasmuch as what is non-contradictory and consequent can always be thought as possible), they style a negative and medi- ate criterion of material truth : as what is self-con- tradictory and logically inconsequent is in reality impossible; at the same time, what is not self-con- tradictory and not logically inconsequent is not, how- ever, to be regarded as having an actual existence. a See Kant, Logih, Einleitung, (jik, § 42. — Eu. vii. ; Knig, Lor/ik, § 22 ; Fries, Lo- LECTURES ON LOGIC. 107 But here the foundation is treacherous ; the notion of lect. VL truth is false. When we speak of truth, we are not satisfied with knowing that a thought harmonises what.' with a certain system of thoughts and cognitions ; but, over and above, we require to be assured that what we think is real, and is as we think it to be. Are we satisfied on this point, we then regard our thoughts as true ; whereas if we are not satisfied of this, we deem them false, how well soever they may quadrate with any theory or system. It is not, there- fore, in any absolute harmony of mere thought that truth consists, but solely in the correspondence of our thoughts with their objects. The distinction of for- mal and material truth is thus not only unsound in itself, but opposed to the notion of truth universally held, and embodied in all languages. But if this distinction be inept, the title of Logic, as a positive standard of truth, must be denied ; it can only be a negative criterion, being conversant with thoughts and not with things, with the possibility and not with the actuality of existence.* The preceding inaccuracy is, however, of little mo- 2. The Ab- ment compared with the heresy of another class of pro"ccc.fon a philosophers, to whose observations on this point lofthe'^og?- can, however, only allude. Some of you may, per- *"* haps, find a difficulty in believing the statement, that there is a considerable party of philosophers, illus- trious for the highest speculative talent, and whose systems, if not at present, were, a few years ago, the most celebrated, if not the most universally accredited, in Europe, who establish their metaphysical theories on the subversion of all logical truth./^ I refer to those philosophers who hold that man is capable of a Easer, Lofjik, \>. 65-G. — Ed. /3 See above, p. 90, note o. — Ed. 108 LECTURES ON LOGIC. LK(T. mow than a ivlative notion of existence, — that he VI is competent to a knowledge of absolute or infinite being, (for these terms they use convertibly,) in an identity of knowledge and existence, of himself and the Divinity. This doctrine, which I shall not now attempt to make you understand, is developed in very various schemes, that is, the different philosophers attempt, by very different and contradictory methods, to arrive at the same end ; all these systems, how- ever, agree in this, — they are all at variance with the four logical laws. Some, indeed, are established on the express denial of the validity of these laws ; and others, without daring overtly to reject their autho- rity, are still built in violation of their precept. In fact, if contradiction remain a criterion of falsehood, if Loofic and the laws of thousfht be not viewed as an illusion, the philosophy of the Absolute, in all its forms, admits of the most direct and easy refutation. But on this matter I only now touch, in order that you may not be ignorant, that there are philosophers, and philosophers of the highest name, who, in pursuit of the phantom of absolute knowledge, are content to repudiate relative know'ledge, logic, and the laws of thought. This hallucination is, however, upon the wane, and as each of these theorists contradicts his brother, Logic and Common Sense will at length re- fute them all. Mistake of Bcforc Icaviug the consideration of this subject, it regarrto is ncccssary to notice a mistake of Dr Eeid, which it ouccption. .^ ^^^ more remarkable that he should have commit- ted, than that others have been found to follow and applaud it, as the correction of a general error. In the fourth Essay on the Intellectual Powers, and in the third chapter, entitled Mistakes concerning Con- LECTUKES ON LOGIC. 109 ception,"" there is the following passage, which at once lect. exhibits not only his own opinion, but the universality '— of the doctrine to which it is opposed : — "There remains," he says, *' another mistake con- Reid I'll 1 • T X quoted. cerning conception, which deserves to be noticed. It is — That our conception of things is a test of their possibility, so that, what we can distinctly conceive, we may conclude to be possible ; and of what is im- possible, we can have no conception. " This opinion has been held by philosophers for more than a hundred years, without contradiction or dissent, as far as I know ; and, if it be an error, it may be of some use to inquire into its origin, and the causes that it has been so generally received as a maxim whose truth could not be brought into doubt." I may here observe that this limitation of the pre- valence of the opinion in question to a very modern period is altogether incorrect ; it was equally pre- valent in ancient times, and as many passages could easily be quoted from the Greek logicians alone as Dr Reid has quoted from the philosophers of the cen- tury prior to himself. Dr Reid goes on : — " One of the fruitless questions agitated among the scholastic philosophers in the dark ages was — What is the criterion of truth ? as if men could have any other way to distinguish truth from error, but by the right use of that power of judgment which God has given them. " Descartes endeavoured to put an end to this con- troversy, by making it a fundamental principle in his system, that whatever we clearly and distinctly per- ceive, is true." " To understand this principle of Descartes, it must a Collected Worlc>^, p. 37G-8.— Ed. 110 LECTURES ON LOOIC. LKtT. bo obsorvod. l1i:it ho «';ivo tho namo of perception to ; evoiy powor of (ho luiman iiiulorstaiidiiig ; and in exphiining this vory maxim, lie tolls us that sense, imagination, and pure intellection, are only differont modes of perceiving, and so the maxim was under- stood by all his followers. "The learned Dr Cudworth seems also to have adopted this principle. * The criterion of true know- ledge,' says he, * is only to be looked for in our know- ledge and conceptions themselves : for the entity of all theoretical truth is nothing else but clear intel- ligibility, and whatever is clearly conceived is an entity and a truth ; but that which is false. Divine power itself cannot make it to be clearly and dis- tinctly understood. A falsehood can never be clearly conceived or apprehended to be true.' [Eternal and Immutable Morality, p. 172, &c.) " This Cartesian maxim seems to me to have led the way to that now under consideration, which seems to have been adopted as the proper correction of the former. "When the authority of Descartes declined, men began to see that we may clearly and distinctly conceive what is not true, but thought, that our con- ception, though not in all cases a test of truth, might be a test of possibility. *' This indeed seems to be a necessary consequence of the received doctrine of ideas ; it being evident that there can be no distinct image, either in the mind or anywhere else, of that which is impossible. The ambiguity of the word conceive, which we observed. Essay i. chap, i., and the common phraseology of saying, we cannot conceive such a thing, when we would signify that we think it impossible, might likewise contribute to the reception of this doctrine. LECTURES ON LOGIC. Ill " But whatever was the origin of this opinion, it lect. seems to prevail universally, and to be received as a — maxim. " * The bare having an idea of the proposition proves the thing not to be impossible ; for of an im- l^ossible proposition there can be no idea.' — Dr Samuel Clarke. " ' Of that which neither does nor can exist we can have no idea.' — Lord Bolingbroke. " ' The measure of impossibility to us is inconceiv- ableness, that of which we can have no idea, but that reflecting upon it, it appears to be nothing, we pro- nounce to be impossible.' — Abernethy. " ' In every idea is implied the possibility of the existence of its object, nothing being clearer than that there can be no idea of an impossibility, or conception of what cannot exist.' — Dr Price. " ' Impossibile est cujus nullam notionem formare possumus ; possibile e contra, cui aliqua respondet notio.' — Wolfii Ontologia. " * It is an established maxim in metaphysics, that whatever the mind conceives, includes the idea of possible existence, or, in other words, that nothing we imagine is absolutely impossible.' — D. Hume. " It were easy to muster up many other respectable authorities for this maxim, and I have never found one that called it in question. " If the maxim be true in the extent which the famous Wolfius has given it in the passage above quoted, we shall have a short road to the determina- tion of every question about the possibility or imj^os- sibility of things. We need only look into our own breast, and that, like the Urim and Thummim, will cfive an infalliljlc answer. If we can conceive the 112 LECTUKES ON LOGIC. LECT. thing, it is possible ; if not, it is impossible. And, '■ — siiivly, every man may know whether he ean conceive what is atKrmeil, or not. *' Other philosophers have been satisfied with one lialf of the maxim of Woltius. They say, that what- ever we can conceive is possible ; but they do not say, that whatever we cannot conceive is impossible," On this I may remark, that Dr Reid's criticism of Wolf must be admitted in so far as that philosopher maintains our inability to conceive a thing as possible, to be the rule on which we are entitled to pronounce it impossible. But Dr Reid now advances a doctrine which 1 cannot but regard as radically erroneous. " I cannot help thinking even this to be a mis- take which philosophers have been unwarily led into, from the causes before mentioned. My reasons are these : — "1. Whatever is said to be possible or impossible is expressed by a proposition. Now, what is it to conceive a proposition "? I think it is no more than to understand distinctly its meaning. I know no more that can be meant by simple apprehension or conception, when applied to a proposition. The axiom, therefore, amounts to this : — Every proposi- tion, of which you understand the meaning dis- tinctly, is possible. I am persuaded that I under- stand as distinctly the meaning of this proposition, Any two sides of a triangle are together equal to the third, as of this, Any two sides of a triangle are to- gether greater than the third ; yet the first of these is impossible." Criticise.!, Now this is a singular misunderstanding of the sense in which it has been always held by philoso- phers, that what is contradictory is conceived as LECTURES ON LOGIC. 113 inconceivable and impossible.'* No philosopher, I lect. make bold to say, ever dreamt of denying that we - ^^' can distinctly understand the meaning of the pro- position, the terms of which we recognise to be con- tradictory, and, as contradictory, to annihilate each other. When we enounce the proposition, A is not- A, we clearly comprehend the separate meaning of the terms A and not- A, and also the import of the asser- tion of their identity. But this very understanding consists in the consciousness that the two terms are contradictories, and that as such it is impossible to unite them in a mental judgment, though they stand united in a verbal proposition. If we attempt this, the two mutually exclusive terms not only cannot be thought as one, but in fact annihilate each other; and thus the result, in place of a positive judgment, is a negation of thought. So far Dr Reid is wrong. But he is not guilty of the absurdity attributed to him by Dr Gleig; he does not say, as by that writer he is made to say, that "any two sides of a triangle may be conceived to be equal to the third, as distinctly as any two sides of a triangle may be conceived to be greater than the third." ^^ These are not Dr Reid's words, and nothing he says warrants the attribution of such expressions to him, in the sense in which they are attributed. He is made to hold, not merely that we can understand two terms as contra- dictory, but that we are able to combine them in the unity of thought. After the passage already quoted, Reid goes on to illustrate, in various points of view, the supposed error of the philosophers ; but as all he a See the Author's notes, Ecid's pcedia Uritannica, 7th edit. , p. 620. lVork.% p. 377.— Ed. —Ed. j3 Art. "Metaphysics," Encych- VOL. r. H 114 LKCTUKES ON LOGIC. LKiT. Siivs on this head oriuiuatcs in the misconce])tion VI . . . . ' already sliown of the opinion he controverts, it la needless to take any furtlier notice of his argu- ments, rimuiau-s We have thus considered the conditions of Logic, in so far as certain laws or principles are prescribed ; we have now to consider its conditions, in so far as certain postulates are demanded. Of these there are more than one, but one alone it is here requisite to signalise ; for although it be necessarily supposed in the science, strange to say, it has, by logical writers, not only been always passed over in silence, but frequently and inconsistently violated. This postu- late I comprise in the following paragraph : — Par.xviii. If XVIII. The only postulate of Logic which re- postuhTto. quires an articulate enouncement is the demand, that before dealing with a judgment or reasoning ex]Dressed in language, the import of its terms should be fully understood ; in other words, Lo- gic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought.'' This postu. This postulate cannot be refused. In point of fact, late cannot t i •it"1 i it 'i* be refused, as I havc saiQ, Logic has always proceeded on it, in overtly expressing all the steps of the mental process in reasoning, — all the propositions of a syllogism ; whereas, in common parlance, one at least of these steps or propositions is usually left unexpressed. This postulate, as we shall have occasion to observe in the sequel, though a fundamental condition of Logic, has not been consistently acted on by logicians a See Appendix VI. — Ed. LECTURES ON LOGIC. 115 ill their development of the science ; and from this lect. omission have arisen much confusion and deficiency '. — and error in our present system of Logic. The illus- tration of this postulate will appropriately find its place on occasion of its applications. I now articu- lately state it, because it immediately follows in order the general axioms of the science ; and, at present, I only beg; that you will bear it in mind. I may, how- This postu- •^ *=> -^ / 1 1 I'i'te implied ever, before leavinsr the sumect, observe, (what hasinthedoc- 11 X 1 1- 1 • i\ 1 A • 1 trine of Syl- already, I believe, been mentioned), that Aristotle logism, ac- f r~i It • ' 1 f» 1 • cording to states of Syllogistic, and, oi course, his statement Aristotle. applies to Logic in general, that the doctrine of syllo- gism deals, not with the external expression of rea- soning, in ordinary language, but with the internal reasoning of the mind itself.'* But of this again and more fully, in the proper places. In like manner, we might here, as is done in Mathematics, premise certain definitions; but these it will be more convenient to state as they occur in the progress of our development. I, therefore, pass on to the Second Section of the Doctrine of Elements, which is occupied with the products of thought ; in other words, with the processes regulated by the pre- vious conditions. a Anal. Post., i. 10. — Ed. 110 LECTURES ON LOC.IC LECTURE VIJ. STOICHEIOLOGY. SECTION II. — OF THE PRODUCTS OF THOUGHT. I. ENNOEMATIC — OF CONCEPTS OR NOTIONS. A. OF CONCEPTS IN GENERAL. LECT. I CONCLUDED, ill inv last Lccture, all that I think it VIL . necessary to say in regard to the Fundamental Laws of Thought, or the necessary conditions of the thinkable. The discussion, I am aware, must have been found somewhat dry, and even abstruse ; not that there is the smallest difficulty in regard to the apprehension of the laws themselves, for these are all self-evident propositions, but because, though it is necessary in a systematic view of Logic to commence with the elementary principles of thought, it is impossible, in speaking of these and their application, not to employ expressions of the most abstract generality, and even not to suppose a certain acquaintance with words and things, which, however, only find their explanation in the subsequent development of the science. ThoPro- Having considered, therefore, the four Laws of 'iTiought,— Thought, with the one Postulate of Logic, which con- Judgments, stitutc tlic First Scction of the Doctrme of Logical ings. Elements, I now proceed to the Second, — that which is conversant about Logical Products. These pro- LECTURES ON LOGIC. Il7 ducts, though identical in kind, are of three different lect. • VII degrees ; for while Concepts, Judgments, and Reason- _ ings, are all equally the products of the same Faculty aii products of Comparison, they still fall into three classes, asson/anraii the act, and, consequently, the result of the act, isuonso? of a greater or a less simplicity. These three degrees ■"" ^^''*' are all in fact, strictly, only modifications of the second, as both concepts and reasonings may be re- duced to judgments ; for the act of judging, that is, the act of affirming or denying one thing of another in thought, is that in which the understanding or Faculty of Comparison is essentially expressed. By anticipation : — A concept is a judgment ; for, on the one hand, it is nothing but the result of a foregone judgment, or series of judgments, fixed and recorded in a word, — a sign, and it is only amplified by the annexation of a new attribute, through a continuance of the same process. On the other hand, as a concept is thus the synthesis or complexion, and the record, I may add, of one or more prior acts of judgment, it can, it is evident, be analysed into these again ; every concept is, in fact, a judgment or a fasciculus of judg- ments, — these judgments only not explicitly developed in thought, and not formally expressed in terms. Again, a reasoning is a judgment ; for a reasoning is only the affirmation of the connection of two things with a third, and, through that third, with each other. It is thus only the same function of thought w^hich is at work in Conception, Judgment, and Reasoning; and these express no real, no essential, distinction of opera- tion, but denote only the different relations in which we may regard the indivisible act of thought. Thus, the consideration of concepts cannot be effected out of all relation to, and without even some anticipation of. 118 LECTUKES ON LO(Jir. i.F.rr. the doctrine of jiulujnieuts. Tliis being premised, I now proceed to tlie consideration of tlie Products of Thought, viewed in the three rehitions or the tliree degrees, of Concepts, Judgments, and Reason- ings. Under the Second Section of Stoicheiology, Con- cepts or Notions form the First Chapter. I. Of Con- Now in treating of Concepts, the order I shall fol- Notions,- low is this, — I shall, in the first place, treat of thcni discussion, in general ; in the second, treat of them in special. Under the former, or general, head, will be considered, 1°, What they are ; 2°, How they are produced. Under the latter, or special, head, they will be con- sidered under their various relations. And here, I may observe, that as you obtain no information from Dr Whately in regard to the primary laws of tliought, — these laws being in fact apparently un- whateiy's kuowTi to cvcry British logician old or new, — so you ti^TJarinc will find but little or no aid from his Elements towards onccpts. ^^ understanding of the doctrine of concepts. Ilis omission, in this respect, cannot be excused by his error in regard to the object-matter of Logic ; that object, you will recollect, being on his view, or rather one of his views, not thought in general or the pro- ducts of the comparative faculty in their three degrees, but reasoning or argumentation alone ; for even on the hypothesis that Logic is thus limited, still as the doctrine of reasoning can only be scientifically evolved out of the doctrine of concepts, the consideration of the latter forms the indispensable condition of a satis- factory treatment of the former. But not only is o [Hume, TreoAisc of Human Xa- iireheusion is impossible without lure, Bk. L part iii. § 7. Jac. Tho- judgment. Compare also Krug, Lo- masius, Plujalai, p. 205] [c. xlix. § fj'ik, g 23, Anm. ii. p. 70. — Ed.] 112, where he holds that simple ap- LECTURES ON LOGIC. 119 Wliately's doctrine of concepts, or, in his language, of lect "the process of simple apprehension," meagre and len- sion as con- imperfect, it is even necessary to forewarn you, that it abuTi'vefy leads to confusion and error. There is a fundamental lorLs^Ix-'" distinction of what is called the Extension and the compel" Comprehension of notions, — a distinction which, in vertibL! fact, as you will find, forms the very cardinal point on which the whole theory of Logic turns. But not only is this distinction not explained, it is not even arti- culately stated, nay, the very words which logicians have employed for the expression of this contrast, are absolutely used as synonymous and convertible. In- stead, therefore, of referring you for information in regard to our present object of consideration to Dr Whately, I am sorry to be compelled to caution you * against putting confidence in his guidance. But to return. The following I dictate as the title of the first head to be considered. A. Of Concepts or Notions in General : What are a. of Con- , n cepts or tney i Notions in general. — What they In answering this question, let us, first, consider the '""'^' meaning of the expressions ; and, secondly, the nature of the thing expressed. IF XIX. Concept or notion, {ewoia, ivuorjixa, Par. xix. v6r)[xa, iiTLvoia,'^ conceptio, notio), are terms em- noS,— a 111 Greek, the terms ipvoia (eVj/oTj- Simple Apprehension. See Blemmi- riK6s), iuvorifia (Svvor]/xaTiK6s), inlvoia d;is, Epitoriic Logica [c. v. Vlfpl (eVij/oTjTiKJs), v()7]ixa, to say nothing 'Eirivolas, p. 31, ed. 1G05. — Ed.]; of iirifdrifx.a (iTnuor^fiariKtU), are all Eugenios, Logica [AoyiKr], c. ii. p. more or less obj<'ctionable, as all 170, Leipsic, 1766. — Ed.] Stcphan- more or less ambiguously used for us, 2'hr.snurus, v. NoCs; Hocker, the object or product of thought, in (.'hivis Phil. ArisL, v. t^orj/mara, p. an act of Conception, or, as it has 2'27 ct ncif ; Micrrelius, Lexicon Phi- been usually called by the logicians, losophicum, v. tiurifia, p. 8*JU, and p. IL'O LECTUUKS (IN LOGIC. LKir. VU. t«rim. ployoil us convertible, but while they ileiiote the same thing, they denote it in a ditl'ercnt point of \ie\v. Conception, the act of which concept is the result, expresses the act of comprehending or grasping up into unity the various qualities by which an object is characterised ; Notion (notio), again, signities either the act of apprehending, signalising, that is, the remarking or taking note of the various notes, marks, or characters of an object, which its qualities afibrd ; or the result of that act. Illustrated — cinploy- inent of the terms rt«i'Hiy vil mciUe coiiciptre, and atiimi concept ws. Of conci- pere, coii- ceptus, and conceptio, without ad- junct. In Latin, the word cojicipere, in its many various applications, always expresses, as the etymology would indicate, the process of embracing or comprehending the many into the one, as could be shown by an articulate analysis of the phrases in which the term occurs. It was, accordingly, under this general signi- fication, that this word and its derivatives were ana- logically applied to the operation of mind. Animo vel mente concipere, as used by Cicero, Pliny, Seneca, and other Roman writers, means to comprehend or understand, that is, to embrace a multitude of differ- ent objects by their common qualities in one act of thought ; and animi conceptus was, in like manner, applied by the ancient waiters to denote this operation, or its result. The employment of concipere, conceptus, and concep)tio, as technical terms, in the philosophy of mind, without the explanatory adjunct, was of a later 80 [y. AlffOvfiaTCL. Cf. p. 310, V. Cmiceptus ; p. 633, v, Intentio. — Ed.] On fo-fip-ara, see Aristotle, De In- teryr., c. i., and Waitz, Commenta- rius, p. 327. In Aristotle, De Ani- ma, L. iii. cc. 6 (7), 7 (8), 8 (9), etc., vo-fiiJMTa are clearly equivalent to concepts in our meaning ; [c. G, 'H fx.fi' oiiv rwf aSiaiptTcov vorjais eV TOUTOIJ, TTfpl & OVK ^CTTt T^ XpfvSoi' if ols si KCil Th \p(vSos Kol rh aXTjOfs, avvOfcxis ris ^Stj vorjixaTuy, wcnrtp %v uvToiv. K.r.K. — Ed.] LECTURES ON LOGIC. 121 introduction, — was, indeed, only possible after they lect. had been long familiarly used in a psychological rela tion. But when so introduced, they continued to be employed by philosophers in general in their proper signification as convertible with thought or compre- hension, and as opposed to the mere apprehension of Sense or Imagination. Not, indeed, that examples enough may not be adduced of their abusive applica- tion to our immediate cognitions of individual objects, long before Mr Stewart formally applied the term conception to a certain accidental form of representa- tion, — to the simple reproduction or repetition of an act of perception in imagination." In using the terms conception and concep)t in the sense which I have ex- plained, I, therefore, employ them not only in strict conformity to their grammatical meaning, but to the meaning which they have generally obtained among philosophers. The term notion, like conception, expresses both an The term -'■ ^ notion, — act and its product. I shall, however, as has com- how em- . . . , . ployed by monly been done, use it only in this latter relation, the Auti.or This word has, like conception, been sometimes abus- ively applied to denote not only our knowledge of things by their common characters, but, likewise, to include the mere presentations of Sense and represen- tations of Phantasy. This abusive employment has, however, not been so frequent in reference to this term as to the term conception ; but it must be ac- knowledged, that nothing can be imagined more vague and vacillating than the meaning attached to notion in the writings of all British philosophers, without exception. So much for the expressions concept and notion. I now go on to that which they express. a See Lectures on Mdaphynics, vol. ii. p. 261. — Ed. 122 LECTURES ON LO(;u;. i.KiT. 'I XX." — 111 our c'oiisciousuess, — apprclieiisioii, _\'il_ of an imlividiinl ohject, there may be distinguished Iw4i'- tl'«-' ^^^'^ tollowing cognitions : — 1°, The immediiitc IiKMhiu^"^ Jiiid irrespective kuowledge we have of the indi- vidual object, as a complement of certain qualities or characters, considered simply as belonging to itself; 2°, The mediate and relative knowledge we have of this object, as comprising qualities or characters common to it with other objects. The former of these cognitions is that contained in the Presentations of Sense, external and inter- nal, and Representations of Imagination. They are only of the individual or singular. The latter is that contained in the Concepts of the Under- standing, and is a knowledge of the common, general, or universal. The conceiving an object is, therefore, its re- cognition mediately through a concept; and a Concept is the cognition or idea of the general character or characters, point or points, in which a plurality of objects coincide. Concepts,- This requircs some illustration, and it will be best iui'tr^aS*' afforded by considering the history of our knowledge. S thJ'hi'r^ Our mental activity is not first exerted in an appre- knowfed^. hension of the common properties of things. On the Objects are Contrary, objects are originally presented to us in con- prle°nica in fused aud imperfect perceptions. The rude materials anSper- fumishcd by Sense, retained in Memory, reproduced Sns^^'^*^^^ by Reminiscence, and represented in Imagination, the Understanding elaborates into a higher knowledge, o On this and three following par- ledge, see Opera II. i. p. 14 et seq. — agraphs apply Leibnitz's distinction [Meditationes de Cognitione, Veritate, of Intuitive and Symbolical Know- ct Iilcis, — Eo.] LECTUHES ON LOGIC. 123 simply by means of Comparison and Abstraction. The lect. primary act of Comparison is exerted upon the indi- vidual objects of Perception and Imagination alone. compLlsou In the multitude and complexity of these objects, gtractioii or certain attributes are found to produce similar, others ^"''"^'"" to produce dissimilar, impressions. The observation of this fact determines a reflective consideration of their properties. Objects are intentionally compared together for the purpose of discovering their similari- ties and difierences. When things are found to agree or to disagree in certain respects, the consciousness is, by an act of volition, concentrated upon the objects which thus partially agree, and, in them, upon those qualities in or through which they agree ; and by this concentration, — which constitutes the act called Attention, — what is efiected 1 On the objects and qualities, thus attentively considered, a strong light is shed; but precisely in proportion as these are illuminated in consciousness, the others, to which we do not attend, are thrown into obscurity. The result of Attention, by concentrating the mind upon certain qualities, is thus to withdraw or abstract it from all else. In technical language, we are said to prescind the phpenomena which we exclusively con- sider. To i^rescind, to attend, and to abstract, are Precision, merely difi'erent but correlative names for the same aud'^Ab""' process ; and the first two are nearly convertible. Snck'ti'v'!^'' When we are said to 'prescind a quality, we are merely the'smne' supposed to attend to that quality exclusively ; and '^^'^^'^'"" when we abstract, we are properly said to abstract from, that is, to throw other attributes out of account. I may observe that the term abstraction is very often abusively employed. By Abstraction we are frequently said to attend exclusively to certain pha3nomena, — 124 I.KCTUIIKS ON LOGIC. LF.(X tlioso, to wit, whirh wo abstract; whereas, the term 1_ abstraction is j)i(>piily applied to the qualities which we abstract from, and by abstracting from some, we are enabled to consider others more attentively. At- tention and Abstraction are only the same process viewed in diflerent relations. They arc, as it were, the positive and negative poles of the same act.* By Comparison, the points of resemblance among things being thus discovered, and by Attention consti- tuted into exclusive objects; by the same act they are also reduced in consciousness from multitude to unity. What is meant by this will be apparent from the following considerations. The rc.iuc AVe are conscious to ourselves that we can repeat jcctsfrom our acts of consciousness, — that we can think the to unity.- same thought over and over. This act, or this and iuus- thought, is always in reality the same, though mani- fested at different times : for no one can imagine that Thought is in the repetition of one and the same thought, he has s^me^hiie a plurality of thoughts ; for he is conscious, that it is L^ldentl-^ one and the same thought w^hich is repeated, so long *^ ■ as its contents remain identical. Objects are Now^ this relation of absolute similarity which sub- same when sists between the repetitions of the same thought, is TiL^'todb- found to hold between our representations of the th^'i^cogni- resembling qualities of objects. Two objects have similar qualities only as these qualities afford a similar presentation in sense or a similar representation in imagination, and qualities are to us completely simi- lar, when \ve are unable to distinguish their cognitions. But what we cannot distinguish, is, to us, the same ; therefore, objects which determine undistinguishable o See Lectures on Metaphysics, vol. Logik, § 49. — Ed. [Schulze, Zogik, ii. p. 292, and Bachmann, Lo(jlk, § § 28 ; Drobisch, Logik, % 14, p. 11 e< 44. CompareKaut,ioj/i/.-, § 6; Kriig, seq.'] tlODS. LECTURES ON LOOIC. 125 impressions upon us, are perceived and represented in lect, the same mental modification, and are subjectively to us precisely as if they were objectively identical. But the consciousness of identity is not merely the The con- ^ . sciousness result of the indiscernible similarity of total objects, of identity is . f 1 • equally the it is equally the result of the similarity of any of their result ottiie ^ '' • 1 similarity of parts, — partial characters. For by abstractmc; ob- any of the . . . .,. Trc 1 partial cha- servation from the points in which objects diner, andractersof . . objects. limiting it to those in which they agree, we are able to consider them as identical in certain respects, how- ever diverse they may appear to be in others, which, for the moment, we throw out of view\ For example, let B, C, and D represent a series of individual objects, which all agree in possessing the resembling attributes <5f I/} y> y> ^^^ severally differ in each respectively possessing the non-resembling attributes i, o, u. Now, in so far as we exclusively attend to the resembling qualities, we, in the first place, obscure or remove out of view their non-resembling characters, i, o, u, while we remain exclusively conscious of their resembling- qualities, y, y, y. But in the second place, the quali- ties expressed by y, y, y, determine in us cognitive energies which we are unable to distinguish, and which we, therefore, consider as the same. We, therefore, view the three similar qualities in the three different objects as also identical ; we consider the y in this, the y in that, and the y in the third object, as one, and in so far as the three objects participate in this oneness or identity, we regard them also as the same. In other words, we classify B, C, and D under y ; y is the genus, B, C, and D are its individuals or species, severally distinguished from each other by the non-resembling properties, i, o, u. Now it is the points of similarity thus discovered and identified in 120 LEOTUniv'"^ ON LOnT(\ LECT. tlio uiiitv i>t' oonsciousness, which constitute Concepts VII. 1— or Notions. (K-ncniiisa. It is ovitlont tluit tlic stimc process of Comparison ami Ahstriiction may be again performed on the con- cepts thus formed. They are, in like manner, com- pared together, and their points of resemblance noted, exchisively considered, and reduced to one in tlic synthesis of thouglit. This process is called General- isation ; that is, the process of evolving the general Concepts or or ouc, out of thc individual and manifold. Notions p"rfluou^iy and concepts are also sometimes designated by the Hl ^"" style of general notions, — general conceptions. This is superfluous, for, in propriety of speech, notions and concepts are, in their very nature, general ; while the other cognitive modifications to which they are op- posed, — perceptions and imaginations, — have, in like manner, their essence in their individuality. Idea,— By the way, you may have noticed that I never use reason why not the term idea. The reason of my non-employment rGtrulnrlv cm].ioyelot«\ tlic cll'crts wliicli llicv (IcU'iHiiiu' ill us 1_ ari\ l>v us, iutlisccriiiMc. To us, they aiv, tlicretoiv, virtually tho same, and the same we, accordingly, con- sider them to be, tiiough in ditierent objects; pre- cisely as we consider the thouglit of the same o)»ject to be itself the same, Avlien repeated at intervals, — at ditlerent times, in consciousness. This l)y way of preface being understood, I showed that in the for- mation of a concept or notion the process may bo analysed into four momenta. In the first place, we must have a plurality of objects presented or repre- sented by the subsidiary faculties. These faculties must furnish the rude material for elaboration. In the second place, the objects thus supplied are, by an act of the Understanding, compared together, and their several qualities judged to be similar or dissimilar. In the third place, an act of volition, called Attention, concentrates consciousness on the qualities thus re- cognised as similar ; and that concentration, by atten- tion on them, involves an abstraction of consciousness from those which have been recognised and thrown aside as dissimilar ; for the power of consciousness is limited, and it is clear or vivid precisely in propor- tion to the simplicity or oneness of its object. Atten- tion and abstraction are the two poles of the same act of thought ; they are like the opposite scales in a balance, the one must go up as the other goes down. In the fourth place, the qualities, which by compari- son are judged similar and by attention are consti- tuted into an exclusive object of thought, — these are already, by this process, identified in consciousness ; for they are only judged similar, inasmuch as they produce in us indiscernible effects. Their synthesis in consciousness may, however, for precision's sake, be LECTURES ON LOGIC. 133 stated as a fourth step in the process ; but it must be i^ct. remembered, that at least the three latter steps are not, in reality, distinct and independent acts, but are only so distinguished and stated, in order to enable us to comprehend and speak about the indivisible operation, in the different aspects in which we may consider it. In the same way, you are not to sup- pose that the mental sentence which must be analysed in order to be expressed in language, has as many parts in consciousness, as it has words, or clauses, in speech; for it forms, in reality, one organic and indivisible whole. To repeat an illustration I have already given : — The parts of an act of thought stand in the same relation to each other as the parts of a triangle, — a figure which we cannot resolve into any simpler figure, but whose sides and angles we may consider apart, and, therefore, as parts ; though these are, in reality, inseparable, being the necessary condi- tions of each other. — But this by the way. The qualities of difi'erent individual things, thus identified in thought, and constituting concepts, under which, as classes, these individual things themselves are ranged ; — these primary concepts may themselves be subjected to the same process, by which they were elaborated from the concrete realities given in Percep- tion and Imagination. We may, again, compare differ- ent concepts together, again find in the plurality of at- tributes which they comprehend, some like, some unlike; we may again attend only to the similar, and again identify these in the synthesis of consciousness ; and this process of evolving concepts out of concepts we may go on performing, until the generalisation is arrested in that ultimate or primary concept, the basis itself of all attributes, — the concept of Being or Existence. K>4 I.IXTI'KKS l)N I.OCH'. LKtT. llaviii'^ thus (.Mulcavoiut'd to givt' y»»ii a <^a'iifral ^"'' viow of what concepts arc, aiul by what process they of CouccjiU. aiv fornu'd, 1 statcil hy way of corollary, some of their ujenoral charai'toristics. The first of these I mentioned is their partiality or inadecpaey, — that is, they com- prehend only a larger or smaller portion of the whole attributes belonging to the things classified or con- tained under them. KcUiv.ty The second is their relativity. Formed by compari- son, they express only a relation. They cannot, there- fore, be held up as an absolute object to consciousness, — they cannot be represented, as universals, in ima- gination. They can only be thought of in relation to some one of the individual objects they classify, and, Avhen viewed in relation to it, they can be represented in imagination ; but then, as so actually represented, they no longer constitute general attributions, they fall back into mere special determinations of the individual object in wliich they are represented. Thus it is, that the generality or universality of concepts is potential, not actual. They are only generals, inasmuch as they may be applied to any of the various objects they contain ; but while they cannot be actually elicited into consciousness, except in application to some one or other of these, so, they cannot be so applied with- out losing, i^ro tanto, their universality. Take, for example, the concept horse. In so far as by horse we merely think of the word, that is, of the combination formed by the letters, h, o, r, s, e, — this is not a con- cept at all, as it is a mere representation of certain individual objects. This I only state and eliminate, in order that no possible ambiguity should be allowed to lurk. By horse, then, meaning not merely a re- presentation of the word, but a concept relative to LECTURES ON LOGIC. 135 certain objects classed under it ; — the concept horse, lect I say, cannot, if it remain a concept, that is, a uni- vin. versal attribution, be represented in imagination ; i,,aveTpo- but, except it be represented in imagination, it cannot anlttn^"!, be applied to any object, and, except it be so applied, "°"'®''^*'y it cannot be realised in thought at all. You may try to escape the horns of the dilemma, but you cannot. You cannot realise in thought an absolute or irre- spective concept, corresponding in universality to the application of the word ; for the supposition of this involves numerous contradictions. An existent horse is not a relation, but an extended object possessed of a determinate figure, colour, size, &c. ; horse, in general, cannot, therefore, be represented, except by an image of something extended, and of a determinate figure, colour, size, &c. Here now emerges the con- tradiction. If, on the one hand, you do not represent something extended and of a determinate figure, colour, and size, you have no representation of any horse. There is, therefore, on this alternative, nothing which can be called the actual concept or image of a horse at all. If, on the other hand, you do represent something extended and of a determinate figure, colour, and size, then you have, indeed, the image of an individual horse, but not a universal concept co- adequate with horse in general. For how is it pos- sible to have an actual representation of a figure, which is not a determinate figure ? but if of a deter- minate figure, it must be that of some one of the many different figures under which horses appear ; but then, if it be only of one of these, it cannot be the general concept of the others, which it does not repre- sent. In like manner, how is it possible to have the actual representation of a thing coloured, which is loG i.KcrrKKs on i.ocic i.Krr. not tlio ri'|tivsi'ntalion of a detcnninate I'oloiir, lliat ^"'' is, oithor white, or l>lack, or grey, or brown, &c.'? but if it be any one of these, it can only represent ;i horse of this or that partieuhvr colour, and cannot be the general concept of horses of every colour. 'I'he same result is given by the other attributes ; antt what I originally stated is thus manifest, — that concepts liavc only a potential, not an actual, universality, that is, they are only universal, inasmuch as they may be applied to any of a certain class of objects, but as actually applied they are no longer general attribu- tions, but only special attributes. But con- But it does not from this follow that concepts are not, there- mere words, and that there is nothing general in woni""' "^ thought itself. This is not indeed held in reality by any philosopher ; for no philosopher has ever denied that we are capable of apprehending relations, and in particular the relation of similarity and difference ; so that the whole controversy between the conceptualist and nominalist originates in the ambiguous employ- ment of the same terms to express the representations of Imagination and the notions or concepts of the Understanding. This is significantly showm by the absolute non-existence of the dispute among the philo- sophers of the most metaphysical country in Europe. In Germany the question of nominalism and concep- tualism has not been agitated, and wdiy ? Simply be- cause the German language supplies terms by which concepts, (or notions of thought proper), have been contradistinguished from the presentations and repre- sentations of the subsidiary faculties." But this is not a subject on which I ought at present to have a See the Author's note, lieid's tcqjhi/sccs, vol. ii. \k 290 ct ^eq. — Worku, i>. 412 ; and Ledures on Me- Ed. LECTURES ON LOGIC. 137 touched, as it is, in truth, foreign to the domain of lect. Logic ; and I have only been led now to recur to it L_ at all, in consequence of some difficulties expressed to me by members of the class. — All that I wish you now to understand is, — that concepts, as the result of comparison, that is, of the apprehension and affirma- tion of a relation, are, necessarily, in their nature re- lative, and, consequently, not capable of representa- tion as absolute attributes. I shall terminate the consideration of concepts in general by the following paragraph, in which is stated, besides their inadequacy and relativity, their depend- ence on language : — IF XXIII. The concept thus formed by an ab- Par.xxiii. straction of the resembling from the non-resem- c °tS^' bling qualities of objects, would again fall back on^Lan-"'"*' into the confusion and infinitude from which it has ^*^^' been called out, were it not rendered permanent for consciousness, by being fixed and ratified in a verbal sign. Considered in general, thought and language are reciprocally dependent ; each bears all the imperfections and perfections of the other; but without language there could be no know- ledge realised of the essential properties of things, and of the connection of their accidental states. This also is not a subject of which the considera- The relation tion properly belongs to Logic, but a few words may u. Sght not be inexpedient to make you aware, in general, of I'nflulnce the intimate connection of thought and its expression, excrtlm and of the powerful influence which language exerts oJerTtioi". upon our mental operations. Man, in fact, only ob- tains the use of his faculties in obtaining the use of speech, for language is the indispensable mean of the 138 LECTri;i:s on iahwc LKtT. Vlll. uuiuv»'>-Miry in oortitiu nu-ut4il o)H.*raliuus. Mental oiicrations to which language is indispen- sable, and its relation to these. lUvoIitpnuMit of his natural powers, wliother intellec- tual or moral. l'\»r rerei'ption, iiulecil, for tlie mere consciousness o( the similarities and dissimilarities in the ohjeets perceived, for the ap})rehension of the causal connec- tion of certain thiiii;s, and for tlie a}>plication of this knowledge to the attainment of certain ends, no lan- guage is necessary ; and it is only the exaggeration of a truth into an error, when philosophers maintain that language is the indispensable condition of even the simpler energies of knowledge. Language is the attribution of signs to our cognitions of things. But as a cognition must have been already there, before it could receive a sign ; consequently, that knowledge which is denoted by the formation and application of a word, must have preceded the symbol which denotes it. Speech is thus not the mother, but the godmother, of knowdedge. But though, in general, we must hold that language, as the product and correlative of thought, must be viewed as posterior to the act of thinking itself; on the other hand, it must be admitted, that we could never have risen above the very lowest degrees in the scale of thought, without the aid of signs. A sign is necessary, to give stability to our intellectual progress, — to establish each step in our advance as a new starting-point for our advance to another beyond. A country may be overrun by an armed host, but it is only conquered by the establishment of fortresses. AVords are the fortresses of thought. They enable us to realise our dominion over what we have already overrun in thought ; to make every intellectual con- quest the basis of operations for others still beyond. — (Jr another illustration : — You have all heard of the LECTURES ON LOGIC. 139 process of tunnelling, of tunnelling through a sand- lect. bank. In this operation it is impossible to succeed, unless every foot, nay almost every inch in our pro- gress, be secured by an arch of masonry, before we attempt the excavation of another. Now, language i^'"'^ ^* to the mind precisely what the arch is to the tunnel. The power of thinking and the power of excavation nre not dependent on the word in the one case, on the mason- work in the other ; but without these subsi- diaries, neither process could be carried on beyond its rudimentary commencement. Though, therefore, we allow that every movement forward in language must be determined by an antecedent movement forward in thought ; still, unless thought be accompanied at each point of its evolution, by a corresponding evolution of language, its further development is arrested. Thus it is, that the higher exertions of the higher faculty of Understanding, — the classification of the objects pre- sented and represented by the subsidiary powers in the formation of a hierarchy of notions, the connection of these notions into judgments, the inference of one judgment from another, and, in general, all our con- sciousness of the relations of the universal to the par- ticular, consequently all science strictly so denomin- ated, and every inductive knowledge of the past and future from the laws of nature : — not only these, but all ascent from the sphere of sense to the sphere of moral and religious intelligence, are, as experience proves, if not altogether impossible without a language, at least possible only to a very low degree. Admit- ting even that the mind is capable of certain ele- mentary concepts without the fixation and signature of language, still tlicse are but sparks which would twinkle only to expire, and it requires words to give 140 LKcTlKKS ON LOdlC. i.KcT. tluMu i>ri>nHiu'n('i\ ;nul, by eiiablin<]j us t(> colloet niul VIII. . — elaborate tluin into now concepts, to raisi> ontof what would (ithcrwise W only scattered and transitory scin- tillations a vivid and enduring light. B. ofCim- I here terminate the General and proceed to the Nations in Spei-ial consideration of Concepts — that is, to view sp«.H.ia. ^]^QYn in their several Relations. Now, in a logical point of view, there are, it seems to me, only three possible relations in which concepts can be considered; for the only relations they hold are to their objects, to their subject, or to eacli other. In relation to their objects, — they are considered as inclusive of a greater or smaller number of attributes, that is, as applicable to a greater or smaller number of objects ; this is tech- nically styled their Quantity. In relation to their subject, that is, to the mind itself, they are considered as standing in a higher or a lower degree of conscious- ness, — they are more or less clear, more or less distinct ; this, in like manner, is called their Qualify. In rela- tion to each other, they are considered as the same or different, co-ordinated or subordinated to each other ; this is their Relation, strictly so called." Under these three heads, I now, therefore, proceed to treat them ; and, first, of their Quantity. Piir. XXIV. ^ XXIV. As a concept, or notion, is a thought cwptl of in wdiich an indefinite plurality of characters is a On their relation to tlieir origin havethequantityofextension. These as direct or indirect, see Esser, two thus quantity in general. [System der Logik, § 49, p. 96. — Ed.] 3°, By relation to each other they Mem. — N.B. Notions may be thus have relation strictly so called, better (?; divided : — 4°, By relation to their subject 1°, By relation to themselves they they have clearness and distinctness, have the quantity of coni])rehenHion. (This last had better be relegated 2°, By relation to their objects they to Methodology.) — Memoranda. LECTURES ON LOGIC. 141 bound up into a unity of consciousness, and ap- lect VIIL plicable to an indefinite plurality of objects, a , „ ., . , two kinds, concept IS, tnereiore, necessarily a quantity, and intensive , . , and Exten- a quantity varying m amount according to the sive. greater or smaller number of characters of which it is the complement, and the greater or smaller number of things of which it may be said. This quantity is thus of two kinds ; as it is either In- tensive or Extensive. The Internal or Intensive Quantity of a concept is determined by the greater or smaller number of constituent characters con- tained in it. The External or Extensive Quantity of a concept is determined by the greater or smaller number of classified concepts or realities contained under it. The former (the Intensive Quantity) is called by some later Greek logicians depth, (/3a^os) ; by the Latin logical writers com- prehension, [comiDvehensio, quantitas compre- hensionis, complexus, or quantitas complexus). The latter (the Extensive Quantity) is called by the same later Greek Logicians the breadth, (TrXarog) ; by Aristotle, 17 Trepio^r], to Trepie^eiv, TO Trepiix^crBai ; " by the logical writers of the western or Latin world, the extension or circuit, {extensio, quantitas extensionis, ambitus, quan- titas ambitus) and likewise the domain or sphere of a notion, [regio, sphcera).^ a See Lectures on Metaphy.ncs, vol. cahilin, cc. i. ii. ] [p. 37 ed. 1579; ii. p. 290 n. Aristotle does wot use prefixed to his Commentary on the ireptoxv as a substantive, though C'atnjoHcs, first published in 149G : the verb, both active and passive, "Ad hoc breviter dicitur, quod esse is employed in this signification, magis colluctivum multorum potest e.g. Anal. Prior., i. 27; Jihet., iii. 5. intoUigi dupliciter : uno modo iiWm- — Ed. slve, et sic species magis eat colloc- /3 [Cf. Porphyrii, hagoye, cc. i. ii. tiva, quia magis unit adunata ; alio viii. ; Cajctan, In Porphyrii Pncdi- raodo f.;!TiOij- antipredicamental rule, C'ateg. iii. 1, (reroi. — Ed. "Offo Kara tov KaTrjyopovfXfvov X^yerai LECTURES ON LOGIC. 145 importance with that which they have exclusively lect. developed, and which is founded on the other kind of L quantity exhibited by concepts, and to which I now proceed. But a concept may also be considered externally, 2. Exten- that is, as a unity which contains under it a plurality of classifying attributes or subordinate concepts, and, in this respect, it has another quantity which may be called its external or extensive quantity. This is commonly called its extension ; sometimes its sphere or domain, (sphcera, regio, quantitas, ambitus) ; and, by the Greek Logicians, its breadth or latitude, {nXd- Tos.y Here the parts which the total concept contains, are said to be contained under it, because, holding the relation to it of the particular to the general, they are subordinated or ranged under it. For example, the concepts 7nan, horse, dog, &c., are contained under the more general concept a^mnal, — the con- cepts triangle, square, circle, rhombus, rhomboid. Sec, are contained under the more general concept figure ; inasmuch as the subordinate concepts can each or any be thought through the higher or more general. But as each of these subordinate concepts is itself a whole or general, which contains under it parts or more particular concepts, it follows, again, on the axiom or self-evident truth, that a part of a part is a part of the whole, — an axiom which, you will here- after see, constitutes the one principle of all Deductive reasoning, — it follows, on this axiom, that whatever is contained under the partial or more particular con- cept is contained under the total or more general concept. Thus, for example, triangle is contained ■ander figure ; all, therefore, that is contained under o See above, p. 141, notes a, /3. — Ed. VOL. I. K UG LKCTIRKS ON lAHilV. LECr. VUl. Intensive ami Kxtou- sive quau- titics are opposed to each other. h'iaiK/Ji', as nr(((tK/h'd (riaiujie, equilateral triangle, kc, will, likoNvisc, bo coiitaiuod undov Jig lire, by which wo may, aoroiHliiioly, think and describe them. ISiR'h, ill general, is what is meant by the two Quantities of concepts, — their Comprehension and Extension. But these quantities are not only different, they are opposed, and so opposed, that though each supposes the other as the condition of its own existence, still, however, within the limits of conjunct, of correlative existence, they stand in an inverse ratio to each other, — the maximum of the one being necessarily the minimum of the other. On this I give you the fol- lowing paragraph : — Par. XXV. Law ref- lating the mutual re- lations of Extension and Com- preheosion. H XXV. A notion is intensively great in pro- portion to the greater number, and intensively small in proportion to the smaller number, of determinations or attributes contained in it. Is the Comprehension of a concept a minimum, that is, is the concept one in which a plurality of attributes can no longer be distinguished, it is called simple ; whereas, inasmuch as its attri- butes still admit of discrimination, it is called complex or compound.'^ A notion is extensively great in proportion to the greater number, and extensively small in proportion to the smaller number, of determina- tions or attributes it contains under it. When the Extension of a concept bcomes a minimum, that is, when it contains no other notions under it, it is called an individual.^ These two quantities stand always in an inverse o Krug, Loglk, § 28.— Ed. /3 Knig, ibid., § 29.— Ed. LECTURES ON LOGIC. 147 ratio to each other : For the neater the Compre- lect. vm. hension of a concept the less is its Extension, and the greater its Extension the less its Com- prehension." To illustrate this : — When I take out of a concept, iiiustratiou. that is, abstract from one or more of its attributes, I diminish its comprehension. Thus, when from the concept man, equivalent to rcUioncd animal, I abstract from the attribute or determination rational, I lessen its internal quantity. But by this diminution of its comprehension I give it a wider extension, for what remains is the concept a^iimal, and the concept animal embraces under it a far greater number of objects than the concept man. Before, however, proceeding further in illustrating the foregoing paragraph, it may be proper to give you also the following : — 1i XXVI. Of the logical processes by which these Par.xxvL , , • , • f , T r> 1 Processes counter quantities oi concepts are amplined, — by which the one which amplifies the Comprehension ispreheuslon called Determination, and sometimes called Co7i- sk)u of '^^ cretion, the other which amplifies the Extension is are Lmpn- called Abstraction or Generalisation. Definition vlLuU. and Division are severally the resolution of the Comprehension and of the Extension of notions, into their parts. A Simple notion cannot be de- fined ; an Individual notion cannot be divided./^ a Krug, Locjik, § 27. — Ed. ; /3 [Synonyms of Abstraction: — 1, [Scliulze, Logik, § 33. Cf . Porphyry, Analysis (of Comprehension) ; 2, Syu- Isfuprje, c. viii. §§ 9, 10.] ["En to. thesis; .'}, Generification ; 4, Induc- fiiv yevri irXeovd^eL t^ tSiv vit' avra tion ; 5, Amplification. elSwv TTfpiox^' TO 5e efSrj raiv ytyoju Synonyms of Determination or ■nXeovd^fi Ta7s o'lKeiais Siacpopals. "Eti Concretion : — I, Analysis (of Exten- ovT€ rh flSos y^voiT av yeuiKooraTov sion) ; 2, Synthesis ; .3, Specification; ovre rh y4vos elSiKwraroi'. — Ed.] 4, Restriction ; 5, Individuation.] 1 IS LECTURES ON LOGIC. Lv.cv. Tlie ivasDii o( this opposition of the two c|iuiiilities VIII. •. .• ■_ is nianifost in a inoiiiont, from the consideration of i.fiiKMwo" thoir several natures. The comprehension of a con- ,r^J™Hi>. t'l^pt is nt)thing more than a sum or complement eonipr^hou- ^f tlie distinouisliinjT characters, of which the con- sion ami O O ' Esiousiou cept is made up; and tlie extension of a concei)t in au in- ^g nothin^r morc than the sum or complement of verse ratio _ *-' -•■ toeaoh the objects themselves, whose resembling characters other. J ' _ <=» , were abstracted to constitute the concept. Now, it is evident, that the more distinctive characters the concept contains, the more minutely it will distinguish and detennine, and that if it contain a plenum of distinctive characters, it must contain the distinctive, — the determining, characters of some individual ob- ject. How do the two quantities now stand ? In regard to the comprehension or depth, it is evident, that it is here at its maximum, the concept being a complement of the whole attributes of an individual object, which, by these attributes, it thinks and dis- criminates from every other. On the contrary, the extension or breadth of the concept is here at its minimum ; for, as the extension is great in propor- tion to the number of objects to which the concept can be applied, and as the object is here only an individual, it is evident it could not be less, without ceasing to exist at all. Again, to reverse the process ; — throwing out of the comprehension of the concept, that is, abstracting from those attri- butes, which belonging exclusively to, exclusively distinguish, the individual, we at once diminish the comprehension, by reducing the sum of its at- tributes, and amplify the extension of the concept, by bringing within its sphere all the objects, which the characteristics, now thrown out of the comprehen- LECTUKES ON LOGIC. 149 sion, had previously excluded from the extension, lect. Continuing the process, by abstraction we throw out _ of the sum of qualities constituting the comprehension, other discriminating attributes, and forthwith the extension is proportionally amplified, by the entrance into its sphere of all those objects which had pre- viously been debarred by the determining character- istics last discarded. Thus proceeding, and at each step ejecting from the comprehension those characters which are found the proximate impediments to the amplification of the extension of the concept, we at each step diminish the former quantity precisely as we increase the latter ; till, at last, we arrive at that concept which is the necessary constituent of every other, — at that concept which all comprehension and all extension must equally contain, but in which com- prehension is at its minimum, extension at its maxi- mum, — I mean the concept oi Being or Existence.'^ We have thus seen, that the maximum of compre- Definition hension and the minimum of extension are found in sL.-Ir'e the concept of an individual, — that the maximum of ex- cessesTy .. Ill'' p 1' i^i which Com- tension and the mmimum oi comprehension are lound prehension in the concept of the absolutely simple, that is, in the sL of^con- concept of existence. Now comprehension and exten- TIoi-^cl sion, as quantities, are wholes ; for wholes are only the complement of all their parts, and as wholes are only by us clearly comprehended as we distinctly comprehend their parts, it follows : — 1°, That com- prehension and extension may each be analysed into its parts ; and, 2", That this analysis will afibrd the mean by which each of these quantities can be clearly and distinctly understood. But as the two quantities o This, like other logical relations, [See below, p. 152.^Ed.] may be typified by a sensible figure. 150 l.ECTrUES ON I.OCIIC. LKiT. are of an opposite nature, it is manifest that the two processes of analysis w ill, likewise, be opposed. The analysis of the intensive or comprehensive quantity oi' concepts, tliat is, their dei)tli, is accom])lished by 1 )eliuition; that of their extensive quantity or breadth, by Division. On Definition and Division I at present touch, not to consider them in themselves or on their own account, that is, as the methods of clear and of distinct thinking, for this will form the matter of a special discussion in the Second Part of Logic or Methodology, but simply in so far as it is requisite to speak of them in illustration of the general nature of our concepts. Definiiion Thc cxpository or explanatory analysis of a concept, considered as an intensive whole or quantum, if pro- perly effected, is done by its resolution into two con- cepts of which it is proximately compounded, that is, into the higher concept under which it immediately stands, and the concept which affords the character by which it is distinguished from the other co-ordi- nate concepts under that higher concept. This is its Definition ; that is, in logical language, its expo- sition by an analysis into its Genus and Differential Quality ; — the genus being the higher concept, under which it stands ; the differential Cjuality the lower concept, by which it is distinguished from the other concepts subordinate to the genus, and on a level or co-ordinate with itself, and which, in logical language, are called Sj^ecies. For example, if we attempt an expository or explanatory analysis of the concept 7nan, considered as an intensive quantity or complexus of attributes, we analyse it into animal, this being the higher concept or genus under which it stands, and rational, the attribute of reason being the character- LECTURES ON LOGIC. 151 istic or differential quality by which man is dis- lect. tinguished from the other concepts or species which L stand co-ordinated with itself, under the genus animal, — that is, irrational animal or brute. Here you will observe, that though the analysis be of the comprehension, yet it is regulated by the ex- tension ; the extension regulating the order in which the comprehension is resolved into its parts. The expository analysis of a concept, an extensive Division. whole or quantum, is directly opposed to the preceding, to which it is correlative. It takes the higher con- cept, and, if conducted aright, resolves it into its proxi- mately lower concepts, by adding attributes which afford their distinguishing characters or differences. This is division : — Thus, for example, taking the high- est concept, that of ens or existence, by adding to it the differential concepts per se. or substantial, and non per se or accidental, we have substantial existence or exist- ence per se, equivalent to substance, and accidental existence or existeyice non per se, equivalent to acci- dent. We may then divide substance by simple and not-simple, equivalent to compound, and again simple by material and non-material, equivalent to imma- terial, equivalent to spiritual ; — and matter or material substance by organised and not-organised, equivalent to brute matter. Organised matter we may divide by sentieiit or animal, and non-sentient or vegetable. Animal we may divide hj rational and irrational, and so on, till we reach a concept which, as that of an individual object, is, in fact, not a general concept, but only in propriety a singular representation. Thus it is manifest, that as Definition is the analysis The indc- of a complex concept into its component parts or at- imnlisibiL tributes, if a concept be simple, that is, if it contain in i:.2 i.iX'Tri;i:s on iahwv LECT. it only a .siiiirlo attrilmti', it must be iiuloliiiable ; ami Vlll. ..... JiiX^nn, that as Division is the analysis of a higher (»r move general concept into others lower and less gen- eral, if a concept be an individual, that is, only a bundle of individual qualities, it is indivisible, is, in fact, not a proper or abstract concept at all, but only a concrete representation of the Imagination, Dimrram "" Xlic followino- Diao;ram represents Breadth and rcpivseutiug o o i Ksiciusiou Depth, with the relations of Affirmation and Necjation and t i>iu- ^ ^ prvhensiou to thesc Quantitics. of Concepts. ^ Schemes of the Two Quantities. Line of Breadth. Aff. Neg- Explana- tion. n. D. vi. 1. V. 2. iv. 3. iii. 4. ii. 5. i. 6. A A A A A A \A E E E E E IE 1 I I I I 10 \I U U 1^ Y \Y z z' z" I I! m Ground of Reality. In the preceding Table there are represented : — by A, A, &c., the highest genus or widest attribute ; by Y, the lowest species or narrowest attribute ; whilst the other four horizontal series of vowels typify the subaltern genera and sj^ecies, or the intermediate attributes. The voiuels are reserved exclusively for classes, or common qualities; whereas the consonants z, z', z", (and which to render the contrast more ob- a Tlie Diagram and relative text to end of Lecture arc extracted by the Editors from the Author's Dis- cusdio/m, p. 699-701. — Ed. LECTURES ON LOGIC. 153 trusive are not capitals,) represent individuals or sin- lect. gulars. Every higher class or more common attribute - is supposed (in conformity with logical precision) to be dichotomised, — to be divided into two by a lower class or attribute, and its contradictory or negative. This contradictory, of which only the commencement appears, is marked by an italic vowel, preceded by a perpendicular line ( | ) signifying not or non, and analogous to the minus (— ) of the mathematicians. This being understood, the Table at once exhibits the real identity and rational differences of Breadth and Depth, which, though denominated quantities, are, in reality, one and the same quantity, viewed in counter relations and from ojDposite ends. Nothing is the one, which is not, pro tanto, the other. In Breadth : the supreme genus (A, A, &c.) is, as it appears, absolutely the greatest whole ; an indivi- dual (z) absolutely the smallest part ; whereas the intermediate classes are each of them a relative part or species, by reference to the class or classes above it ; a relative whole or genus, by reference to the class or classes below it. — In Depth : the individual is ab- solutely the greatest whole, the highest genus is abso- lutely the smallest part ; whilst every relatively lower class or species, is relatively a greater whole than the class, classes, or genera, above it. — The two quantities are thus, as the diagram represents, precisely the in- verse of each other. The greater the Breadth, the less the Depth ; the greater the Depth, the less the Breadth : and each, within itself, affording the corre- lative differences of whole and part, each, therefore, in opposite respects, contains and is contained. But, for distinction's sake, it is here convenient to employ a difference, not altogether arbitrary, of expression. 154 LECTUKKS ON I.OCIC. LKCT. We should s;i y : — "containing and contaiiu'd unih'7;" _ i'ov liri'adtli ; "containing and contained in," for Dcjtlli. This distinction, \vhich has been taken by some modern logicians, though unknown to many ot" them, was not observed by Ai'istotle. We find liim, (to say nothing of otlier ancient logicians), using the expression eV oXm eTi^ai or virdpyeiv, for either whole. Though dilierent in the order of thought {ratione), the two quantities are identical in the nature of things (re). Each supposes the other; and Breadth is not more to be distinguished from Depth, than the relations of the sides, from the relations of the angles, of a triangle. In effect it is precisely the same reasoning," whether we argue in Depth, — " z' is (i.e. as subject, contains in it the inherent attribute) some Y ; all Y is some U ; all U is some ; all is some I ; all I is some E ; all E is some A ; — there- fore, z' is some A:" or whether we argue in Breadth, — " Some A is {i.e. as class, contains under it the subject part) all E ; some E is all I ; some I is all ; some is all U ; some U is all Y ; some Y is z' ; — therefore, some A is z'." The two reasonings, internally iden- tical, are externally the converse of each other ; the premise and term, which in Breadth is major, in Depth is minor. In syllogisms also, where the con- trast of the two cj[uantities is abolished, there, with the difference of figure, the differences of major and minor premise and term fall likewise. In truth, how- ever, common language in its enouncement of pro- positions, is here perhaps more correct and philoso- phical than the technical language of logic itself. For as it is only an equation — only an affirmation of identity or its negation, which is, in either quantity, proposed ; therefore the substantive verb, {is, is 7iot,) LECTUKES ON LOGIC. 155 used in both cases, speaks more accurately, than the lect expressions, contained, (or not contained) in of the '- one, contained, (or not contained) under of the other. In fact, the tivo quantities and the two qiamtijications have by logicians been neglected together. This Table, (the principle of which becomes more palpably demonstrative, when the parts of the table are turned into the parts of a circular machine**), exhibits all the mutual relations of the counter quan- tities. — 1°, It represents the classes, as a series of resemblances thought as one, (by a repetition of the same letter in the same series,) but as really distinct, (by separating lines). Thus, A is only A, not A, A, A, &c. ; some Animal is not some Animal ; one class of Animals is not all, every, or any other ; this Animal is not that ; Socrates is not Plato ; z is not z\ On the other hand, E is E A ; and Y is YUOIEA; every lower and higher letter in the series coalescing uninterruptedly into a series of reciprocal subjects and predicates, as shown by the absence of all discrim- inating lines. Thus, Socrates (z'), is Athenian (Y), Greek (U), European (0), Man (I), Mammal (E), Ani- mal (A). Of course the series must be in gram- matical and logical harmony. We must not collate notions abstract and notions concrete. — 2°, The Table shows the inverse correlation of the two quantities in respect of amount. For example : A, (i.e. A, A, &c.), the highest genus, is represented as having six times the Breadth of Y ; whilst Y, (i.e. Y — A), the lowest species, has six times the Depth of A. — 3°, The Table mani- fests all the classes, as in themselves unreal, subjective, a A machine of this kiiul was con- trine of the text. For a description structed by the Author, and usi'd in of it see Memoir of f-'ir W. Jfarni/foii, the class-room to ilhistrate the doc- \). 2i9-'252. — Ed. 150 LECTURES ON L0(;1C. LECT. iilial ; for tlu'so arc merely fictions or artifices of the VIII. ... — mind, for the coiivenieiice of thiukiiig. Universals only exist in iiatuiT, as they cease to be universal in tlioucjht ; that is, as they are reduced from general and abstract attributes to individual and concrete qualities. A — Y are only truly objective as distri- buted through z, //, z", &c. ; and in that case they are not universals. As Boethius expresses it : — " Omne quod est, eo quod est, singulare est." — 4°, The opposition of class to class, through contradictory attributes, is distinguished by lines different from those marking the separation of one part of the same class from another. Thus, Animal, or Sentiently- orgauised, (A), is contrasted "with Not-animal, or Not- sentieutly - organised, ( | A), by lines thicker than those which merely discriminate one animal (A), from another (A).*^ o See further iu Discussmis, p. 701 et seq. — Ed. LECTURES ON LOGIC. 157 LECTURE IX. STOICHEIOLOGY. SECT. II. OF THE PRODUCTS OF THOUGHT. I. ENNOEMATIC. B. OF CONCEPTS IN SPECIAL. — II. THEIR SUBJECTIVE RELATION — QUALITY. Having concluded the consideration of the relation lect. of concepts to their objects, — the relation in which — — — their Quantity is given, I now proceed to consider concept "o their relation to their conceiving subject — the relation jJcT ^" ' in which is given their Quality. This consideration of the quality of concepts does not, in my opinion, belong to the Doctrine of Elements, and ought, in scientific rigour, to be adjourned altogether to the Methodology, as a virtue or perfection of thought. As logicians, however, have generally treated of it likewise under the former doctrine, I shall do so too, and commence with the following paragraph. U XXVII. A concept or notion is the unity in Par.xxvn, consciousness of a certain plurality of attributes, of Conccpu 1 • , .1 ,1 p ,^ • 1 consists in and it, consequently, supposes the power of thmk- its logical ing these, both separately and together. But as or'^impir" there are many gradations in the consciousness with which the characters of a concept can be thought severally and in conjunction, there will consequently be many gradations in the actual 1 :.s LEcrrinis on i.ociic. LKlT. IX. IVrfociion or lin[H rl'ocliou of a notion. It is this ju'i-frititMi or imperfection which constitutes the logical Quality of a concept." ll is thus the o-ivater or smaller decree of conscious- ncss which accompanies the concept and its object, that determines its quality, and according to which it is called logically perfect or logically imperfect. Now there may be distinguished two degrees of this logical perfection, the nature of which is summarily expressed in tlie following j)aragraph. Par.XXVllI. Tlie two ilegrecs of tlie logical Perfect ion and Imper- fection of Concepts, — their Clear- ness anil Distinct- ness, and their Ob- scurity and Indistinct- ness. "i XXVIII. There are two deo^rees of the looical perfection of concepts, — viz. their Clearness and their Distinctness, and, consequently, two opposite degrees of their corresponding imperfection, — viz. their Obscurity and their Indistinctness. These four qualities express the perfection and imper- fection of concepts in extremes ; but between these extremes, there lie an indefinite number of intermediate degrees. A concept is said to be clear {clara), when the deoTce of consciousness is such as enables us to distinguish it as a whole from others ; and obscure {obscura), when the degree of conscious- ness is insufficient to accomplish this. A concept is said to be distinct {distincta, perspicua), when the degree of consciousness is such, as enables us to discriminate from each other the several characters, or constituent parts of which the con- cept is the sum ; and indistinct or confused {indistincta, confusa, imp>e7^spicua), wdien the amount of consciousness requisite for this is a Knig, LogiTc, § 30. Cf. Esser, Loyik, % 45 tt »eq. — Ed. LECTURES OX LOGIC. 159 wanting. Confused (confusa) may be employed lect as the genus including obscure and iridistinct."' — — The expressions clearness and ohscuritij, and dis- Original tinctness and indistinctness, as applied to concepts, ofthetx- originally denote certain modifications of vision ; from t/ea™^*, vision they were analogically extended to the other &c."'" ^' senses, to imagination, and finally to thought. It may, therefore, enable us the better to comprehend their secondary application, to consider their primitive. To Leibnitz^ we owe the precise distinction of concepts into clear and distinct, and from him I borrow the following illustration. In darkness, — in the complete illustrated obscurity of night, — we see nothing, — there is no per- tJvrsron."'^^ ception — no discrimination of objects. As the light dawns, the obscurity diminishes, the deep and uniform sensation of darkness is modified, — we are conscious of a change, — we see something, but are still unable to distinguish its features, — we know not what it is. As the light increases, the outlines of wholes begin to appear, but still not with a distinctness sufficient to allow us to perceive them completely ; but when this is rendered possible, by the rising intensity of the light, we are then said to see clearly. We then re- cognise mountains, plains, houses, trees, animals, &c., that is, we discriminate these objects as wholes, as unities, from each other. But their parts, — the mani- fold of which these unities are the sum, — their parts still lose themselves in each other, they are still but a Compare Knig, Logik, 31 et seq. L. ii., ch. xxix. The illustration, — Ed. [Buffier, Lo;jiqne, § 345 et seq. however, does not occur iu either of Kant, Kr.d.r. Fer)iuiift,}j. ii. Trans, these passages. It was probably Dial., art. i. p. 414, 3cl ed., 1790.] borrowed from Krug, Lo(/ik, § 31, j8 .See his Meditatioiies de Cogiil- and attributed to Leibnitz by an tlnne, Veritate, et Idcis, {Opera, ed. oversight. — -Ed. Erdmann, p. 71)), Nouveaux Esuals, 160 LKCrrUKS ON logto LECT. imlistiiu'tly visible. At longth when the daylight lias IX fiillv sprung, we are enabled likewise to discriminate their parts ; we now see distinctly what lies around us. But still we see as yet only the wholes which lie proximately around us, and of these, only the parts which possess a certain size. The more distant wholes, and the smaller parts of nearer wholes, are still seen by us only in their conjoint result, only as they con- cur in making up that whole which is for us a visible minimum. Thus it is, that in the distant forest or the distant liill, we perceive a green surface ; but we see not the several leaves, which in the one, nor the several blades of grass, which in the other, each con- tributes its effect to produce that amount of impres- sion which our consciousness requires. Thus it is, that all which we do perceive is made up of parts which we do not perceive, and consciousness is itself a complement of impressions, which lie beyond its apprehension." Clearness and distinctness are thus only relative. For between the extreme of obscurity and the extreme of distinctness, there are in vision an infinity of intermediate degrees. Now the same thing occurs in thought. For we may either be conscious only of the concept in general, or we may also be conscious of its various constituent attributes, or both the concept and its parts may be lost in themselves to consciousness, and only recognised to exist by effects which indirectly evidence their existence. Clearness The pcrfcction of a notion, as I said, is contained in *c°urity as two degrccs or in two virtues, — viz. in its clearness nccpts. ^^j ^ .^g distinctness ; and, of course, the opposite vices of obscurity and indistinctness afford two de- grees or two vices, constituting its imperfection. " A a Sec Lfcturea mi MetapJiT/sirs, vol. i. \>. .348 ct seq. — Ed. LECTURES ON LOGIC. 161 concept is said to be clear, when tlie degree of con- lect sciousness by which it is accompanied is sufficient to '- — discriminate what we think in and through it, from what we think in and through other notions ; whereas if the degree of consciousness be so remiss that this and other concepts run into each other, in that case, the notion is said to be obscure. It is evident that clearness and obscurity admit of various degrees ; each being capable of almost infinite gradations, ac- cording as the object of the notion is discriminated with greater or less vivacity and precision from the obiects of other notions. A concept is absolutely '^'^^^ shio- clear, when its obiect is distinguished from all other aud abso- . . -7777 1-1 ^"^'''y ''^• objects; a concept is absolutely obscure, when its ob-scure. ject can be distinguished from no other object. But it is only the absolutely clear and the absolutely ob- scure which stand opposed as contradictory extremes ; for the same notion can at once be relatively or com- paratively clear, and relatively or comparatively ob- scure. Absolutely obscure notions, that is, concepts whose objects can be distinguished from nothing else, exist only in theory ; — an absolutely obscure notion being, in fact, no notion at all. For it is of the very essence of a concept, that its object should, to a cer- tain degree at least, be comprehended in its peculiar, consequently, in its distinguishing, characteristics. But, on the other hand, of notions absolutely clear, that is, notions whose objects cannot possibly be con- founded with aught else, whether known or unknown, — of such notions a limited intelligence is possessed of very few, and, consequently, our human concepts are, properly, only a mixture of the opposite qualities; — clear or obscure as applied to them, meaning oidy that the one quality or the other is the preponderant. VOL. \. L 162 LECTUKKS ON LOCK'. i.KCY. Ill a lo;j;u-al rclalioii, (lu- illustration of notions con- _1__ sists in the raising tliein from a preponderant obscu- rity to a preponderant clearness — or from a lower decree of clearness to a hiojhcr."" So much for the (piality of clearness or obscurity considered in itself. Ti.o Pi*- P>ut a Clear concept may be either Distinct or ludis- I'lui I'miL- tinct ; the distinctness and indistinctness of concepts coucopTs" are, therefore, to be considered apart from their clear- ness and obscurity. Historical But before entering upon the nature of the distinc- this dislinc- tion itsclf, I may observe that we owe the discrimina- tion of Distinct and Indistinct from Clear and Ol^scure Due to notions to the acuteness of the great Leibnitz. By the ' °"'^' Cartesians the distinction had not been taken ; though the authors of the Port Royal Logic come so near, that we may well marvel howthey failed explicitly to enounce Locke. it.'^ Though Locke published his Essay Concernincj Human Understanding some five years subsequent to the paper in which Leibnitz — then a very young man — had, among other valuable observations, pro- mulgated this distinction, Locke did not advance be- yond the limit already reached by the Cartesians ; — indeed, the praises that are so frec[uently lavished on this philosopher for his doctrine concerning the dis- tinctions of Ideas, — the conditions of Definition, &c., — only prove that his encomiasts are ignorant of what had been done, and, in many respects, far better done, by Descartes and his school : — in fact, with regard to the Cartesian Philosophy in general, it must be con- fessed, that Locke has many errors to expiate, arising o Esser, pj). 91, 92, [Lofjik, §46. — Leibnitz, see the Appendix to Mr Ed.] Baynes'a translation of the Port Part 1. oh. ix. — For a compari- Royal Locjlc, p. 423 (second edition.) son of this statement of the distinc- — Ed. tion with those of Descartes aud LECTURES ON LOGIC. 163 partly from oversight, and partly from the most un- lect. accountable misapprehension of its doctrines. It is — — — almost needless to say, that those who, in this country, have written on this subject, posterior to Locke, have not advanced a step beyond him ; for though Leib- nitz be often mentioned, and even occasionally quoted, by our British philosophers, I am aware of none who possessed a systematic acquaintance with his philo- sophy, of none, I might almost say, who were even superficially versed, either in his writings, or in those . of any of the illustrious thinkers of his school. But to consider the distinction in itself. — We have The dis- . -, -t T 1 tinctiou in seen that a concept is clear, when we are able to re- itself. cognise it as different from other concepts. But we may discriminate a whole from other wholes, we may discriminate a concept from other concepts, though we have only a confused knowledge of the parts of which that whole, of the characters of which that concept, is made up. This may be illustrated by the iiiustrat- analogy of our Perceptive and Representative Faculties, analogy of We are all acquainted with many, say a thousand, andXpre- ■,..-,,,. . 1 -, 1 sentation. individuals ; that is, we recognise such and such a countenance as the countenance of John, and as not the countenance of James, Thomas, Richard, or any of the other 999. This we do with a clear and certain knowledge. But the countenances, which we thus distinguish from each other, are, each of them, a com- plement made up of a great number of separate traits or features ; and it might, at first view, be supposed that, as a whole is only the sum of its parts, a clear cognition of a whole countenance can only be realised through a distinct knowledge of each of its constituent features. But the slightest consideration will prove that this is not the case. For how few of us arc able ICA LECTUKKS ON LOGIC. i.Kscs the , f, , • • ,^ • • p .iiiTcix'uce the perpetrator oi a certain crime, the commission oi Jurr^Aua" which he had chanced to see, — would the counsel be kuowi"dge. allowed to invalidate the credibility of the witness by, first of all, requiring him to specify the various ele- ments of which the total likeness of the accused was compounded, and then by showing that, as the witness either could not specify the several traits, or specified what did not agree with the features of the accused, he was, therefore, incompetent to prove the identity or non-identity required 1 This would not be allowed. For the court would hold that a man might have a clear perception and a clear representation of a face and figure, of w^hich, however, he had not separately considered, and could not separately image to himself, the constituent elements. Thus, even the judicial de- termination of life and death supposes, as real, the difference between a clear and a distinct knowledge : for a distinct knowledge lies in the knowdedge of the constituent parts ; wdiile a clear knowledge is only of the constituted Avhole. Further Continuing our illustrations from the human coun- illustration ,, , ■■•, ^ -\ p r from the tcuance, — we all have a clear knowledge oi any lace which w^e have seen, but few of us have distinct knowledge even of those with which ^ve are familiar : but the paintr, who, having looked upon a counte- nance, can retire and reproduce its likeness in detail, has necessarily both a clear and a distinct know- human counte- nance. LECTURES ON LOGIC. 1G5 ledge of it. Now, what is tlius the case with percep- lect. tions and representations, is equally the case with ^— notions. AVe may be able clearly to discriminate one concept from another, although the degree of con- sciousness does not enable us distinctly to discrimin- ate the various component characters of either con- cept from each other. The Clearness and the Distinct- ness of a notion are thus not the same ; the former involves merely the power of distinguishing the total objects of our notions from each other; the latter in- volves the power of distinguishing the several charac- ters, the several attributes, of which that object is the sum. In the former, the unity, in the latter, the mul- tiplicity, of the notion is called into relief. The Distinctness of a concept supposes, however, the special Clearness ; and may, therefore, be regarded as a higher of the dis- degree of the same quality or perfection. "To the a Concept, distinctness of a notion, over and above its general degrees. clearness, there, are required three conditions, — 1°, The clear apprehension of its several characters or component parts ; 2°, The clear contrast or discrimination of these ; and, 3°, The clear recognition of the nexus by which the several parts are bound up into a unity or whole. " As the clearness, so the distinctness, of a notion is susceptible of many degrees. A concept may be called distinct, when it involves the amount of con- sciousness required to discriminate from each other its principal characters ; but it is so much the more dis- tinct, 1°, In proportion to the greater number of the characters apprehended ; 2°, In proportion to the greater clearness of their discrimination ; and, 3°, In proportion to the precision with which the mode of their connection is recognised. But the greater dis- tinctness is not exclusively or even principally deter- 1G6 LECTURES ON LOGIC. Lv.cT. niinoil by the greater nuiuber of the clearly appre- — — — liendecl characters ; it depends still more ou their superior iin})ortance. In particular, it is of moment, whether the characters be positive or negative, inter- nal or external, permanent or transitory, peculiar or common, essential or accidental, original or derived. From the mere consideration of the differences sub- sisting between attributes, there emerge three rules to be attended to in bestowing ou a concept its requisite distinctness. " In the first place, we should endeavour to discover the positive characters of the object conceived ; as it is our purpose to know what the object is, and not what it is not. When, however, as is not unfrequently the case, it is not at once easy to discover what the positive attributes are, our endeavour should be first directed to the detection of the negative ; and this not only because it is always an advance in knowledge, when we ascertain what an object is not, but, likewise, because the discovery of the negative characters con- ducts us frequently to a discovery of the positive. " In the second place, among the positive qualities we should seek out the intrinsic and permanent before the extrinsic and transitory ; for the former give us a purer and more determinate knowledge of an object, though this object may likewise at the same time present many external relations and mutable modifi- cations. Among the permanent attributes, the proper or peculiar always merit a preference, if for no other reason, because through them, and not through the common qualities, can the proper or peculiar nature of the object become known to us. " In the third place, among the permanent charac- ters we ought first to hunt out the necessary or essen- LECTURES ON LOGIC. 167 tia], and then to descend from them to the contingent lect. . IX or accidental ; and this not only because we thus give '. — order and connection to our notions, but, likewise, be- cause the contingent characters are frequently only to be comprehended through the necessary." " But before leaving this part of our subject, it may Thedis- be proper to illustrate the distinction of Clear and ciear and Distinct notions by one or two concrete examples. Of notions many things we have clear but not distinct notions, by concrete Thus we have a clear, but not a distinct, notion Qf '^^'^"'p '^"• colours, sounds, tastes, smells, &c. For we are fully able to distinguish red from white, to distinguish an acute from a grave note, the voice of a friend from that of a stranger, the scent of roses from that of onions, the flavour of sugar from that of vinegar ; but by what plurality of separate and enunciable charac- ters is this discrimination made "? It is because we are unable to do this, that we cannot describe such perceptions and representations to others. " If you ask of me," said St Augustin, " what is Time, I know not ; if you do not ask me, I know."/^ What does this mean 1 Simply that he had a clear, but not a distinct, notion of Time. Of a triangle we have a clear notion, when we distinguish a triangle from other figures, without spe- cially considering the characters which constitute it what it is. But when we think it as a portion of space bounded by three lines, as a figure whose three angles are equal to two right angles, &c., then we obtain of it a distinct concept. We now come to the consideration of the question, — now tho How does the Distinctness of a concept stand afi'ected of'fconccpt a Esser, Lorjik, § 47, p. 9.3-95. — /3 Confesmons, xi. c. 14. — Ed. Ed. 168 I.KCTriJKS ON \A)C,\C. i.KiT. l»v tilt' two (luaiitit ics of" ;i conci'itt ? -and in reference L!__ to this point I wnuM, in the lirst place, dictiite to you is afffctotl 1 ■• 1 1 • 1 bytiuMwo llie tollowuiLi; paragrapli : — t|uau(itio( of » C\>UOC|ll. pm.xxix. H XXIX. As a concept is a plurality of cliar- Distiiu-t- ^ . . . 1 1 1 T ni'>s. lutor- acters Ixnnul up into unity, ami as that plurality nitl auil . . ^ . . . y . . . Kxicru:J. IS contamed, partly in its Intensive, partly under its Extensive, quantity ; its Distinctness is, in like manner, in relation to these quantities, partly an Internal or Intensive, partly an External or Extensive Distinctness.* Espiication. In cxplanatioii of this, it is to be observed, that, as the distinctness of a concept is contained in the clear apprehension of the various attributes of which it is the sum, as it is the sum of these attributes in two opposite relations, which constitute, in fact, two oppo- site quantities or wholes, and as these wholes are severally capable of illustration by analysis, — it follows, that each of these analyses will contribute its peculiar share to the general distinctness of the concept. Thus, if the distinctness of a notion bears reference to that plurality which constitutes its comprehension, in other words, to that which is contained in the concept, the distinctness is denominated an internal or intensive distinctness, or distinctness of compi^eliensioii. On the other hand, if the distinctness refers to that plurality which constitutes the extension of the notion, in other words, to what is contained under it, in that case, the distinctness is called an external or extensive distinct- ness, a distinctness of extension. It is only when a notion combines in it both of these species of distinct- ness, it is only when its parts have been analysed in a Krug, Logik, § 34 ; Esser, Logik, § 48. — En. LECTURES ON LOGIC. 160 reference to the two quantities, that it reaches the lect. highest degree of distinctness and of perfection. — U — The Internal Distinctness of a notion is accom- Definition plished by Definition, that is, by the enumeration of sion. the characters or partial notions contained in it ; the External Distinctness, again, of a notion is accom- plished through Division, that is, through the enu- meration of the objects which are contained under it. Thus the concept man is rendered intensively more distinct, when we declare that man is a 7^ational ani- mal ; it is rendered extensively more distinct, when we declare that man is partly male, partly female man."' In the former case, we resolve the concept man into its several characters, — into its partial or constituent attributes ; in the latter, we resolve it into its subordinate concepts, or inferior genera. In simple no- simple notions, there is thus possible an extensive, ofLexten- but not an intensive, distinctness ; in individual dual notions notions, there is possible an intensive, but not an sive°dU extensive, distinctness.^ Thus the concepts existence, green, sweet, &c., though as absolutely or relatively simple, their comprehension cannot be analysed into any constituent attributes, and they do not, therefore, admit of definition ; still it cannot be said that they are incapable of being rendered more distinct. For do we not analyse the pluralities of which these con- cepts are the sum, when we say, that existence is either ideal or real, that green is a yellowish or a bluish green, that sweet is a pungent or a mawkish sweet "? — and do we not, by this analysis, attain a greater degree of logical perfection than when we think them only clearly and as wholes 'i'^ "A con- a Krug, p. 95, [Logik,% .34. — Ed.] y Krug, Logik, § .34, Annicrk., i. /3 Esser, Lnrjlk, § 48.— Ed. pp. 95, 90.— iio. 170 LECTURES ON LOfilC. i.vxT. oe})t has, therofoiv, attaiuod its highest point of dis- tinctness, ^vhen there is such a consciousness of its Ji'jwim characters that, in rendering its comi)rehensi()n dis- n[-iof'.r'" tinct, w'c, touch on notions which, as simple, admit of * ""'"^J"- no definition, and in rendering its extension distinct, we touch on notions which, as individual, admit of no ulterior division. It is true, indeed, that a distinct- ness of this degree is one which is only ideal ; that is, one to which we are always approximating, but which we never are able actually to reach. In order to approach as near as possible to this ideal, we must always inquire, what is contained in, and what under, a notion, and endeavour to obtain a distinct conscious- ness of it in both relations. What, in this research, first presents itself we must again analyse anew, with reference always both to comprehension and to exten- sion ; and descending from the higher to the lower, from the greater to the less, we ought to stop only when our process is arrested in the individual or in the simple." " o Esser, Lof/ik, § 48, p. 96.— Ed. LECTURES ON LOGIC. l7l LECTURE X. STOICHEIOLOGY. SECT. IL— OF THE PRODUCTS OF THOUGHT. I.— ENNOEMATIC. IMPERFECTION OF CONCEPTS. It is now necessary to notice an Imperfection to which lect. concepts are peculiarly liable, and in the exposition of which I find it necessary to employ an expression, ti^no^f cmi- which, though it has the highest philosophical author- ''^^^^' ity for its use, I would still, in consequence of its ambi- guity in English, have avoided, if this could have been done without compromising the knowledge of what it is intended to express. The expression I mean, is intuitive, in the particular signification in which it is used by Leibnitz'' and the continental philosophers in general, to denote what is common to our direct and ostensive cognition of individual objects, in Sense or Imagmation, (Presentation or Representation), and in opposition to our indirect and symbolical cognition of general objects, through the use of signs or language, in the Understanding. But, on this head, I would, first of all, dictate to you the following paragraph. H XXX. As a notion or concept is the fac- Par. xxx. titious whole or unity made up of a plurality of tionofcou- ccpts. a Mpditationes de Cognitione, Veri- p. 80. — Ed. talc, et Ideis, Opera, ed. Erdmann, 172 l.KCTrKES ON l.OC.W. i.Kcr. attrilmti's, — a wliolc too often of a very complex —U— multiplicity; and as this multiplicity is ouly nuMitally heltl together, inasmuch as the concept is llxetl and ratified in a sign or word ; it frc- cjueutly happens, that, in its employment, the ^vord does not sufjfjest tlie whole amount of tliought for which it is the ade(piate ex})ression, but, on the contrary, we frequently give and take the sign, either with an obscure or indistinct con- sciousness of its meaning, or even without an actual consciousuesss of its signification at all. niustratiou. Tliis liability to the vices of Obscurity and Indis- tinctness arises, 1°, From the very nature of a concept, which is the binding up of a multiplicity in unity ; and, 2°, From its dependence upon language, as the necessary condition of its existence and stability. In consequence of this, when a notion is of a very com- plex and heterogeneous composition, we frequently use the term by which it is denoted, without a clear or distinct consciousness of the various characters of wdiich the notion is the sum ; and thus it is, that we both give and take words without any, or, at least, without the adequate complement of thought. I may exemplify this ; — You are aware, that in coun- tries where bank-notes have not superseded the use of the precious metals, large payments are made in bags of money, purporting to contain a certain number of a certain denomination of coin, or, at least, a certain amount in value. Now, these bags are often sealed up and passed from one person to another, without the tedious process, at each transference, of counting out their contents, and this upon the faith, that, if examined, they will be found actually to contain the X. LECTURES ON LOGIC. 173 number of pieces for which they are marked, and for lect, which they pass current. In this state of matters, it is, however, evident, that many errors or frauds may be committed, and that a bag may be given and taken in payment for one sum, which contains another, or which, in fact, may not even contain any money at all. Now the case is similar in regard to notions. As the scaled bag or rouleau testifies to the enumerated sum, and gives unity to what would otherwise be an uncon- nected multitude of pieces, each only representing its separate value ; so the sign or word proves and ratifies the existence of a concept, that is, it vouches the tying up of a certain number of attributes or characters in a single concept, — attributes which would otherwise exist to us only as a multitude of separate and uncon- nected representations of value. So far the analogy is manifest; but it is only general. The bag, the guaranteed sum, and the constituent coins, represent in a still more proximate manner the term, the con- cept, and the constituent characters. For in regard to each, we may do one of two things. On the one hand, we may test the bag, that is, open it, and ascertain the accuracy of its stated value, by counting out the pieces which it purports to contain ; or we may accept and pass the bag, without such a critical enumeration. In the other case, we may test the general term, prove that it is valid for the amount and quality of thought of which it is the sign, by spreading out in consciousness the various characters of which the concept professes to be the complement ; or we may take and give the term without such an evolution." a A hint of this illustration i.i to vol. i. chap. viii. p. 200. — Eu. be found in Degcrando, iJes Sitjncv, 17 I l.KlTrKKS ON I.OCIC. LF.CY. It is ('\ iilriit from this, lliat notions or concepts are _J___ pei'iiliarlv li;il>K> to i;re;it vagueness and ambiguity, and that tlieir symbols are liable to be passed about witliout the proper kind, or the adequate amount, of thought. The liability Tliis iutercstiug subject has not escaped the obser- wuItIi^uc-" vatiou of the philosophers of this country, and by ^pts^no" them it has, in fact, with great ingenuity been illus- UHtishpiii- trated ; but as they are apparently ignorant, that the "*"'' """^ matter had, before them, engaged the attention of sundry foreign philosophers, by whom it has been even more ably ean^'assed and expounded, I shall, in the exposition of this point, also do justice to the illustrious thinkers to whom is due the honour of hav- ing originally and most satisfactorily discussed it. Stewart The following passage from Mr Stewart will afford ttsubjITct. the best foundation for my subsequent remarks. " In the last section I mentioned Dr Campbell as an in- genious defender of the system of the Nominalists, and I alluded to a particular application which he has made of their doctrine. The reasoninc-s which I had then in view, are to be found in the seventh chapter of the second book of his FhilosojyJiy of Rhetoric, in which chapter he proposes to explain how it happens, ' that nonsense so often escapes being detected, both by the waiter and the reader.' The title is somewhat ludicrous in a gi'ave philosophical work, but the disquisition to which it is prefixed, contains many acute and profound remarks on the nature and power of signs, both as a medium of communication, and as an instrument of thought. Refers to " Dr CampbcH's speculations with respect to lan- guage as an instrument of thought, seem to have been suggested by the following passage in Mr Hume's LECTURES ON LOaiC. l75 Treatise of Human Nature ;" — ' I believe every one lect. who examines the situation of his mind in reasoning, — 1^ will agree with me, that we do not annex distinct and complete ideas to every term we make use of ; and that in talking of Government, Church, Negotiation, Conquest, we seldom spread out in our minds all the simple ideas of which these complex ones are composed. It is, however, observable, that notwithstanding this imperfection, we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a full comprehension of them. Thus if, instead of saying, that in war the weaker have always recourse to negotiation, we should say, that they have always recourse to conquest ; the custom which we have acquired, of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that pro- position.' " In the remarks which Dr Campbell has made on this passage, he has endeavoured to explain in what manner our habits of thinking and speaking gradually establish in the mind such relations amono; the words we employ, as enable us to carry on processes of reasoning by means of them, without attending in every instance to their particular signification. With most of his remarks on this subject I perfectly agree ; but the illustrations he gives of them are of too great extent to be introduced here, and I would not wish to run the risk of impairing their perspicuity, by attempting to abridge them. I must, therefore, refer such of my readers as wish to prosecute the specula- tion, to his very ingenious and philosophical treatise. " ' In consequence of these circumstances,' says Dr a Part i. § 7.— Ed. iTl") LKlTl'lvKS ON LOCK'. LKtT. C'ain])lK'll, ' it liMpiu'iis tliat, in luatlcrs w liirli are pcr- fi'i'tlv laniiliar to us, w t' are aMo to reason l)y means Ml. *"*"'*' *^>t' wonls, witlioiit examining, in every instance, their siLrnitication. Almost all the possible a})plie,ations of tlie terms (in other words, all the act^uired relations of the signs) have become customary to us. The con- sequence is, that an unusual aj)plication of any term is instantly detected ; this detection breeds doubt, and this doubt occasions an immediate recourse to ideas. The recourse of the mind, when in any de- gree puzzled witli the signs, to the knowledge it has of the things signified, is natural, and on such subjects perfectly easy. And of this recourse the discovery of the meaning, or of the unmeaningness of what is said, is the immediate effect. But in matters that are by no means familiar, or are treated in an uncommon manner, and in such as are of an abstruse and intricate nature, the case is widely different.' The instances in ^\'hich we are chiefly liable to be imposed on by words without meaning, are (according to Dr Campbell), the three followinor : — o "First, Where there is an exuberance of metaphor. " Secondly, When the terms most frequently occur- ring denote things which are of a complicated nature, and to which the mind is not sufficiently familiarised. Such are the words — Government, Church, State, Con- stitution, Polity, Power, Commerce, Legislature, Juris- diction, Proportion, Symmetry, Elegance. " Thirdly, When the terms employed are very abstract, and consequently of very extensive signifi- cation. " * The more general any word is in its signification, it is the more liable to be abused by an improper or unmeaning application. A very general term is appli- LECTURES ON LOGIC. 177 cable alike to a multitude of different individuals, a lect, X particular term is applicable but to a few. When the '. — rightful applications of a word are extremely numer- ous, they cannot all be so strongly fixed by habit, but that, for greater security, we must perpetually recur in our minds from the sign to the notion we have of the thing signified ; and for the reason aforemen- tioned, it is in such instances diflicult precisely to ascertain this notion. Thus the latitude of a word, though different from its ambiguity, hath often a similar effect.'"" Now, on this I would, in the first place, observe, Locke an- ticipntcd that the credit attributed to Hume by Dr Campbell Hume in and Mr Stewart, as having been the first by whom the empioy- the observation had been made, is, even in relation to terms with- British philosophers, not correct. Hume has stated meaning, nothing which had not, with equal emphasis and an equal development, been previously stated by Locke, in four different places of his Essay. ^ Thus, to take only one out of at least four passages directly to the same efiect, and out of many in which the same is evidently maintained, he says, in the chapter entitled — Of the Abuse of Wo7^ds: — "Others Locke there be who extend this abuse yet farther, who take so little care to lay by words which, in their primary notation, have scarce any clear and distinct ideas which they are annexed to, that by an unpardonable negligence they familiarly use words which the pro- priety of language has affixed to very important ideas, without any distinct meaning at all. Wisdom, glory, grace, &c., are words frequent enough in every a Elements, vol, i., chap. iv. § 4, §7; ii.i xxix. 9; ii., xxxi. 8; iii., JFort^, vol. ii., p. 19.S-195. ix. 6 ; iii., x, 2,— Ed. /3 Compare Essay, B. ii., ch. xxii., VOL. L M ITS LKCTURES ON LOCIC. LKt'T. iiKin's iiKHitli ; luit if a oreat many- of those wlio iiso ' them slioulil l)o askt-d wliat they mean hy thorn, tliey woiiKl 1)0 at a stand, and not know what to answer : a phiin proof, tliat though they have learned those soiuuls, and have them ready at their tongue's end, yet there are no determined ideas laid up in their minds, which are to be expressed to others by them. Men havinfj been accustomed from their cradles to learn words, which are easily got and retained, before they know or had framed the complex ideas to which tliey were annexed, or which were to be found in the things they were thought to stand for, tliey usually continue to do so all their lives ; and without taking the pains necessary to settle in their minds determined ideas, they use their words for such unsteady and confused notions as they have, contenting themselves with the same words other people use ; as if their very sound necessarily carried with it constantly the same meaning. This though men make a shift with in the ordinary occurrences of life, where they find it necessary to be understood, and therefore they make signs till they are so ; yet this insignificancy in their words, when they come to reason concerning either their tenets or interest, manifestly fills their discourse with abundance of empty unintelligible noise and jar- gon, especially in moral matters, where the words, for the most part, standing for arbitrary and numerous col- lections of ideas, not regularly and permanently united in nature, their bare sounds are often only thought on, or at least very obscure and uncertain notions annexed to them. Men take the words they find in use among their neighbours, and that they may not seem ignorant what they stand for, use them confi- dently, without much troubling their heads about a LECTURES ON LOGIC. 179 certain fixed meaning : whereby, besides the ease of it, lect. they obtain this advantage, that as in such discourses ' they seldom are in the right, so they are as seldom to be convinced that they are in the wrong; it being all one to go about to draw those men out of their mistakes who have no settled notions, as to dispossess a vagrant of his habitation, who has no settled abode. This I guess to be so ; and every one may observe in himself and others, whether it be or no." ° From a comparison of this passage with those which I have given you from Stewart, Campbell, and Hume, it is manifest that, among British philosophers, Locke is entitled to the whole honour of the observa- tion : for it could easily be shown, even from the iden- tity of expression, that Hume must have borrowed it from Locke ; and of Hume's doctrine the two other philosophers profess only to be expositors. This curious and important observation was not. The disfmc- however, first made by any British philosopher ; for tuitive and Leibnitz had not only anticipated Locke, in a publi- knowledge cation prior to the Essay, but afforded the most pre- by Leibnitz. cise and universal explanation of the phsenomenon, which has yet been given. To him we owe the memorable distinction of our This disUnc- knowledge into Intuitive and Symbolical, in which superseded distinction is involved the explanation of the pha3no- vcrsyofNo- menon in question. It is the establishment of this and concep- distinction, likewise, which has superseded in Ger- Germany, many the whole controversy of Nominalism and Conccptualism, — which, in consequence of the non- establishment of this distinction, and the relative imperfection of bur philosophical language, has idly a Essay concerning Human Under- x. §§ 3, 4. — Ed.] standing, vol. i. p. 228; [B. in., ch. 180 LECTl'KKs ON i.ocir. LKCT. l'u»<.'x|uaiul- alio- of {he • IikUiiu-9 <.<( {■^■ll'liltx. Manner in which he gave his writings to the world. His paper Jje Voijiii- tione, I'eri- tate,et Ideit. agit;itod tlio }tsyi'liology of this country and oi' Fraiu'o. Tliat tlie tloc'trines of Leibnitz, on this and other i-ardinal points of psychology, should have remained a|>parently unknown to every philosopher of this country, is a matter not less of wonder than of regret, and is only to be excused by the mode in which Leibnitz iiavc his writinos to the world. His most valuable thoughts on the most important subjects were generally thrown out in short treatises or letters, and these, for a long time, were to be found only in partial collections, and sometimes to be laboriously sought out, dispersed as they were in the various scientific Journals and Transactions of every country of Europe ; and even when his works were at length col- lected, the attempt of his editor to arrange his papers according to their subjects (and what subject did Leibnitz not discuss '() was baffled by the multifari- ous nature of then- contents. The most important of his philosophical writings, — his Essays in refutation of Locke, — were not merely a posthumous publication, but only published after the collected edition of his Works by Dutens ; and this treatise, even after its publication, was so little known in Britain, that it remained absolutely unknown to Mr Stewart, (the only British philosopher, by the way, who seems to have had any acquaintance with the works of Leib- nitz), until a very late period of his life. The matter, however, with which we are at present en- gaged, was discussed by Leibnitz in one of his very earliest writings ; and in a paper entitled De Cogni- tione, Veritate, et Ideis, published in the Acta Eru- ditorum of 1684, we have, in the compass ef two quarto pages, all that has been advanced of principal LECTURES ON LOGIC. 181 importance in regard to the peculiarity of our cognitions lect. by concept, and in regard to the dependence of our concepts upon language. In this paper, besides estab- lishing the difference of Clear and Distinct knowledge, he enounces the memorable distinction of Intuitive and Symbolical knowledge, — a distinction not cer- tainly unknown to the later philosophers of this coun- try, but which, from their not possessing terms in which precisely to embody it, has always remained vague and inapplicable to common use. Speaking of the analysis of complex notions, he says — " For the Leibnitz most part, however, especially in an analysis of any intuitive , , ' . ^ •' . . 7 . X andSymbo- lengtn, we do not view at once {71071 si^niU i7%tuemur) Hcai know- the whole characters or attributes of the thinsf, but in place of these we employ signs, the explication of which into what they signify, we are wont, at the moment of actual thought, for the sake of brevity, to omit, knowing or believing that we have this expli- cation always in our power. Thus, when I think a chiliogon, (or polygon of a thousand equal sides), I do not always consider the various attributes, of the side, of the equality, and of the number a thousand, but use these words, (whose meaning is obscurely and im- perfectly presented to the mind), in lieu of the notions which I have of them, because I remember, that I possess the signification of these words, though their application and explication I do not at present deem to be necessary. This kind of thinking I am used to call blind or symbolical. We employ it in Algebra and in Arithmetic, and in fact universally. And certainly, when the notion is very comj)lex, we cannot think at once all the ingredient notions ; but where this is pos- sible, — at least, inasmuch as it is possible, — I call the cognition intuitive. Of the primary elements of our ISli LKCTUHKS ON LOUlf. LECT. notions, tliere is jj^ivcn no other knowlecW than tho X ... ' intuitive; as o\' «nir composite notions, there is, ior the most part, possible only a symbolieul. From these considerations it is also evident, that of the tliinj^s whieli we distinctly know we are not conscious of the iileas, except in so far as we employ an intuitive cog- nition. And, indeed, it happens that we often falsely believe tluit we have in (jur mind the ideas of things, erroneously supposing that certain terms which we employ had been applied and explicated ; and it is not true, — at least it is ambiguously expressed, what some assert, — that we cannot speak concerning any- thing, understanding what we say, without having au idea of it actually present. For we frequently apply any kind of meaning to the several words, or wc merely recollect us that we have formerly understood them, but because we are content with this blind thinking, and do not follow out the resolution of the notions, it happens, that contradictions are allowed to lie hid, which perchance the composite notion involves. . . Thus, at first sight, it must seem, that we could form an idea of a maximum velocity (motus celerrimics), for in using the terms we understand what we say ; we shall find, however, that it is impossible, for the notion of a quickest motion is shown to be con- tradictory, and, therefore, inconceivable. Let us sup- pose, that a wheel is turned with a velocity absolutely at its maximum ; every one perceives that if one of its spokes be produced, its outer end will be moved more rapidly than the nails in the circumference of the wheel ; the motion, therefore, of these is not a maximum, which is contrary to the hypothesis, and, therefore, involves a contradiction." This quotation will' suffice to show you how cor- LECTURES ON LOGIC. 183 rcctly Leibnitz apprehended the nature of concepts, lect. as opposed to the presentations and representations of the subsidiary faculties; and the introduction of thi^dis'tiuc- the term Symbolical knowledge, to designate the LdbnL on former, and the term Intuitive knowledge to compre- pi,yof Ger- hend the two latter, — terms which have ever since ™'^°^' become classical in his own country, — has bestowed on the German language of philosophy, in this re- spect, a power and precision to which that of no other nation can lay claim. In consequence of this, while the philosophers of this country have been all along painfully expounding the phsenomenon as one of the most recondite arcana of psychology, in Germany it has, for a century and a half, subsided into one of the elementary doctrines of the science of mind. It was in consequence of the establishment of this distinction by Leibnitz, that a peculiar expression, {Begriff, con- ceptus), was appropriated to the symbolical notions of the Understanding, in contrast to the intuitive pre- sentations of Sense and representations of Imagination, which last also were furnished with the distinctive appellation of intuitions, (Anschauungen, intuitus). Thus it is, that, by a more copious and well-appointed language, philosophy has, in Germany, been raised above various controversies, which, merely in conse- quence of the poverty and vagueness of its English nomenclature, have idly occupied our speculations. But to return to the mere logical question. The doctrine of Leibnitz in regard to this natural The distinc- imperfection of our concepts was not overlooked by his ciiUod by disciples, and I shall read to you a passage from the of LcH Lesser Logic of Wolf, — a work above a century old, and which was respectably translated from German into English in the year 1770. This translation is tlic di8cii)lcs 184 LECl'lTKKS ON LOCIC. LKUT. X. now raivly to be nwl with, which may account lor its being apparently totally unknown to our J)ritish })lii- losophers ; and yet. u[)on tlu' whole, with all its faults ami imperfections, it is perhaps the most valuable work on Logic, (to say nothing of the Port Roijal Logic), in the English lanr nioanini; can possibly be joined willi these — — — wonls. To tliis head also belonpj tlie Natural Sym- pathy and Anli[)athy of Plants; llie Wnud ol' lviL;ht or law {rincu/nni juris), used in tiie delinition ol" Obliui;ation, by Civilians ; the Principle of Evil of the Manicheans," &c." a Loyic or Rdlional Thouijhts on man of Baron Wolfias, c. ii., p. 54- the Powers qf the Human Under- 57; LoirImii, 1770. — Ei). staiulinij. Translakd from the Gcr- LECTUIIES ON LOGIC. 187 LECTURE XL STOICHEIOLOGY. SECT. I. OF THE PRODUCTS OF THOUGHT. I. ENNOEMATIC. III. RECIPROCAL RELATIONS OF CONCEPTS. A. QUANTITY OF EXTENSION — SUBORDINATION AND CO-ORDINATION. I NOW proceed to the third and last Relation of Con- lect. cepts, — that of concepts to each other. The two '— former relations of notions, — to their objects and to their subject, — gave their Quantity and Quality. This, the relation of notions to each other, gives what is emphatically and strictly denominated their Relation. In this rigorous signification, the Relation of Concepts may be thus defined. H XXXL The Relation proper of notions con- Par.xxxi. 1 -, . . ., 1 • 1 Reciprocal sists m those determmations or attributes which Relations belong to them, not viewed as apart and in them- selves, but as reciprocally compared. Concepts can only be compared together with reference, cither, 1°, To their Extension ; or, 2°, To their Comprehen- sion. All their relations are, therefore, dependent on the one or on the other of these quantities." H XXXIL As dependent upon Extension, con- Par.xxxii. cepts stand to each other in the five mutual tuusiou. « Cf. Knig, Lxjik, § 36.— Ed. 188 LKCTUUES DN LOGIC. l.KtT. relations, 1 , ( M" Ivxclusicm ; i2 , OT Cooxlension ; :V, Of Subonlinatitui ; 4°, Of Co-onlinatioii ; and, 5°, Of Intersection. 1. One ('oneei)t excludes another, when no part of the one coincides with any part of the othci'. "2. One concept is coextensive with another, when each has the same number of subordinate concepts under it. 3. One concept is sul)ordinatc to an- other, (which may be called the Superonlinate), when the former is included within, or makes a l>art of, the sphere or extension of the latter. 4. Two or more concepts are co-ordinated when each excludes the other from its sphere, but when both go immediately to make up the extension of a third concept, to which they are co-subordi- nate. 5. Concepts intersect each other, when the sphere of the one is partially contained in the sphere of the other." Examples of the five tuutuAl rc- hitiung of Cuucopts. Of Exclusion, liorse, syllogism, arc examples. There is, however, no absolute exclusion. As examples of Coextension, — the concepts, living being, and organised being, may be given. For, using the term life as applicable to plants as well as to animals, there is nothinsj liviner which is not oroi'an- ised, and nothing organised which is not living. This reciprocal relation will be represented by two circles covering each other, or by two lines of equal length and in positive relation. As examples of Subordination and Co-ordination, man, dog, horse, stand, as correlatives, in subordina- tion to the concept animal, and, as reciprocal correla- tives, in co-ordination with each other. o C'f. Krug, Lo'jik, § 41. — Ed. LECTURES ON LOGIC. 189 What I would call the reciprocal relation of In- tersection, takes place between concepts, when their spheres cross or cut each other, that is, fall partly within, partly without, each other. Thus, the con- cepts hlach and heavy mutually intersect each other, for some black things are heavy, some not, and some hea^y things are black, some not. CONGErTS, THEIK KELATIONS PEOPER : TO WIT OF 1. Exclusion'' 2. Coextension 3. Subonlination 4. Co-oi\lination 5. Intersection, or Partial Co- inclusion and Coexclusion LECT. XI. Of these relations those of Subordination and Co- Suimniina- ordination are of principal importance, as on them co-oniiua- o The notation by straight lines 1848. — Ei). was first employed by the Author in 190 l.ECTDRES ON LOOIC. LKCT. iviK>sos till' whole systoiu of chissificatioii ; iiiul to tlioin alone it is, therefore, necessary to accord a more lion of principal purticiihir eonsiiloration. iin|H,nauct<. i^^nJ^.i. the Subordination of notions, there are vari- Term* ex- prtwivoof Qns terras to express the diiTerent modes of tliis rehi- tho .iiffoixiil ^ ■•■ nuHU-sofiiio tion : these it is necessary that you shouhl now learn norior ninl Inferior, Hroaiteraoil Narrower, notious. H XXXIII. Of notions which stand to cacli other in the relation of Subordination, — the one is the Higher or Superior, {notio, conceptiis, supe- rior), the other tlie Lower or Inferior, {notio, con- ceptus, inferior). The superior notion is likewise called the Wider or Broader {iatior), the inferior is likewise called the Narrower (angtistior)."' Explication. Thc meaning of these expressions is sufficiently manifest. A notion is called thc higher or superior, inasmuch as it is viewed as standinsj over another in the relation of subordination, — as including it within its domain or sphere ; and a correlative notion is called the lower or inferior, as thus standing under a supe- rior. Again thc higher notion is called the wider or hroader, as containing under it a greater number of things ; the lower is called the narrower, as contain- ing under it a smaller number. Par.XXXIV. Universal and Particu- lar notiuns. H XXXIV. The higher or wider concept is also called, in contrast to the lower or narrower, a Universal or General Notion, {p6r)fxa KaOoXov, a Cf. Knig, Logik, § 42.— Ed. LECTURES ON LOGIC. ' 191 notio^ co7iceptus, universalis, generalis) ; the lower lect. or narrower concept, in contrast to the higher or wider, a Particular Notion, (vorjixa fjiepcKov, notio, conceptus, 'particular is) ."' The meaning of these expressions, likewise, requires Explication, no illustration. A notion is called universal, inas- much as it is considered as binding up a multitude of parts or inferior concepts into the unity of a whole ; for universus means in unum versus or ad unum versus, that is, many turned into one, or many re- garded as one, and universal is employed to denote the attribution of this relation to objects. A notion is called particular, inasmuch as it is considered as one of the parts of a higher concept or whole. H XXXV. A superior concept, inasmuch as it Par.xxxv. constitutes a common attribute or character for species'. a number of inferior concepts, is called a General Notion, {uorjfxa KaOoXov, notio, conceptus, genera- lis), or, in a single word, a Genus, {yeuo, luit is, 1 think, more properly tlividcil in the lol- K)\\iiig manlier : — Ik'nuj hi/ accident is viewed cither as absolute or as relative. As absolute, it Hows cither from the matter, or from the form of things. If from the matter, it is Quantity, Aristotle's secoml cate- gory ; if from the form, it is Quality, Aristotle's third category. As relative, it corresponds to Aristotle's fourth category. Relation; and to Relation all the other six may be reduced. For the category Where is the relation of a thing to other things in space ; the category Whe7i is the relation of a thing to other things in time ; Action and Passion constitute a single relation, — the relation of the agent and the patient; Posture is the relation of the parts of a body to each other ; finally, Habit is the relation of a thing containing and a thing contained." The little I have now said in regard to the categories of Aristotle is more, perhaps, than I was strictly war- ranted to say, considering them, as I do, as wholly extralogical, and I have merely referred to them as exhibiting an example of the application of the doc- trine of classification.^ a This classification of the Catego- Crassaque MaUrief, dcdcrunt exordia ries is given by Paciiis, In Arist. Ca- rebus." terj., c. 3, p. 40, ed. 1597. Cf. Aqui- Second line better— nas, In Arist. Metaph., L. v. lect. 9; ,, „ ,^ c 7-.- ^ ^- nr A 1 ■ Sunt, cum Materia, cunctarum cx- Suarez, Disputatioties Mctaphysiccc, .. „ ^. ' .„,^,„ -^'"^ ordia rerum. Disp. xxxix. §§ 12, 15.— Ed. /3 There is nothing in regard to RevVs Account of Aristotle's Lor/k, which a greater diversity of opinion c. ii, §§ 1, 2, Worl:s, p. 685 et setj. has prevailed, even among Logicians, See Facciolati, Logica, t. i., Eudi- than the number of the Categories, rnenta Logica, P. I. c. iii. p. 32. For some allow only two— Substance Purchot, Insiit. Philos., t. i. Logica, and Mode ; others three — Substance, p. 82, ed. 1716. Chauvin, Xex/co;i Mode, and Kelation ; others four — Philosoiihicum v. Caterjornim. [For Mind, Space, ]\latter, and Motion ; various attempts at reduction and others seven, which are comi)rehend- classification of the categories, see ed in the following distich :— Plotinus, Enncad., VI. L. ii. c. 8 ct " Mm, Meiisura, Quies, Motus, Po- «^- (Tennemann, Gesch. der Phil. , situra, Figv.ru, vi. p. 175 et seq.) ; David the Arme- LECTURES ON LOGIC. 201 1 may, likewise, notice, by the way, that in the lect, physical sciences of arrangement, the best instances of which are seen in the different departments of thniffer"cut Natural History, it is found necessary, in order to SsTf '^ mark the relative place of each step in the ascending ti.Tphys'icai IT T • PI ,ij • 1 sciences of and descending series oi classes, to bestow on it a anange- particular designation. Thus kingdom, class, order, ™^° * tribe, family, genus, subgenus, species, subspecies, vari- ety, and the like, are terms that serve conveniently to mark out the various degrees of generalisation, in its application to the descriptive sciences of nature. With such special applications and contingent differ- ences. Logic has, however, no concern. I, therefore, proceed to the last relative denomination of concepts under the head of Subordination in Extension. It is expressed in the following paragraph : — H XXXVII. A genus as containing under it Par.xxxvii. . . *" , . . Logical and species, or a species as containing under it m- Metiuihysi- dividuals, is called a Logical, or Universal, or and Parts. Subject, or Subjective, or Potential Whole ; while species as contained under a genus, and indivi- duals as contained under a species, are called Logical, or Universal, or Subject, or Subjective, or Potential Parts. E converso, — an individual as containing in it species, or a species as con- taining in it genera, is called a Metaphysical, or nian, in Brandis, Scholia ad Aristot., On history of categories in antiquity, p. 49; Ramus, Animad. Aristot. , [L. see Petersen, Chrysijipea: Phil. Fim- iv. p. 80c< scg., ed. 1550. — Ed.]; Jo. damenta, p. 1 ct seq. For the doc - Picus Mirandiilamis, Condusioncs, trines of the Platonists and Stoics Opera, p. 90, ed. BasiL, 1572 ; Lan- on the subject of the Categories, see rentius Valla, [Dialectics D'lsputa- 'Fa.ccioXa.W, Ivstit. Log.,{Lo(jica,\,. W. tiones, CO. i. ii.— Ed.] ; Eugenios, p. ii., p. 84 et seq. Cf. Trendclen- AoyiKT), p. 225 ct seq. On categoric burg, G'cschichtc dcr Kulcfjorienlchrc, tables of various authors, see Den- pj). 251, 267. — Ed.] zingcr, IiLit. Log., ii. § 008, p. 55. 202 LEcrruuEs on i.ov.w. u:rv. Fitrmal, or Actual Wliolc ; wliilc species as coii- — — taiiH'J in an individual, and genera as contained in species, are called Metaplnjsical, or Formal, or Actual Parts."' This nomenclature, however, in so far as nietajihysical is opposed to logical, is inept ; for we shall see that both these wholes and parts are equally logical, and that logicians liave been at fault in considering one of them, ill their doctrine of reasoning, to the exclusion of the other. Expiica- A whole is that which contains parts ; a part is that which is contained in a whole. But as the rela- tion of a whole and parts is a relation dependent on the point of view from which the mind contemplates the objects of its knowledge, and as there are differ- ent points of view in which these may be considered, it follows that there may also be different wholes and parts. Philosophers have, accordingly, made various enumerations of wholes ; and, without perj)lexing you with any minute discussion of their various divi- sions, it may be proper, in order to make you the better aware of the two wholes with which Logic is conversant, — (and that there are two logical wholes, and, consequently, two grand forms of reasoning, and not one alone, as all logicians have hitherto taught, I General shall hercaftcr endeavour to convince you), — to this various end, I say, it may be expedient to give you a general ^vhoics. view of the various wholes into which the human mind may group up the objects of its speculation. Wholes may be first divided into two genera, — into a See Timpler, Logica, [p. 232 et gica Rcstituta, P. III., c. ii. § 2, 8cq. — Ed.] Facciolati, [Logica, t. i., ed. Geneva?, 1G68. — Ed.] Burgers- liwUrnenta Logica, P. II. c. vi., p. dyk, [InstitutioiKS Logical, p. 51. — 51-52.— Ed.] Derodon, p. 447, [>^o- Ed.] LECTURES ON LOGIC. 203 a Whole by itself (totum per se), and a Whole by lect. accident (totum per accidens). A Whole per se is '— that which the parts of their proper nature neces,- se,'^uV^^ sarily constitute ; thus body and soul constitute the accTdniT man. A Whole j^er accidens is that which the parts make up contingently ; as when man is considered as made up of the poor and the rich. A whole per se may, again, be subdivided into five kinds, into a Logical, a Metaphysical, a Physical, a Mathematical, and a Collective. 1°, A Logical, styled also a Uni- whole pei- versal, a Subject or Subjective, a Potential Whole ; into, r, and 2°, A Metaphysical, styled also a Formal or an 2% mcu- Actual Whole, — these I have defined in the paragraph. It is manifest, that the logical and metaphysical wholes are the converse of each other. For as the logical whole is the genus, the logical parts the species and individual ; in the metaphysical, e contra, an in- dividual is the whole of which the species, a species the whole of which the genera, are the parts. A metaphysical whole is thus manifestly the whole de- termined by the comprehension of a concept, as a logical whole is that whole determined by its exten- sion ; and if it can be shown that the whole of com- prehension afibrds the conditions of a process of rea- soning equally valid, equally useful, equally easy, and, to say the least of it, equally natural, as that afforded by the whole of extension, it must be allowed that it is equally well entitled to the name of a logical whole, as the whole which has hitherto exclusively obtained that denomination. 3°, A Physical, or, as it is like- 3°. piiysi- wise called, an Essential Whole, is that which consists of matter and form, in other words, of substance and accident, as its essential parts. 4°, A Matlie- r, Matiic- matical, called likewise a Quantitative, an Integral, 204 LiHTiKKs ON nunc. LK(T. iiioiv propoilyan liiti'gratc,Whole, (^)/»;yi hitajnitioii), — '— — is that which is composed of integral, or, more properly, o{ integrant, parts, (partes integrantcs). In this whole every })art lies out of every other part, whereas, iu a physical whole, the matter and form, the sub- stance and accident, permeate and modify each other. Thus in the integrate whole of a human body, the head, body, and limbs, its integrant parts, arc not con- s', Coiiec- tained in, but each lies out of, each other. 5°, A Col- lective, styled also a Whole of Aggregation, is that which has its material parts separate and accidentally tlu'own together, as an army, a heap of stones, a pile of wheat, &c.* But to proceed now to an explanation of the terms in the paragraph last dictated. Of these, none seem to require any exposition, save the words subjective and potential, as synonyms applied to a Logical or Universal whole or parts. The terms Thc formcr of these, — the term subjective, or more 7uhjecHve properly subject, as applied to the species as parts sub- t^ L^^cai jacent to, or lying under, a genus, — to the individuals, whole aud j^ l • ^ j. 1 • l • • parts. as parts subjacent to, or lying under, a species, is a clear and appropriate expression. But as applied to the genus or species, considered as w^holes, the term subject is manifestly improper, and the term subjective hardly defensible. In like manner, the term universal, as applied to genus or species, considered as logical wholes, is correct ; but as applied to individuals, con- sidered as logical parts, it is used in opposition to its proper meaning. The desire, however, to obtain epithets common both to the parts and to the w^hole, and thus to indicate at once the relation in general, has caused logicians to violate the proprieties both of o See above, p. 202, note. — Ed. LECTURES ON LOGIC. 205 language and of thought. But as the terms have lect. been long established, I think it sufficient to put you '— on your guard by this observation. In regard to the term potential, — I shall, before The term ° ^ potential. saying anything, read to you a passage from the L^d Mon- Antient Metaphysics of the learned Lord Monboddo.* quoted, " In the first place, it is impossible, by the nature of things, that the genus should contain the species as a part of it, and the species should likewise contain the genus, in the same respect. But, in different respects, it is possible that each of them may contain the other, and be contained by it. We must, therefore, try to distinguish the difierent manners of containing, and being contained. And there is a distinction that runs through the whole of ancient philosophy, solving many difficulties that are otherwise insurmountable, and which, I hope, will likewise solve this difficulty. The distinction I mean is the distinction betwixt what exists Swdfiei, or potentially only, and that which ex- ists iuepyeia, or actually. In the first sense, every- thing exists in its causes ; and, in the other sense, nothing exists but what is actually produced. Now, in this first sense, the whole species exists in the genus; for the genus virtually contains the whole species, not only what actually exists of it, but what may exist of it in any future time. In the same manner, the lowest species, below which there is no- thing but individuals, contains virtually all those indi- viduals, present and future. Thus, the species man, comprehends all the individuals now existing, or that shall hereafter exist ; which, therefore, are said to be parts of the species man. On the other hand, the genus is actually contained in the species ; o Vol. i. p. 479. 206 LECTUKES (^N LOO TO. LECT. :iiiJ the species, likewise, in each of the individuals *^'* under it. Thus, the genus animal is actually con- taineil in the species man, without which it could not be conceived to exist. And, for the same reason, the species ma)i is actuidly contained in each indivi- dual. — It is a piece of justice which I think I owe to an author, hardly known at all in the western parts of Europe, to acknowledge that I got the hint of the so- lution of this difficulty from him. The author I mean is a living Greek author, Eugenius Diaconus, at present Professor, as I am informed, in the Patriarch's Univer- sity at Constantinople, who has written an excellent system of logic, in very good Attic Greek." Stewart's This, or rather a similar passage at p. 73 of the fourth strictures on this j.ass.ife'c volume of the Antient MetapJujsics, affords Mr Stewart *""* """^ ■ an opportunity of making sundry unfavourable stric- tures on the technical language of Logic, in regard to which he asserts, "the adepts are not, to this day, unanimously agreed ; " and adds, that " it is an extraordinary circumstance, that a discovery on which, in Lord Monboddo's opinion, the whole truth of the syllogism dejifends, should be of so very recent a date."" Now this is another example which may serve to put you on your guard against any confidence in the assertions and arguments even of learned men. You may be surprised to hear, that so far is Eugenius from being the author of this observation, and of the term potential as applied to a logical wholQ, that both are to be found, with few exceptions, in all the older sys- tems of Logic. To quote only one, but one of the best and best known, that of Burgersdyk, — he says, speaking of the logical whole : " Et quia universale subjectas species et indi vidua nan actu continet sed o Elements, vol. ii., c. iii., § 1 ; Worksy vol. iii., p. 199 and p. 200, note. LECTURES ON LOGIC. 207 jpotentia ; factum est, ut hoc totum dictum sit totum lect. potentiale, cum ceterse species totius dicantur totum — actuale, quia partes suas actu continent." " Aristotle notices this difference of the two wholes. ^^ Having thus terminated the consideration of con- cepts as reciprocally related in the perpendicular line of Subordination, and in the quantity of Extension, in so far as they are viewed as containing classes, — I must, before proceeding to consider them under this quantity in the horizontal line of Co-ordination, state to you two terms by which characters or concepts are denominated, in so far as they are viewed as differ- ences by which a concept is divided into two sub- ordinate parts. IT XXXVIII. The character, or complement of Par.xxxviii. G'cuGric characters, by which a lower genus or species is Specific,' distinguished, both from the genus to which it is dual Diffcr- subordinate, and from the other genera or species with which it is co-ordinated, is called the Generic or the Specijic Difference, {^la^opa yevLKTj, and hia<^opa dhiKTi, differentia generica, and differen- tia specijica). The sum of characters, again, by which a singular or individual thina; is discrim- inated from the species under which it stands, and from other individual thino-s along with which it stands, is called the hidividual or Singular or Numerical Difference, {differentia iiidividualis vel singularis vel numerica)?' Two things are thus said to be generically dif- Expiica ferent, inasmuch as they lie apart in two different genera ; specifically different, inasmuch as they lie o Lib. L c. xiv., p. 43, ed. IGGO. c. i, De Toto ct Parte.— Ev.] — Ed. y Krug, Lo;/ik, § 45.— Ed. $ Vide Timplcr, Lofjica, [L. II. tion. 208 LEOTlTiES ON LOGIC. LK(T. apart in two ilillbrcnt sjiocios ; indiviilually or numc- U rirally ilitliiviit. iiiasinucli as tliey do not constitute tjfucric one and tlic same reality. Thus conmxd and stone iMTi-rl^Ve.*^ uuiy 1)0 Said to 1)0 generieally dilleront ; ho)'sc and ox to be specitieally ditKeront; UiijlijUjer and Eclipse to be numerically or individually different. It is evi- dent, however, that as all genera and species, except the highest of the one and the lowest of the other, may be styled inditferently either genera or species ; generic dilf'erence and specific difference are in gen- eral only various expressions of the same thing, and, accordingly, the terms heterogeneous and homogene- ous, which apply properly only to the correlation of genera, are usually applied equally to the correlation of species. Individual " Individual existences can only be perfectly discri- or Sjnirular . i • t~» • ^ • i i i • Difference, mniatcd lu rcrccption, external or internal, and their numerical differences are endless ; for of all possible contradictory attributes the one or the other must, on the principles of Contradiction and Excluded Middle, be considered as belonging to each individual thing. On the other hand, species and genera may be perfectly discriminated by one or few characters. For example, man is distinguished from every genus or species of animal by the one character of 7Xitionality ; triangle, from every other class of mathematical figure, by the single character of trilaterality. It is, therefore, far easier adequately to describe a genus or species than an individual existence ; as in the latter case, we must select, out of the infinite multitude of characters which an individual comprises, a few of the most prominent, or those by which the thing may most easily be recognised." " But as those which we a Knig, Lofjlh, § 45, p. 134-5. — Ed. LECTURES ON LOGIC. 209 thus select are only a few, and are only selected with lect. reference to our faculty of apprehension and our capa- city of memory, they always constitute only a petty, and often not the most essential, part of the numeri- cal differences by which the individuality of the object is determined. Having now terminated the consideration of the Subordination of concepts under Extension, it is only necessary to observe that their Co-ordination under that quantity affords nothing which requires explana- tion, except what is contained in the following para- graph : — H XXXIX. Notions, in so far as they are Par.xxxix. . n -I Co-ordina- considered the co-ordinate species oi the same Hon of Con- genus, may be called Consjoecies ; and in so far as Conspecies are considered to be different but not contradictory, they are properly called Dis- crete or Disjunct Notions {notiones discretce vel disjunctce). The term Disparate {notiones dis- paratce) is frequently applied to this opposition of notions, but less properly ; for this ought to be reserved to denote the corresponding opposi- tion of notions in the quantity of Comprehension. I conclude the consideration of concepts, as depend- ent on Extension, by a statement of the two general laws, by which both Subordination and Co-ordination of notions, under this quantity, are regulated. H XL. The whole classification of things by Par. xl. Genera and Species is governed by two laws. gcnerTiaws The one of these, the law of Homogeneity {prin- subordina- cipium Homogeneitatis), is, — That how different oniiuluion,*'' VOL. L LMU LECTIRKS ON lAXilC. LKCT XI. uuilor Kx- tvusitni, nrv r«guUtvj)position, t-allod *_. likowi.sc Repugnance, (to dtrtc/jaTtKw? o-vtik^I- (jOul, arrt(/)acri9, op2>osi(io ininwiliitta sive contra- didoria, rcpugnantia) ; :uk1, 2°, Afediate or Con- tra nj Opposition, (to luavTioi^ avTiKeiaOai, kvav- TLOTrji;, oppositio nicdiata vel contraria). The fonnor emerges when one concept abolishes (tol- lit) directly or by simple negation, what another establishes (ponit) ; the latter, when one concept does this not directly or by simple negation, but throuoli the affirmation of somethino- else." o o Expiica- " Identity is not to be confounded with Agreement ,7" .-. 1 or ConoTuence, nor Diversity with Confliction. All Iilenlity and O ' J i^f^Ritv"' identical concepts are, indeed, congruent ; but all S ^"°"'*'' congruent notions are not identical. Thus, learning and virtue, beauty and riches, magnanimity and sta- ture, are congruent notions, inasmuch as, in thinking a thing, they can easily be combined in the notion we form of it, although in themselves very different from each other. In like manner, all conflictive no- tions are diverse or different notions, for unless differ- ent, they could not be mutually conflictive. But, on the other hand, all different concepts are not conflic- tive ; but those only whose difference is so great that each involves the negation of the other ; as, for ex- ample, virtue and vice, beauty and deformity, ivealth and poverty. Thus these notions are by pre-emin- ence — /car' i^o^r^v — said to be 02')p)0sed, although it is true, that in thinking we can oppose, or place in antithesis, not only different, but even identical, concepts." " To speak now of the distinction of Contradictory a [Cf. Drobisch, Logik, p. 17, § 25 ct aeq.] LECTURES ON LOGIC. 215 and Contrary Opposition, or of Contradiction and lect. Contrariety ; — of these the former, — Contradiction, — '— is exemplified in the opposites, — yellow, not yellow, twy and"' tvalking, not ivalking. Here each notion is directly, OpposTtLi. immediately, and absolutely, repugnant to the other, — they are reciprocal negatives. This opposition is, therefore, properly called that of Contradiction or of Repugnance ; and the opposing notions themselves are conti^adictory or repugnant notions, in a single word, conti'adictories. The latter, or Contrary Oppo- sition, is exemplified in the opposites, yellow, blue, red, &c., walking, standing, lying, &c." " In the case of Contradictory Opposition, there are only two confiictive attributes conceivable ; and of these one or other must be predicated of the object thought. In the case of Contrary Opposition, on the other hand, more than two confiictive characters are possible, and it is not, therefore, necessary, that if one of these be not predicated of an object any one other must. Thus, though I cannot at once sit and stand, and consequently sitting and standing are at- tributes each severally incompatible with the other ; yet I may exist neither sitting nor standing, — I may lie ; but I must either sit or not sit, I must either stand, or not stand, &c. Such, in general, are the oppositions of Contradiction and Contrariety." "It is now necessary to say a word in regard to Logical sig- their logical significance. Immediate or Contradictory courradlc- Opposition constitutes, in Logic, affirmative and nega- contrTry tive notions. By the former something is posited or "I'l'*"''"*"- affirmed {p)onitur, affirmatur) ; by the latter, some- thing is sublated or denied {tollitur, negatur). This, however, is only done potentially, in so far as concepts are viewed apart from judgments, for actual affirm a- 210 LECTURES UN LOGIC. LKtT. tion and actual nogatiou suppo.so an act oi" judguiont ; hut, at the saiuo time, in so far as two concepts iitionl the elcnuuts, auri)UL;lit into relation, necessitate the formation, i>r an atlirmative or negative proposi- tion, they may be considered as in themselves negative and aiHrmative. " ''Further, it is evident that a notion can be logi- cally ilenied only by a contradiction. For when we abstract from the matter of a notion, as Logic does, it is impossible to know that one concept excludes another, unless the one be supposed the negation of the other. Logically considered, all positive or affir- mative notions are congruent, that is, they can, as far as their form is concerned, be all conceived or thought together ; but whether in reality they can coexist, — that cannot be decided by logical rules. If, therefore, we would, with logical precision and cer- tainty, oppose things, we must oppose them not as contraries, {A. B. C), but as contradictories, {A. — not A. B. — not B. C. — 7iot C.) — Hence it also follows, that there is no negation conceivable without the con- comitant conception of an affirmation, for we cannot deny a thing to exist, without having a notion of the existence which is denied." " There are also certain other relations subsisting be- tween notions, compared together in reference to their Comprehension. Par.xLiii. ^\ XLIII. Notions, as compared with each other and"Extrin- iu rcspcct of their Comprehension, are further distinimished into Intrinsic and Extrinsic, The former are made up of those attributes which are essential, and, consequently, necessary to the o Krug, Logik, p. 118-120.— Ed. SIC notions. LECTURES ON LOGIC. 2l7 object of the notion : these attributes, severally lect. considered, are called Essen tials or hiternal .De- ^— nominations, {ovcncoSr}, essentialia, denominati- ones internee, intrinsicce), and, conjunctly, the Ess ence [ovcria, essentia). The latter, on the con- trary, consist of those attributes which belong to the object of the notion only in a contingent manner, or by possibility ; and which are, there- fore, styled Accideiijts, or Extrinsic Denomina- tions, {crvixjSe/BTjKOTa, accidentia, denominationes externce or extrinsicw.) " Having thus given you the distinctions of notions, invoiu- as founded on their more general relations under the Co-ordina- „ ^-^, - . _ . tion of Con- quantity oi Comprehension, i now proceed to con- cepts under . -, , - - . . . , . . Comprelien- sider them under this quantity m their proximate sion,— these relations ; that is, in the relation of Involution and giected by the relation of Co-ordination. These relations have "^'" been, I may say, altogether neglected by logicians : who, in consequence, have necessarily overlooked Hence one of the two great divisions of all reasoning ; for in compie- ...-.(. Ill 1 hension all our reasoning is either from the whole to the parts overlooked T f> 1 1 1 1 • 1 • f t>y logicians. and irom the parts to the whole, m the quantity oi extension, or from the whole to the parts and from the parts to the whole, in the quantity of comprehen- sion. In each quantity there is a deductive, and in each quantity there is an inductive, inference ; and if the reasoning under either of these two quantities were to be omitted, it ought, perhaps, to have been the one which the logicians have exclusively cultivated. For the quantity of extension is a creation of the mind itself, and only created through, as abstracted from, the quantity of comprehension ; whereas the o. Krug, Lorjik, § 39. — ^Ed. LECT. XII. 21S LKCirKKS ox LOOIC. t|U;uitit> of cDnnirclu'iisioii is at oiu'e l' things. The fonnor (jiiantity is thus secDmlary and factitious, (he latter })iiniaiy and na- tural, liui prx.- Tiiat h>gieians should have ueglected the process ol" tempi«7i"i reasoning which is competent between the parts and riMoto. ^j^^^ xvhole of tlie quantity of comprehension, is tlie more remarkable, as, after Aristotle, they have in gen- eral articulately distinguished the two quantities from each other, and, after Aristotle, many of them have explicitly enounced the special law on which the logic of comprehension proceeds. This principle established, but not applied, is expressed in the axiom, — The char- acter of the character is the character of the thing ; or, The predicate of the predicate is the predicate of the subject, (Nota notce est nota rei ipsius; PtcbcU- catitm prcedicati est lynedicatum suhjecti). This axiom is enounced by Aristotle ; " and its application, I have little doubt, "was fully understood by him. In fact 1 think it even possible to show in detail, that his whole analysis of the syllogism has reference to both quantities, and that the great abstruseness of his Prior Analytics, the treatise in which he develops the general forms of reasoning, arises from this, — that he has endeavoured to rise to formulae sufficiently general to express at once what was common to both kinds ; — an attempt so far beyond the intelligence of subsequent logicians, that they have wholly misun- derstood and perverted his doctrine. They under- stood this doctrine, only as applied to the reasoning in extensive quantity ; and in relation to this kind of reasoning, they have certainly made palpable and easy what in Aristotle is abstract and diflficult. But then o Caicg., c. iii. — Ed. LECTURES ON LOGIC. 219 tliey did not observe that Aristotle's doctrine applies lect. to two species, of which they only consider one. It '— was certainly proper to bring down the Aristotelic logic from its high abstraction, and to deliver its rules in proximate application to each of the two several species of reasoning. This would have been to fill up the picture of which the Stagirite had given the sketch. But by viewing his Analytic as exclu- sively relative to the reasoning in extension, though they simplified the one-half of syllogistic, they alto- gether abolished the other. This mistake, — this par- tial conception of the science, — is common to all logicians, ancient and modern : for in so far as I am aware, no one has observed, that of the quantities of comprehension and extension, each affords a reason- ing proper to itself ; and no one has noticed that the doctrine of Aristotle has reference indifferently to both ; although some, I know, having perceived in general that we do reason under the quantity of com- prehension, have on that founded an objection to all reasoning under the quantity of extension, that is, to the whole science of Logic as at present constituted. I have, in some degree, at present spoken of matters which properly find their development in the sequel ; and I have made this anticipation, in order that you should attend particularly to the relation of concepts, under the quantity of comprehension, as containing and contained, inasmuch as this affords the foundation of one, and that not the least important, of the two great branches, into which all reasoning is divided. IF XLIV. We have seen that of the two quan- Par. xl[v. titles of notions each affords a logical Whole and anrco-o" Parts ; and that, by opposite errors, the one of ' '"' '""' 220 LFXTURES ON LOGIC. i.KCT tlio.^o has, tliiouijjli over inclusion, been called the _* L /o(/ii'((I, whilst the other has, througli over exclu- sion, been called the metaphysical. Thus, in respect of their Comprehension, no less than of their Extension, notions stand to each other in a relation of Containing and Contained ; and this relation, which in the one quantity (extension) is styled that of Subordination, may in the other (comprehension), for distinction's sake, be styled that of In i'olutio7i. Co-ordination is a term which may be applied in either quantity." In the quantity of comprehension, one notion is involved in another, when it forms a part of the sum total of characters, which together con- stitute the comprehension of that other; and two notions are in this quantity co-ordinated, when, whilst neither comprehends the other, both are immediately comprehended in the same lower concept. tion, Eipiica- From what has been formerly stated, you are aware that the quantity of comprehension, belonging to a notion, is the complement of characters which it con- tains in it ; and that this quantity is at its maximum in an individual. Thus the notion of the individual Socrates, contains in it, besides a multitude of others, the characters of Son of Soplironiscus, Athenian, Greek, European, man, animal, organised being, &c. But these notions, these characters, are not all equal!}' proximate and immediate ; some are only given in and throusfh others. Thus the character Athenian is O applicable to Socrates only in and through that of Son of Sopjhroniscus, — the character of Greek, only in and a [Cf. Drobisch, Logik, §§ 22, 23 ; Fischer, Logik, § 49] LECTURES ON LOGIC. 221 through that of Athejiian, — the character of Europe- lect. cm, only in and through that of Qreeh, — and so forth ; 1- in other words, Socrates is an Athenian only as the son of Sophroniscus, only a Greek as an Athenian, only a European as a Greek, only a man as a Euro- pean, only an animal as a man, only an organised being as an animal. Those characters, therefore, that are given in and through others, stand to these others in the relation of parts to wholes ; and it is only on the principle, — Part of the 'part is a part of the whole, — that the remoter parts are the parts of the primary whole. Thus, if we know that the individual Socrates comprehends the character son of Sophron- iscus, and that the character son of Sophroniscus comprehends the character Athenian ; we are then warranted in saying that Socrates comprehends A the- nian, in other words, that Socrates is an Athenian. The example here taken is too simple to show in what manner our notions are originally evolved out of the more complex into the more simple, and that the pro- gress of science is nothing more than a progressive unfolding into distinct consciousness of the various elements comprehended in the characters, originally known to us in their vague or confused totality. It is a famous question among philosophers, — Controversy Whether our knowledge commences with the gen- 'lpredicate, {7rpo(TKarriyopovii€vov, ap2:)7'CBdicatmn).^ The Subject and Predicate of a proposition together are, after Aristotle, called its Terms or Extremes,'^ a See De Interp. , c. 3, where the yopovfifvov to denote the predicate of f>rifjia, or verb, includes the predicate a proposition, see Ammonius on Dc and copula united. — Ed. Interp., p. 110 b, ed. Aid., Venetiis, /3 See De Interpretatione, c. 10, 1546. See below, p. 230. — Ed. § 4 : 'Oraf 5e rh I(tti rpirov irpocr- [For the origin of this distinction KarriyopriTai, — an expression to which see Blemmidas (after Aristotle), may be traced the scholastic dis- Logica, p. 186.] tinction between secundi and tertii y Anal. Trior., I. 1, 4.— Ed. adjacentis. For the term TrpoaKarr]- LECTURES ON LOGIC, 229 {opoL, oLKpa, TTepara, termini) ; as a proposition lect is by him sometimes called an Interval, (Stct- arrjixa),"' being, as it were, a line stretched out between the extremes or terms. We may, there- fore, articulately define a judgment or proposi- tion to be the product of that act in which we pronounce, that of two notions thought as sub- ject and as predicate, the one does or does not constitute a part of the other, either in the quantity of Extension, or in the quantity of Comprehension. Thus in the proposition, iron is magnetic, we have lUustratiou. iron for the Subject, magnetic for the Predicate, and the substantive verb is for the Copula. In regard to this last, it is necessary to say a few words. " It is not always the case, that in propositions the copula is expressed by the substantive verb is or est, and that the copula and predicate stand as distinct words. In adjective verbs the copula and predicate coalesce, as in the proposition, the sun shines, sol lucet, which is equivalent to the sun is shining, sol est lucens. In existential propositions, that is, those in which mere existence is predicated, the same holds good. For when I say / am, Ego sum, the am or sum has here a far higher and more emphatic import than that of the mere copula or link of connection. For it expresses, / am existent, Ego sum existens. It might seem that, in negative propositions, when the copula is affected by the negative particle, it is converted into a non-copula. But if we take the word copula in a wider meaning, for that through which the subject and predicate are connected in a mutual relation, it' a Anal. Prior., I. 15, 16, 25.— Ed. 230 LECTURES ON LOGIC. LECT. will apply not only to aftirmativc but to negative, not -J — only to categorical but to hypothetical and disjunc- I'wposi- tive, propositions."" I may notice that propositions ii'iirVA.!-' with the subject, predicate, and copula, all three arti- cnlntely expressed, have been called by the school- men those of the third adjacent, [propositiones tertii adjaceiitis, or tertii adjecti), inasmuch as they mani- festly contain three parts. This is a barbarous ex- pression for what the Greeks, after Aristotle, called TrpoTctcret? eV rpiTov {eaTi) Kar-qyopovixevov. For the same reason, propositions with the copula and pre- dicate in one were called those of the second ad- jacent.^ Concepts " What has now been said will enable you to per- mems.- ccivc how far concepts and judgments coincide, and thJy cohi- how far they differ. On the one hand, they coincide differ*" in the following respects : — In the first place, the concept and the judgment are both products; the one the product of a remote, the other the product of an immediate, act of comparison. In the second place, in both, an object is determined by a character or attribute. Finally, in the third place, in both, things relatively different in existence are reduced to a rela- tive identity in the unity of thought. On the other hand, they differ in the following respects : — In the first place, the determination of an object by an attri- bute is far more express in the judgment than in the concept ; for in the one it is developed, in the other only implied. In the second place, in the concej)t the unity of thought is founded only on a similarity of quality; in the judgment, on the other hand, it is a Krug, Logik, § 52, Anm. ii, p. p. 74 ; Crakanthorpe, Logica, pp. 153-154. — Ed. [Compare Bach- IGO, 1C7.] mann, Logik, p. 127 j Schulze, Zojrii*, ^ See above, p. 228, note )3. — Ed. LECTURES ON LOGIC. 231 founded on a similarity of relation. For in the lect. notion, an object and its characters can only be con- 1- ceived as one, inasmuch as they are congruent and not conflictive, for thus only can they be united into one total concept. But in the judgment, as a subject and predicate are not necessarily thought under a similarity of quality, the judgment can comprehend not only congruent, but likewise conflictive, and even contradictory, notions; for two concepts which are compared together can be recognised as standing in the relation either of congruence or of repugnance. Such is the sameness, and such is the diversity, of concept and judgment." " We have thus seen that a judgment or pro23osition consists of three parts or correlative notions, — the notion of a subject, the notion of a predicate, and the notion of the mutual relation of these as determined and determining. Judgments may^ I think, be primarily divided in judgments,, two ways, — the divisions being determined by theaFvidld. general dependencies in which their component parts stand to each other, — and the classes afi'orded by these divisions, when again considered, without distinction, in the difi'erent points of view given by Quantity,. Quality, and Eelation, will exhaust all the possible forms in which judgments are manifested. IF XL VIII. The first great distinction of Judg- Par. xlviii. ments is taken from the relation of Subject and Jio" Vf'^'' Predicate, as reciprocally whole and part. If the -Spre!' Subject or determined notion be viewed as the Extensive.'^ containing whole, we have an Intensive or Com- prehensive proposition ; if the Predicate or dc- o Esser, Logik, § 56, p. Ul. 232 LECTURES ON LOGIC. LETT. termiiiing notion be viewed as the containing ^"'' whole, we have an Extensive proposition. Expiioa. This distinction of propositions is founded on the diitinctiou distinction of the two quantities of concepts, — their the Com- Comprehension and their Extension. The relation of »n.i Exten- subjcct and predicate is contained within that of copu. whole and part, for we can always view either the determining? or the determined notion as the whole which contains the other. The whole, however, which the subject constitutes, and the whole which the pre- dicate constitutes, are different, being severally de- termined by the opposite quantities of comprehension and of extension ; and as subject and predicate neces- sarily stand to each other in the relation of these inverse quantities, it is manifestly a matter of indiffer- ence, in so far as the meaning is concerned, whether we view the subject as the whole of comprehension, which contains the predicate, or the predicate as the whole of extension, which contains the subject. In point of fact, in single propositions it is rarely appar- ent which of the two wholes is meant ; for the copula IS, est, &c., equally denotes the one form of the relation as the other. Thus, in the proposition mem is tivo- legged, — the copula here is convertible with compre- hends or contains in it, for the proposition means man contains in it two-legged, that is, the subject man, as an intensive whole or complex notion, com- prehends as a part the predicate tivo-legged. Again, in the proposition onan is a hilled, the copula corre- sponds to contained under, for this proposition is tantamount to, mxxn is contained wider hiped, that is, the predicate biped, as an extensive whole or class, contains under it as a part the subject 7nan. But, in LECTURES ON LOGIC. 233 point of fact, neither of the two propositions unam- lect. biguously shows whether it is to be viewed as of an _ intensive or of an extensive purport ; nor in a single proposition is this of any moment. All that can be said is, that the one form of expression is better accommodated to express the one kind of proposition, the other better accommodated to express the other. It is only when propositions are connected into syllo- gism, that it becomes evident whether the subject or the predicate be the whole in or under which the other is contained ; and it is only as thus constituting two different, two contrasted, forms of reasoning, — forms the most general, as under each of these every other is included, — that the distinction becomes neces- sary in regard to concepts and propositions. The dis- tinction of propositions into Extensive and Intensive, it is needless to say, is, therefore, likewise the most general ; and, accordingly, it is only in subordination to this distinction that the other distinctions, of which we are about to treat, are valid. I now proceed to the second division of Judgments, and commence with the following paragraph. H XLIX. The second division of Judgments Par. xlix. ° Second is founded on the different mode in which the re- division of . Judgments, lation of determination may subsist between the — Categon- subject and predicate of a proposition, ihis re- ditionai,— lation is either Simple or Conditional, (propositio of which is • • 7' • T \ /-\ 1 c subdivided Simplex, loropositio conditionalis). On the former into Hypo- alternative, the proposition is called Cateqoincal;"' Disjunctive, on the latter, inasmuch as the condition lies either matic. o [Categorical had better be called as by Mocenicus, who has also Abso- Absolute, as is done by Gassendi, lute. See Co7itemj7lationes Pcripate- Loyica, p. 287, cd. Oxon.; or Perfect, tica, ii. c. 2, p. 39 ct scj'.] 234 LECTURES ON LOGIC. LECT. in the subject, or in the predicate, or iu botli tlie ••^"'' subject ami i)redicate, there are three species of proposition. In the first case, the proposition is JTi/pothctical, in the second. Disjunctive, in the third, Dilemmatic or Hypothetico-disjunctive.'^ Expiica- I shall consider these in their order ; and, first, of Cau'i^ricai Catcgorlcal propositions. But here it is proper, be- TKm''' fore proceeding to expound what is designated by the attgotica . ^^^.^ catcgoHcal, to commence with an explanation of the term itself. This word, as far as is now known, was first employed by Aristotle in a logical signifi- cation. I have already explained the meaning of •the term category ;^ but you are not to suppose that categorical has any reference to the ten summa genera of the Stagirite. By Aristotle the term Karr)- yopLKos is frequently employed, more especially in the books of the Prior Analytics, — and in these books alone it occurs, if I am correct in my estimate, eighty- its signifi- seven times. Now you will observe, that in no single cation as . . , . , t i i a • i • used by instance is this word applied by Aristotle except m Aristotle. . . . .^"^^ . ^ • ^ . .^ . one unambiguous signincation, that is, the signmcation of affirmative ; and it is thus by him used as a term convertible with /cara^artKos, and as opposed to the two s}'non}Tns of negation he indifierently employs, — dno- ^art/cos and (jTepr)rLKo<^? Such is the meaning of the Its meaning worcl in Aristotclic usagc. Now you will observe, that ingsof his it obtained a totally difi'erent meaning in the writings disciples of his disciples. This new meaning it probably ob- tained from Theophrastus, the immediate discijole of Aristotle, for by him and Eudemus we know that it a Cf. Krug, Lorjik, § 57. — Ed. fi See above, p. 197. — Ed. [Mocenicus, loc. C('<. ; Schulze, io^tl", y Compare Discussions, p. 152. — §§ 45, 52, 60-69.] Ed. LECTUEES ON LOGIC. 235 was so employed ; — and in this new meaning it was lect. exclusively applied by all tlie Greek and Latin expo- 1- sitors of the Peripatetic philosophy, in fact, by all subsequent logicians without exception. In this second signification, the term categorical, as applied to a proposition, denotes a judgment in which the predicate is simply afiirmed or denied of the subject, and in contradistinction to those propositions which have been called hypothetical and disjunctive. In this change of signification there is nothing very remark- able. But it is a singular circumstance that, though This differ- the Aristotelic employment of the word be in every n^ficaLn^' , 1 , , 1 1 1 1 • iwt hitherto instance altogether clear and unambiguous, no one, observed. either in ancient or in modern times, should ever have made the observation, that the word was used in two difierent meanings ; and that in the one meaning it was used exclusively by Aristotle, and in the other exclusively by all other logicians. I find, indeed, that the Greek commentators on the Organon do, in refer- ence to particular passages, sometimes state that KaTiq- yoptKog is there used by Aristotle in the signification of affirmative ; but, in so far as I have been able to ascertain, no one has made the general observation, that the word was never applied by Aristotle in the sense in which alone it was understood by all other logical writers. So much for the meaning of the term categorical; as now employed for simple or absolute, and as opposed to conditional, it is used in a sense difi'erent from its original and Aristotelic meaning. In regard to the nature of a Categorical Judgment Nature of a itself, it is necessary to say almost nothing. For, as Judgment this judgment is that in which the two terms stand to each other simply in that relation which every 236 LECTURES ON LOGIC. LKiT. jiulii:meiit implies, to the exclusion of all extrinsic conditions, it is evident, that what we have already said of the essential nature of judgment in general, allords all that can be said of categorical judgments in particular. A categorical proposition is expressed in the formulae, A is B, A is not B. I proceed, therefore, to the genus of propositions as opposed to categorical, — viz., the Conditional, — Conditioned. II. Con.ii- This irenus, as stated in the paraejraph, comprises lueuts.— two species, according as the condition lies more Tlioso com- . 1 • 1 1 • • 1 T prise three proximately in the subject, or m the predicate; to which is to be added, either as a third s})ecies, or as a compound of these two, those propositions in which there is a twofold condition, — the one belonging to the subject, the other to the predicate. The first of these, as stated, forms the class of Hypothetical, the second that of Disjunctive, the third that of Dilem- Variations matic, propositions. I may notice, by the way, that theappiica- thcrc IS a good deal of variation in the language of terms co?i- logiciaus ill icgard to the terms Conditional and &uiH>/po- Hypothetical. You are aware that conditio nalis, in Latin, is commonly applied as a translation of vvo- OeTLKos in Greek ; and by Boethius, who was the first among the Latins who elaborated the logical doctrine of hypothetical, the two terms are used convertibly with each other.* By many of the schoolmen, how- ever, the term hypothetical [hypotheticus) was used to denote the genus, and the term conditional, to denote the species, and from them this nomenclature has passed into many of the more modern compends of logic, — and, among others, into those of Aldrich and Whately. This latter usage is wrong. If either o Compare Discussions, p. ^150. Syllogismo Hypothetico, L. i.— Ed. For Boethius, see his treatise De LECTURES ON LOGIC. 237 term is to be used in subordination to tlie other, con- lect. ditioncd, as the more extensive term, ought to be '— applied to designate the genus ; and so it has accord- ingly been employed by the best logicians. But to pass from words to things. I said that Hypothetical propositions are those in i. Hvpo- ,.,, T- Tr'-i 1- T thetical. which the condition qualiiying the relation between the subject and predicate lies proximately in the subject. In the proposition, B is A, the subject B is unconditionally thought to exist, and it thus consti- tutes a categorical proposition. But if we think the subject B existing only conditionally, and under this conditional existence enunciate the judgment, we shall have the h}'p)othetical proposition, If B is, A is,- — or, in 'a concrete example, — Rainy iveather is wet iveather, is a categorical proposition — If it rains, it will he ivet, is an hypothetical. In an hypothetical proposition the objects thought stand in such a mutual relation, that the one can only be thought in so far as the other is thought ; in other words, if we think the one, we must necessarily think the other. They thus stand in the relation of Keason and Consequent. For a reason is that which, being affirmed, necessarily entails the affirmation of something else ; a con- sequent is that which is only affirmed, inasmuch as something previous is affirmed. The relation between reason and consequent is necessary. For a reason followed by nothing, would not be the reason of any- thing, and a consequent which did not proceed from a reason, would not be the consequent of anything. An hypothetical proposition must, therefore, contain a reason and its consequent, and it thus presents the appearance of two members or clauses. The first clause, — that which contains the reason, — is called the 23S LECTURES ON LOGIC. LKCT. Antecedent, also the Reason, the Condition, or the Ilt/- J pothesis, {h)/pothe;iis, conditio, ratio, antecedens, — i.e., niemhruni ^\\(} propositio) ; the second, which contfiins the coiisetj^ueut necessitated by this ground, is called the Consequent, also the Thesis, {co'nsequens, thesis, ra- tionatum, conditionatuni). The relation between the two clauses is called the Consequence, [consequentia), and is expressed by the particles if on the one hand, and then, so, therefore, &c., on the other, which are, therefore, called the Consecutive particles, {particulce consecutivcs)."' These are frequently, however, not formally expressed. An hypo- "This couscqucnce {if is — then is) is the copula in jud^ent hypothetical propositions ; for through it the concepts posite!" ' are brought together, so as to make up, in conscious- ness, but a single act of thought ; consequently, in it lies that synthesis, that connection, which constitutes the hypothetical judgment. Although, therefore, an h}^othetical judgment appear double, and may be cut into two different judgments, it is nevertheless not a composite judgment. For it is realised through a simple act of thought, in which if and then, the ante- cedent and the consequent, are thought at once and as inseparable. The proposition if B is, then A is, is tantamount to the proposition, A is through B. But this is as simple an act as if we categorically judged B is A, that is, B is under A. Of these two, neither the one, — If the sun shines, nor the other, — then it is day, — if thought apart from the other, will constitute a judgment, but only the two in conjunction. But if we think, — The sun shines, and it is day, each by itself, then the whole connection between the two thoughts is abolished, and we have nothing more than o Krug, Lorjik, § 57, Aiim. 2, p. 1G9. — Ed. LECTURES ON LOGIC. 239 two isolated categorical judgments. The relatives if lect. and then^ in which the logical synthesis lies, constitute 1_ thus an act one and indivisible. " For the same reason, an Hypothetical iudgment Not con- vertible into cannot be converted into a Cates-orical. For the a Categori- cal. thought, A is through B, is wholly different from the thought, A is in B. The judgment, — If God is righteous, the7i will the wicked he punished, and the judgment, — A righteous God punishes the ivicked, are very different, although the matter of thought is the same. In the former judgment, the punishment of the wicked is viewed as a consequent of the righteous- ness of God ; whereas the latter considers it as an at- tribute of a righteous God. But as the consequent is regarded as something dependent from, — the attribute, on the contrary, as something inhering in, it is from two wholly different points of view that the two judg- ments are formed. The hypothetical judgment, there- fore, A is through B, is essentially different from the categorical judgment, A is in B ; and the two judg- ments are regulated by different fundamental laws. For the Categorical judgment, as expressive of the relation of subject and attribute, is determined by the laws of Identity and Contradiction ; the Hypothetical, as expressive of the relation of Reason and Conse- quent, is regulated by the principle of that name." " So much for Hypotheticals. "Disjunctive judgments are those in which the 2. Disjimc- condition qualifying the relation between the subject and predicate, lies proximately in the predicate, as in the proposition, D is either B, or C, or A. In this class o Krug, Lofjlk, § 57, p. 168, Anm. (consequentia.) Heiice the logical 2. — Ed. [Hypotheticals take account rule, Propositio Conditionalis nihil not of the correctness of the two 2)omt in esse. Christian Weiss, Lekr- clauses, but only of their connection, buck dcr Logik, p. 109, ed. ISOl.] tive. 240 LECTURES ON LOGIC LECT. of iiulirments a certain i>luiality of attributes is prcdi- XIII Jo J •< X ^ rated of the subject, but in such a manner that this plurality is not predicated conjunctly, but it is only judged that, under conditions, some one, and only some one, of this bundle of attributes appertains to the subject. When I say that Men are cither Blacl-, or White y or Tawny, — in this proposition, none of tliese three predicates is unconditiouall}^ affirmed; but it is only assumed that one or other may be affirmed, and that, any one being so affirmed, the others must, eo ipso, be denied. The attributes thus disjunctively predicable of the subject, constitute together a certain sphere or whole of extension ; and as the attributes mutually exclude each other, they may be regarded as reciprocally reason and consequent. A disjunctive proposition has two forms, according as it is regulated by a contradictory, or by a contrary, opposition. A is either B or not B, — This mineral is either a metal or not, — are examples of the former ; A is either B, or C, or D, — This mineral is either lead, or tin, or zinc, — are examples of the latter. The opposite attri- butes or characters in a disjunctive proposition are called the Disjunct Members [memhra disjuncta) ; and their relation to each other is called the Disjunction, (disjunctio), which in English is expressed by the rela- tive particles either, or, (aut, vel), in consequence of which these words constitute the Disjimctive j^articles, (particulcB disjunctivce). In propositions of this class the copula is formed by either is, — or is, for hereby the concepts are brought together so as to constitute a single object of consciousness, and thus a synthesis or union of notions is effected. A DUjunc- " Now, although in consequence of the multiplicity mrntnofin of its prcdicatcs, a disjunctive proposition may be LECTURES ON LOGIC. 241 resolved into a plurality of judgments, still it is not lect. on that account a complex or composite judgment. ^^' For it is realised by one simple energy of thought, in p^^e^ 3'' which the two relatives,— the either and the or, — are fbteln^oT' thought together as inseparable, and as binding up categorical, the opposite predicates into a single sphere. In con- sequence of this, a disjunctive proposition cannot be converted into a categorical. For in a categorical judgment a single predicate is simply affirmed or de- nied of a subject ; whereas in a disjunctive judgment there is neither affirmation nor negation, but the op- position of certain attributes in relation to a certain subject constitutes the thought. Howbeit, therefore, that a disjunctive and a categorical judgment may have^a certain resemblance in respect^of their object- matter ; still in each the form of thought is w^hoUy different, and the disjunctive judgment is, conse- quently, one essentially different from the cate- gorical."" Dilemmatie propositions are those in which a condi- 3, Diiem- tion is found both in the subject and in the predicate, and, as thus a combination of an hypothetical form and of a disjunctive form, they may also appropriately be denominated Hypothetico-disjunctive. If X is A, it is either B or C — If an actio?i be prohibited, it is p>rohibited either by natural or by positive laiv — If a cognition be a cognition of fact, it is given either through an act of external perception or through an act of self-consciousness. In such propositions, it is not necessary that the disjunct predicates should be limited to two ; and besides what are strictly called dilemmatie judgments, we may have others that would properly obtain the names of trilemmatic, tetralem- a Krug, LogiJc, pp. 170, 171. Compare Kant, LogiJc, § 29. — Ed. VOL, L Q 242 LECTURES ON LOGIC. LECT. matic, poli/lem viatic, kc. But in roforeuce to proposi- ^"'' tions, as iu reference to syllogisms, dilemma is a won' used not merely to denote the cases where there are onlv two disjunct members, but is, likewise, extended to any plurality of opposing predicates. There re- mains here, however, always an ambiguity ; and per- haps, on that account, the term hypothetico-disjunctive might with propriety be substituted for dilcmmatic. A Diicm- A proposition of this class, though bearing both an mcLTmdi^ h^'i^othetical and a disjunctive form, cannot, however, loiTcdiT' be analysed into an hypothetical and a disjunctive piu^U)* judgment. It constitutes as indivisible a unity of U^Tofoli- thought as either of these ; and can as little as these """■ be reduced without distinction to a plurality of cate- gorical propositions. Eveiy form of Judgments which we have hitherto considered, has its coiTCsponding form of Syllogism ; and it is as constituting the foundations of different kinds of reasoning, that the consideration of these dififerent kinds of propositions is of principal import- judgments ance. These various kinds of propositions may, how- fn reference cvcr, bc cousidcrcd iu tlic different points of view of to Quantity. Q^g^j^^j^y^ Quality, and Relation. And first of Quan- tity ; in reference to which I give you the following paragraph. Par. L. ^ L, The Quantity of Judgments has refer- coinmon cucc to thc wholc of Extcusion, to the number the division of thc objccts concemiug which wc judge. On mentsL- this I shall State articulately, 1°, The doctrine of their "^uan- the Logiciaus ; and, 2°, The doctrine which I con- 2°^"Thedoc- ceive to be the more correct. AmUron^ 1°. (The doctriuc of the Logicians.) The point. common doctrine, which, in essentials, dates from LECTURES ON LOGIC. 243 Aristotle," divides Propositions according to their lect, Quantity into four classes ; viz., (A), the Universal '- or General (pr. universales,generales^'npord(Tei^ at KaOoXov) ; (B), the Particular (pr. particulares, TrpoTd(reL<; [xepLKai, at eV jaepet) ; (C), the Indivi- dual or Singular {pr. individuales, si^igidares, exposiloricB, TrpoToicreLq at Ka9' eKacnov, ra aro/xa) ; (D), the Indefinite {pr. imprcefinitw, indefinitce, TrpoTd(TeLhrastus is cited in illustration of a very ob- scure statement concerning the opposition of indesignate proposi- tions. — Ed.] 246 LECTURES ON LOGIC. LECT iiess or totality in the form of oneness, indivisible unity, IS involyed. Particular Partifular Jiulgmenta are those in ^vllich, among whiii. tlic objects \yitliin a certain sphere or class, ^ve judge concernincf some indefinite number less than the whole, — as Some men are virtuous — Many hoys are courage- ous — Most u'omen are compassionate ; the indefinite plurality, Ayithin the totality, being here denoted by w..r,is the \yord3 some, many, most. There are certain words to mark out whicli scrvc to mark out the quantity in the case 'un/vcrLr of Universal, Individual, and Particular propositions, aud Parti-' Tlic words wliicli dcsiguatc universality are all, the poshion? ichole of, every, both, each, none, no one, neither, always, everywhere, &c. The words which mark out particu- larity are some, not all, one, two, three, &c., sometimes, somewhere, &c. There are also terms which, though they do not reach to an universal whole, approximate to it, as many, most, almost all, the greatest part, &c., few, very few, hardly any, &c., which, in the common employment of language, and in reference to merely probable matter, may be viewed as almost tantamount to marks of universality. Distinction By logiciaus in general it is stated, that in a logical and ind17i- relation, an Individual is convertible with an Universal ParticdTr proposition ; as in both something is predicated of a whole subject, and neither admits of any exception. But a Particular Judgment, likewise, predicates some- thing of a whole subject, and admits of no exception ; for it embraces all that is viewed as the subject, and excludes all that is viewed as not belongino; to it. The whole distinction consists in this, — that, in Uni- a Individuum (proprium) signatum, gum. The former of each, and the and individuum vagura. So particti- latter of each, corresponding. — Me- lare signatum, and particulare va- moranda. Judgments. LECTURES ON LOGIC. 247 versal and in Individual Judoiments, the number of lect. XIII the objects judged of is thought by us as definite ; whereas, in Particular Judgments, the number of such objects is thought by us as indefinite. That Indivi- dual Judgments do not correspond to Universal Judg- ments, merely in virtue of the oneness of their subject, is shown by this, — ^that, if the individual be rendered indefinite, the judgment at once assumes the character of particularity. For example, the propositions, — A German invented the art of printing, — AnEnglishman generalised the law of gravitation, — are to be viewed as particular propositions. But, if we substitute for the indefinite expressions a German and an Englishman, the definite expressions Fust and Newton, the judg- ment obtains the form of an universal. With regard to quantity, it is to be observed, say categorical the logicians, that Categorical Judgments are those aionefac-^ alone which admit of all the forms. " Hypothetical the io|- '^ and Disjunctive propositions are always universal. mtt°of aii For in hypothetical, by the position of a reason, there quLtky! " is posited every consequent of that reason ; and in disjunctives the sphere or extension of the subject is so defined, that the disjunct attributes are predicated of the whole sphere. It may, indeed, sometimes seem as if in such propositions something were said of some, and, consequently, that the judgment is par- ticular or indefinite. For example, as an hypo- thetical, — If some men are learned, then others are unlearned; as a disjunctive, — Those men who are learned are either philosophers or not. But it is easily seen that these judgments are essentially of a general character. In the first judgment, the real consequent is, — then all others are unlearned ; and in the second, the true subject is, — all learned men, irinc erro- UOOUJ. -48 LECTURES ON LOCJIC. LErr. for this is involved in the expression — TJiose men — — — who are learned, &c." " Thu doc- Such is the doctrine of the Logicians. This I cannot but hold to be erroneous ; for we can easily construct propositions, whether hypothetical or disjunctive, which cannot be construed either as universal or singular. For example, when we say, hypothetically, — If some Dodo is, then some animal is; or, disjunctively, — Some men are either rogues or fools: — in either case, the proposition is indefinite or particular, and no inge- nuity can show a plausible reason why it should be viewed as definite, — as general or individual. a Krug, Logik, §' 57, Addi. 4, p. mcinen Logik, i, § 122; Schulze, Lo- 171 €t se*?.— Ed. [Cf. Hoffbauer, (/(!-,§ 60. Contra :—EmeT, Logik, % Anfangsgrilnde der Logik, § 2^3 ; Sig- 92, p. 177. — See below, pp. 333, wart, Logik, § 164 e< seq., ed. 1835 ; 334, note o.— Ed.] Kiesewetter, Grundriss einer allge- LECTURES ON LOGIC. 249 LECTURE XIV. STOICHEIOLOGY. SECTION II. — OF THE PRODUCTS OF THOUGHT. II. APOPHANTIC* JUDGMENTS — THEIK QUALITY, OPPOSITION, AND CONVEKSION. The first part of our last Lecture was occupied with lect, the doctrine of Judgments, considered as divided into ; — Simple and Conditional ; Simple being exclusively tion, Categorical, Conditional, either Hypothetical, Disjunc- tive, or Hypothetico-disjunctive. We then proceeded to treat of the Quantity of propositions, and, in this respect, I stated that they are either Definite or Inde- finite ; the Definite comprising the two subordinate classes of General or Universal, and of Singular or Individual propositions, while the Indefinite are cor- respondent to Particular propositions alone. In regard to the terms definite and indefinite, I warned you that I do not apply them in the sense given by logical writ- ers. With them, Indefinite propositions denote those in which the quantity is not explicitly declared by one of the designatory terms, all, every, some, many, &c. Such propositions, however, ought to be called pre- indesignate { prceindesignatw, aTr/aoo-Stdptorrot), that is, not marked out hy a prefix, — a term better adapted to indicate this external accident of their enunciation; for, in point of fact, these preindesignate propositions 250 LECTURES i>N I.OCIC. LKCT. aiv I'ithor ilolinito or iii(lfrnii(t\ niid (luite as dcllnito XIV. ... ... . 1— or iiulotiniti' in luoaiiini;-, as if tlioir »[uan(ity liad hoeii cxpivssly niarki'il out by tlic predesigiiatory terms. Sccouii 'I'liis liiiiiL!^ preniisoil, 1 now 2^0 on to tlie next divi- (iiviuou 1' I 1 * 1 1 • • • T 1 ofjujg- ."^lun ot .ludpnenis, — the division proceeding on that ui»t nrxHini. ground wliich by Logicians has been called tlie Qiia- Quaiity. ///y of Judgments. In itself the term quality is hero a very vague and arl)itrary expression, for we miglit, with equal propriety, give the name of quality to several other of the distinguishing j)rinciples of pro- positions. For example, the truth or falsehood of pro- positions has been also called their quality ; and. some logicians have even given tlie name of quality to the ground of the distinction of judgments into categorical, h}'pothetical, and disjunctive. What, however, has been universally, if not always exclusively, styled the quality of propositions, both in ancient and modern times, is that according to which they are distributed into Affirmative and Negative. 'O" tive. Par. LI. II LI. In respect of their Quality, Judgments inr^ectof arc dlvldcd into two classes. For either the lity/are^Af- Subjcct aud Prcdicatc may be recognised asreci- and n'J^ procally containing and contained, in the opposite quantities of Extension and Comprehension ; or they may be recognised as not standing in this relation. In the former case, the subject and predicate are affirmed of each other, and the proposition is called an Affirmative, (Trporacrts KarafftaTLKij or KaT-qyopLK-q, judicium affirmati- vum or 2>ositivum) ; in the latter case, they are denied of each other, and the proposition is called a Negative, {TrpoTaa-t^ anocfiaTLKTJ or o-TeprjTLKtj, judicium negativum). LECTURES ON LOGIC. 251 In this paragraph, I have enounced more generally lect. than is done by logicians the relation of predication, in its affirmative and negative phases. For their defi- tion. "^'^ nitions only apply either to the subject or to the predi- ofThTde?- cate, taken as a whole ; whereas, since we may indiflfer- preXcaUon ently view either the subject as the whole in relation '^aph.^'^'^'' to the predicate, or the predicate as the whole in rela- tion to the subject, according as we consider the pro- position to express an intensive or to express an exten- sive judgment, — it is proper in our definition, whether of predication in general, or of affirmation and negation in particular, to couch it in such terms that it may indifi"erently comprehend both these classes, — both these phases, of propositions. As examples of Affirmative and Negative proposi- Affirmative tions, the following may suffice : — A is B — A is not B tive Propo- — God is merciful — God is not vindictive. In an Affirmative judgment, there is a complete inclusion of the subject within the predicate as an extensive whole, or of the predicate within the subject as an intensive whole. In Negative judgments, on the contrary, there is a total exclusion of the subject from the sphere of the predicate (extensively), or of the predicate from the comprehension of the subject (intensively). In affirmative propositions there is also distinctly enounced through what predicate the notion of the subject is to be thought, that is, what predicate must be annexed to the notion of the subject ; in negative propositions, in like manner, it is distinctly enounced through what predicate the notion of the subject is not to be thought, that is, what predicate must be shut out from the notion of the subject. In negative judgments, therefore, the negation essentially belongs to the Copula ; for otherwise all propositions 252 LFXTUKES ON lAHiU'. LECT. without ilistiiu'tioii would be aflirmative. This, liow- *^'^" I'ViT. lias boon a point of controversy among modern Th«j ui>:«- logicians; for many maintain that the negation Ix'longa nThcW to the predicate, on the following grounds : — If the luJ^Md'by negation pertained to the copula, there could be no "^.''^'" synthesis of the two terms, — the whole act of judgment would be subverted ; while at the same time a non- connecting copula, a non-copulative, is a contradiction in terms. But a negative predicate, that is, a predicate by which something is taken away or excluded from the subject, involves nothing contradictory ; and, there- fore, a judgment with such a predicate is competent." The oppo- The opposite doctrine is, however, undoubtedly the mainuine.r more corrcct. For if we place the negation in the pre- .vliUior. dicate, negative judgments, as already said, are not different in form from affirmative, being merely affir- mations that the object is contained within the sphere of a negative predicate, or that a negative predicate forms one of the attributes of the subject. This, how- ever, the advocates of the opinion in question do not venture to assert. The objection from the apparent contradiction of a non-connecting copula is valid only if the literal, the grammatical, meaning of the term copula be coextensive with that which it is applied logically to express. But this is not the case. If lit- erally taken, it indicates only one side of its logical True import meaning. What the word copula very inadequately Li'copX denotes, is the form of the relation between the subject and predicate of a judgment. Now, in negative judg- ments, this form essentially consists in the act of tak- a Krug, Logik, § 55, Anm. 3. — erslen Logik, § 12 ; Derodou, Logica, Ed. [Compare, on the same side, p. 642; cf. p. 515 et seq. Ctyntra: Buffier, Logique, i. § 75 et seq.; Bol- — Kant, Logik, § 22, Anm. 3; Bach- zano, Wissensclmftslehre, Logik, vol. mann, Logik, § 84, p. 127 j Esser, ii. §§ 127, 129, 136 ; Schulze, Logik, Logik, § 59, p. 115.] § 50, p. 74 ; Bardili, Grundriss der LECTURES ON LOGIC. 253 ihg a part out of a wliole, and is as necessary an act of lect. thought as the putting it in. The notion of the one — contradictory in fact involves the notion of the other. '^ The controversy took its origin in this, — that every originofthe , ^ ^ . nn • controversy negative ludojment can be expressed m an amrmative regardiug r 11 . . , „ , 1 the place of lorm, when the negation is taken irom the copula negation. and placed in the predicate. Thus, A is not B may be changed into, — A is 7iot-B. The contrast is better expressed in Latin, A non est B — A est no/i-B. In fact, we are compelled in English to borrow the Latin non to make the difference unambiguously apparent, saying, A is non-^, instead of A is not-^. But this proves nothing ; for by this transposition of the negation from the copula to the predicate, we are also enabled to express every affirmative proposition through a double negation. Thus, A is B, in the affir- mative form is equivalently enounced by A is not 7ion- B — A no7i est no72-B, in the negative. This possibility of enunciating negative propositions Negative ,„ . 1 fr> • ... terms, — m an amrmative, and amrmative propositions in ahowdesig- negative, form, has been the occasion of much perverse Aristotle. refinement among logicians. Aristotle^ denominated the negative terms, such as non B, non homo, non alhus, &c., ovofxara dojotcrra, literally, indefinite nouns. Boethius,"^ however, unhappily translated Aristotle's By Greek term ao/Difrros by the Latin infinitus, reserving the term indefinitus to render dSioptcrro? as applied to propositions, but of which the notion is more ap- propriately expressed, as we have seen, by the word indesignate {indesignatus) , or better preindesignate [prwindesignatus). The Schoolmen, following Boethi- By the us, thus called the ouofxara aopiara of Aristotle no- a Baclimann, Logik, p. 127. — Ed. y In De Interprctalionc, L. ii. § 1. i3 De Interpretatione, c. 2.— En. Opera, p. 250.— Ed. 254 LECTURES OX LOO 10. LEiT. mina injinita: ami tlir iion (hoy .stylctl the 2^nrticnla !_ inflnilans. Out of such olomeiits they also coustructed Pfvpoti- Propositio Ill's Injinita'; that is, jiulgmcnts in ^vhicll ii7/ffofO?o either the subject or the i»reilicate was a negative — wh.r notion, as non homo est ririats, and noino est non- riridls, and these they distinguished from the simple On this negative, homo — non est — viricUs. Herein Boethius CiiV and the schoolmen have been followed by Kant,*^ *"'■ through the Woliian logicians ; for he explains Infi- nite Judgments as those which do not simply indicate, that a subject is not contained under the sphere of a predicate, but that it lies out of its sphere, some- where in the infinite sphere. He has thus considered them as combining an act of negation and an act of atfirmation, inasmuch as one thing is afiirmed in them through the negation of another. In consequence of this view, he gave them, after some Wolfians, the name of Limitative, which he constituted as a third form of judgments under quality, — all propositions being thus eitlier Affirmative, Negative, or Limitative. The whole question touching the validity of the dis- tinction is of no practical consequence ; and consists merely in whether a greater or less latitude is to be given to certain terms. I shall not, therefore, occupy your attention by entering on any discussion of what Kant's may be urged in refutation or defence. But if what division of I have already stated of the nature of negation and SfSed^ its connection with the copula, be correct, there is no ground for regarding Limitative propositions as a class distinct in form, and co-ordinate with Affirma- tive and Negative judgments. ^^ If we consider the quantity and quality of judg- a Logik, § 22. Compare Wolf, tion, see Bachmann, Logik, § 84, p. Philos. Ration., § 209.— Ed. 128; Hchnlze, Logik, §50; Drobisch, /3 Compare Krug, Logik, § 55. Logik, % 42.] Anm. 2. — Ed. [Against the distinc- LECTURES ON LOGIC. 255 LECT. XIV. ments as combined, there emerges from this juncture four separate forms of propositions, for they are either Universal Affirmative, or Universal Negative, Particu- lar Affirmative, or Particular Negative. These forms, in order to facilitate the statement and analysis of the syllogism, have been designated by letters, and as it is necessary that you should be familiar with these symbols, I shall state them in the following paragraph. H LII. In reference to their Quantity and Par. lii. Quality together, Propositions are designated by Propositions the vowels A, E, I, 0. The Universal Ajffirona-thlk qxln^ tive are denoted by A ; the Univei^sal Negative Qu^aiity by E ; the Particular Affirmative by I ; the getuer." Particular Negative by 0. To aid the memory, these distinctions have been comprehended in the following lines : — Asserit A, negat E, sed universaliter ambse, Asserit I, negat O, seel particulariter ambo.'' I may here, likewise, show you one, and perhaps the best, mode, in which these different forms can be expressed by diagrams. E a Petrus Hispanus, Summulcr, Tataretiis, Expositio in Summulas, Tract, i. partic. 4, f. 9. Cf. Petrus Tract, i. f. 9 b.— Ed. 236 LECTURES ON LOGIC. LKi'i. The invention t>l' this mode of seiisualisiiig by *^'^* circles tlio abst met ions of Logic is generally given to Iiupi'r' Kuler, who innjiloys it in his Letters to a German omi'iil^ J'riiiccss on different matters of J^hysics and Phdoso- in^Sr pf'!/-'' ^^^^y t'-"* »:\^' nothing of other methods, tliis by wcriUHrto eireles is of a much earlier origin. For I find it in To£ found tl^tj Nueleu^ LogiccB Weisiance, which appeared in Ive^i"*'"*" 1712 ; but this was a posthumous publication, and the author. Christian Weise, who was Kector of Zit- i.nnbert's tau, dicd in 1708. I may notice, also, that Lambert's r* fouud'iu method of accomplishing the same end, by parallel AUu-a.us. Yii^^Q of different lengths, is to be found in the Logic of Alstedius, published in 1614, consequently above a century and a half prior to Lambert's ]\^eites Orga- non.^ Of Lambert's originality there can, however, I think, be no doubt ; for he was exceedingly curious about, and not over-learned in, the history of these subsidia, while in his philosophical correspondence many other inventions of the kind, of far inferior in- terest, are recorded, but there is no allusion whatever to that of Alstedius. Distinction Bcforc Icaviug this part of the subject, I may take tk)Mint°o'" notice of another division of Propositions made by mXi""^ all logicians, — viz., into Pure and Modal. Pure pro- positions are those in which the predicate is categori- cally affirmed or denied of the subject, simply, without any qualification ; Modal, those in which the predicate is categorically affirmed or denied of the subject, under some mode or qualifying determination. For example, — Alexander conquei'ed Darius^is a pure, — Alexander a Partie ii. Lettre xxxv., ed. logistic figure, is given in the ZojrJcfB Coumot. — Ed. Hy sterna Harmonicum of Alstedius j3 A very imperfect diagram of (1614), p. 395. Lambert's diagrams this 'kind, with the lines of equal (Neues Organon, vol. i. p. \l\ et seq.) length, in illustration of the first syl- are much more comjJete. — Ed. LECTURES ON LOGIC. 257 conquered Darius honourably, is a modal proposi- lect. tion." Nothino; can be more futile tliaii this distinc- tion. The mode in such propositions is nothing more tiuTtion than a part of the predicate. The predicate may be a notion of any complexity, it may consist of any number of attributes, of any number even of words, and the mere circumstance that one of these attributes should stand prominently out by itself, can establish no difference in which to originate a distinction of the kind. Of the examples adduced, — the pure proposi- tion, Alexander conquered Darius, means, being re- solved, Alexander was the conqueror of Darius, — Alexander being the subject, was the copula, and the conqueror of Darius the predicate. Now, if we take the modal, — Alexander conquered Darius honourably, and resolve it in like manner, we shall have Alexander ivas the honourable conqueror of Darius ; and here the whole difference is, that in the second the predicate is a little more com.plex, being the honourable conqueror of Darius, instead of the conqueror of Darius. But logicians, after Aristotle,^ have principally con- Division of sidered as modal propositions those that are modified posittonsby by the four attributions of Necessity, Impossibility, Modais as Contingence, and Possibility. But in regard to these, the°consf-^ the case is precisely the same ; the mode is merely a the matter part of the predicate, and if so, nothing can be more sitionaT unwarranted than on this accidental, on this extra- diT "^' logical, circumstance to establish a great division of logical propositions. This error is seen in all its fla- grancy when applied to practice. The discrimination a These modais are not acknow- by the Schoolmen. Compare Am- ledged by Aristotle, who allows only monius, In De Interp., p, 148 b, ed. the four mentioned below. Theyap- 1546. — Ed. pear, however, in his Greek commen- /3 De Interp., c. 12. Compare tators, and from them were adopted Anal, Prior., i. 2. — Ed. VOL. I. K 2:)S LECTURES ON LOGIC. LF.cT. o( ]>ropositions into Pure and Modal, and the discri- niinatiou of Modal propositions into Necessary, Im- possible, Contingent, Possible, and tlie recognition of tliese as logical distinctions, rendered it imperative on the logician, as logician, to know what matter was necessary, impossible, contingent, and possible. For rules were laid down in regard to the various logical operations to which propositions were subjected, ac- cording as these were determined by a matter of one of these modes or of another, and this too when the modal character itself was not marked out by any peculiarity or form of expression. Thus, to take one of many passages to the same effect in^Miately. Speaking whateiy of the quality of propositions, he says : — " When the subject of a proposition is a Common- term, the uni- versal signs (' all, no, every ') are used to indicate that it is distributed, (and the proposition consequently is universal) ; the particular signs (' some, &c.') the contrary. Should there be no sign at all to the com- mon term, the quantity of the proposition (which is called an Indefinite proposition) is ascertained by the matter ; i. e. the nature of the connection between the extremes : which is either Necessary, Impossible, or Contingent. In necessary and in impossible matter, an Indefinite is understood as a universal: e. g., birds have wings ; i. e. all: birds are not cjuadrupeds ; i. e. none: in contingent matter, ({. e. where the terms partly {i. e. sometimes) agree, and partly not) an Indefinite is understood as a particular ; e. g., food is necessary to life ; i. e. some food ; birds sing ; {. e. some do ; birds are not carnivorous : i. e. some are not, or, all are not." * Criticised. Now, all this procccds upon a radical mistake of the nature and domain of Logic. Logic is a purely a Elements of Lorjlc, book ii. chap. ii. § 2, jip. C3, 64. LECTURES ON LOGIC. 259 formal science, it knows nothing of, it establishes l^ct, nothing upon, the circumstances of the matter, to XIV. which its form may chance to be applied. To be able po'^sition'"^" to say that a thing is of necessary, impossible, or con- takes cTg- tingent matter, it is requisite to generalise its nature tile modality from an extensive observation ; and to make it in- this science cumbent on the logician to know the modality of all exbten^ce"" the objects to which his science may be applied, is at once to declare that Logic has no existence ; for this condition of its existence is in every point of view impossible. It is impossible — 1°, Inasmuch as Logic would thus presuppose a knowledge of the whole cycle of human science ; and it is impossible — 2°, Because it is not now, and never will be, determined what things are of necessary or contingent, of possible or impossible existence. Speaking of things impossible in nature. Sir Thomas Brown declared, that it is im- possible that a quadruped could lay an egg, or that a quadruped could possess the beak of a bird ; and, in the age of Sir Thomas Brown, these propositions would have shown as good a title to be regarded as of im- possible matter as some of the examples adduced by Dr Whately. The discovery of New Holland, and of the Ornithorhynchus, however, turned the impossible into the actual ; for, in that animal, there is found a quadruped which at once lays an egg and presents the bill of a duck. On the principle, then, that Logic is exclusively conversant about the forms of thought, I have rejected the distinction of propositions and syllogisms into pure and modal, as extra -logical. Whatever cannot be stated by A, B, C, is not of logi- cal import ; and A, B, C, know nothing of the neces- sary, impossible, and contingent." a See Discussions, p. 145 et scq. 72, and § 23, p. 79 ; Schulze, LorjiJc, — Ed. [Compare Bachmann,io^i^-, § 52, p. 78.] § 73, p. 115; Richter, Lo(jik, % 19, p. 2G0 LEOTlTvES OX LOGIC. LF.CT. XIV. It may bo proper, however, to explain to you tlie meaning of three terms wliich arc used in relation to Srlnliw* r*ure and Modal propositions. A proposition is called iu™tvil'ui. Assert on/, when it enounces what is known as actual; wiuTiw ■l^rohlcniatic, when it enounces what is known as pos- po«tH»M. g^^i^^ . ^IpoJcictic or Demonstrative, when it enounces what is knoA\ni as necessary." Ti.iniDivi. The last point of view in which judgments are con- inenw-Ke- sidcred, IS thcu' Kolatiou to each other. In respect e*ch other, of tlicsc rclatious, propositions have obtained from Logicians particular names, which, hov/ever, cannot be understood without at the same time regarding the matter which the judgments contain. As the dis- tinctions of Judgments and of Concepts are, in this respect, in a great measure analogous, both in name and nature, it will not be necessary to dictate them. When the matter and form of two judgments are considered as the same, they are called Identical, Con- vertible, Equal or Equivalent (jorojoositiones identicce, pares, convertibiles, cequipollentes) ; on the opposite alternative, they are called Different (2'>r. diversw). If considered in certain respects the same, in others dif- Keiativeiy fcrcut, they arc called Relatively Identical, Similar, or Cognate {pr. relative identicce, similes, affines, cog- nates). This resemblance may be either in the subject and comprehension, or in the predicate and extension. Disparate. If tlicy havc a similar subject, their predicates are Disparate {disparata) ; if a similar predicate, their Disjunct, subjects are Disjunct (disjuncta). When two judgments differ merely in their quan- tity of extension, and the one is, therefore, a parti- cular, the other a general, they are said to be subor- dinated, and their relation is called Subordination a Kant, Lorjik, § 30.— Ed. Judgments, Identical. Different. LECTURES ON LOGIC. 261 (suhordinatio). Tlie subordinating (or, as it might, lect. perhaps, be more properly styled, the swperordinate) '— judgment is called the Suhalternant {suhalternans) jnant! ^'^' the subordinate judgment is called the Suhalternate Subaiter- (suhalternatum). When, of two or more judgments, the one aflSrms, Opposition the other denies, and when they are thus reciprocally ments. different in quality, they are said to be Opposed or Conjiictive {pr. oppositce, avriKeip.a/ai), and their re- lation, in this respect, is called Opposition (oppositio). This opposition is either that of Contradiction or contradic- Repugnance {contradictio, avri(j>acrii), or that of Con- contrariety trariety {contrarietas, havrioTqi). If neither contradiction nor contrariety exists, the congruent judgments are called Congruent {pr. congruentes, con- " ^^^ ^' sonantes, consentientes). In regard to this last state- subcon- ment, you will find in logical books, in general," that JtTon.°^^°' there is an opposition of what are called Suhcontraries (suhcontraria), meaning by these particular proposi- tions of different quality, as, for example. Some A are B, some A are not B, or. Some men are learned, some men are not learned ; and they are called Suhcontra- 7'ies, as they stand subordinated to the universal con- trary propositions, — All A are B, no A is B, or. All men are learned, no man is learned. But this is a Not a real mistake, there is no opposition between Suhcontraries ; ^^^^'^ '**"* for both may at once be maintained, as both at once must be true if the some be a negation of all. (They cannot, however, both be false.) The opposition in this case is only apparent ;^ and it was probably only aEle'mentsofLogic,\>yT>rWha,te\Y, p. 190. — Ed.] part ii. cliap. ii. § 3, p. 68, 3d edit. /3 For which reason Aristotle de- But see Scheibler, Opera JLogica, scribes it aa an opposition in language, Pars iii. c. xi. p. 487, ed. 1665 ; but not in reality. Anal. Prior., XJlrich, [Instit. Lvy. et Met. § 183, ii. 15.— Ed. [Compare Fonseca, //i- '2u'2 LECTURES ON LOGIC. LECT. laiil ilinvn from a Itno of svninictry, in order to make XIV. . . . ' . — — — out the opposition t»f all (lie eoniors in the square of Opi>osit ion, which you will find in almost every work on I.oixie. Conrrrwou Finally, various relations of iudfjmcuts arise from of l^vposi- . . . tiotu. what is called their Conversion. When the subject and predicate in a categorical proposition, (for to this we now limit our consideration), are transposed, the proposition is said to be converted ; the proposition given and its product are both called the jiidicia con- versa ; the relation itself in which the judgments stand is called Conversion or Reciprocation, sometimes Obversion or Transposition {convcrsio, reciprocatio, Terms cm- ohvCrSlO, tranSJ^OSlt 10 , lX€Td6e(TL<;, IXeTa/BoXTJjdvTLCTTpOcfiy]) . denote the Thc glvcn proposition is called the Converted or Con- ori^ual aud , . , . . . . . converted vcrsc, (judiciiim, couvevsuni, ^:)rcp;ace?i5, pi^opositio ' conversa) ; the other, into w^hich it is converted, the Converting, {jud., prop.,convertens, suhjacens). There is, however, much ambiguity, to say the least of it, in the terms commonly employed by Logicians to desig- nate the two propositions, — that given, and that the product of the logical elaboration. The prejacent and subjacent may pass, but they have been very rarely employed. The term p)ropositio conversa^ the con- verse or converted judgment, specially for the original proposition, is worse than ambiguous ; it is applied generally to both judgments ; it may, in fact, more appropriately denote the other, — its product, — to which indeed it has, but through a blunder, been actually slit. Dialect., L. iii. c. 6, p. 129, ed. Denzinger, Instilutiones Logicce, vol. 1604; Conimhricensis Nova Logira, ii. § 713, p. 138; Caramuel, p. 33.] Tract, iii. Disp. iii. § 2, p. 124, ecL [Rationalls et Jiealis Philosojjhia, 1711. Kant expressly rejects Sub- author c I oarme Caramuel Lohkovntz, contrariety, Loglk, g 50, Anm. Com- S. Th. Lovanknsi Doctore, Ahhate pare Krug, Logik, § 64, Anm. 4; Melrosensi. Lovanii, 1642. — Ed.] Braniss, Grwadriss der Loglk, p. 105; LECTURES ON LOGIC. 263 applied by Aldrich," and he is followed, of course, by lect. AVliately. The original proposition ought to be called 1^ the Convertencl or Convertible (jyr. convertenda, con- vertihilis).^ The term Converting {co7ivertens), em- ployed for the proposition, the product of conversion, marks out nothing of its peculiar character. The ex- pression 'pr. exposita applied to this judgment hj PropodUo Aldrich,'*' without a word of comment, is only another uTuse'by" instance of his daring ignorance ; for the phrase pr. ex- ronedus/'^' posita had nothing to recommend it in this relation, and was employed in a wholly different meaning by logi- cians and mathematicians.^ In this error Aldrich is followed by Whately, who, like his able predecessor, is wholly unversed in the literature and language of Logic. The logicians after Aristotle have distinguished two, species of or, as we may take it, three, or even four, species of dis^in^ish- Conversion. c?aS '*'^" 1. The first, which is called Simple or Pure Con- version {conversio simplex, avTia-rpo^r) airXr}, roi? opoi^ irpoq eavT7]v, Aristotle, i.e., cum terminis recip>rocatis) ,^ is when the quantity and quality of the two judgments o Eudimenta Logicce, L. i. c. ii. sensed), iu order to prove a general j3 [So Noldius, p. 263, ] [Logica Be- relation between notions apprehend- co^rruto, Hafnise, 1766. — Ed.] ed by the intellect. This method is 7 Crakanthorpe, Sanderson, and used by Aristotle in proving the con- Wallis [denominate the original pro- version of propositions and the reduc- position ^jr. conversa, its product ^;r. tion of syllogisms, ^ee Anal. Prior., convcrtens. See Crakanthorpe, Logi- i. 2 ; i. 6 ; i. 8. The instance se- ca, L. iii. c. 10, p. 179, ed. 1677 ; lected is called the cxpositum, (rh Sanderson, Logica, L. ii. c. 7, p. 76, fKnQiv) ; and hence singular propo- ed. 1741 ; Wallis, Institutio Logicce, sitions and syllogisms are called ex- it, ii. c. 7, p. 113, edit. 1729. Wallis pository. Compare Pacius on Anal. also uses 25^. convertenda as a syno- Pr., i. 2, and Sir W. Hamilton's nym iov pr. conversa. — Ed.] note, Reid's Works, p. 696. — Ed. 5 The term exposition {eK0effis) is eToh Spots avTicrrpfcfxiy, Anal. Pr., employed by Aristotle, and by most i. 2, i. c, when each term is the exact subsequent logicians, to denote the equivalentof the other. SeeTrendel- selection of an individual instance enburg, Elcmcnta Log. Arist., § 14; whose qualities may be perceived In De Anima, p. 408 ; Waitz, In by sense {iKTidivai, cxponere, ohjicere Arist. Org., vol. i. p. 373. — Ed. 204 LECTURES ON LOGIC. ijx:t. XIV. Mnemonic Verses ex- pressing conversion. aiv tho same. It lu^Uls in T^niversal Negative tmd Partioular Atlinnativi' propositions. i2. The second, wliicli is called Conversion hj/ Acci- dent {c. per acciilens, atrtcrr/jo^T) cV fiepcL, Kara jxepo^, Aristotle), is when, the quality remaining unaltered, the quantity is reduced. It holds in Universal Aflirma- tives. These two are the species of the conversion of propositions acknowledged by all ; they arc evolved by .Vristotle, not, as might have been expected, in his treatise On Enouncement, but in the second chapter of the first book of his Prior Analytics."' 3. The third, which is called Conversion hy Contra- position (c. per oppositionem, c.j^cr contrapositionem, both by Boethius,'^ contrap>ositio, aimcrrpor) avv avri- OccrcL, Alexander'*'), is when, instead of the subject and predicate, the quantity and quality remaining the same, there is placed the contradictory of each. This holds in Universal Affirmatives, and most logicians allow it in Particular Negatives. It is commemorated by Aristotle in the eighth chapter of the second book of his Topics : it is there called the inverse consecution from contradictions. I shall here mention some mnemonic verses in which the doctrine of conversion is expressed. 1°. Kegarding conversion as limited to the Simple a [Boethius seems the first who gave the name of Conversio per Acci- dans. With him it is properly both Ampliative and Restrictive. (So Ptidiger, De Sc/isu Veri et Falsi, pp. 250, 303, 2d edit. 1722; Fischer, Lo'jik, p. 108). It is opposed as a conspecies to c. generalis ; and both are species of c. simplex, which is op- posed to Contraposition. See Opera, De Syllorjitmo Catcgorico, L. L p. 687. Thus conversio is divided pri- marily into e. simplex and c. per con- trapositionem. Aristotle does not use a.vTiffTpo-potheses. Hypotheses, that is, propositions which are assumed wdth probability, in order to explain or prove some- LECTURES ON LOGIC. 267 tliinoj else which cannot otherwise be explained or lect. ... XIV proved. Lemmata, that is, propositions borrowed L from another science in order to serve as subsidiary ^'^"^^''• propositions in the science of which we treat. Finally, Scholia, that is, propositions which only serve as illus- Schoiia. trations of what is considered in chief. The clearest and most appropriate examples of these various kinds of propositions are given in mathematics." " a Esser, LogiTc, § 79, pp. 147, 148.— Ed. [Compare Knig, Logilc, §§ 67, 68.] 268 LECTURES OX LOGIC. LECTURE XV. STOICIIEIOLOGY. SECTION II. — OF THE PRODUCTS OF THOUGHT. III. — THE DOCTRINE OF REASONINGS. REASONING IN GENERAL — SYLLOGISMS THEIR DIVISIONS ACCORDING TO INTERNAL FORM. LECT. In my last Lecture, I terminated the Doctrine of Judgments, and now proceed to that of Reasonings. The act of " AMien the necessity of the junction or separation of — whw'."^' a certain subject-notion and a certain predicate-no- tion is not manifest from the nature of these notions themselves, but when, at the same time, we are desir- ous of knowing whether they must be thought as inclusive, or as exclusive, of each other, — in this case, we find ourselves in a state of doubt or indecision, from our ignorance of which of the two contradictory- predicates must be affirmed or denied of the subject. But this doubt can be dissipated, — this ignorance can be removed, only in one way, — only by producing in us a necessity to connect with, or disconnect from, the subject one of the repugnant predicates. And since, ex Itypothesi, this necessity does not, at least does not immediately, arise from the simple knowledge of the subject in itself, or of the predicate in it- self, or of both together in themselves; it follows LECTURES ON LOGIC. 269 that it must be derived from some external source, lect. XV and derived it can only be, if derived from some other '— knowledge which affords us, as its necessary conse- quence, the removal of the doubt originally harboured. But if this knowledge has for its necessary conse- quence the removal of the original doubt, it must stand to the existing doubt in the relation of a general rule ; and, as every rule is a judgment, it will con- stitute a general proposition. But a general rule does not simply and of itself reach to the removal of doubt and indecision ; there is required, and necessarily required, over and above, this further knowledge, — that the rule has really an application, or, what is the same thing, that the doubt really stands under the general proposition, as a case which can be de- cided by it as by a general rule. But when the general rule has been discovered, and when its ap- plication to the doubt has likewise been recognised, the solution of the doubt immediately follows, and therewith the determination of which of the contradic- tory predicates must or must not be affirmed of the subject ; and this determination is accompanied with a consciousness of necessity or absolute certainty.'"^ A illustrated simple example will place the matter in a clearer light, ampie.^^ When the notion of the subject ma7i is given along with the contradictory predicates /ree agent and 7ie- cessary agent, there arises the doubt, — with which of these contradictory predicates the subject is to be con- nected ; for, as contradictory, they cannot both be affirmed of the subject, and, as contradictory, the one or the other must be so affirmed ; in other words, I doubt whether man be a free agent or not. The no- tion 7nan, and the repugnant notions free agent and o Esser, Logik, § 82, p. 153. 270 LEI.TURES ON LOGIC. LE17. ht'C€S.^arj/ at ; and I must endeavour to discover some I'ther notion ulucli will enable nic to decide. Now, taking the predicate yVcc aycnt, this leads me to the closely connected notion morally responsible agent, which let it be supposed that I otherwise know to be necessarily a free agent. I thus obtain the pro- position, — Every morally responsible agent is a free agent. But this proposition docs not of itself contain the solution of the doubt, for it may still be asked, does the notion morally responsible agent constitute a pre- dicate which appertains to the notion of mail, the sub- ject 1 This question is satisfied, if it is recognised that the notion man involves in it the notion of a morally responsible agent. I can then say, — Man is a morally responsible agent. These two propositions being thus formed, and applied to the subsisting doubt, the removal of this doubt follows of itself ; and in place of the previous indecision, Avhether man be a free agent or not, there follows, w^ith the conscious- ness of necessity or absolute certainty, the connected judgment that, Man is also a free agent. The wdiole process, — the whole series of judgments, — will stand thus : — Every morally responsible agent is a free agent ; Man is a morally responsible agent; Therefore, man is a free agent. The exam- Lct US consldcr in what relation the different consti- ple given is /• i • i tit* a Reason- tueut parts ot this proccss stand to each other. It is whole of evident that the whole process consists of three no- and may be tlons aud their mutual relations. The three notions b^thr^ are, free agent, responsible agent, and man. Their mutual relations are all those of whole and part, — and whole and part in the quantity of exten- LECTUEES ON LOGIC. 271 sion ; for the notion frm agent is seen to contain lect under it the notion responsible agent, and the notion 1 responsible agent to contain under it the notion man. Thus, these three notions are like three circles of three various extensions, severally contained one within another ; and it is evident, that the process by which we recognise that the narrowest notion, man, is con- tained under the widest notion, responsible agent, is precisely the same by which we should recognise the inmost circle to be contained in the outmost, if we were only supposed to know the relation of these to- gether by their relation to the middle circle. Let ABC denote the three circles. Now, ex hypothesi, we know, and only know, that A contains B, and that B contains C ; but as it is a self- evident principle that a part of the part is a part of the whole, we cannot, with our knowledge that B contains C, and is contained in A, avoid recognising that C is contained in A. This is precisely the case with the three notions, — -free agent, — responsible agent, — man; not knowing the relation between the notions/ree agent and man, but knowing tb.a,tfree agent contains under it responsible agent,siiid that responsible agent contains under it man, we, upon the principle that the part of a part is a part of the whole, are compelled to think, as a necessary consequence, that free agent contains under it man. It is thus evident, that the process shown in the example adduced is a mere recognition of the relation of three notions in the quantity of ex- tension ; our knowledge of the relation of two of these notions to each other being not given immediately, but obtained through our knowledge of their relation to the third. 272 LECTURES l)X LOGIC. LEcT. r»ut lot US consiiltT tills process a lit iKm1os(M-. The rcliitions of tin- tlnci' notions, in tlio ;il)OV(' example, ^'.TkI'" i^i"*-' those givin in the (jiiantity of JJrejidth or Exten- [^""^.i,'",^'! sion. r)Ut every notion has not only an Extensive, ircMM-T"" hut likewise an Inti'nsive quantity, — not only a /rai^l.""' quantity in hreaJth, hut a quantity in depth ; and these two tjuantities stand to eaeh other, as we liave seen," always in a determinate ratio, — the ratio of in- vei*sion. It would, therefore, appear a 2^>'iori, to be a necessary presumption, that if notions bear a certain relation to each other in the one quantity, they must bear a counter relation to each other in the other quantity ; consequently, that if w^e are able, under the quantity of extension, to deduce from the relations of two notions to a third their relation to each otlier, a correspondent evolution must be competent of the same notions, in the quantity of comprehension. Let us tiy w^iether this theoretical presumption be war- ranted a posteriori and by experiment, and whether, in the example given, the process can be inverted, and the same result obtained with the same necessity. That example, as in extension, was : — All resjionsihle agents are free agents ; But man is a responsible agent ; Tlierefore, man is a free agent. In other words, — the notion resj^onsible agent is con- tained under the notion free agent ; but the notion man is contained under the notion responsible agent ; therefore, on the principle that the part of a part is a part of the whole, the notion man is also contained under the notion free agent. Now, on the general doctrine of the relation of the two quantities, we must, a See above, p. 146. — Ed. LECTURES ON LOGIC. 273 if we would obtain the same result in the compre- lect. . XV. hensive which is here obtained under the extensive 1- quantity, invert the whole proqess, that is, the notions which in extension are wholes become in comprehen- sion parts, and the notions which in the former are parts become in the latter wholes.^ Thus the notion free agent, which, in the example given, was the great- est whole, becomes, in the counter process, the smallest part, and the notion inan, which was the smallest part, now becomes the greatest whole. The notion res'pon- sihle agent remains the middle quantity or notion in both, but its relation to the two other notions is re- versed ; what was formerly its part being now its whole, what was formerly its w^hole being now its part. The process will, therefore, be thus explicitly enounced : — The notion man comprehends in it the notion resjjonsihle agent ; But the notion responsible agent comp7'ehends in it the notion free agent ; Therefore, on the principle, that the part of a part is a part of the whole, the notion man also compreheJids in it the notion free agent. Or, in common language : — Man is a responsible agent ; But a responsible agent is a free agent ; Therefore, man is a free agent. This reversed process, in the q^uantity of comprehen- sion, gives, it is evident, the same result as it gave in the quantity of extension. For, on the supposition, that we did not immediately know that the notion man comprehends free agent, but recognised that man comprehends responsible agent, and that respon- sible agent comprehends free agent, we necessarily are compelled to think, in the event of this recogni- VOL. L s 274 LECTURES ON LOGIC. LECT. tion, that tin' luUioii man coniprt'lu'ixls the notion XV. free agent. Thcc..|.uu It is only necessary further to obscrvT, that in the »naci.mivrx< one process, — tluit, to Wit, 111 extension, the co[)ula ^s- cw^tct" 'means is contained under, whereas in the other, it °*'**""^" means eomjirehends in. Thus the proposition, — God is merciful, viewed as in the one (quantity, signifies God is contained under merciful, that is, the notion God is contained under the notion merciful ; viewed as in the other, means God compile! tends merciful, that is, the notion God comprehends in it the notion mei'ciful. Now, this process of thought, (of which I have en- deavoured to give you a general notion), is called Reasoning ; but it has, likewise, obtained a variety of other designations. The definition of this process, with its principal denominations, I include in the fol- lowing paragraph : — Par. LIII. Definition of the pro- cess of Reasoning with the principal denomina- tions of pro- cess and product. ^ LIII. Reasoning is an act of mediate com- parison or Judgment ; for to reason is to recog- nise that two notions stand to each other in the relation of a whole and its parts, through a recognition, that these notions severally stand in the same relation to a third. Considered as an act, Reasoning or Discourse of Reason, {ro Xoyil^eaOaL, XoyicrfJios, SidvoLa, to ^LavoeiaOai), is, likewise, called the act or process of Argumenta- tion (argumentationis) , of Ratiocination {ratio- cinationis), of Inference or Illation {inferendi), of Collecting {colligendi), of Concluding [con- cludendi), of Syllogising {tov crvWoyitfiaOaL, barbarously syllogisandi). The term Reasoning is, likewise, given to the product of the act ; and LECTURES ON LOGIC. 275 a reasoning, in this sense, (ratiocinatio, ratioci- lect. XV nium), is, likewise, called an Argumentation '— {argumentatio) ; also frequently an Argument {argumentum), an Inference or Illation (illatio), a Collection (collectio), a Conclusion {conclusio, avixTrepaa-fxa) ; and, finally, a Syllogism (crvXXo- A few words in explanation of these will suffice ; Expiica- and, first, of the thing and its definition, thereafter of its names. In regard to the act of Reasoning, nothing can be i. The Act ^ 1 , ,. , . . . ^ „ , . of Reason- more erroneous than the ordinary distinction oi this ing. process, as the operation of a faculty difierent in kind from those of Judgment and Conception. Concep- tion, Judgment, and Reasoning, are in reality only various applications of the same simple faculty, that of Comparison or Judgment. I have endeavoured to show, that concepts are merely the results, ren- dered permanent by language, of a previous process of comparison ; that judgment is nothing but com- parison, or the results of comparison, in its immediate or simpler form; and, finally, that reasoning is nothing but comparison in its mediate or more complex application." It is, therefore, altogether a reason erroneous to maintain, as is commonly done, that a orfan reasoning or syllogism is a mere decompound whole, made up of judgments ; as a judgment is a compound whole, made up of concepts. This is a mere mecha- nical mode of cleaving the mental phsenomena into parts ; and holds the same relation to a genuine analysis of mind which the act of the butcher does to that of the anatomist. It is true, indeed, that a a See above, pp. 116, 117. — Ed. ing IS one organic whole. 276 LELTUUES ON LOOIC. LE«.*r. syllofrism can be soparatod into tliivi' parts or pro- !_ positions; nnd that these propositions have a certain meaiiinu". \\\\cn considcri'tl apart, aiiil out of I'clation to cai'h other. lUit when thus consicU'red, tlicy h)se the whole significance which they liad wlien united in a reasoning ; for their whole significance consisted in their reciprocal relation, — in the light wliich they mutually reflected on each other. We can certainly hew an animal body into parts, and consider its members apart ; but these, though not al)solutely void of all meaning, when viewed singly and out of relation to their whole, have lost the })rincipal and peculiar significance which they possessed as the coefticicnts of a one organic and indivisible whole. It is the same with a syllogism. The parts which, in their organic union, possessed life and importance, when separated from each other, remain only enunciations of vague generalities, or of futile identities. Though, when expressed in language, it be necessary to analyse a reasoning into parts, and to state these parts one after another, it is not to be supposed that in thought one notion, one proposition, is known before or after another ; for, in consciousness, the three notions and their reciprocal relations constitute only one identical and simultaneous cognition. Error of Thc logiciaus havc indeed all treated the syllogism their'^ai" as if this w^ere not the case. They have considered s/uo^Sm."' one proposition as naturally the last in expression, and this they have accordingly called the conclusion ; whilst the other two, as naturally going before the conclusion, they have styled the premises, forming tov wliicli this in'oces5? is (K'lioininatcd, XV ...... ' Rt'aso)iin(j i.s a inoililicatioii iVom ihc b'rciu'h r(tis- tiwhiUc' onner, {-Aud thi.s a ilorivatit)ii fnnu tlio Latin nido), ^^^i^i^\ng J^i^d i'OiTi'.>(»iul.s to r(.(f I OiUimt 10, wliivli lia.s iiuU'cd boon nsf^.**^' immodiatily tran.stoirLHl into our language under tlie luuttoniiig torni ratiocination. Ratiocination denotes i)roperly KaliiK-iim- . . 1 i i i /■ «ion. the process, but, improperly, also the product ot rea- soning ; Hatiocinium marks exclusively the product. The original meaning of ratio was comjjutation, and from the calculation of numljers it was transferred to Dixcoureo. the process of mediate comparison in general. Dis- course {(Uscursus, Stai^ota) indicates the operation of comparison, the running backwards and forwards be- tween the characters or notes of ol)jects, {disciirrere inter notas, BiavoeladaL) ; this term may, therefore, be properly applied to the Elaborative Faculty in general, which I have thus called the Discursive. The terms discourse and discursus, as BidvoLa, are, however, often, nay generally, used for the reasoning process, strictly considered, and discursive is even applied to denote mediate, in opposition to intuitive, judgment, as is done by Milton." The compound term discourse of reason^ unambiguously marks its employment in Argumenta- this scuse. Argumentation is derived from argumen- Arjiment. tari, which means argumentis uti; argument again, argiiriientum, — what is assumed in order to argue something, — is properly the middle notion in a reason- ing, — that through which the conclusion is established; and by the Latin Khetoricians it was defined, — " pro- a Paradise Lost, v. 486, — " Whence the soul R«a£OD receives, and reason is her being, DiBcursive or intuitive ; discourse Is oftest yours." —Ed. 8C. 2,— " A beast, that wants discourse of reason. Would have mourned longer." Hooker, E. P., iii. 8, 18 : "By Dis- course of reason, aided with the in- )3 Shakespeare, Hamlet, act. 1, fluence of divine grace. " — Ed. LECTURES ON LOGIC. 279 babile inventum ad faciendam fidem." " It is often, lect. XV however, applied as coextensive with argumentation. sion. Inference or illation, (from infer 6), indicates the carry- inference ing out into the last proposition what was virtually contained in the antecedent judgments. To conclude To con- {concludere), again, signifies the act of connecting and shutting into the last proposition the two notions which stood apart in the two first. A conclusion Conciusi (conclusio) is usually taken, in its strict or proper sig- nification, to mean the last proposition of a reasoning ; it is sometimes, however, used to express the product of the whole process. To syllogise means to form syl- to syiio- logisms. Syllogism (crvXXoyta-jaos) seems originally, |yito,ris„ like ratio, to have denoted a computation, — an adding up, — and, like the greater part of the technical terms of Logic in general, was borrowed by Aristotle from the mathematicians.^ This primary meaning of these two words favours the theory of those philosophers who, like Hobbes'*' and Leidenfrost,^ maintain that all rea- soning, that all thought is in fact at bottom only a cal- culation, a reckoning. 2^vXXoyto-/ao? may, however, be considered as expressing only what the composition of the word denotes, — a collecting together; for o-vWoyitr ecrOai comes from avWeyeiv, which signifies to collect.'^ a Cicero, Orator-ice Partitiones, c. S De 3Iente Humana, c. viii. §§ 4, 2. Cf. Discussions, p. 149.— Ed. 10, pp. 112, 118, ed. 1793.— Ed. ;3 [See Piccartus, Org. ArisL, pp. e Eugenios, AoyiK^, p. 405, et ibi 467, 468 ; Ammonius, In Quinque Blemmidas : [Kal rb nlv ovofxa, Sti Voces, i. 1 ; Philoponus, In An. crvWoyf} ns iarX \6ywv irAeiSvwv iv Prior., f. 17 b; Pacius, Comm. in avT

1_ reason collirfcre. 'i'liis refers to tlie act of collecting ni ro»«cUo. ^|j^^ conclusion the two notions scattered in tlu' premises. ..nu " From what has already been said touching the •Mu eharactor of the reasoning process, it is easy to see wliat an' the general conditions which every syllogism supposes. For, as the essential nature of reasoning consists in this, — that some doubt should be removed by the application to it of some decisive general rule, there are to every syllogism three, and only three requi- sites necessary ; 1°, A doubt, which of two contra- dictory predicates must be affirmed of a certain sub- ject, — the problem or question, (problema, quassitum) ; 2°, The a]>plication of a decisive general rule to the doubt; and, 3°, The general rule itself. But these requisites, when the syllogism is constructed and ex- pressed, change their places ; so that the general rule stands first, the application of it to the doubt stands second, and the decision in regard to the doubt it- self stands last. Each of these necessary constituents of a syllogism forms by itself a distinct, though a cor- relative, proposition ; every syllogism, therefore, con- tains three propositions, and these three propositions, in their complement and correlation, constitute the syllogism."* It will be proper, however, here to dictate a paragraph, expressive of the denominations techni- cally given to the parts, which proximately make up the syllogism. Par. Liv. H LIV. A Reasoning or Syllogism is composed f?onsTf the of two parts, — that which determines or precedes, fro.vimate'iy and that which follows or is determined. The make up ihe syllogism, gi^gio infertur ; quare a concluflione est syllogismnB."— Ed.] potiufl, quamapropositionibusdictus a Esser, Logik, § 83, p. 156. LECTURES ON LOGIC. 281 one is called tlie Antecedent (antecedens) ; the lect, other, the Consequent (consequens). The Ante- - cedent comprises the two propositions, the one of which enounces the general rule, and the other its application. These, from their naturally pre- ceding the Consequent, are called the Premises [propositiones prcemissce, sumptiones, membra antecedentia, Xrj^ixara). Of the premises, the one which enounces the general rule, or the re- lation of the greatest quantity to the lesser, is called the Major Premise, or Major Proposition, or the Proposition simply, {propositio major, pro- positio prima, propositio, sumptum, siimptio ma- jor, sumptio, thesis, exjyositio, intentio, TrpocrXyj-^L^, TT/aoracrts rj }xeitfiiv, Xrjjxixa to ixeitpv). The other premise, which enounces the application of the ge- neral rule, or the relation of the lesser quantity to the least, is called the Minor Pi^emise, the Minor Pi'oposition, the Assumption!, or the Subsumption, {prop>ositio minor, propositio altera, assumptio, subsimnptum, suhsumptio, sumptio minor, Trporacriq Tj ikojTTOiv, Xrjfjifia to eXarrov). It is manifest that, in the counter quantities of Breadth and Depth, the two premises will hold an opposite relation of major and minor, of rule and appli- cation. The Consequent is the final proposi- tion, which enounces the decision, or the relation of the greatest quantity to the least, and is called the Conclusion (conclusio, conclusum, propositio conclusa, collectio, complexio, summa, connexio, illatio, intentio, and, in Greek, crvixTrepacn^a, to (rvvayojxevov,"' to iin^epoixevov). , This part is usually designated by the conjunction, Therefore a [Eugenios, AoyiK^, pansim.] 2S2 LECTLTKES OX l.OCAC. 1 KiT (f r./.'. cipaV and its svnon\nis. The Conclusion -1—1- is till' Problem {2>robh'ma), Question {qita'stio, ipuvsi'tiim)y wliicli Avas oriLjinally askod, stated now as a decision." The Problem is usually omit- ted in the ex]^rcssion of a syllogism ; hut is one of its essential parts. 'J'he whole nomenclature of the syllogistic parts, be it observed, has refer- ence to the one-sided views of the logicians in regard to the process of reasoning.'^ Kxpiica- The Syllogism is divided into two parts, the Ante- Tmooo.iini cedent and the Consequent : — the antecedent compre- .•uidCi.n>o- hendinof the two propositions, in which the middle notion is compared with the two notions we would compare together ; and the consequent comprising the one proposition, which explicitly enounces the relation implicitly given in the prior of these two notions to each other. Premises. The two propositions which constitute the antece- dent are called, among other names, the Premises. Of these the proposition expressing the relation of whole which one of the originally-given notions holds to the assumed or middle notion as its part, is called, among Major. other appellations, the Major Pivposition, the Major Premise, or The Proposition, Kar e^o^r^v. The other proposition of the antecedent enouncing the relation of whole, which the assumed or middle notion holds to the other of the given notions as its part, is called, .M,„or. among other appellations, the Minor Proposition, the a [See Alex. Aplirodisiensis, In sura Veri, L. ii. p. GOG et srq., ed. Anal. Prior., i. c. 4, f. 17 b; Boethi- 1555. — Ed.] ; Bachmann, Logik, p. us, III TopkaCiceronis, L. i., Opera, 184; Facciolati ; Sextus Empiricus. p. 764. ] [Facciolati, Kudirnenta Logica, c. iii. /3 [See E. Agricola, De Invenliona p. 83, ed. 1750 ; Sextus Empiricus, DialecticcB, L. ii. c. xiv. pp. 401, 417, Hypotyposes, L. ii. p. 86 et alibi. — 420; Vives, Opera, [t. i., Dc Cen- Ed.] LECTURES ON LOGIC. 283 Mi7ior Premise, the Assumption, or the Subsumption. lect. These, as terms of relation, vary, of course, with the _ relation in the counter quantities. The one proposi- tion which constitutes the consequent is called, among other appellations, the Conclusion. Perhaps the best Sumption, names for these three relative propositions oi a syllo- tion, and „ • 07 • /-i 1 • Conclusion. gism would be bumpUon, bubsumption, Uoncmsion, as those which express most briefly and naturally the nature and reciprocal dependence of the three judg- ments of a syllo2:ism. In the first place, the expres- Grounds of ^ .,<^7 . ., their adop- sions bumption and l:^uosiimption are appropriate tion as best , . 1 . . p 1 • 1 1 1 names for logical expressions, in consequence 01 their both show- the three 1 -r • • 1 1 Till propositions mg that Logic considers them, not as absolutely, but ofasyiio- only as hypothetically true ; for Logic does not war- rant the truth of the premises of a syllogism, it only, on the supposition that these premises are true, guar- antees the legitimacy of the inference, — the necessity of the conclusion. It is on this account that the pre- Lemma, mises have, by the Greek logicians, been very properly styled hjixfiaTa,"' corresponding to the Latin sump- tiones ; and were there any necessity to resort to Greek, the Major Proposition, which I would call Sumption {siimptio), might be well denominated Lemma simply ; and the Minor Proposition, which I would call the Suhsump>tion (suhsumptio), might be well denominated the Hypolemma. In the second Hypoiem- place, though both premises are sumptions or lem- ™''" mata, yet the term sumption, as specially applied to the Major Premise, is fully warranted both by prece- dent and by principle. For, in like manner, the major proposition, — the major lemma, has always obtained both from the Greek and Latin logicians the generic term ; — it has been called, The Proposition, The a See Alexander, In An. Prior., f. 14 b; Scholia, ed. Brandis, p. 150. — Ed. •JS4 LECTURES ON I.ocic. 1 .1 /.(•DUUd, { pntpositio, r) 7TpoTa(rL<;, to X)}/.(/ia') ; and as tliis is tlio jiulunu'iit which includes and aUoNvs bolli the others, it is ^vcll rulith'd, as llic princiital proposi- tion, to tlio style and title of (Itc j>r(>jn>si(ioii, f/ic \«..uM.i. Itiiuna, the sumption by pre-cnunonce.'* In tlio third place, the term subitui7ij)tion is preferable to (he term assumj>tio>i,n?i a denomination of the IMinor Premise; for the term subsumptioti precisely marks out its rela- tion of subordination to the major premise, Avhercas the term asiiU7npiion does not. Assumption would indeed, in contrast to subsumjytio?}, have been an unexceptionable word by which to designate the major proposition, had it not been that logicians have very generally em])loyed it to designate the minor, so that to reverse its application would be productive of inevitable confusion. But for this objection, I should certainly have preferred the term assumption to that of sumption, for the appellation of the major proposi- tion ; not that in itself it is a preferable expression, but simply because assump)tion is a word of familiar usage in the English langtiage, which sumption and suhsumption certainly are not. Objections Thc picccding are reasons why the relative terms ^^lizuoTi'^of sum2)tion and subsumj^tion ought to be employed, as ifoDs o7th*e' being positively good expressions ; but the expediency mSn^ of their adoption becomes still more manifest, when "^^' they are compared and contrasted with corresponding >jajor Pro- denominatious in ordinary use. For the terms major position and . . -. . . . • • -t Premise. p/Toposition and majov premise, minor proposition and Minor Pro- . . i j • i • j.* T position and muioi' jwcmise, are exposed to various objections. In the first yjlace, they are complex and tedious expres- o See Cicero, Z/c Z)iv. , ii. 53 :'* Sed .... assumjHio tamen, quam demus tibi istaa duaa sumptiones, ea Trp6(T\ri\pti' iidem vocant, non dabi- qu» K-fiiifjMTa appellant dialectic! : tur."— Ed. LECTURES ON LOGIC. 285 sious, whereas sumption and subsumption are simple lect. and direct. In the second place, the abbreviations in common use, (the major proposition being called the Qiiajor, the minor proposition being called the minor,) are ambiguous, not only in consequence of their vague- ness in general, but because there are two other parts of the syllogism to which these expressions, major and minor, may equally apply. For, as you will soon be informed, the two notions which we compare together through a third, are called the major and the minor terms of the syllogism ; so that when we talk of majors and minors in reference to a syllogism, it re- mains uncertain whether we employ these words to denote the propositions or the terms of a reasoning. Still more objectionable are the correlative terms, Pro- Propositiou. position and AssuTnption, as synonyms for the major Assump- and minor premises. The term proposition is a word in too constant employment in its vague and general sense, to be unambiguously used in a signification so precise and special as the one in question ; and, in consequence of this ambiguity, its employment in this signification has been in fact long very generally aban- doned. Again, the term assumption does not express the distinctive peculiarity of the minor premise, — that of being a subordinate proposition, — a proposition taken or assumed under another; this word would indeed, as I have noticed, have been applied with far greater propriety, had it been used to denote the major in place of the minor premise of a syllogism. These are among the reasons which have inclined The use of me to employ, at least along with the more ordinary ludfuC denominations, the terms sumption and subsumption. sanctioned Nor is it to be supposed, that this usage is destitute ent^''^'^ of precedent, for I could adduce in its favour even the 286 LECTUKES ON LOGIC. LECT. liivrh aiithoritv ul' Uoctliius." In «>i'iK'r;il, and wilh- XV . . r» ' out ivferenco to Logic, it api)cars marvellous how, in Englisli pliiloso|tliy, wo eould so long do witliont the noun ituhsuvijttion, and the verb to aubsumc, for these ilenote a relation which we have very frequently oc- casion to express, and to express which there arc no other terms witliin «)ur reacli. We have already in English assumjition and asaunie, presumption and ynr-funnc, cotisu)nj>tio)i and consume, and there is no imaginable reason why we should not likewise enrich the language, to say nothing oi surnjition, hy the ana- logous expressions suhsumption and subsume. ThcConciu- In regard to the proposition constituting the con- sequent of a syllogism, the name which is generally bestowed on it, — the Conclusion, — is not exposed to any serious objections. There is thus no reason why it should be superseded, and there is in fact no other term entitled to a preference. — So much in reference to the terms by which the proximate parts of a syllo- gism are denoted. I now proceed to state to you in general the Divi- sion of Syllogisms into Species determined by these parts, and shall then proceed to consider these several species in detail. But I have first of all to state to you a division of Syllogisms, which, as comprehend- ing, ought to precede all others. It is that of Syllo- gisms into Extensive and Comprehensive. Par. Lv. H LV. The First Division of Syllogisms is sionofSyi- takcu from the different kinds of quantity under logisnu into i • i i • i t-i i • i Extensive wuich thc rcasonmof proceeds. J^or while every and Com- ° ^ -^ prehensive. a " Quoniam enim omnis syllo- vocatur; secundaverocM«M»z/)." — gismus ex propositionibus texitur, Boethius, £>e Syllogmao Hypothetico, prima vel propositio, vel sumptum lib. i. — Ed. LECTURES ON LOGIC. 287 syllogism, infers that tlie part of a part is a part lect. of tlie whole, it does this either in the quantity of Extension, — the Predicate of the two notions compared in the Question and Conclusion being the greatest whole, and the Subject the smallest part ; or in tlie counter quantity of Comprehen- sion, — the Subject of these two notions being the greatest whole, and the Predicate the smallest part. After what I have already stated in regard to the nature of these opposite quantities, under the doctrine of Concepts and Judgments,'' and after the illustrations I have given of the possibility of con- ducting any reasoning in either of these quantities at will,'^ — every syllogism in the one quantity being convertible into a syllogism absolutely equi- valent in the other quantity, — it will be needless to enlarge here upon the nature of this distinction in general. This distinction comprehends all others ; its illustration, therefore, supposes that the nature of the various subordinate classes of syllogisms should be previously understood. It will, therefore, be expe- dient, not at present to enter on any distinct consider- ation of this division of reasonings, but to show, when treating of syllogisms under their various subaltern classes, how each is capable of being cast in the mould of either quantity, and not, as logicians suppose, in that of extensive quantity alone. The next distinction of Syllogisms is to be sought Matter and for either in the constituent elements of which they log^sms.^^ are composed, or in the manner in which these are connected. The former of these is technically called a See above, p. 140 ct seq. — Ed. ;3 See above, p. 272 etseq. — Ep. 2SS LECTURJIS ON LOGIC. LKrr. the matter o[ a svUoiiisin, tlio latter its /(>/•//), You J must, however, observe that these terms are here used in a restrieted meaning. JJoth matter anil form under thisdistinetiou are inehided in the form of asylh\i^asm, when we speak of form in contrast to tlie empirical matter Avhieli it may eontaiii. 'i'liis, tlicrefore, is a distinction under that form with which Logic, as you know, is exclusively conversant ; and the matter here spoken of should be called, for distinction's sake, the formal or necessai^i/ 'matter of a syllogism. In this sense, then, the matter of a syllogism means merely the propositions and terms of which every syllogism is necessarily made up ;a whereas, otherwise, the form of a syllogism points out the way in which these consti- tuents are connected.^ This being understood, I repeat that the next distinction of syllogisms is to be sousfht for either in their matter or in their form. Their form, " Now in regard to their matter, syllogisms cannot of u^"n"e« differ, for every syllogism, without exception, requires ^tfon of the same constituent parts, — a question, the subsump- SyUogisms. ^^^^ ^£ ^^ under a general rule, and the sumption of the general rule itself; which tliree constituents, in the actual enunciation of a syllogism, change, as I have already noticed, their relative situation ; "'^ — what was first in the order of thought being last in the order of expression. The form " The difference of Syllogisms can, therefore, only SoidfiT be sought for in their different forms ; so that their Emra^.'^ distinctions are only formal. But the form of a syllo- o Proximate and remote matter. — propositionum, proxima vero sunt Marfjinal Jotting. [See Hurtado de propositiones ipsse, quibns coalescit Mendoza, Disput. Phil., Dwp. Logi- syllogismus." — Ed.] ccE, t. i. d. X. § 48, p. 4G5 : "Ma- )8 Krug, Logik, § 72, Anm., i.— teria (syllogismi) alia est proxima, Ed. [Cf. Fries, Logik, § 44.] alia remota. Remota sunt termini y Esser, Logik, § 85, p. 159. — Ed. LECTURES ON LOGIC. 289 gism, considered in its greatest generality, is of a lect twofold kind, viz. either an Internal and Essential, '- or an "External and Accidental. The former of these depends on the relations of the constituent parts of the syllogism to each other, as determined by the na- ture of the thinking subject itself; the latter depends on the external expression of the constituent parts of the syllogism, whereby the terms and propositions - are variously determined in point of number, position, and consecution. We must, therefore, in conformity to the order of nature, first of all, consider what classes of syllogism are given by their internal or essential form ; and thereafter inquire what are the classes afforded by their external or accidental modifications. First, then, in regard to the Internal or Essential Form of Syllogism. " A Syllogism is only a syllogism when the con- clusion follows from the premises with an absolute certainty ; and as this certainty is determined by a universal and necessary law of thought, there must, consequently, be as many kinds of Syllogism as there are various kinds of premises affording a consequence in virtue of a different law. Between the premises there is only one possible order of dependency, for it is always the sumption, — the major premise, which, as the foundation of the whole syllogism, must first be taken into account. And in determining the difference of syllogisms, the sumption is the only premise which can be taken into account as affording a difference of syllogism ; for the minor premise is merely the sub- sumption of the lesser quantity of the two notions, concerning whose relation we inquire, under the question, and this premise alw^ays appears in one and the same form, — in that, namely, of a catego- VOL. I. T .Hi; :.,i 1 ■uiioo- Iu'dIk-IwiOU I'.id conclu- :-ion. 200 LECTURES ON LOGIC. LKCT rioal proposition. 'riu> .same i.s, likc\vis»>, tlio ca.se in r. i^anl to the conclu.sion, ami, thorofoiv, we can no moiv look towanls the conclusion for a detcrniitia- tion of the ilivcrsity of .syllosjjism than towanls the snlvsiimption. We have thu.s only to inquire in reganl to the various possible kinds of major pro- position."" sviiocisnu Now as all sumptions arc judgments, and as we » 'corVins "i . li''i^'<^ already found that the most general division of lorofui^r judgments, next to the primary distinction of inten- "uw sive and extensive, is into simple and conditional, this division of judgments, which, when developed, affords the classes of categorical, disjunctive, hypothetical, and h}^3othetico-disjunctive propositions, will furnish us with all the possible differences of major premises. " It is also manifest that in any of these aforesaid pro- positions, (categorical, disjunctive, h}"pothetical, and hypothetico-disjunctive,) a decision of the question, — which of two repugnant predicates belongs to a certain subject, — can be obtained according to a universal and necessary law. In a categorical sump- tion, this is competent through the laws of Identity and Contradiction ; for what belongs or does not belong to the superordinate notion, belongs or does not belong to the subordinate. In disjunctive sump- tions, this is competent through the law of Excluded Middle ; since of all the opposite determinations one alone belongs to the object ; so that if one is affirmed the others must be, conjunctively, denied, and if one is denied the others must be, disjunctively at least, affirmed. In hypothetical sumptions, this is competent through the law of Reason and Consequent ; for where the reason is, there must be the consequent, and where o Esser, Logik, % 85. — Ed. LECTURES ON LOGIC. 291 the consequent is, there must he the reason." " There lect. are thus obtained three or four great classes of Syllo- gisms, whose essential characteristics I shall comprise in the following paragraph : — H LVI. Syllogisms are divided into different Par. lvi. •' '-' _ Second classes, according as the connection between the grand divi- ' '^ _ _ , sion of Syl- premises and conclusion is determined by the logisms— ■"- . '' according to different fundamental laws, 1°, Of Identity andtbeiawre- '' eulatingthe Contradiction; 2°, Of Excluded Middle; 3°, Of inference. Eeason and Consequent ; these several determi- nations affording the three classes of Categoiical, of Disjunctive, and of Ilypotlietical Syllogisms. To these may be added a fourth class, the Hypo- ihetico-disjunctive or Dilemmatic Syllogism, which is determined by the two last laws in combina- tion. Before proceeding to a consideration of these seve- Examples . . ° . . of the four ral syllogisms in detail, I shall, first of all, give you species of examples of the four species together, in order that you may have, while treating of each, at least a gene- ral notion of their differences and similarity. 1. — Op a Categorical Syllogism. i. Catego- rical. Sumption All matter is created ; Subsumption But the heavenly bodies are material; Conclusion Therefore, the heavenly bodies are created. a See Esser, Logih, § 8G, p. 161. cdytic of Logical Forms, the Author's This classification of syllogisms can- later view is expressed as follows : not be regarded as expressing the " All Mediate inference is one — Author's final view ; according to that incorrectly called Categorical ; which, as before observed, the prin- for the Conjunctive and Disjunctive ciple of Reason and Consequent is forms of Hypotheticcd reasoning are not admitted as a law of thought, reducible to immediate inferences." See above, p. 86, note a. In a note Compare Disciission-s, p. 651 et seq. by Sir W. Hamilton, appended to — Ed, Mr Baynes's Essay on tlie New An- 292 LECTURES ON LOtJlC. LFOT XX.' -• — ^'* ^ Disjunctive Syllogism. a. nujunc- Sumption The hope of immortal it ij in cither a rational ex- pectation or an illu^sion ; Subsumption But the hope of immortality ii a rational expec- tation ; Conclusion Thercfore,the hopcof immortality is not an illusion. 3. n\-T>o- 3. — Of an IlYroTHETicAL Syllogism. I helical. Sumption If Lojic do not profess to he an inMrumcnt of invention, the rejiroach that it discovers nothing is unfounded ; Subsumption But Logic does not profess to he an instrument of invention ; Conclusion Tlierefore, the rejyt'oach that it discovers nothing is unfo?inded. 4. iiyi.u- -i. — Of the DiLE>rMA OR Hypothetico-disjunctive Syllogism, thctico-dis- junctire. Sumption If man icere suited to live out of society, he would either he a god or a beast ; Subsumption But man is neither a god nor a beast ; Conclusion Tlierefore, he is not suited to live out of society. LECTURES ON LOGIC. 293 LECTURE XVI. STOICHEIOLOGY. SECTION II. — OF THE PRODUCTS OF THOUGHT. III. — DOCTRINE OF REASONINGS. SYLLOGISMS. THEIR DIVISIONS ACCORDING TO INTERNAL FORM. A. SIMPLE — CATEGORICAL. — I. DEDUCTIVE IN EXTENSION. In our last Lecture, I entered on the Division of lect, . . XVI. Syllogisms. I first stated to you the principles on - — — which this division must proceed ; I then explained tion?^' the nature of the first great distribution of Reason- ings into those of Intensive and those of Extensive Quantity ; and, thereafter, that of the second great distribution of reasonings into Simple and Condi- tional, the Simple containing a single species, — the Categorical ; the Conditional comprising three species, — the Disjunctive, the Hypothetical, and Hypothetico- disjunctive.'' These four species, I showed you, were severally determined by difierent fundamental Laws of Thought : the Categorical reposing on the laws of Identity and Contradiction ; the Disjunctive on the law of Excluded Middle ; the Hypothetical on the law of Reason and Consequent; and the Hypothe- tico-disjunctive on the laws of Excluded Middle and Reason and Consequent in combination. a Compare above, p. 236. — Ed. 294 LECTURES ON LOGIC. i.Krr 1 now •!»> on to tlio special eousidoration of the first XVI ® . of tlioso olasses of Syllogism — viz. the Syllogism Svii^H.m". whieh has beeu denominatecl Categorical. And iu Konc*!*"' regard to the meaning and liistory of the term cate- tfon'c((l, it will not be necessary to say anything in addition {o what I liave already stated in speaking of : .0 icrin judgments.'* As used originally by Aristotle, the term I rJ^wlw . ^.^^^^,g^^^,^^^^l YHQuwt merely affirmative, and was opposed to negative. By Theophrastus it was emjJoyed in the sense of absolute, — simple, — direct, and as opposed to conditional; and in this signification it has continued to be employed by all subsequent logicians, without their having been aware that Aristotle never employed it in the meaning iu Avliich alone they used it. Par. Lvii. % LVII. A Categorical Sylloo^ism is a reasoning The Cate- . t> J n t> eoricai Syi- whosc form is determined by the laws of Identity what. ' and Contradiction, and whose sumption is thus a categorical proposition. In a Categorical Syllo- gism there are three principal notions, holding to each other the relation of whole and part; and these are so combined together, that they constitute three propositions, in which each prin- cipal notion occurs twice. These notions are called Terms {termiiii, opoi), and according as the notion is the greatest, the greater, or the least, it is called the Major, the Middle, or the Minor Term.^ The Middle Term is called the Argument {argumentum, Xoyos, ttlo-tls) ; the Major and a See above, y. 234 et seq. — Ed. vi. c. xii. p. 343 ; Hurtado de Men- j3 [On principle of name of Major doza, p. 469.] [Lisjiut. Philosojahi- and Minor terms, see Alex. Aphro- cce, t. i. ; Disp. Logicce, d. x. § 50 et disiensis, In An. Prior., L. i. cc. iv. scq. Tolosae, 1617. See also Dis- V. ; Philoponufl, In An. Prior., L. L cussions, p. 666 et seq. — Ed.] 1 23 b; Fonseca, Inetit. Dialect., L. LECTURES ON LOGIC. 295 Minor Terms are called Extremes {extrema, aKpa). lect. If the syllogism proceed in the quantity of Ex- L tension, (and this form alone has been considered by logicians,) the predicate of the conclusion is the greatest whole, and, consequently, the Major Term ; the subject of the conclusion, the smallest part, and, consequently, the Minor Term. If the syllogism proceed in the quantity of Compre- hension, the subject of the conclusion is the greatest whole, and, consequently, the Major Term ; the predicate of the conclusion, the small- est part, and, consequently, the Minor Term. In either quantity, the proposition in which the rela- tion of the major term to the middle is expressed, is the Sumption or Major Premise, and the pro- position in which is expressed the relation of the middle term to the minor, is the Subsumption or Minor Premise. The general forms of a Cate- gorical Syllogism under the two quantities are consequently the following : — AN EXTENSIVE SYLLOGISM. AN INTENSIVE SYLLOGISM. B ^s A C is B C is B B is A G is A * C is A All man is mortal ; Caius is a man ; But Caius is a man ; But all man is mortal ; Therefore, Cains is mortal. Therefore, Caius is mortal. In these examples, you are aware, from what has Exi,iica- previously been said,* that the copula in the two different quantities is precisely of a counter meaning ; in the quantity of extension, signifying is contained under ; in the quantity of comprehension, signifying a See above, p. 274. —Ed. 206 LEiTUKKS ON I.OCJIC. LECT. contains in it. Tlius, taking the several formula^ the _^_'l_ Extensive SyUogisni will, when explicitly enounced, be r.\»mi>lo of r 11 the Kxto as follows : — f^^T^c^^ Svl- Tfw Middle (t rm 15 is contained under the Major term A ; But the Minor term C As contdined under the Middle term B ; Therefore, the Minor term C is also contained under the Major term A. U>gi»iu. tCUMVC. Or, to take the concrete example : — The Middle tenn all men is contained under the Major term mortfd. But the Minor term Caiu^ i^ contained tmder the Middle term all men ; Therefore, the Minor term Caius is also contained under the Major tenn mortal. oi tiie lu- On the contrary, the Intensive Syllogism, when ex- plicated, is as follows : — The Major term C contains in it the Middle term B ; But the Middle term B contains in it the Minor term A ; Therefore, the Major term C also contains in it the Minor term A. Or, in the concrete example : — The Major term Caius contains in it the Middle term man; But the Middle term man contains in it the Minor terra mortal ; Therefore, the Major term Caius also contains in it the Minoi' term mortal. Thus you see that by reversing the order of the two premises, and. by reversing the meaning of the copula, we can always change a categorical syllogism of the one quantity into a categorical syllogism of the other. "^ In this paragraph is enounced the general nature of a categorical syllogism, as competent in both the quantities of extension and comprehension, or, with more propriety, of comprehension and extension ; for comprehension, as prior to extension in the order of a Not in Inductive Syllogisms. — Jotting. [See below, p. 323. — Ed.] LECTURES ON LOGIC. 297 nature and of knowledge, ought to stand first. But lect XVI. as all logicians, with the doubtful exception of Aris- totle, have limited their consideration to that process of reasoning given in the quantity of extension, to the exclusion of that given in the quantity of compre- hension, it will be proper, in order to avoid misappre- hension, to place some of the distinctions expressed in this paragraph in a still more explicit contrast- In the reasonings under both quantities, the words The reason- expressive of the relations and of the things related prehension . -, rni 1 • I'll • • ^^^ ^^^^ '^^ are identical, ihe things compared m both quantities Extension are the same in nature and in number. In each there compared , . , , 1 . . and con- are three notions, three terms, and three propositions, trasted. combined in the same complexity ; and, in each quantity, the same subordination of a greatest, a greater, and a least. The same relatives and the same relations are found in both quantities. But though the relations and the relatives be the same, the relatives have changed relations. For while the relation between whole and part is the one uniform relation in both quantities, and while this relation is thrice realised in each between the same terms ; yet, the term which in the one quantity was the least, is in the other the greatest, and the term which in both is intermediate, is in the one quantity contained by the term which in the other it contained. Now, you are to observe that logicians, looking Narrow and only to the reasoning competent under the quantity d"finiti'ons of extension, and, therefore, looking only to the possi- StheMa"^ bility of a single relation between the notions or terms i^'a MiS*^' of a syllogism, have, in consequence of this one-sided *"'""' consideration of the subject, given definitions of these relatives, which are true only when limited to the kind of reasoning which they exclusively contem- 20S LErn'REs on Loau\ I KIT platoil, Tliis is seen in their (Icriiiitioiis of the Maior, -MiJiUe, aiul Minor Ti-rnis. ■' In rt>uaril to the lirst, they all sinii)ly define the Major term to be the predicate of the conelnsion. This is true of the reasoning; under extension, but of that exclusively. For the ]Major term, that is, the term which contains both the others, is, in the reason- ing of comprehension, the subject of the conclusion. Minor Again, the Minor term they all simply define to be the subject of the conclusion ; and this is likewise true oidy of the reasoning under extension : for, in the reasoning under comprehension, the ]\Iiuor term is the Mia.iic, predicate of the conclusion. Finally, they all simply define the Middle term as that which is contained under the predicate, and contains under it the subject of the conclusion. But this definition, like those of the two other terms, must be reversed as applied to the reasoning under comprehension. I have been thus tediously explicit, in order that you should be fully aware of the contrast of the doctrine I propose, to what you will find in logical books ; and that you may be prepared for the further development of this doctrine, — for its application in detail. In regard to the nomenclature of Major, Minor, and Middle terms, it is not necessary to say much. The expression term {terminus, opoi) was first employed by Aristotle, and, like the greater part of his logical vocabulary, was, as I have observed, borrowed from the language of mathematics." You are aware that the word term is applied to the ultimate constituents both of propositions and of syllogisms. The terms of a proposition are the subject and predicate. The terms o See Scheibler, [Opera Logica, 279, note fi. — Ed.] Pars. iii. c. 2, p. 398, and above, p. LECTURES ON LOGIC. 299 of a syllogism are the three notions which in their lect. . . . . XVI. threefold combination form the three propositions of a syllogism. The major and minor terms Aristotle, by another mathematical metaphor, calls the extremes (a/cpa), the major and minor extremes ; and his defi- Aristotle's •• ^1 ifi • -\ ^^ • Ti 1 definitiou of nition 01 these and of the middle term is, unlike those the terms 01 the subsequent logicians, so general, that it will gism. apply with perfect propriety to a syllogism in either quantity. " I call," he says, " the middle term that which is both itself in another and another in it ; and which, by its position, lies in the middle ; the extremes I call both that which is in another and that in which another is."* And in another place he says, " I define the major extreme that in which the middle is ; the minor extreme that which is subordinated to the middle."^ I may notice that the part of his definition of the His defini- middle term, where he describes it as " that which, by Middle its position, lies in the middle," does not apply to the middle by mode in which subsequent logicians enounce the syl- appiicTbie" logism. For let A be the major, B the middle, and C in which the minor term of an Extensive Syllogism, this will logidlus" I 1.1 enounce the be expressed thus : — syllogism. Sumption B ?'s A, i. e. B ?'s contained imder A. Subsumption C is ^, i. e. C is contained under B. Conclusion C is A, i. e. C ?'s also contained under A. In this syllogism the middle term B stands first But quite and last in the premises, and, therefore, Aristotle's t^fiie rea^ definition of the middle term, not only as middle by Con!)frohcn- nature, containing the minor and contained by the major, but as middle by position, standing after the major and before the minor, becomes inept. It will apply, however, completely to the reasoning in com- ^ a Anal. Prior., L. i., c. 4, § 3. /3 Ibid., §8. sion. 300 LECrrRES ON LOGIC. LL\T. prehensiou ; I\tr tlio extensive .syllo<;isiii given al)Ove \ V I _; L. beinij converted into an intensive, by reversing the twct premises, it will stand as follows : — Sumption C /.•* B, i. c. C confos not Ix-ltmL;,' [o ;i wliolc docs not lu'loni;" to Y V I J. its part: and on tlir otlicr, lookinii; iVtun the parts to their whole, to say, — What niaUosup all the parts con- stitutes the whole ; and wiiat does not make up all the parts does not eonstitule the whole. Now, these two applications of the principles of Identity and Contra- diction, as we look from one term of the relation of whole and part, or from the other, determine two dif- ferent kinds of reasoning. For if we reason down- wai'ds from a containing whole to a contained part, we shall have one sort of reasoning which is called the Deductive ; whereas, if we reason upwards, from the constituent parts to a constituted whole, we shall have another sort of reasoning, which is called the Inductive. This I briefly express in the following paragraph : — Par. Lviij. ^ LVIII. Categorical Syllogisms are Deductive, syEs'ms' if, on thc principles of Identity and Contradic- ivitive'*" tion, we reason downwards, from a containing M.i Indue- whole to a contained part ; they are Inductive, if, on these principles, we reason upwards, from the constituent parts to a constituted whole. I. Deduc- This is sufficient at present to afford you a general pricarsyi- conception of the difference of Deductive and Induc- ogisras. ^^^^ Catcgoricals. The difference of these two kinds of reasoning will be properly explained, when, after having expounded the nature of the former, we proceed to consider the nature of the latter. We shall now, therefore, consider the character of the deductive pro- cess, — the process which has been principally, and certainly most successfully, analysed by logicians ; for though their treatment of deductive reasoning has LECTURES ON LOGIC. 303 been one-sided and imperfect, it is not positively lect. erroneous ; whereas tlieir analysis of the inductive — process is at once meagre and incorrect. And, first, of the proximate canons by which Deductive Cater goricals are regulated. IF LIX. In Deductive Categoricals the uni- Par. lix. ^ , , Deductive versal laws of Identity and Contradiction take categon- -. cals, — their two modified forms, according as these syllo- canons, gisms proceed in the quantity of Comprehen- sion, or in that of Extension. The peculiar canon by which Intensive Syllogisms of this class are regulated, is, — What belongs to the predicate belongs also to the subject ; what is repugnant to the predicate is repugnant also to the subject. The peculiar canon by which Extensive Syllogisms of this class are regulated, is, — What belongs to the genus belongs to the species and individual ; what is repugnant to the genus is repugnant to the species and individual. Or, more briefly, AVhat pertains to the higher class, pertains also to the lower. Both these laws are enounced by Aristotle," and Expiica- both, from him, have passed into the writings of subsequent logicians. The former, as usually ex- pressed, is, — Prcedicatum prmdicati est etiam prcedi- catum subjecti; or, Hota notce est etiawb nota rei ipsius. The latter is correspondent to what is called the Dicta de Omni et de Nullo ; the Dictum de Omni, when least ambiguously expressed, being, — Qidcquid de omni valet, valet etiam de quibusdam et singulis; — and the Dictum de Nidlo being, — Quicquid de nidlo a Catcfj., c. 3. Anal. Prior., i. 1. — Ed. r^04 LECTURES ON LOGIC. LECT XTl. Conucction of Uio pri'- jHwitions anit (onus of the Calo- porical Syl- logism iiliis- trntotl bv sensible svmUils, i'(r/t7, )u'C lie (]nibusrelK'nsion,tliev have, eonsiMiiuMitly, not perceived tlie jtropcr a}>i>lieation of the lornu'r canon ; ^vllicll, therefore, remained in their systems either a mere hors d\vuvn', or else was only forced into an un- natural connect ion with the principle of the syllo- irism of extension. Before stating to you how the preceding canons are again, in their proximate application to categorical syllogisms, for convenience sake, still more exj^licitly enounced in certain special rules, it will be proper to show you the method of marking the connection of the propositions and terms of a categorical syllogism by sensible symbols. Of these there are various kinds, l)ut, as I formerly noticed, the best upon the w^hole, because the simplest, is that by circles.a According to this metliod, syllogisms with affirmative and nega- tive conclusions would be thus represented^ : — Ext. AFFIRMATIVE. Int. Ext. — P -M -M -M a [An objection to the mode of syllogiHtic notation by circles is, tiiat we cannot, by this mode, show that the contained exhausts the con- taining; for we cannot divide the area of a circle between any number of contained circles, representing in extension all co-ordinate species, in comi)rehension all the immediate attributes.] [For the Author's final scheme of notation, see Tabular Scheme at end of Volume II. — Ed.] $ See above, p. 256. Of. Krug, Logik, § 79, p. 245.— Ed. LECTURES ON LOGIC. 305 Ext. NEGATIVE. Int. LECT. XVI. You are now prepared for the statement and illus- Proximate tration oi the various proximate rules by which all categorical ^ -,, . 1 T ' i T n ' Syllogisms. categorical syllogisms are regulated. ' And, lirst, m i. Exten- regard to these rules in relation to the reasoning of Extension. "Aldrich," says Dr Whately, "has given twelve rules, which I find might be more conveniently re- duced to six. No syllogism can be faulty which violates none of these rules."" This reduction of the syllogistic rules to six is not original to Dr Whately ; but had he looked a little closer into the matter, he might have seen that the six which he and other logicians enumerate, may, without any sacrifice of precision, and with even an increase of perspicuity, be reduced to three. I shall state these in a paragraph, and then illustrate them in detail. IF LX. An Extensive Categorical Syllogism, Par. lx. if regularly and fully expressed, is governed by ruIcs ohu the three following rules : — Catcgorkai I. It must have three, and only three. Terms, ^ '*^'^'"* constituting three, and only three. Propositions. o Elements of Logic, B. ii. c. iii, § 2, p. 85, 8th edit. — Ed. VOL. L U 306 LECTURES ON LOP. 10. LECT. H. <^t tilt' ]>ivmises, tlic Siimi)tion must in ^^' quantity )>»> Dolinitc (/. r. universal or singular), ami the 8ul)suniption in quality Allirniativo. 111. The Conchhsion must correspond in (,)uan- tity with the Subsumption, luul iu Quality with the Sumption." iuu5iraiiou. These three simple laws comprise all the rules which First Hulc. , . . , , . , r • • a logicians lay down with so coiiiusiiig a minuteness.^ The first is : — A categorical syllogism, if regular and perfect, must have three, and only three, ^propositions, made up of three, and only three, terms. " The neces- sity of this rule is manifest from the veiy notion of a categorical syllogism. In a categorical syllogism the relation of two notions to each other is determined through their relation to a third ; and, consequently, each must be compared once vAih. the intermediate notion, and once with each other. It is thus mani- fest that there must be three, and cannot possibly be more than three, terms ; and that these three terms must, in their threefold comparison, constitute three, What is and only three, propositions. It is, however, to be KTe^dJd obsen^ed, that it may often happen as if, in a valid as^ogica gy^QgisjjQ^ there were more than three principal notions, — three terms. But, in that case, the terms or notions are only complex, and expressed by a plurality of words. Hence it is, that each several notion extant in a syllogism, and denoted by a separate word, is not on that account to be viewed as a logical term or o Krug, Lorjih, § 80.— Ed. [Cf. Schulze, Lorjik, § 79; Fries, Logik, Alexander Aphrodisiensis, In An. § 55, p. 224.] Prior., L. i., f. 17, Aid. ; Derodon, )3 See Scheibler, Opera Logica, Logica Restitute, p. 639 c< stq.; Hoff- pars, iv., p. 516; Keckermann, Sys- bauer, An/angsgriinde der Logik, § te7>ui Logicoe Minus, Opera, t. i. p. 317, p. 164; Bachmann, Logik, § 239.— Ed. 122, p. 187 ; Esser, Logik, §§ 88, 89. LECTURES ON LOGIC. 307 terminus, but only those which, either singly or in lect. connection with others, constitute a principal momen- — turn of the syllogism."* Thus, in the following syllo- gism, there are many more than three several notions expressed by three several words, but these, we shall find, constitute in reality only three principal notions or logical terms : — Sumption He ivlio conscientiously performs his duty is a truly good man ; Subsumption Socrates conscientiously performs Ms duty ; Conclusion Tlierefore, Socrates is a truly good man. Here there are in all seven several notions denoted by seven separate words : — 1. Conscientiously, 2. Per- forms, 3. Duty, 4. Truly, 5. Good, 6. Man, 7. Socrates ; but only three principal notions or logical terms, — viz., 1. Conscientiously jpei'forms Ms duty, 2. Truly good man, 3. Socrates. " When, on the other hand, the expression of the Quatemio middle term m the sumption and subsumption is used rmn. in two significations, there may, in that case, appear to be only three terms, while there are in reality four ; or, as it is technically styled in logic, a quaternio ter- minorum.^ On this account, the syllogism is vicious in point of form, and, consequently, can afford no in- ference, howbeit that the several propositions may, in point of matter, be all true. And why % — because there is here no mediation, consequently no connection be- tween the different terms of the syllogism. For ex- ample ; — The animals are void of reason ; Man is an animal ; Tlierefore, man is void of reason. a Krug, Logik §80, p. 246; Anm. $ [Cf. Fonseca,] [Instit. Dial., L. 1.— Ed. vi. c. 20, p. 359.— Ed.] 308 LECTURES ON LOCK'. LECT. " lli'iv tluMoiicliisii)n is iiivalul, though each propo- sition. bv itsolf, and in a ciTtaiu sense, may bo true. For hi ix' tlio middle term animal is not taken in the s;inu' nu-aninjj; in tlie major and minor propositions. For in the former it is taken in a narrower signilica- tion, as convertible with brute; in i the latter in a wider yiiinification, as convertible Avilh animated or- gani^m.'"^ ^«cond The second rule is : — Of the premises, the sumption must in quantity be definite, (universal or singular), the subsumption must in quality be affirmative. — The sumption must in reference to its quantity be definite ; because it aflbrds the general rule of the syllogism. For if it were indefinite, that is, particular, we should have no security that the middle term in the sub- sumption comprised the same part of the sphere which it comprised in the sumption, p Thus : — I M Some M are P ; ^ All S are M ; All S are P. Or, in a concrete example : — Some works of art are cuNcal ; All pictures are works of art ; Therefore, all pictures are culncal. In regard to the subsumption, this is necessarily affirmative. The sumption is not limited to either quality, because the proposition enouncing a general rule may indifi'erently declare All M is P, and No M is P. The assumption is thus indeterminate in regard to quality. But not so the proposition enouncing the application of a general rule. For it must subsume, a Ej-ug, Logik, p. 247. — Ed. LECTURES ON LOGIC. 309 that is, it must affirm, that somethincj is contained lect. *^ . XVI. under a condition ; and is, therefore, necessarily affir mative. We must say S is M. But in respect of quantity it is undetermined, for we can either say All S is M, or Some S is M. If the subsumption is nega- tive, there is no inference ; for it is not necessary that a genus should contain only things of a certain species. This is shown in the following example : — All men are animals; No horse is a man ; Therefore, no horse is an animal. Or, as abstractly expressed, — All M are P ; But no S is M ; ■ " iVo S is P. Thus it is, that in a regular extensive categorical syllogism, the sumption must be always definite in quantity, the subsumption always affirmative in quality, a I have, however, to add an observation requisite to Misconcci. prevent the possibility of a misconception. In stating gard to de- it as a rule of extensive categoricals, that the sumption of sump- must be definite (i.e. universal or singular), if you are at comi'n.ie all conversant with logical books, you will have noticed "'"•''■ that this rule is not in unison with the doctrine therein taught, and you may, accordingly, be surprised that I should enounce as a general rule what is apparently con- tradicted by the fact that there are syllogisms, — valid syllogisms, — of various forms, in which the sumption is a particular, or the subsumption a negative, proposi- tion. In explanation of this, it is enough at present to say, that in these syllogisms the premises are trans- o Krug, Logik, p. 248. Bachmann, Logik, § 124. — Ep. 310 LECTURES ON LOOK'. UCT. i>ose(l in tho oxpivssion. You will, 1i(>rcaftcr, luul that XYI 1_ the sumption is not always tlu' jU'oposition which i»xicr"T stands first in the enunciation, as the conclusion is not a^not"" always the proposition which stands last. Such trans- th*.umV* i>ositions are, however, only external accidents, and Il^ptuu." the mere order in which the premises and conclusion ID • rvasou- of a syllogism are enounced, no more changes their nature and their necessary relation to each other, than does the mere order in which the grammatical parts of a sentence are expressed, alter theii- essential char- acter and reciprocal dependence. In the phrases m' bonus and bonus vir, — in both, the vir imi substantive and the bonus an adjective. In the sentence variously enounced, — Alexander Darium vicit, — AJexander vicit Darium, — Darium Alexander vicit, — Darium vicit Alexander, — Vicit Alexander Darium, — Vicit Darium Alexander: — in these, a difiference of order may denote a difference of the interest we feel in the various constituent notions, but no difference of their What truly grammatical or logical relations. It is the same with the sump- syllogisms. The mere order of enunciation does not su*bsump- change a sumption into a subsumption, nor a sub- reasoning, sumption into a sumption. It is their essential rela- tion and correlation in thought which constitutes the one proposition a major, and the other a minor pre- mise. If the former precede the latter in the expres- sion of the reasoning, the syllogism is technically regular ; if the latter precede the former, it is techni- cally irregular or transposed. This, however, as you will hereafter more fully see, has not been attended to by logicians, and in consequence of their looking away from the internal and necessary consecution of the premises to their merely external and accidental arrangement, the science has been deformed and per- .LECTURES ON LOGIC. 311 plexed by the recognition of a multitude of different .lect. . . . . XVI. forms, as real and distinct, which exist only, and are — only distinguished, by certain fortuitous accidents of expression. This being understood, you will not mar- vel at the rule in regard to the quantity of sumptions in extensive syllogisms, (which, however, I limit to those that are regularly and fully expressed), — that it must be definite. Nor will you marvel at the counter canon in regard to the quality of sumptions in intensive syllogisms, — that it must be affirmative.'' The necessity of the last rule is equally manifest as that of the preceding. It is : — The conclusion must Third Rule, correspond in quantity with the subsumption, and in quality with the sumption. " This rule is otherwise enounced by logicians : — The conclusion must always follow the weaker or worser part, — the negative and the particular being held to be weaker or worser in relation to the affirmative and universal. The con- clusion, in extensive categoricals (with which we are at present occupied) is made up of the minor term, as subject, and of the major term, as predicate. Now, as the relation of these two terms to each other is de- termined by their relation to the middle term, and as the middle term is compared with the major term in the sumption; it follows that the major term must hold the same relation to the minor in the conclusion which it held to the middle in the sumption. If then the sumption is affirmative, so likewise must be the conclusion ; on the other hand, if the sumption be negative, so likewise must be the conclusion. In the subsumption, the minor term is compared with the a [See Bachmann, Logik, § 124, Krug, LogiJc, § 82, p. 249; Cf. § pp. 192, 194, Anm. 3; Drobisch, 83, p. 264, and § 109, p. 362; Fac- Logik, § 73, p. 65, §§ 42, 44, pp. 34, ciolati, Rudimenta Logica, P. iii. c. 36; Schulze, Logih, § 79, p. 114; iii. p. 91.] ;U2 LECTURES ON LOGIC. LECT, iiiiilillo ; tliat is, (lu^ minor is aftinnod as under th<' — --- miiKUo, In the cont'liision, the major term cannot, tlierelbro, be predieated of more things than were atlirnicd aa under tlie midiUe term in the subsumption. I3 the subsumption, therefore, universal, so likewise must be the conclusion ; on the contrary, is the for- mer particular, so likewise must be the latter."" a Krug, Logik, § 80, p. 250-51.— Ed. LECTURES ON LOGIC. 313 LECTURE XVII. STOICHEIOLOGY. SECTION II. — OF THE PRODUCTS OF THOUGHT. III. DOCTRINE OF REASONINGS. SYLLOGISMS. THEIR DIVISIONS ACCORDING TO INTERNAL FORM. A. SIMPLE. — CATEGORICAL — II. DEDUCTIVE IN COMPRE- HENSION — III. INDUCTIVE IN EXTENSION AND COM- PREHENSION. — B. CONDITIONAL. DISJUNCTIVE. In my last Lecture, after terminatins^ the considera- lect. .' '^ XVII tion of the constituent elements of the Categorical — '— Syllogism in general, whether in the quantity of Com- tion*^'*" "" prehension or of Extension, I stated the subdivision of Categorical Syllogism into Deductive and Induc- tive, — a division determined by the difference of reasoning from the whole to the parts, or from the parts to the whole. Of these, taking the former, — the Deductive, — first into consideration, I was occupied, during the remainder of the Lecture, in giving a view of the laws which, in their higher or lower universality, — in their remoter or more proximate application, govern the legitimacy and regularity of Deductive Categorical Syllogisms. Of these laws, the highest are the axioms of Identity and Contradiction, by which all Categorical Syllogisms are controlled. These, when 314 LECTURES ON LOGIC. LECT, ]>roxim;itilv appliiJ to tlu' two loniis of Deductive XVII *. L Catogoricals, dotonniiieil by the two ijuautities of Com})ivlioiisioii and Extension, constitute two canons, — the canon of the Intensive Syllogism l>cing, — What belongs to the predicate belongs also to the subject, — what is repugnant to the predicate is repugnant also to the subject ; — the canon of the Extensive Syllogism beiuix, — AVhat belono-s to the i^cnus bcloncfs also to the species and individual, — what is repugnant to the genus is repugnant also to the species and individual. Each of these, however, in its more proximate appli- cation, is still further developed into a plurality of more explicit rules. In reference to Extensive Syllo- gism, the general law, or the Dictum de Omni et de Nidlo (as it is technically called), is evolved into a series of rules, which have been multiplied to twelve, are usually recalled to six, but w^hich, throwing out of account irregular and imperfect syllogism, may be conveniently reduced to three. These are, I. An Ex- tensive Categorical Deductive Syllogism must have tliree, and only three, terms, constituting three, and only three, propositions. II. The sumj)tion must in quantity be definite, {i. e. universal or singular) ; the subsumption must in quality be afiirmative. III. The conclusion must correspond in quantity with the sub- sumption, and in quality with the sumption. The Lecture concluded with an explanation of these rules in detail. 2. The In- We have next to consider into what rules the law Caicgoricai of Intensivc or Comprehensive Syllogism is developed, SyUogism. in its more proximate application. Now, as the in- tensive and extensive syllogisms are always the coun- terparts of each other, the proximate rules of the two forms must, consequently, be either precisely LECTURES ON LOGIC. 315 the same, or precisely the converse of each other, lect. Accordingly, taking the three rules of extensive syllo- — L. gisms, we find that the first law is also, without dif- ference, a rule of intensive syllogisms. But the second and third, to maintain their essential identity, must be externally converted ; for to change an extensive syllogism into an intensive, we must transpose the order or subordination of the two premises, and re- verse the reciprocal relation of the terms. The three general rules of an Intensive Categorical Deductive Syllogism will, therefore, stand as follows : — H LXI. An Intensive Categorical Deductive Par. lxi. Syllogism, that is, one of Depth, if regularly and iiuensi*ve '^ fully expressed, is governed by the three follow- Deductive 1 Syllogism. mg rules. I. It must have three, and only three, Terms, constituting three, and only three. Propositions. II. Of the premises, the Sumption must in quality be Affirmative, and the Subsumption in quantity Definite, (that is, universal or sin- gular). III. The Conclusion must not exceed the Sump- tion in Quantity, and in Quality must agree with the Subsumption. In regard to the first of these rules, — the rule which Expiica- is identical for syllogisms whether extensive or inten- First Rule, sive, — it is needless to say anything ; for all that I stated in regard to it under the first of these forms, is valid in regard to it under the second. I proceed to the second, which is, — The sumption second must in quality be affirmative, the subsumption must in quantity be definite, (that is, universal or singular). Ilir. LECTURES OX LOGIC. LECT. Alul, heiv, wi' \\a\o to answer the question, — Why in '— an intensive syllogism must the sumption be affirma- tive in quality, the subsumption definite in quantity? Let us take tlie following syllogism as explicated : — M docii not comprehend P ; Therefore f S does not comprehend P. Pinidencc comprehends virtue ; But virtue does not comprehend blameworthy ; Tlierefore prudence does not comprehend blameworthy. Here all goes on regularly. AVe descend from the major term prudence to the middle term virtue, and from the middle term virtue to the minor term blame- worthy. But let us reverse the premises. We at once see that though there is still a discoverable meaning, it is not directly given, and that we must rectify and restore in thought what is perverse and preposterous in expression. In the previous example, the sumption is affirmative, the subsumption negative. Now let us take a negative sumption : — S does not comprehend M ; But M compreJiends P. Here there is no conclusion competent, for we can neither say S comprehends P, nor S does not coynpre- hend P. Or to take a concrete example, — Prudence does not comprehend learning ; But learning comprehends praiseicorthy. We can draw, it is evident, no conclusion ; for we can neither say, from the relation of the two proposi- tions, that Prudence comprehends praiseworthy, nor that Prudence does not comprehend praiseworthy. Grounds of The icason why an extensive syllogism requires a 'regarding uuivcrsal sumption, and an intensive syllogism an LECTURES ON LOGIC. 31 7 affirmative, and wliy the one requires an affirmative lect. and the other a definite subsumption, is the following. The condition common to both syllogisms is that the anrsub" sumption should express a rule. But in the extensive eSsWc'" syllogism this law is a universal rule, that is, a rule prehensTve to which there is no exception ; but then it may be ^y^^^'^ism*- expressed either in an affirmative or in a negative form, whereas in the intensive syllogism this law is expressed as a position, — as a fact, and, therefore, admits only of an affirmative form, but, as it is not necessarily universal, it admits of limitations or ex- ceptions. This opposite character of the sumptions of the two forms of syllogisms is correspondent to the opposite character of their subsumptions. In the extensive syllogism, the subsumption is, and can only be, an affirmative declaration of the application of the sumption as a universal rule. In the intensive syllogism, the subsumption is either an affirmation or a negation of the application of the sumption as a positive law. Hence it is that in an intensive syllo- gism the major premise is necessarily an affirmative, while the minor may be either an affirmative or a negative proposition. In regard to the second clause of the second rule, the reason why the subsumption in an intensive syllo- gism must be definite in quantity, is because it would otherwise be impossible to affirm or deny of each other the minor and the major terms in the conclusion. For example : — Sumption Prudence is a virtue, i. e. Prudence comprehends virtue ; Siibsumption... ^ome virtue is praiseworthy, i.e. Some virtue comprehends praiseworthy. From these we can draw no conclusion, for the inde- 31S LECTURES ON LOOK'. L8CT tiuilo some vl )•(>{(• (loos not eonnect tlic major term *^^'l_ prucfvnce niul llio minor term p raise irortht/ into the noiossarv relation of whole and part. Hurvi Kuio. In ren^anl to the third rule — The eonclusion must he eorrespondent in quantity with the sumption, and in quality with the subsumption — it is not necessary to say anything. Here, as in the extensive syllogism, the conclusion cannot be stronger than the weakest of its antecedents, that is, if any premise be negative the conclusion cannot but be negative also; and if any premise be particular, the conclusion cannot but be particular likewise, and as a w^eaker quality is only found in the subsumption and a weaker quantity in the sumption, it follows that (as the rule declares) the conclusion is regulated by the sumption in re- gard to its quantity, and by the subsumption in regard to its quality. It is, however, evident, that thouffh warranted to draw a universal conclusion from a general sumption, it is always competent to draw- only a particular. II. Indue- So much for the proximate laws by which Cate- eoricafsyi- gorical Dcductivc Syllogisms are governed, when con- ogisms. gidered as perfect and regular in external form. We shall, in the sequel, have to consider the special rules by which the varieties of Deductive Categorical Syl- logisms, as determined by their external form, are governed ; but at present we must proceed to the general consideration of the other class of categorical syllogisms afforded by their internal form, — I mean those of Induction, the discussion of which I shall commence by the following paragraph. Par. Lxii. 1" LXII. An Inductive Categorical Syllogism Inductive , . . , . , n i Categorical IS a rcasoiimg in which we argue irom the notion LECTURES ON LOGIC. 319 of all the constituent parts discretively, to the lect. notion of the constituted whole collectively. Its general laws are identical with those of the —what!™' Deductive Categorical Syllogism, and it may be expressed, in like manner, in the form either of an Intensive or of an Extensive Syllogism. We shall, in the sequel, have to consider more The views 111 1 T • • /»T'T°'^ logicians particularly the nature and peculiarities of Logical regarding T 1 • 1 n 1 TT f ^^^ nature Induction when we come to treat of the Figure of of Logical Syllogism, and when we consider the nature of Logi- erroneous. cal or Formal, in contrast to Philosophical or Real In- duction, under the head of Modified Logic. At pre- sent, I shall only say, that all you will find in logical works of the character of logical induction is utterly erroneous ; for almost all logicians, except Aristotle, consider induction, not as regulated by the necessary laws of thought, but as determined by the probabilities and presumptions of the sciences from which its matter has accidentally been borrowed. They have not con- sidered it, logically, in its formal, but only, extra- logically, in its material conditions. Thus, logicians have treated in Logic of the inductive inference from the parts to the whole, not as exclusively warranted by the law of Identity, in the convertibility of the whole and all its parts, but they have attempted to establish an illation from a few of these parts to the whole ; and this, either as supported by the general analogies of nature, or by the special presumptions afi'orded by the several sciences of objective existence." Logicians, with the exception of Aristotle, who is, The charac- however, very brief and unexplicit in his treatment of caiVr For^' this subject, have thus deformed their science, andRcaio" Material, a ComTpa,re Discussions, p. 159. — Ed. Induction. 320 LECTURES ON LOCIO. LKiT. pcruloxril t lu' vory .simnlo tli)cti'inc of logical induction, XVII * by confounding formal with niatdial induction. All inductive reasoning is a reasoning from the parts to the whole ; but the reasoning from the parts to the whole in the various material or objective sciences, is Aery different from the reasoning from the parts to the whole in the one formal or subjective science of Logic. In the former, the illation is not simply founded on the law of Identity, in the convertibility of a whole and all its parts, but on certain presump- tions di*awn from an experience or observation of the constancy of nature ; so that, in these sciences, the inference to the whole is rarely from all, but generally from a small number of, its constituent parts ; conse- quently, in them, the conclusion is rarely in truth an induction properly so called, but a mixed conclusion, drawn on an inductive presumption combined with a deductive premise. For examj^le, the physical philo- sopher thus reasons : — T7iis, that, and the other magnet attract iron; But this, that, and the other magnet represent all magnets/ Therefore, all magnets attract iron. Now, in this syllogism, the legitimacy of the minor premise, This, that, and the other magnet represent all magnets, is founded on the principle, that nature is uniform and constant, and, on this general principle, the reasoner is physically warranted in making a few parts equivalent to the w^hole. But this process is wholly incompetent to the logician. The logician know^s nothing of any principles except the laws of thought. He cannot transcend the sphere of neces- sary, and pass into the sphere of probable, thinking ; nor can he bring back, and incorporate into his own formal science, the conditions which regulate the LECTURES ON LOGIC. 321 procedure of tlie material sciences. This beino; tlie lect. ^ S XVII. case, induction is either not a logical process dijBferent from deduction, for the induction of the objective philosopher, in so far as it is formal, is in fact deduc- tive ; or there must be an induction governed by other laws than those which warrant the induction of the objective philosopher. Now, if logicians had looked to their own science, and not to sciences with which, as logicians, they had no concern, they would have seen that there is a process of reasoning from the parts to the whole, as well as from the whole to the parts, that this process is governed by its own ^ laws, and is equally necessary and independent as the other. The rule by which the Deductive Syllo- canons of - . TTTi 11 ^ -^ the Deduc- gism IS governed is, — What belonojs, or does not tive and in- f, °, .. Till 1 '^"'^''ve Syl- belong, to the contammg whole, belongs, or does not logisms — belong, to each and all of the contained parts. The mai. rule by which the Inductive Syllogism is governed is, — What belongs, or does not belong, to all the constituent parts, belongs, or does not belong, to the constituted whole. These rules exclusively deter- mine all formal inference ; whatever transcends or violates them, transcends or violates Logic. Both are equally absolute. It would be not less illegal to infer, by the deductive syllogism, an attribute belonging to the whole of something it was not conceived to contain as a part ; than, by the inductive, to conclude of the whole what is not conceived as a predicate of all its constituent parts. In either case, the con- sequent is not thought as determined by the ante- cedent ; the premises do not involve the conclusion." To take the example previously adduced, as an o [Cf. Knxg, Logik, §§ 166, 167 ; tionalis, §§ 477, 478 ; ScotusJ [Quoes- Sanderson, Compendiujn Log. Artls, tionea in An. Prior., L. ii. q. viii. p. L. iii. c. X. p. 112; Wolf, PhU. Pa- :516, cd. 610.— Ed.] vor.. I. X LECrUIlES UN LDCU". LKcr. illustration oi' a luatorial or pliilosopliical iiuUu-lioii, it wouUl l>e thus expressed as ii formal or logical in- XVII. »..n.i.i:,ii- iluction : — lustr^tctl. T/ii.>; fhnt, ami the other magnet attraet iron ; But this, that, and the other magnet are all magurt.-^ ; Therefore, all magnets attract iron. Hero the inference is determined exclusively 1 »y a law of thought. In the subsumption it is said — 77/ /x, that, ((ud the other magnet are all magnets. Tliis means, This, that, and the other magnet are, that is, constitute, or rather, are conceived to constitute, all magnets, that is, the ivhole — the class — the genius magnet. If, therefore, explicitly enounced, it will be as follows : — This, that, and the other magnet are con- ceived to constitute the ivhole class magnet. The con- clusion is — Tlierefore, all magnets attract iron. This, if explicated, will give — Therefore the whole class magnet is conceived to attract iron. The whole syllo- gism, therefore, as a logical induction, will be : — Tliis, that, and the other magnet attract iron ; But this, that, and the other magnet are conceived to constitute the genus magnet ; Tlierefore, the genus magnet attracts iron. Objection It is almost needless to advert to an objection, which, ** "**^'' I see, has misled Whately among others. It may be said, that the minor, This,that,and the other magnet are all magnets, is manifestly false. This is a very super- ficial objection. It is very true that neither here, nor indeed in almost any of our inductions, is the state- ment objectively correct, — that the enumerated parti- culars are really equivalent to the whole or class which they constitute, or in which they are contained. But as an objection to a logical syllogism, it is wholly incompetent, as wholly extralogical. For the logician LECTURES ON LOGIC. 323 has a right to suppose any material impossibility, any lect. material falsity ; he takes no account of what is ob- '— jectively impossible or false, and has a right to assume what premises he please, provided that they do not involve a contradiction in terms. In the example in question, the subsumption — This, that, and the other magnet are all magnets — has been already explained to mean not that they really are so, but merely that they are so thought to be. It is only on the sup- position of this, that, and the other magnet being conceived to constitute the class magnet, that the inference proceeds, and, on this supposition, it will not be denied that the inference is necessary. I stated Formula that an inductive syllogism is equally competent in uve Syiio- comprehension and in extension. For example, let us compreheu- suppose that x, y, z represent parts, and the letters Extension. A and B wholes, and we have the following formula of an inductive syllogism in Comprehension : — X, y, z constitute A ; A comiorehends B ; Therefore, x, j, z compreliend B. This, if converted into an extensive syllogism, by transposing the premises and reversing the copula, gives : — A is contained under B ; X, y, z constitute A ; Therefore, x, y, z are contained under B. But in this syllogism, it is evident that the premises are in an unnatural order. We must not, therefore, here transpose the premises, as we do in converting a de- ductive categorical of comprehension into one of ex- tension. We may obtain an inductive syllogism in two different forms, and in either comprehension or extension, according as the parts stand for the major. :v2i LKCrUUKS ON LOCIC. LKrr. XVII. or I'or till' niiiKlk' term. U" the minor term is formed of tlie }Kirts, it is evident there is no induction ; for in til is »';ise tlu\y oidy constitute tliiit tjuanlity of the syllogism which is always a part, and never a whole. Let X, y, z re})resent the parts ; where not su[)erseded by X, y, z, S will represent the major term in a com- prehensive, and the minor term in an extensive, syllo- gism ; V will represent the major term in an exten- sive, and the minor term in a comprehensive, syllo- gism ; and j\I the middle term in both. I shall, first, take the Inductive Syllogism of Comprehension. FiRiST Cask, — (Tho parts hold- ing the place of the major term S). X, y, z constitute M ; J M comprehends P ; Therefore, x, y, z comprehend P. Skcond Case, — (Tho parts hold- ing the place of the middle term). S comprehends x, y, z; X, y, z constitute P; Therefore, 8 comprehends P. Again, in the Inductive Syllogism of Extension : — First Case, — (The parts holding the place of the major term P). X, y, z constitute M ; S is contained under M ; Therefore, S is contained under X, y, z. Second Case, — (The parts hold- ing the place of the middle term). X, y, z are contained under P ; X, y, z constitute S ; Tlierefore, S iscontained underV. Whately aud otiiers erroneously make the Inductive Syllogism Deductive Before leaving this subject, I may notice that the doctrine of logical induction maintained by Whately and many others, diverges even more than that of the older logicians from the truth, inasmuch as it makes this syllogism a deductive syllogism, of which the sumption, which is usually understood and not ex- pressed, is always substantially the same — viz. " What belongs (or does not belong) to the individuals we have examined belongs (or does not belong) to the whole class under which they arc contained." This LECTURES ON LOGIC. 325 doctrine was first, I think, introduced by Wolf," for lect. XVII the previous logicians viewed the subsumption as the — — ^ common, and, therefore, the suppressed premise, this the older lo- premise always stating that the individuals or parti- ^''"''°^' culars enumerated made up the class under which they were severally contained/ For example, in the instance from the magnet we have already taken, the subsumption would be — This, that, and the other mag- 7iet and so forth, are the ivhole class raagnet. This Correct as doctrine of the older logicians is correct as far as it gtes!* ' goes ; and to make it absolutely correct, it would only have been necessary to have established the distinc- tion between the logical induction as governed by the a priori conditions of thought, and philosophical in- duction as legitimated by the a posteriori conditions of the matter about which the inquiry is conversant. This, however, was not done, and the whole doctrine of logical induction was corrupted and confounded by logicians introducing into their science the considera- tion of various kinds of matter, and admittino- as logical an induction supposed imperfect, that is, one in which there was inference to the whole from some only of the constituent parts. This Imperfect Induction Doctrine of they held in contingent matter to be contingent, — iXcUon. o [Of. Wolf, Philosoi)hia Ration- c. xx. p. 217, ed. 1677.] [Cf. Discus- alls, § 479, first ed. 1728. So, before sions, p. 170, note.— Ed.] Wolf, Schramm, Aristot. Philos. fi [On Induction in general, see Princijnn, p. 27, ed. Helmst., 1718: Zabarella, Tabuloe in An. Prior., p. " Inductione ex multis singularibus 170 ct scq., 0-pera Lorjica, (Ajipen- coUigitur universale supposito loco dix) ; Molinaeus, Elementa Lorjica, majoris propositionis hoc canone : — L. i. c. ii. p. 99 ; Isendoorn, Cursiis Quicquid competit omnibus partibus, Lof/icus, L. iii. q. ii. p. 361 ; Crellius hoc competit toti ; in isto (Enthy- /saonendo tollens, or Negative, constituting the Modus tollens, or Modus tollendo ponens. In each of these modes there are two cases, which I comprehend in the following mnemonic verses : — (A) Affirmative, or Modus ponendo tollens : — 1 . Falleris aid fallor ; fallor ; non fallerls ergo. 2. Falleris aut fallor ; tu falleris ; ergo ego nedum. (B) Negative, or Modus tollendo ponens : — 1. Falleris aut fallor ; non fallor ; falleris ergo."- 2. Falleris aut fallor ; non falleris ; ergo ego fallor. In illustration of this paragraph, I have defined a Expiica- disjunctive syllogism, one whose form is determined by the law of Excluded Middle, and whose sumption is, accordingly, a disjunctive proposition. I have not, a syllogism as logicians in general do, defined it directly, — a syllo- j^nctiVc gism whose major premise is a disjunctive proposition. S'liuo't For though it be true that every disjunctive syllogism liisjuu^tivc '' rciisoiiing. o This line is from Purchot, The others are the Author's own. — Instil. I'hilos. Loyica, t. i. p. 184. Ed. 328 l.KcTUKKs ox i,(u;ic. LK(T. has a ilisium'tivt.' luaior itrcinisi' the converse is not XN'll . ... — '— true ; for owry syllogism that has a disjunctive sumption is not, on that account, necessarily a dis- junctive syllogism. For a disjunctive syllogism only emerges, when the conclusion has reference to the relation of reciprocal alKrmation and negation subsist- ing between the disjunct members in the major pre- mise, — a condition not, however, contained in the mere existence of the disjunctive sumption." For example, in the syllogism : — B is either C or D ; But A is B ; Therefore, A is either C or I). This syllogism is as much a reasoning determined, not by the law of Excluded Middle, but solely by the law of Identity, as the following : — B is C. A is B. There/ore, Ai s C. For in both we conclude, — C (in one, C or D) is an attnhute q/'B ; hut B is an attribute of A ; therefore, C (C or D) is an attribute of A, — a process, in either case, regulated exclusively by the law of Identity.'^ This being premised, I proceed to a closer con- sideration of the nature of this reasoning, and shall, first, give you a general notion of its procedure; then, secondly, discuss its principle ; and, thirdly, its con- stituent parts. V. General 1°. Tlic general form of the Disjunctive Syllogism ili^sjunetive may be given in the following scheme, in which you Syllogism. a Cf. Scheibler, Opera Lo'jka, tione. " — Ed. Pars iv. p. 553 : "Neque enim syl- /3 Sigwart, pp. 154, 157. [Hand- logismus di.'^junctus semper est, cum huch zur Vorlamngen iibcrdic Lo(jik, propositio est disjunctiva, sed cum von H. C. W. Sigwart, 3ded., Tiibin- tota qiiaestio disjwuitur in proposi- gen, 1835, §§ 245, 24S. — Ed.] LECTURES ON LOGIC. 329 will observe there is a common sumption to the nega- lect. tive and affirmative modes : — • A is either B or C. »• Fo^miila tor a oyllo- ISTegativb, or Modus tollendo gism with two disjunct PONENS— mcnbers. Affirmative, or Modus pon ENDO TOLLENS Nolo AisB ; Now A is not B ; Therefore, A is not C. Therefore, A is C. Or, in a concrete example : — Sempronitis is either honest or dishonest. Affirmative, or Modus pon- ENDO TOLLENS Now Sempronius is honest ; Therefore, Semproniits is not dishonest. Negative, or Modus tollendo PONENS Noto Semi^ronius is not honest ; Therefore, Sempronius is dis- honest. " This formula is, however, only calculated for the b. Formula ,. . foraSyllo- case in which there are only two disjunct members, gism with •' _ more than that is, for the case of negative or contradictory op- two disjunct ^ ° , members. position ; for if the disjunct members are more than two, that is, if there is a positive or contrary opposi- tion, there is then a twofold or manifold employment of the Models ponendo tollens and Modus tollendo 200716718, according as the affirmation and negation is determinate or indeterminate. If, in the Models po- ne7ido tolle7is, one disjunct member is determinately affirmed, then all the others are denied ; and if several disjunct members are indeterminately affirmed except one, then only that one is denied. If, in the Modus tolleTido 2'>07ie7fis, a single member of the disjunction be denied, then some one of the others is indetermin- ately affirmed ; and if several be denied, so that one alone is left, then this one is determinately affirmed." " This will appear more clearly from the following for- mulae. Let the common Sumption both of the Modus 2)0)ie7ido tollens and Modus tolle7ido ponens be : — a Ebser, Louik, % 93, p. ISO. — Eu. 330 LECTUKES ON LO(U(". I. Kit. xvn. Fil-st (asc, A is either \\ or C or I>. UK Modus PoNENDtt Toi-licns- A is cither 1> or C or 1 ) ; Now A /.•>• B ; There/ore, A /*• neither C nor D. Second Case. A in either B or C or D ; Now A in either B w C ; There/ore, A is not I). II. The ^Iodus Tollendo Ponens. First Case. A /*■ either B or C or D ; Now A is not V> ; Therefore, A is either C or D. Secoiul Case. A /■;.• either B or Corl); Now A is neither B 7ior C j Therefore, A u- D. Or, to take these in concrete examples, let tlic Com- mon Sumption be : — The ancients were in genius either superior to tlie moderns, or inferior, or equal. I. The Modus Ponendo Tollens. First Case. The ancients icere in genius either superior to the modems, or inferior, or equal ; Now the ancients were superior ; Therefore, the ancients were neither inferiw nor equal. Second Case. Tlie ancients were in genius either superior to the moderns, or inferior, or equal ; Now the ancients icere either superior or equal ; Tlierefore, the ancients xcere not inferior. II. The Modus Tollendo Ponens. First Case. The ancients were in genius either superior to the moderns, or inferior, or equal ; Noiv the ancients were not inferior ; Therefore, the ancients icere either superior or equal. Second Case. The ancients icere in genius either superior to the moderns, or inferior, or equal ; Now the ancients were neitJier inferior nor equal; Therefore, the ancients were superior. LECTURES ON LOGIC. 331 Such is a general view of its procedure. Now, 2°, lect. . XVII for its principle. " If the essential character of the Disjunctive Syllo- cipieonue' gism consist in this, — that the affirmation or negation, syllogism.^ or, what is a better expression, the position or subla- tion, of one or other of two contradictory attributes follows from the subsumption of the opposite ; — there is necessarily implied in the disjunctive process, that, when of two opposite predicates the one is posited or affirmed, the other is sublated or denied; and that, when the one is sublated or denied, the other is posited or affirmed. But the proposition, — that of two repugnant attributes, the one being posited, the other must be sublated, and the one being sublated, the other must be posited, — is at once manifestly the law by which the disjunctive syllogism is governed, and manifestly only an application of the law of Ex- cluded Middle. For the Modus ponendo toUens there is the special rule, — If the one character be posited, the other character is sublated ; and for the Modus tollendo ponens there is the special rule, — If the one character be sublated, the other character is posited. The law of the disjunctive syllogism is here enounced, only in reference to the case in which the members of disjunction are contradictorily opposed. An oppo- sition of contrariety is not of purely logical concern- ment; and a disjunctive syllogism with characters opposed in contrariety, in fact, consists of as many pure disjunctive syllogisms as there are opposing pre- dicates." "" 3°. I now go on to the third and last matter of 3°.Theseve- consideration, — the several parts of a Disjunctive Disjunctive O 11 • Syllogism. ISyllogism. a Esscr, Lo(jik, § 94. — Ed. 332 i.ixTi'UKs ON Loaio. i.Krr. •• 'The (iiicstion toiiccrniiiL!" tlu' s])0('ial laws of a dis- juiictivo svlloij,isin, (tr, what is the same thing, what is the «,)rii;iiial and iieeessary form of a disjunctive syllogism, as tletermined by its general j)rincij»Ie or law, — this cjuestion may be asked, not only in rcfer- eiiee to the whole syllogism, but likewise in reference to its several parts. The original and necessary form of a disjunctive syllogism consists, as we have seen, in the reciprocal position or sublation of contradic- tory characters, by the subsumption of one or other. Hence it follows, that the disjunctive syllogism must, like the categorical, involve a threefold judgment — viz. 1°, A judgment in which a subject is determined by two contradictory predicates ; 2°, A judgment in which one or other of the opposite predicates is sub- sumed, that is, is afhrmed, either as existent or non- existent ; and, 3°, A judgment in which the final decision is enounced concerning the existence or non- existence of one of the repugnant or reciprocally ex- clusive predicates. But in these three propositions, as in the three propositions of a categorical syllogism, there can only be three principal notions — viz. the notion of a subject, and the notion of two contradic- tory attributes, which are generally enounced in the sumption, and of which one is posited or sublated in the subsumption, in order that in the conclusion the other may be sublated or posited. The case of contrary opposition is, as we have seen, easily re- conciled and reduced to that of contradictory oppo- sition." " The laws of the several parts of a disjunctive syllogism, or more properly the original and necessary form of these several parts, are given in the following paragraph : — a Esser, Lojik, § 95. — Ed. >junc- gism. LECTURES ON LOGIC. 333 If LXIV. — 1°, A regular cand perfect Disjunc- lect. tive Syllogism must have three propositions, in ^^^ ^^j^ which, if the sumption be simple and the disjunc- The laws of ' i . . , . the Disjunc- tion purely logical, only three principal notions tive Syiio can be found. 2°, The Sumption, in relation to its quantity and quality, is always uniform, being Universal and Affirmative ; but the Subsumption is suscep- tible of various forms in both relations. 3°, The Conclusion corresponds in quantity with the subsumption, and is opposed to it in quality." The first rule is, — A regular and perfect disjunctive Expiica- syllogism must have three propositions, in which, if First Rule, the sumption be simple and the disjunction purely logical, only three principal notions can be found. " Like the categorical syllogism, the disjunctive con- sists of a sumption, constituting the general rule ; of a subsumption, containing its application ; and of a conclusion, expressing the judgment inferred. Dis- junctive syllogisms are, therefore, true and genuine reasonings ; and if in the sumption the disjunction be contradictory, there are in the syllogism only three principal notions. In the case of contrary disjunc- tions, there may, indeed, appear a greater number of notions; but as such syllogisms are in reality composite, and are made up of a plurality of syllo- gisms with a contradictory disjunction, this objection to the truth of the rule is as little valid as the cir- cumstance, that the subject in the sumption is some- times twofold, threefold, fourfold, or manifold ; as, for example, in the sumption — Jolm, James, Thomas, are a Esser, I. e. Krug, Lo(jik, § 8G. — Ed. 384 LECTUHKS ON LOOTC. i.EcT. either n'rtuoiis or ricions. For tliis is a c'()i)iilative ^^"' proposition, which is composed of tlirec simple pro- positions — viz., John is, &c. If, tlierefore, there be such a sumjition at the liead of a disjunctive syllogism, it is in this case, likewise, composite, and may be analysed into as many simple syllogisms with three principal notions, as there are simple propositions into which the sumption may be resolved."" Socona The second rule is, — The sumption is, in relation to its quantity and quality, always uniform, — being universal and affirmative ; but the subsumption is susceptible of different forms in botli relations. If we look, indeed, to the subject alone, it may seem to be possiljly equally general or particular ; for we can equally say of some as of all A that they are either B or C. But as all universality is relative, and as the sumption is always more extensive or more compre- hensive than the subsumption, it is thus true that the sumption is ahvays general. Again, looking to the predicate, or, as it is complex, to the predicates alone, they, as exclusive of each other, appear to involve a negation. But in looking at the whole proposition, that is, at the subject, the cojoula, and the predicates in connection, we see at once that the copula is affirmative, for the negation involved in the predicates is confined to that term alone. ^^ Third Rule. In regard to the third rule, which enounces, — That the conclusion should have the same c[uantity with the subsumption, but an opposite quality, — it is requisite a Krvig, Logilc, I. c. — Ed. G7G.] [" Propositio Disjimctivanul- $ See Krug, Logik, § 86, Anm. 2. lam habet quantitatem nisi suarum — Ed. [Bachmann, Logik, § 141, p. partium . . . sicut Propositio 354. Contra ;— Twesten, Logik, § Hypothctica habet tantum quanti- 1.37, ed. 1825, p. 119. Esser, Logik, tatem suarum pai-tium." See above, § 95. Derodon, Logica licstituta, p. j). 247, and ji. 248, note a. — Ed.] LECTURES ON LOGIC. 335 to say nothing, as the first clause is only a special lect. application of the rule common to all syllogisms that — the conclusion can contain nothing more than the premises, and must, therefore, follow the weaker part ; and the second is self-evident, as only a special appli- cation of the principle of Excluded Middle, for, on this laAV, if one contradictory be affirmed in the subsump- tion, the other must be denied in the conclusion, and if one contradictory be denied in the subsumption, the other must be affirmed in the conclusion. The Disjunctive, like every other species of syllo- The pis- gism, may be either a reasoning in the quantity of syiiogbm Comprehension, or a reasoning in the quantity of Ex- hensiou and tension. The contrast, however, of these two quan- tities is not manifested in the same signal manner in the disjunctive as in the categorical deductive syllo- gism, more especially of the first figure. In the cate- gorical deductive syllogism, the reasonings in the two counter quantities are obtrusively distinguished by a complete conversion, not only of the internal signifi- cance, but of the external appearance of the syllogism. For not only do the relative terms change places in the relation of whole and part, but the consecution of the antecedents is reversed ; the minor premise in the one syllogism becoming the major premise in the other. This, however, is not the case in disjunctive syllogisms. Here the same proposition is, in both c[uantities, always the major premise ; and the whole change that takes place in converting a disjunctive syllogism of the one quantity into a disjunctive syllo- gism of the other, is in the silent reversal of the copula from one of its meanings to another. This, however, as it determines no apparent difference in single pro- positions, and as the disjunctive sumption remains 336 LECTURES ON LOOIC. Lv.cT. always the saiuo ]>ropositii)ii, out of wliicli the sub- -^^■•'- ' • 111- , 1 . . sumptum and the conclusion avo evolved, in the one quantity as in the other, — the reversal of the sump- tion, from extension to comprehension, or from com- prehension to extension, occasions neither a real nor Kx:uni.us. an apparent change in the syllogism. Take, for ex- ample, the disjunctive syllogism : — Plato is either learned or unlearned ; But Plato is learned ; Tlierefore, Plato is not unlearned. Now let us explicate this into an intensive and into an extensive syllogism. As an Intensive Syllogism it will stand : — Plato compreJiends either the attribute learned or the attrihnte unlearned ; But Plato comprehends the attribute learned; Therefore, ^c. As an Extensive Syllogism it will stand : — Plato is contained either under the class learned, or under the class unlearned ; But Plato is contained under the class learned ; Tlierefore, Sfc. From this it appears, that, though the difference of reasoning in the several quantities of comprehension and extension obtains in disjunctive, as in all other syllogisms, it does not, in the disjunctive syllogism, determine the same remarkable change in the external construction and consecution of the parts, which it does in categorical syllogisms. LECTURES ON LOGIC. 337 LECTURE XVIII. STOICHEIOLOGY. SECT. IL — OF THE PKODUCTS OF THOUGHT. ITI. DOCTRINE OF REASONINGS. SYLLOGISMS. — THEIR DIVISIONS ACCORDING TO INTERNAL FORM. B. CONDITIONAL. — HYPOTHETICAL AND HYPOTHETICO- DISJUNCTIVE. Having now considered Catesforical and Disjunctive lect. XVIII Syllogisms, the next class of Reasonings afforded by L the difference of Internal or Essential Form is the Hypothetical ; and the general nature of these syllo- gisms is expressed in the following paragraph : — ^ LXV. An Hypothetical Syllogism is a rea- Par. lxv. soning whose form is determined by the law of ticai syiio- Reason and Consequent. It is, therefore, regu- general lated by the two principles of which that law is the complement, — the one, — With the reason, the consequent is aiiirmed ; the other, — With the consequent, the reason is denied : and these two principles severally afford the condition of its Af- firmative or Constructive, and of its Negative or Destructive, form {Modus ponens et Modus tol- lens). The sumption or general rule in such a syllogism is necessarily an hypothetical proposi- tion {If A is, then B is). In such a proposition VOL. I. Y ooS LECrrUKS ON LOGIC. LECT. it is nu'U'ly oiiouiuihI tluit the luior member (A) will. . .1 L niul llu' posterior meniher (B) stand to eacli other in the rehitiou of reason and consequent, if cxist- m(i, but "without it bein^: determined whether they really exist or not. Such determination must follow in the subsumption and conclusion ; and that, either by the absolute affirmation of the antecedent in the subsumption, and the illative affirmation of the consequent in the conclusion (the modus 2^onens); or by the absolute negation of the consequent in the subsumption, and the illa- tive negation of the antecedent in the conclusion (the modus tollens)."' The general form of an hypo- thetical syllogism^ is, therefore, the following: — Common Sumption — If A is, then B is ; 1 2 J., w, Modus Poxens : IModus Tollens : But A is ; But B is not ; TJierefore, B is. Therefore, A is not. Or, A B 1) Modus Ponens — Si x>oteris possum ; sed tujjotes; ergo ego possum. B A 2) Modus Tollens — Si j^oteris 2)ossum ; nonjwssum ; nec2Jofesergo.y Expiica- In illustrating this paragraph, I shall consider, 1°, This species of syllogism in general ; 2°, Its peculiar principle ; and, 3°, Its special laws. [a For use of terms poncTis and 23, f. 60, Venet., 1536; Magentinus, tollens, nee Boethius, De Sijllogismo In Anal. Prior., i. 16 b; Alex. Hypothetico, Opera, p. 611; Wolf, Aphrodisiensis, In Anal. Prior., S. Phil. Rat, § 406-410. Mark Dun- 87, 88, 109, 130, Aid., 1520; In To- can uses the terms "a positione ad pica, f. 65, Aid., 1513; Anonymous position em," and "a remotione ad Author, On SyUoyiums, f. 44, ed. remotionem."] [Instltutioncs Loyica;, 1536; Scheibler, Opera Logica, pars L. iv. c. 6, § 4, p. 240. Cf. p. 243, iv. p. 548 ; Bolzano, Wisscnschafts- Salmurii, 1812.— Ed.] lehre, Logik, ii. p. 560; Waitz, Or- P [On the Hypothetical Syllogism yanon. In An. Prior., i. c. 23.] in general, see Ammonias, In de In- y These lines are the Author's tcrp., Procem., f. 3, Venetiis, 1540; own. — Ed. Philoi)onus, In Anal. Prior., i. c. tion LECTURES ON LOGIC. 339 1°, " Like every other species of simple syllogism lect. the Hypothetical is made up of three propositions, — '^^"^' a sumption, a subsumption, and a conclusion. There £tSTs i must, in the first place, be an hypothetical proposition Ipf^g^^j''' holdinor the place of a general rule, and from this pro- Contains <~> 1- o ' L three propo- position the other parts of the syllogism must be de- ^'^^°'''- duced. This first proposition, therefore, contains a sumption. But as this proposition contains a relative and correlative member, — one member, the relative clause, enouncing a thing as conditioning ; the other, the correlative clause, enouncing a thing as condi- tioned ; and as the whole proposition enounces merely the dependency between these relatives, and judges nothing in regard to their existence considered apart and in themselves, — this enouncement must be made in a second proposition, which shall take out of the sumption one or other of its relatives, and categori- cally enounce its existence or its non-existence. This second proposition contains, therefore, a subsumption ; and, through this subsumption, a judgment is likewise determined, in a third proposition, with regard to the other relative. This last proposition, therefore, con- tains the conclusion proper of the syllogism. "But as the sumption in an hypothetical syllogism in an hypo- contains two relative clauses, — an antecedent and aiogL'mthere consequent, — it, therefore, appears double ; and as a twofow^'^* either of its two members may be taken in the sub- reasoning, sumption, there is, consequently, competent a twofold dmpmc'ns kind of reasoning. For we can either, in the first place, ^oiielT^'^'^ conclude from the truth of the antecedent to the truth of the consequent ; or, in the second place, conclude from the falsehood of the consequent to the falsehood of the antecedent. The former of these modes of hypo- thetical inference constitutes what is sometimes called 'MO i.KcrntKs on looio. LV.vr. the Coiw^tntcticc JIi/po(In-(ica(, but more properly the J L Moihts Poncih'i : — the hitter what is sometimes called the DcstructiiH' Ili/pothetical, hut more properly the ^[o^hls 7'()//('/Ks\"" As examples of the two modes : — Modus PoiuMis — 1/ Socniti'ii he tu'rfiioiis, he vierifs csfoem ; But Socratea is virtuous ; Therefure, he merits esteem. >roilus Tollons — // Socrdtcs he virtuous, he merits esteem ; But Socrates does not merit esteem ; Therefore, he is not virttious.fi So much for the character of the Hypothetical Syl- logism in general. I now proceed to consider its peculiar principle. 2°, itspocu- 2", " If the essential nature of an Hypothetical cipkN-"he Syllogism consist in this, — that the subsumption son and *"" affimis or denies one or other of the two parts of a onsequcnt. ^|j^Q^^g|^^^ Standing to each other in the relation of the thing conditioning and the thing conditioned, it will be the law of an hypothetical S3dlogism, that, — If the condition or antecedent be affirmed, so also must be the conditioned or consequent, and if the condi- tioned or consequent be denied, so likewise must be the condition or antecedent. But this is manifestly a Knig, Logik, § 81, Anm. 1, p. Yiere, If ithe day, \s cdX[e^\rhT)yov- 254. Compare Esser, Logik, § 90, nevov, both by Peri])atetics and by p_ 172. — Ed. Stoics; the sun is on the earth, is $ [Nomenclature of Theophrastiis, called rh tiroixevovhy Peripatetics, rh Eudemus, and other Peripatetics, in Kriyov by Stoics. The whole, If it he regard to Hyjiothetical Syllogism, in day, the siin is on the earth, is called contrast with that of the Stoics. rh aw-qfjLuivov by Peripatetics, tJi Tlpa-yixara, vovfjiara, cpuval (Peri- rpo-rriKuv by Stoics : But it is day, is patetic), arc called by the Stoics ij.{Td\Ti\f/ts to Peripatetics, Trp6(T\T)\pts respectively, rvyx(i''oi'ra, iK(popiKa., to Stoics. Tlureforc the sun is on A€KTo. the earth is o-uyUTrepao-yua to Peripate- Take this Hypothetical Syllo- tics, eiTi mi^ht be determined by many othei- reasons than A." ° For example : — If there are sharjurs in the company we omjlit not to ijamhic ; lint there are no sharpers in the company; Therefore^ we ought to (jamhle. Here the conclusion is as false as if we conversely in- ferred, that because lue ought not to gamble, there are sharjfcrs in the room. Conversion " Logicians have given themselves a world of j)ains thcticai to in the discovery of general rules for the conversion Syiio^sms, of Hypothetical Syllogisms into Categorical.'^ But, in neccslar)-. thc first placc, this is unnecessary, in so far as it is applied to manifest the validity of an lijqoothetical syllogism ; for the hypothetical syllogism manifests its own validity with an evidence not less obtrusive than does the categorical, and, therefore, it stands in no need of a reduction to any higher form, as if it were of this a one-sided and accidental modification. With equal propriety might we inquire, how a cate- gorical syllogism is to be converted into an hypo- 2°, Not thetical. In the second place, this conversion is not possible, always possible, and, therefore, it is never necessary. In cases where the sumption of an hypothetical syllo- gism contains only three notions, and where of these three notions one stands to the other two in the o Krug, Lofjiky § 82, p. 256. — wetter, AU'jemeine Logik, i. § 239, Ed. p. 115; Esser, Logik, §§ 99, 100. P [For the reduction of Hypothe- Against, see Krug, Logik, p. 356, ticals, see Wolf, P/a7os. ^a<., § 412; and Lexikon, iii. p. 559; Fries, Reusch, Systema Logicum, § 563 ; Logik, § 62, p. 207 ; Baclimann, Molinteus, Elcmenta Logica, L. L Logik, % 89, AjiTa.2; (Inpart), Aris- tract, iii. c. 1, p. 95; Keckermann, totle, Anal. Prior., L. i. c. 44, p. Opera, t. i. pp. 266, 767 ; Crellius, 274, ed. Pacii ; (In part), Pacius, In Isagoge, L. iii. c. 17, p. 243 ; Kiese- Arist. Organon, he. cit, p. 194.] XVIII. LECTUEES ON LOGIC. 343 relation of a middle term, — in these cases, an liypo- lect thetical syllogism may without difficulty be reduced to a categorical. Thus, when the formula. If K is, then B is, signifies, If A. is C, then A is also B, — that is, A is B, inasmuch as it is C, — in this case the categorical form is to be viewed as the original, and the hypothetical as the derivative."" For ex- ample : — If Caius he a man, then he is mortal; Bui Caius is a man ; Therefore, he is mortal. Here the notion man is regarded as comprehending in it, or as contained under, the notion mortal; and as being comprehended in, or as containing under it, the notion Caius: it can, therefore, serve as middle term in the categorical syllogism to connect the two notions Caius and mortal. Thus : — Man is mortal ; Caius is man ; Therefore, Caius is mortal. " In such cases it requires only to discover the middle term, in order to reduce the hypothetical syllogism to a categorical form ; and no rules are requisite for those who comprehend the nature of the two kinds of reasoning. " But in those cases where the sumption of an hypothetical syllogism contains more than three notions, so that the formula. If A is, then B is, signifies, If A. is C, then is B also D, — in such cases an easy and direct conversion is impossible, as a categorical syllogism admits of only three principal notions. To accomplish a reduction at all, we must make a circuit through a plurality of categorical syl- a King, Loijik, p. 258, Anm. 3. — Ed. 344 LECTLIRKS ON LOCIC. i,K(*r. lorrisms boforo we can arrive at an identical con- — '- elusion, — a process whicli, so far from lendinsi; to simplify ami explain, eoncliiees only to perplex ami ohseure." Hvpotheti- " On the other hand, we can always easily convert pisms of au hypothetical syllogism of one form into another, — casiivc.n- tlic modus 2^07ipect ; If the sun he not risen, it is not day. But here the proposition, as an hypo- thetical judgment, is and must be affirmative. For the affirmative in such a judgment is contained in the positive assertion of the dependence of consequent or antecedent; and if such a dependence be not affirmed, an hypothetical judgment cannot exist. In regard to what is stated in the rule concerning The sub- the conditions of the subsumption, — that this may ^'^'"'' '""" either be general or particular, affirmative or nega- tive, — it will not be requisite to say anything in illus- tration. For, as the subsumption is merely an abso- lute assertion of a single member of the sumption, and as such member may, as an isolated proposition, be of any quantity or any quality, it follows, that the sub- sumption is equally unlimited. In reference to the third rule, which states that the Third RuIo. conclusion is regulated in quantity and quality by that member of the sumption which is not subsumed, and this in modo ponente by congruence, 171 modo tollente by opposition, it will not be requisite to say much. " In the conclusion, the latter clause of the sump- tion is affirmed in modo pone7ite, because the former is affirmed in the subsumption. In this case, the conclusion has the same quantity and quality as tlie 350 LECTURES ON LOGIC. LF.CT. clause wliicli it affirms. In modo tollente the antc- L cciJi'ut of the sumptiou is denied in the conclusion; because in the subsumption the consequent clause had been denied. There thus emerges an opposition be- tween that clause as denied in the conclusion, and that clause as affirmed in the sumption. The conclu- sion is thus always opposed to the antecedent of the sumption in quantity, or in quality, or in both together, according as this is differently determined by the differ- ent constitution of the propositions. For example : — If some men zce)'e omniscient, tlien would tliey he as Gods ; But no man is a God ; Therefore, some men are not omniscient, that is, no man is omniscient."'^ 3. Hypothc- I now proceed to the consideration of the last class jun"ctiveor of syllogisms affordcd by the Internal Form, — the SyiiJ^ms. class of Dilemmatic or Hypothetico-disjunctive Syl- logisms, and I comprise a general enunciation of their nature in the following paragraph. Par. LXviL % LXVII. If tlic sumption of a syllosfism be at Hvpothe- , -■■. . . "^ ^ . . , tico-disjunc- once hypothetical and disiunctive, and if in the live Syllo- '' ^ , y . . ' ^'ismor subsumptiou the whole disjunction, as a conse- quent, be sublated, in order to sublate the ante- cedent in the conclusion ; — such a reasoning is called an Hypothetico-disjunctive Syllogism, or a Dilemma. The form of this syllogism is the following : — //' A exist, then either B or C exists ; But neither B nor C exists ; Therefore, A does not exist. a Krug, Logik, § 83, p. 265.— Ed. 19, p. 218. Cf. Fries, Logik, § 60, p. fi Krug, Lor/ik, § 87. — Ed. [Con- 257 ; Alclrich, Eudimenta Lor/icce, c. tra, see Troxler, Logik, ii. p. 103 n*. iv. § 3, p. 107, Oxford, 1852 ; Plat- That the Dilemma is a negative in- ner, PliUosoplmche Ajihurismcn, i. § duction, see Wallis, Logica, L. iii. c. 583, p. 280. ] Dilemma. LECTURES ON LOGIC. 351 We have formerly seen, that an hypothetical may lect. be combined with a disjunctive judgment ; and if a '. proposition of such a character be placed at the head ^on,''*^*" of a reasoning, we have the Hypothetico-disjunctive Syllogism or Dilemma. This reasoning is properly an hypothetical syllogism, in which the relation of the antecedent to the consequent is not absolutely affirm- ed, but affirmed through opposite and reciprocally ex- clusive predicates. If A exist, then either B or C exists. The sumption is thus at once hypothetical and disjunctive. The subsumption then denies the disjunctive members contained in the consequent or posterior clause of the sumption. But neither B nor C exists. And then the inference is drawn in the con- clusion, that the reason given in the antecedent or prior clause of the sumption must likewise be denied. Therefore A does not exist."' For example : — If man be not a morally responsible being, he must wa7it either the power of recognising moral good (as an intelligent agent), or the power of rvilling it (as a free agent) ; But man luants neither the poiver ofrecognis-ing moral good (as an intelligent agent), nor the potoer of loilling it (as a free agent); Therefore, man is a moi'ally responsible being. "An hypothetico-disjunctive syllogism is called the Designa- dilemma or homed syllogism in the broader accep- Hypotiietl tation of the term [dilemma, ceratinus, cornutus sc. trve's^o- syllogismus). We must not, however, confound the^'^"' cor7iutus and erocodilinus of the ancients with our hypothetico-disjunctive syllogism. The former were sophisms of a particular kind, which we are hereafter to consider; the latter is a regular and legitimate form of reasoning. In regard to the application of the terms, it is called the cornutus or horned syllogism, a Krug, loc. cit. — Ed. 352 LECTUllES ON LOO 10. LKtT. because in the sumption the disjunctive members of the consequent are opposed like liorus to the assertion Dilemma. of the adversary ; with these we tlirow it from one side to the other in the subsumption ; in order to toss it altogether away in the conclusion. If the disjunc- tion has only two members, the syllogism is then called a dilemma {hicornis) in the strict and proper signification, literally double sumption. Of this the example previously given is an instance. If it has three, four, or five members, it is called trilemma {tri- cornis), tetralemma [quadricornis), pentalemma {quin- quecornis) ; if more than four, it is, however, usually called 2^oli/le7nma {inulticornis). But, in the looser signification of the word, Dilemma is a generic ex- pression for all or any of these." * Rules for " Considcrcd in itself, the hypothetico-disjunctive projllfsea syllogism is not to be rejected, for in this form of reasoning we can conclude with cogency, provided we attend to the laws already given in regard to the hypothetical and disjunctive syllogisms. It is not, however, to be denied, that this kind of syllogism is very easily abused for the purpose of deceiving, through a treacherous appearance of solidity, and from terrifying a timorous adversary by its horned aspect. In the sifting of a proposed dilemma, we ought, therefore, to look closely at the three following particulars: — 1°, Whether a veritable consequence subsists between the antecedent and consequent of the sumption ; 2°, Whether the opposition in the consequent is thorough-going and valid ; and, 3°, Whether in the subsumption the disjunctive mem- bers are legitimately sublated. For the example of o Krug, he. cU. Antn. 2.— Ed. 268, 7G9.] [Cf. Keckermann, Opera, t. i. pj). LECTURES ON LOGIC. 353 a dilemma which violates these conditions, take the lect. ^ ,, . xvin. lollowing : — • If virtue were a habit worth acquiring, it must insure either lioioer, or wealth, or honour, or pleasure ; But virtue insures none of these ; Therefore, virtue is not a habit wort?i attaining. " Here : — 1°. The inference in general is invalid ; for a thing may be worth acquiring though it does not secure any of those advantages enumerated. 2°. The disjunction is incomplete ; for there are other goods which virtue insures, though it may not insure those here opposed. 3°. The subsumption is also vicious ; for virtue has frequently obtained for its possessors the very advantages here denied." ** Before leaving this subject, it may be proper to The whole make two observations. The first of these is, that cai laws,— though it has been stated that Categorical Syllogisms contradi'c- are governed by the laws of Identity and Contradic- eluded tion, that Disjunctive Syllogisms are governed by the and Reason law of Excluded Middle, and that Hypothetical Syllo- queut,— are gisms are governed by the law of Reason and Conse- each' form quent, — this statement is not, however, to be under- " *^ *'^'^™* stood as if, in these several classes of syllogism, no other law were to be found in operation, except that by which their peculiar form is determined. Such a supposition would be altogether erroneous, for in all of these different kinds of syllogism, besides the law by which each class is principally regulated, and from which it obtains its distinctive character, all the others contribute, though in a less obtrusive manner, to allow and to necessitate the process. Thus, though the laws This iiius- of Identity and Contradiction are the laws which pre- l'^iu cate- eminently regulate the Categorical Syllogism, — still fogisms.' ^ ' o Krug, Logih, § 87, Anm. 3, p. 281.— Ed. VOL. I. Z 354 i.KcTUUiN ON Lonu'. LECT. without tlir hnvs of Excliulcd Middle, and Reason and J L Consequent, all inference in these syllogisms would be inipossiMe. Thus, thouoh the law of Identity ailbrds the basis of all atiirmativc, and the law of Contradic- tion the basis of all negative, syllogisms, still it is the law of Excluded Middle which legitimates the impli- cation, that, besides afhrmation and negation, there is no other possible quality of predication. In like manner, no inference in categorical reasoning could be drawn, were we to exclude the determination of Reason and Consequent. For we only, in deductive reasoning, conclude of a part what we assume of a whole, inasmuch as we think the whole as the reason — the condition — the antecedent — by which the part, as a consequent, is determined ; and we only, in induc- tive reasoning, conclude of the whole what we assume of all the parts, inasmuch as we think all the parts as the reason — the condition — the antecedent — by which The law of the wholc, as a consequent, is determined. In point mam'tL*"^' of fact, logically or formally, the law of Identity and tharorRea- tlic law of Rcasou and Consequent in its affirmative Coii^qucnt. form, are at bottom the same ; the law of Identity constitutes only the law of Reason and Consequent, — the two relatives being conceived simultaneously, that is, as subject and predicate; the law of Reason and Consequent constitutes only the law of Identity, the two relatives being conceived in sequence, that is, as antecedent and consequent." And as the law of Reason and Consequent, in its positive form, is only that of Identity in movement ; so, in its negative form, it is only that of Contradiction in movement. In Disjunctive Syllogisms, again, though the law of o [Compare Koppen, Darstellung c< scg., Niimberg, 1810.] dfs Wesens der Philosophic, p. 102 LECTURES ON LOGIC. 355 Excluded Middle be the principle which bestows on lect. ^ ^ xvni. 2. In Dis- them their peculiar form, still these syllogisms are not independent of the laws of Identity, of Contradiction, jtnctivj and of Eeason and Consequent. The law of Excluded sy»«gi^'"«- Middle cannot be conceived apart from the laws of Identity and Contradiction ; these it implies, and, without the principle of Reason and Consequent, no movement from the condition to the conditioned, that is, from the affirmation or negation of one contradic- tory to the affirmation or negation of the other, would be possible. Finally, in Hypothetical Syllogisms, though the law 3. in Hypo- of Reason and Consequent be the prominent and dis- logisms. tinctive principle, still the laws of Identity, Contra- diction, and Excluded Middle are also there at work. The law of Identity affords the condition of Affirma- tive or Constructive, and the law of Contradiction of Negative or Destructive, Hypotheticals ; while the law of Excluded Middle limits the reasoning to these two modes alone. The second observation I have to make, is one sug- Difficulty in gested by a difficulty which has been proposed to me the'doctrine, in regard to the doctrine, that all reasoning is either reasoning from whole to part, or from the parts to the whole. The from whole difficulty, which could only have presented itself to from the an acute and observant intellect, it gave me much wLL,— ' satisfaction to hear proposed ; and I shall have still greater gratification, if I should be able to remove it, by showing in what sense the doctrine advanced is to be understood. It was to this effect : — In Categorical Syllogisms, deductive and inductive, intensive and extensive, the reasoning is manifestly from whole to part, or from the parts to the whole, and, therefore, in regard to the doctrine in question, as relative to 356 LECTURES ON LOGIC. i.K.cr. catcntM-ical n'asonino-, llicn' \vas no (lilliculty. But J. L this was not tlio caso in ni:;arcl to llypotlictical Syllo- gisms. Those are governed by the law of Reason and Consequent, and it does not appear how the antcce- dtMit and conse(]uent stand to each other in the rela- tion of whole and part. Thisdiffi- III showing how the reason and the consequent arc siIiom7Tvitii to be viewed as whole and part, it is necessary, first, to nvpotho'ti- repeat, that the reason or antecedent means the con- pisms. ' didou, that is, the complement of all without which nu'a couso- something else would not be ; and the consequent 2^3 tT means the couditioncd, that is, the complement of all am" Cou" that is determined to be by the existence of something diiiouiM. ^jg^^ Yqu must further bear in mind, that we have nothing to do with things standing in the relation of reason and consequent, except in so far as they are thought to stand in that relation ; it is with the ratio cognoscendi, not with the 7^atio essendi, that we have to do in Logic ; the former is, in fact, alone properly denominated reason and consequent, while the latter ought to be distinguished as ca,use and effect. The ratio essendi, or the law of Cause and Effect, can indeed only be thought under the form of the ratio cognoscendi, or of the principle of Reason and Conse- quent ; but as the two are not convertible, inasmuch as the one is far more extensive than the other, it is proper to distinguish them, and, therefore, it is to be recollected that Logic is alone conversant with the ratio cognoscendi, or the law of Reason and Conse- (pient, as alone conversant with the form of thought. This beinfj understood, if the reason be conceived as that which conditions, in other words, as that which contains the necessity of the existence of the conse- quent, it is evident that it is conceived as containing Hence the reason or condition unist con- tain the consequent LECTUEES ON LOGIC. 357 tlie consequent. For, in the first place, a reason is lect. . . , . ... XVIII. only a reason if it be a sufficient reason, that is, if it 1- comprise all the conditions, that is, all that necessitates the existence, of the consequent ; for if all the con- ditions of anything are present, that thing must neces- sarily exist, since, if it do not exist, then some con- dition of its existence must have been wantins^, that is, there was not a sufficient reason of its existence, which is contrary to the supposition. In the second place, if the reason, the sufficient reason, be conceived as comprising all the conditions of the existence of the consequent, it must be conceived as comprising the consequent altogether ; for if the consequent be supposed to contain in it any one part not conceived as contained in the reason, it may contain two, three, or any number of parts equally uncontained in the reason, consequently it may be conceived as altogether uncontained in the reason. But this is to suppose, that it has no reason, or that it is not a consequent ; which again is contrary to the hypothesis. The law The Law of of Eeason and Consequent, or of the Condition and the con'equrat Conditioned, is only in fact another expression ofexp^Sn" Aristotle's law, — that the whole is necessarily con- totie's kw, ceived as prior to the part — totum parte 'prius esse, thoie is necesse est."" It is, however, more accurate; for conceived^ Aristotle's law is either inaccurate or ambiguous. thJparV" Inaccurate, for it is no more true to say, that the Aristotle's •' law criti- whole is necessarily prior in the order of thought to ^iscd. a Metaphysics, iv. 11. Aristotle, the whole might be destroyed as a however, allows a double relation, system without the destruction of The whole, when conceived as actu- the parts. Where the whole is not ally constituted, must be regarded conceived as actually constituted, as prior to the parts ; for the latter this relation is reversed. Thus Aris- only exist as i)arts in relation to the totle's rule may be regarded as co- whole. Potentially, however, the extensive with that given in the parts may be regarded as prior ; for text. See the next note. — Ed. 358 LECTUKKS OX LOCIC. i.KCT. the });irts, tlian to say that the itarls ai'O iieccssaiily will • — '- }>rior ill the order of tlioiiglit to the whole. Whole and j>arts are rehitives, and as sueli arc necessarily wiu.ionu.i coexistent in thought. But while each implies the jp.vriviiy other, and the notion of each necessitates the notion v'ov.a in of the other, we may, it is evident, view either, in i-itWr'asti.o thouoht, as the conditioning or antecedent, or as the cinulitioumi; t , • t , riii . i i l or as the couditioucd or conscqucnt. ihus, on the one hand, louti . ^^_^ ^^^^^^ regard the whole as the prior and determining notion, as containing the parts, and the parts, as the posterior and determined notion, as contained by the whole. On the other hand, we may regard the parts as the prior and determining notion, as constituting the whole, and the whole as the posterior and deter- mined notion, as constituted by the parts." In the former case, the whole is thought as the reason, the parts are thought as the consequent ; in the latter, the parts are thought as the reason, the whole is thought as the consequent. Now in so far as the whole is thought as the reason, there will be no difficulty in admitting that the reason is conceived, as containing the parts. But it may be asked, how can the parts, when thought as the reason, be said to contain the whole ? To this the answer is easy. All the parts contain the whole, just as much as the whole contains all the parts. Objectively considered, the whole does not contain all the parts, nor do all the parts contain the whole, for the whole and all the parts are precisely equivalent, absolutely identical. But, subjectively o This is substantially expressed parts are only potentially, existent; by Aristotle, /. c, whose distinction while, on the other hand, Kara is applicable either to the order of (pBopdv {i.e., regarded as disorgan- thoiight or to that of existence. Kara ised elements), the parts exist ac- yivi(nv (I. e. , regarded as a complete tually, the whole only potentially, system), the whole is actually, the — Ed. LECTURES ON LOGIC. 359 considered, that is, as mere thouojhts, we may cither lect. o ^ J XVIII. think the whole by all the parts, or think all the parts - by the whole. If we think all the parts by the whole, we subordinate the notion of the parts to the notion of the whole ; that is, we conceive the parts to exist, as we conceive their existence given through the existence of the whole containing them. If we think the whole by all the pg-rts, we subordinate the notion of the whole to the notion of the parts ; that is, we conceive the whole to exist, as we conceive its existence given through the existence of the parts which constitute it. Now, in the one case, we think the whole as con- ditioning or comprising the parts, in the other, the parts as conditioning or comprising the whole. In the former case, the parts are thought to exist, because their whole exists ; in the latter, the whole is thought to exist, because its parts exist. In either case, the prior or determining notion is thought to comprise or to contain the posterior or determined. To apply Application this doctrine : — On the one hand, every science is true, trine'to the only as all its several rules are true ; in this instance thJaifficuity the science is conceived as the determined notion, stated."' ^ that is, as contained in the aggregate of its constituent rules. On the other hand, each rule of any science is true, only as the science itself is true ; in this instance the rule is conceived as the determined notion, that is, as contained in the whole science. Thus, every single syllogism obtains its logical legitimacy, because it is a consequent of the doctrine of syllogism ; the latter is, therefore, the reason of each several syllogism, and the whole science of Logic is abolished, if each several syllogism, conformed to this doctrine, be not valid. On the other hand, the science of Logic, as a whole, is only necessary inasmuch as its complementary will oOO LECTrKKS ON LOCIC. i.Ki'T. Ji)etriiies are lu'cessaiy ; tiiul these are only necessary inasmuch as their individual applications are neces- sary ; it" Lt>gic, therefore, as a whole be not necessary, the necessity of the parts, which constitute, determine, and comprehend that whole, is subverted. In one relation, therefore, reason and consequent are as tlie whole and a contained part, in another, as all the parts and the constituted or comprised whole.. But in both relations, the reason, — the determining notion, is thought as involving in it the existence of the conse- quent or determined notion. Thus, in one point of view, the genus is the determining notion, or reason, out of which are evolved, as consequents, the species and individual ; in another, the individual is the deter- mining notion or reason, out of which, as consequents, are evolved the species and genus." In like manner, if we regard the subject as that in which the attri- butes inhere, in this view the subject is the reason, that is, the whole, of which the attributes are a part ; whereas if we regard the attributes as the modes through which alone the subject can exist, in this view the attributes are the reason, that is, the whole, of which the subject is a part. In a word, whatever we think as conditioned, we think as contained by something else, that is, either as a part, or as a con- stituted whole ; whatever we think as conditioning, we think either as a containing whole, or as a sum of constituting parts. What, therefore, the sumption of an hypothetical syllogism denotes, is simply this : — If iV, a notion conceived as conditioning, and, there- fore, as involving B, exist, then B also is necessarily conceived to exist, inasmuch as it is conceived as fuUy o This is expressly allowed by quoted from him by Sir W. Hamilton Aristotle, Metaph., iv. 25, and is himself, Biacussions^ 1>. 173.— Ed. LECTURES ON LOGIC. 361 conditioned by, or as involved in, A. I am afraid lect. XVIIL that what I have now said may not be found to have 1 removed the difficulty ; but if it suggest to you a train of reflection which may lead you to a solution of the difficulty by your own effort, it will have done better. So much for Hypothetico-disjunctive syllogisms, the last of the four classes determined by the internal form of reasoning. In these four syllogisms, — the Categorical, the Disjunctive, the Hypothetical, and the Hypothetico-disjunctive, all that they exhibit is conformable to the necessary laws of thought, and they are each distinguished from the other by their essential nature ; for their sumptions, as judgments, present characters fundamentally different, and from the sumption, as a general rule, the validity of syllo- gisms primarily and principally depends. :U)2 LECTURES ON LOGIC. L E C T U K E XIX. STOICHEIOLOGY. SECTION II. — OF THE rPvODUCTS OF THOUGHT. III. DOCTllINE OF KEASONINGS. SYLLOGISMS.^THEIK DIVISIONS ACCORDING TO EXTERNAL FORM. A. COMPLEX, — EPICHEIREMA AND SORITES. LECT. In our treatment of Sylloofisms, we have liitlicrto XIX. J ft ' ; — taken note only of the Internal or Essential Form —their' Ex- of Eeasoning. But besides this internal or essential " form there is another, — an External or Accidental Form ; and as the former was contained in the recip- rocal relations of the constituent parts of the syllo- gism, as determined by the nature of the thinking subject itself, so the latter is contained in the outer expression or enouncement of the same parts, whereby the terms and propositions are variously affected in respect of their number, position, and order of conse- cution. The varieties of Syllogism arising from their external form may, I think, be conveniently reduced to the three heads expressed in the following paragraph : — Par. Lxviii. H LXVIII. Syllogisuis, in respect of tlieir Ex- Syiiogisma tcmal Fomi, admit of a threefold modification. according , , o • 7 i to External For whilc, as purc, they are at once /Simple, and Complete, and Eajidar, so, as qualified, they are LECTURES ON LOGIC. 363 either Complex, or Incomplete, or L^regular: lect. the two former of these modifications regardino; 1- the number of their parts, as apparently either too many or too few ; the last regarding the in- verted order in which these parts are enounced. I shall consider these several divisions in their order ; Expiica- and, first, of the syllogisms which vary from the simple Al^compicx form of reasoning by their apparent complexity. ^ ogisms. But before touching on the varieties of syllogism Relation of afforded by their complexity of composition, it may to eadi"" be proper to premise a few words in regard to the ^ relation of syllogisms to each other. " Every syllogism may be considered as absolute and independent, inas- much as it always contains a complete and inclusive series of thought. But a syllogism may also stand to other syllogisms in such a relation that, along with these correlative syllogisms, it makes up a greater or lesser series of thoughts, all holding to each other the dependence of antecedent and consequent. And such a reciprocal dependence of syllogisms becomes neces- sary, when one or other of the predicates of the prin- cipal syllogism is destitute of complete certainty, and when this certainty must be established through one or more correlative syllogisms."" "A syllogism, viewed classes and as • an isolated and independent whole, is called a ofrdatdr^ Monosyllogism (monosyllogismus), that is, a single MouosyUo'- reasoning ; whereas, a series of correlative syllogisms ^'^™' following each other in the reciprocal relation of antecedent and consequent, is called a Polysyllogism Poiysyiio- {polysyitogismus), that is, a multiplex or composite ciiain of reasoning, and may likewise be denominated a Chain of Reasoning {series syllogistica). Such a chain, — a Esser, Logik, % 104. — Ed. oC4 LKOTlTvES OX LOGIC. i.KCT. such a sories, may, lioAvcver, have such an order of ' depeiuh'iu'o, that cither each successive syllogism is tlic reason of that which preceiled, or the preceding This Ann- syllogism is the reason of that Avhich follows. In the %nth"iic. former case, we conclude analytically or regressivcly ; in the second, synthetically or progressively. That syHogism in the series which contains the reason of Pmsviio- the in-emise of another, is called a Prosyllogism (pro- ^'""' s)/Uog(smus); and that syllogism which contains the Episviio- consequent of another, is called an Einsyllogism {ejn- '"''*'"■ sijJIogismus). Every Chain of Reasoning must, there- fore, be made up both of Prosyllogisms and of E})i- syllogisms."" " When the series is composed of more than two syllogisms, the same syllogism may, in differ- ent relations, be at once a prosyllogism and an cpi- syllogism; and that reasoning which contains the primary or highest reason is alone exclusively a pro- syllogism, as that reasoning which announces the last or lowest consequent is alone exclusively an episyllo- gism. But this concatenation of syllogisms, as ante- cedents and consequents, may be either manifest, or occult, according as the plurality of syllogisms may either be openly displayed, or as it may appear only as a single syllogism. The polysyllogism is, therefore, likewise either manifest or occult. The occult poly- syllogism, W'ith which alone we are at present con- cerned, consists either of partly complete and partly abbreviated syllogisms, or of syllogisms all equally abbreviated. In the former case, there emerges the complex syllogism called E2yicheircma ; in the latter, the complex syllogism called Sorites.''^ Of these in their order. a Krug, Loijik, § 111. — Ed. Eeusch, Systema Lotikum, § 57S, p. /3 Esser, Lu(jik, § 104.— Ed. [Cf, CG4, lecK, 1741.] LECTURES ON LOGIC. 365 IF LXIX. A sylloo^ism is now vulo^arly called lect. an Epicheirema (iTnx^Lp-qfxa), when to either of '— the two premises, or to both, there is annexed axheEpi- " reason for its support. As :— ''"''""*' B is A; But G is'B; for it is D ; Therefore, C is also A.« Or, AU vice is odious; But avarice is a vice; for it makes men slaves ; Therefore, avarice is odious.fi In illustration of this paragraph, it is to be observed, Expiica- that the Epicheirema, or Eeason-rendering Syllogism, is either single or double, according as one or both of the premises are furnished with an auxiliary reason. The single epicheirema is either an epicheirema of the first or second order, according as the adscititious pro- position belongs to the sumption or to the subsump- tion. There is little or nothing requisite to be stated in regard to this variety of complex syllogism, as it is manifestly nothing more than a regular episyllo- gism with an abbreviated prosyllogism interwoven. There might be something said touching the name, which, among the ancient rhetoricians, was used now in a stricter, now in a looser, signification.'^ This, how- ever, as it has little interest in a logical point of view, I shall not trouble you by detailing ; and now pro- ceed to a far more important and interesting subject, o In full, — ationg, see Quintilian, List. Orat., C is D; V. 10, 2, v. 14, 5. Compare also D M B ; Schweighajuser on Epictetus, i. 8 ; Therefore, CisB. Trendelenburg, Ekmenta Logiccs j3 In full, — Aristotelicw, § 33 ; Facoiolati, What makes men slaves is a vice ; Acroases, De Epkhircmatc, ]). 127 But avarice makes 'nien slaves ; ct seq. In Aristotle the term is Therefore, avarice is a vice. used for a dialectic syllogism. See 7 For some notices of these vari- Topica, viii. 11. — Eu. 300 LKciriiKs ON i.oriTO. LKCT. — the sccoiul \;uio(y dI' ooin})lex syllogisms, — the " Sorites. P:u-. i.w. H LXX. Wlioii, oil the common principle of all reasoning, — that the part of a part is a part of the whole, — we do not stop at the second gra- dation, or at the part of the highest ]iart, and conclude that part of the whole, — as All B is a part of the whole A, and all C is a part of the jMrt B, therefore all C is also a part of the whole A, — but proceed to some indefinitely remoter part, as, D, E, F, G, H, &c., which, on the general principle, we connect in the conclusion with its remotest whole, — this complex reasoning is called a Chain-Syllogism or Sorites. If the whole from which we descend be a comprehensive quantity, the Sorites is one of Comprehension ; if it be an extensive quantity, the Sorites is one of Exten- sion. The formula of the first will be : — 1) E ?s D ; that is, E comjyt'ehends D ; 2) J} is C ', that is, D comprehends C ; 3) C is B ; that is, C comjprehends B ; 4) B z's A ; that is, B comxn'cl tends A ; Therefore^ E ?'s A ; in other words, E comprehends A. The formula of the second will be : — 1) B ?'s A j that is, A contains under it B ; 2) C w B ; that is, B contaiyis under it C ; 3) T> is G ; that is, C contains under it D ; 4) E ts D ; that is, D contains under it E ; Therefore, E «s A ; in other words, A contains under it E. These reasonings are both Progressive, each in its several quantity, as descending from whole to part. But as we may also, arguing back from part to whole, obtain the same conclusion, there is also competent in LECTURES ON LOGIC. 367 either quantity a, Regressive Sorites. However, the lect. formula of the Eegressive Sorites in the one quantity, '- will be only that of the Progressive Sorites in the other." 2 3 1 w A B C D E F As a concrete example of these : — I. Progressive Comprehensive Sorites. Bucephalus is a horse ; A horse is a quadruped ; A quadruped is an animal ; An animal is a substance ; Therefore^ Bucephalus is a substance. Explica- tion. Concrete examples of Sorites. a [On the Sorites in general, see Crakanthorpe, Logica, L. iii. c. 22, p. 219 ; Valla, Dialect., L. iii. c. 54, fol. 38, ed. 1509; M.Duncan, Instit. Log., L. iv. c. vii. § 6, p. 255 ; Faccio- lati, Acroases, Dc Sorik., p. 15 et seq. ; Melanchthon, Erotem. Dial., L. iii. DeSorite, p. 74.3; Wolf, Phil. Rat., § 466 et seq. ; Walch, Lcxikon, v. "Sorites;" Fries, Logilc, § 64.] )3 Diagrams Nos. 1 and 2 repre- sent the Affirmative Sorites in the case in which the concepts are coex- tensive. — See above, p. 189, Diagram 2. Diagrams Nos. 3 and 4 represent the Affirmative Sorites in the case in which the concepts are subordi- nate. — See above, p. 189, Diagram 3. Diagram No. 5, taken in connection with No. 3, represents the Negative Sorites. Thus, to take the Progres- sive Comprehensive Sorites : — E is D, D is L\ C is B, B i,v A, no A is P; therefore, no E is P. — Ed. 3G8 LECTURES OX LOGIC. LECT. Or as explicated : — XIX. ' Thr irpriventutioii of tite inAlcldunl Bucephalus comprehends or roiidiiiis in if the notion horse ; Tht' notion hurse coinpreheml^ the notion tju'ulrnped ; The notion quadruped comprehends the notion animal ; The notion animal comprehends thr notion substance ; Therefore, (on tlie coiiiiuou principle that the part of a part is a part of the whole,) the representation of the indi- vidufd, Bucephalus, com2)rehends or contains in it tlie notion substance. II. Ekgressive Comprehensive Sorites. An animal is a substance; A quadruped is an animal ; A horse is a quadruped ; Bucephalus is a horse ; Titer ef ore, Bucephalus is a stibstance. Or as explicated : — The notion animal comprehends the notion substance ; TJie notion qiiadruped comprehends the notion animal ; Tlie notion horse comprehends the notion quadruped ; The representation, Bucephalus, comprehends the notion horse; Tliercfore, (on the common principle, &c.) the rejyre^entation, Bucephalus, comprehends the notion substance. III. Progressive Extensive Sorites, (which is, as enounced by the common copula, identical in expression with the Regressive Comprehensive Sorites, No. II.) An animal is a substance ; A quadruped is an animal ; A horse is a quadruped ; Bucep)halus is a horse; Tlierefore, Bucephalus is a substance. Or as explicated : — 77(6 notion animal is contained under the notion substance ; Tlie notion quadruped is contained under the notion animal; The notion horse is contained under the notion quadruped ; LECTURES ON LOGIC. 369 The representation Bucephalus is contained tinder the notion lecT; , XIX. horse ; - Therefore, (on the common principle, &c.) the representation Bucephalus is contained under the notion substance. IV. The Regressive Extensive Sorites, (which is, as expressed by the ambiguous copula, verbally identical with the Progressive Comprehensive Sorites, No. I.) . Bticephalus is a horse; A horse is a quadruped ; A quadruped is an animal; An animal is a siibstance ; Therefore, Bucephalus is a suhstance. Or as explicated : — The representation Bucephalus is contained under the notion horse ; The notion horse is contained under the notion quadruped ; The notion quadruped is contained under the notion animal ; The notion animal is contained under the notion suhstance; Therefore, the representation Bucephalus is contained under the notion suhstance. There is thus not the smallest difficulty either in regard to the peculiar nature of the Sorites, or in re-, gard to its relation to the simple syllogism. In the i. The for- first place, it is evident that the formal inference in eifce'inSori- the Sorites is equally necessary and equally manifest irecSy^ as in the simple syllogism, for the principle, — the part sJiiogiTm^ ^ of a part is a part of the whole, — is plainly not less applicable to the remotest, than to the most proximate, link in the subordination of whole and part. In the 2. Sorites second place, it is evident that the Sorites can be into simple . •in- ,1 syllogisms. resolved into as many simple syllogisms as there are middle terms between the subject and predicate of the conclusion, that is, intermediate wholes and parts be- tween the greatest whole and the smallest part, which the reasoning connects. Tlius, the concrete example VOL. r. 2 a traUHl. 370 LECTURES ON LO«IO. i.KCT. of a Sorites, already given, is virtually composed of ' three simple syllogisms. It will be enough to show this in one of the quantities ; and, as the most perspi- cuous, let us take that of Comprehension. This iiius- The Progressive Sorites in this quantity was as fol- lows, (and it is needless, I presume, to explicate it) : — Bucephalus is a horse ; A horse is a quadruped ; A quadruped is an animal ; An animal is a substance ; Therefore, Bucejjhulas is a substance. Here, besides the major and minor terms, {Buce- phalus and substance), we have three middle terms, — horse, — quachnvped, — animal. We shall, conse- quently, have three simple syllogisms. Thus, in the first place, we obtain from the middle term horse, the following syllogism, concluding quadruped of Buce- phalus: — I. — Bucephalus is a horse; But a horse is a quadruped; Therefore, Bucephalus is a quadruped. Having thus established that Bucephalus is a quadruped, we employ quadruped as . a middle term by which to connect Bucephalus with animal. We, therefore, make the conclusion of the previous syllo- gism (No. I.) the sumption of the following syllogism (No. n.) II. — Bucephalus is a quadruped ; But a quadruped is an animal ; Tlierefore, Bucejjhalus is an animal. Having obtained another step, we, in like manner, make animal, which was the minor term in the pre- ceding -syllogism, the middle term of the follow^ing ; and the conclusion of No. H. forms the major premise of No. HI. LECTURES ON LOGIC. 37l III. — Bucephalus is an animal ; LECT. But an animal is a substance; Xix. Therefore, Bucephalus is a substance. Ill this last syllogism, we reach a conclusion identi- cal with that of the Sorites. In the third place, it is evident that the Sorites is 3, sorites equally natural as the simple syllogism ; and, as the re- nl^d lation is equally cogent and equally manifest between syllogism. a whole and a remote part, and a whole and a proxi- mate part, that it is far less prolix, and, consequently, far more convenient. What is omitted in a Sorites is only the idle repetition of the same self-evident prin- ciple, and as this can without danger or inconvenience be adjourned until the end of a series of notions in the dependence of mutual subordination, it is plain that, in reference to such a series, a single Sorites is as much preferable to a number of simple syllogisms, as a comprehensive cipher is preferable to the articulate enumeration of the units which it collectively repre- sents. Before proceeding to touch on the logical history of this form of syllogism, and to comment on the doc- trine in regard to it maintained by all logicians, I shall conclude what it is proper further to state con- cerning its general character. ^ LXXI. A Sorites may be either Categorical Par. lxxi. or Hypothetical; and, in both forms, it is governed categorical by the following laws : — Speaking of the Com- thcticaF"" mon or Progressive Sorites, (in which reasoning you will observe the meaning of the word pro- gressive is reversed), which proceeds from the individual to the general, and to which the other form may be easily reduced : — 1°. The number 3*72 LECTURES ON LOCK'. LKfT. XIX. o( tlio }>ivnusc's is imlimited. 2°. All the pre- mises, witli exception of the hist, must be affirm- ative, ami, with exception of tlie first, definite. 3^ The first premise may be either definite or indefinite. 4°. The last may be either negative or affirmative. Form iia of cal ooritcs. Hvputlioci- . . cal Sonus. thctlCal '. I have already given yon examples of the categori- Tlie following is the formula of the hypo- Progukssive. If D is, C is ; If C is, B is ; If B is, A is ; (In modo ponente), Now D is ; Therefore, A is also. (Or in modo tollente), Now A is not ; Therefore, D is not. Degressive. If B is, A is ; If C is, B is ; If D is, C is ; (In modo ponente), Nolo D is ; Therefore, A is. (Or in modo tollente), Noio A is not ; Therefore, D is not. Or to take a concrete example : — Progressive. If Harpagon he avaricious, he is intent on (jain ; If intent on gain, he is discontented ; If discontented, he is unhappy ; Now Harpagon is avaricioiis ; He is, therefore, unhappy. Eegressive. If Harpagon he discontented, he is uyiltappy; If intent on gain, he is discontented; If avaricious, he is intent on gain ; Now Harpagon is avaricious ; Tlierefore, he is unhappy. LECTURES ON LOGIC. 373 In regard to the resolution of the Hypothetical lect. Sorites into simple syllogisms, it is evident that in this Progressive Sorites we must take the first two of Hypo- propositions as premises, and then in the conclusion soHtes into connect the antecedent of the former proposition with logisms!^ ' the consequent of the latter. Thus : — sWeSontes. I. — If Harpagon he avaricious, he is intent an gain ; If intent on gain, he is discontented; Therefore, if Harpagon be avaricious, he is discontented. We now establish this conclusion, as the sumption of the following syllogism :- — II. — If Harpagon he avaricious, he is discontented ; If disconterited, he is unhappy ; Therefore, if Harpagon he avaricious, he is unhap>py. In like manner we go on to the next syllogism : — III. — If Harpagov- he avaricious, he is. unhappy ; Noio Harpagon is avaricious; Therefore, he is unhap>py. In the Regressive Sorites, we proceed in the same n. Regres- fashion ; only that, as here the consequent of the second proposition is the antecedent of the first, we reverse the consecution of these premises. Thus : — I. — If Harpagon he intent on gain, he is discontented ; If discontented, he is unhappnj ; Therefore, if Harpagon he intent on gain, he is unhappy. We then take the third proposition for the sump- tion of the next, the second, syllogism, and the con- clusion of the preceding for its subsumption : — II. — If Harpagon he avaricious, he is intent on gain ; If intent on gain, he is unhapjyy ; Therefore, if IL.apagon be avaricious, he is unhappy. 374 LECTURES ON LOGIC. i.KCT. Wo now tnko tliis last conclusion for tlic sumption ' of the last syllogism : — III. — If Ilarpagon he avaricious, he is unhappy ; Now Ilarpagon is avaricious ; Therefore, he is nnhappy. nis^unctive But It may be asked, can there be no Disjunctive Sorites ? To this it may be answered, that in the sense in which a categorical and hypothetical syllo- gism is possible, — viz., so that a term of the preceding proposition should be the subject or predicate of the following, — in this sense, a disjunctive sorites is im- possible ; since two opposing notions, whether as con- traries or contradictories, exclude each other, and can- not, therefore, be combined as subject and predicate. But when the object has been determined by two opposite characters, the disjunct members may be amplified at pleasure, and there follows certainly a correct conclusion, provided that the disjunction be logically accurate. As : — A is either B or C. Now, B is eitJier D or E ; D is either H or I ; E is either K or L. C is either F orG; ¥ is either M or IST , G is either O or P. TJierefoi'e, A is either H, or I, or K, or L, or M, or K", or 0, or P. Complex Although, thcrcforc, it be true that such a Sorites vLaUe!"^ is correct; still, were we astricted to such a mode of reasoning, thought would be so difiicult, as to be almost impossible. But we never are obliged to employ such a reasoning ; for when we are once assured that A is either B or C, and assured we are of this by one of the fundamental laws of thought. LECTURES ON LOGIC. 375 we have next to consider whether A is B or C, and lect, ' XIX. if A is B, then all that can be said of C, and if A is C, then all that can be said of B, is dismissed as wholly irrelevant. In like manner, in the case of B, it must be determined whether it is D or E, and in the case of C, whether it is F or Gr ; and this being determined, one of the two members is necessarily thrown out of account. And this compendious method we follow in the process of thought spontaneously, and as if by a natural impulsion. . So much for the logical character of the Sorites. It now remains to make some observations, partly historical, partly critical, in connection with this sub- ject. In regard to the history of the logical doctrine of Historical this form of reasoning, it seems to be taken for granted, logical doc- in all the systems of the science, that both the name SorUel Sorites, as applied to a chain-syllogism, and the analysis of the nature of that syllogism, are part and parcel of the logical inheritance bequeathed to us by Aristotle. Nothing can, however, be more erroneous. Neither The name Sorites does not occur in any logical treatise doctrinr of Aristotle ; nor, as far as I have been able to dis- AHstotk. cover, is there, except in one vague and cursory allu- sion, any reference to what the name is now employed to express." Nay, further, the word Sorites is never, I make bold to say, applied by any ancient writer to designate a certain form of reasoning. On the contrary. Sorites, though a word in not unfrequent a The passage referred to is pro- in Aristotle's rule, Categ. , c. 2 : hahly Anal. Prior.,!. 25. But there *' Prsedicatum prcedicati est prse- was no need of a special treatment dicatum subjecti." See also, Anal. of the Sorites, as it is merely a com- Pout, i. 23 et seq. Cf. Pacius, bination of ordinary syllogisms, and Comment., p. 159 ; Bertius, Logica subject to the same rules. — En. [The Peri})atetica, L. iii. Ap2>endix, p. principle of the Sorites is to be found 179.] 376 LECTUKKS ON J.OlilC. LtXT. rnntlovinciit l>v ancient authors, nowhere occurs in XIX. . . any otlier logical meaning than that of a particular J^itTaucicnt ^^^^^^^ <>t sophism, of ^vllich the Stoic Chrysippus was "loir'toao- ivputeil the inventor." to)po<;, you know, in Greek, pntcui'ilr iHt'i^iis a heap or pile of any aggregated substances, -volJilism. ^^ sand, wheat, &c. ; and Sorites, literally a heap)ei\ was a name given to a certain captious argument, which in Latin obtained from Cicero the denomi- Ti.o nature uatiou of acervciUs.^ The nature of the argument oftliis . sophism, was this : — You were asked, for example, whether a certain quantity of something of variable amount were large or small, — say a certain sum of money. If you said it was small, the adversary went on gradually adding to it, asking you at each increment whether it were still small ; till at length you said that it was large. The last sum which you had asserted to be small, was now compared with that which you now asserted to be large, and you were at length forced to acknowledge, that one sum which you main- tained to be large, and another which you maintained to be small, differed from each other by the very pettiest coin, or, if the subject were a pile of wheat, by a single corn. This sophism, as applied by Eubu- lides, (who is even stated by Laertius"^ to be the inventor of the Sorites in general,) took the name of (f)akaKpo^, calvus, the halcL It was asked, — was a man bald who had so many thousand hairs ; you answer, No : the antagonist goes on diminishing and dimin- ishing the number, till either you admit that he who a Persiua, Sat. vi. 80 : P De Divinat'ione, ii. 4 : " Quem- " Inventus, Chrysippe, tul finitor admodiim Soriti resistas ? quern, si acervi." — Ed. necesse sit, Latino verbo liceat acer- [Cicero applies Sorites to an argu- valeni appellare." Cf. Facciolati, ment which we would call a Sorites, Acroascs, p. 17 etseq. — Ed. but it could also be a Chrysippean. 7 L. ii. § 108. — Ed. De Finihus, L. iv. c. 18.] LECTURES ON LOGIC. 377 was not bald with a certain number of hairs, becomes lect, XIX bald when that complement is diminished by a single . '— hair; or you go on denying him to be bald, until his head be hypothetically denuded. Such was the quibble which obtained the name of Sorites, — acerva- lis, climax, gradatio, &c. This, it is evident, had no real analogy with the form of reasoning now known in logic under the name of Sorites. But when was the name perverted to this, its Lamcntius ••r>- y-vPi-T o ■\ Valla the secondary signification \ Of this I am confident, first to use that the change was not older than the fifteenth cen- its present - -J. . p 1 1 • • • acceptation. tury. it occurs m none oi the logicians previous to that period. It is to be found in none of the Greek logicians of the Lower Empire ; nor is it to be met with in any of the more celebrated treatises on Logic by the previous Latin schoolmen. The earliest author to whose writings I have been able to trace it, is the celebrated Laurentius Valla, whose work on Dialectic was published after the middle of the fifteenth century. He calls the chain-syllogism — " coacervatio syllogismorum (quern Graeci crcopov vo- cant.) "" I may notice that in the Dialectica of his contemporary and rival, George of Trebisond, the pro- cess itself is described, but, what is remarkable, no appropriate name is given to it.'^ In the systems of Logic after the commencement of the sixteenth cen- tury, not only is the form of reasoning itself described, but described under the name it now bears. I have been thus particular in regard to the history Thedoctiino of the Sorites, — word and thing, — not certainly on regar^ahig"' account of the importance of this history, considered iiius'tratcr a Dialectics Dispiitationpfi, Lib. Dialectica Libellus, Colonic, 1533, f. iii. c. 12. See Laurentii Valla; Opera., 60 a. Cf. the Scholia of Ncomagus, Basilcic, 1540, p. 742.— Ed. ihid. f. 67 b.— Ed. /3 See Geor(jii Trapezuntii De Re Ol 8 LECTITKES ON LOtllC. i.K.rT. XIX. Logicians have over- looked the Sorites of Extension. ill itself, but because it will enable you the better to iipprelund what is now to be said of the illustration wliieh the doetriue, taught by logicians themselves, of the nature of this particular process, atibrds of the one-sided view which they have all taken of the nature of reasoning in general. I have already shown, in regard to the simple syllo- gism, that all deductive reasonincj is from whole to part ; that there are two kinds of logical whole and two kinds of logical part, — the one in the quantity of comprehension, the other in the quantity of extension ; and that there are consequently two kinds of reason- ing corresponding to these several quantities. I fur- ther showed that logicians had in simple syllogisms marvellously overlooked one, and that the simplest and most natural, of these descriptions of reasoning, — the reasoning in the quantity of comprehension ; and that all their rules were exclusively relative to the reasoning which proceeds in the quantity of extension. Now, in to-day's Lecture, I have shown that, as in simple syllogisms, so in the complex form of the Sorites, there is equally competent a reasoning in com- prehension and in extension, — though undoubtedly, in the one case as in the other, the reasoning in com- prehension is more natural and easy in its evolution than the reasoning in extension, inasmuch as the middle term, in the former, is really intermediate in position, standing between the major and the minor terms, whereas, in the latter, the middle term is not in situation middle, but occupies the position of one or other of the extremes. Now, if in the case of simple syllogisms it be mar- vellous that logicians should have altogether over- looked the possibility of a reasoning in comprehension. LECTURES ON LOGIC. 379 it is doubly marvellous that, with this their prepos- lect, XIX. session, they should, in the case of the Sorites, have altogether overlooked the possibility of a reasoning in extension. But so it is." They have all followed each other in defining the Sorites, as a concatenated syllogism in which the predicate of the proposition preceding is made the subject of the proposition fol- lowing, until we arrive at the concluding proposition, in which the predicate of the last of the premises is enounced of the subject of the first. This definition applies only to the Progressive Sorites in comprehen- sion, and to the Regressive Sorites in extension : but that they did not contemplate the latter form at all is certain, both because it is not lightly to be presumed that they had in view that artificial and recondite form, and because the examples and illustrations they supply positively prove that they had not. To the Progressive Sorites in extension, and to the Difference -n • ci • , • 1 • j1 ' ^ n • , • • between the Kegressive borites m comprehension, this definition is two forms inapplicable; for in these, the subject of the premise*' preceding is not the predicate of the premise following. But the difference between the two forms is better stated thus : — In the Progressive Sorites of compre- hension and the Regressive Sorites of extension, the middle terms are the predicates of the prior premises, and the subjects of the posterior; the middle term is here in position intermediate between the extremes. On the contrary, in the Progressive Sorites of exten- sion and in the Regressive Sorites of comprehension, the middle terms are the subjects of the prior pre- a [Ridiger notices the error of rant vulgo Peripatetici, et cum his those who make Sorites only of Gassendus, qui Soritem sohim ad comprehensive whole. See his De prwdicatum pcrtinere existimat." — Scnsu Veri et Falsi, L. ii. c. 10, § Ed.] 5, p. 400. Cf. p. 343n., g 6.] ["Er- oSO LECTUliES ON lAHWC. i.v.cT. miscs ami the ])ivilicatos of tlic ])ostci'ior ; the niiddlc ' term is here in position not intermediate between the extremes. rroi.fti.io To the question, — wliy, in the case of simple syllo- li^^k'^ins '^ gisms, the logicians overlooked the reasoning in com- Tn UirCv^o' prehension, and, in the case of the Sorites, the reason- 8vnl^?sius, ing in extension, — it is perhaps impossible to afford a incbrom- satisfactory explanation. But we may plausibly con- prciensiou. jg^^^^j.^^ wliat it is out of our power certainly to prove. In regard to simple syllogisms, it was an original dogma of the Platonic school, and an early dogma of the Peripatetic, that philosophy, — that science, strictly so called, — was only conversant with, and was exclu- sively contained in, universals ; and the doctrine of Aristotle, which taught that all our general know- ledge is only an induction from an observation of particulars, was too easily forgotten or perverted by his followers. It thus obtained almost the force of an acknowledged principle, that everything to be known must be known under some general form or notion. Hence the exaggerated importance attributed to defi- nition and deduction : it not being considered, that we only take out of a general notion what we had previously placed therein ; and that the amplification of our knowledge is not to be sought for from above but from below, — not from speculation about abstract generalities, but from the observation of concrete par- ticulars. But however erroneons and irrational, the persuasion had its day and influence ; and it perhaps determined, as one of its efi'ects, the total neglect of one half, and that not the least important half, of the reasoning process. For while men thought only of looking upwards to the more extensive notions, as the only objects and the only media of science, they took LECTURES ON LOGIC. 381 little heed of the more comprehensive notions, and lect. absolutely contemned individuals, as objects which • could neither be scientifically known in themselves, nor supply the conditions of scientifically knowing aught besides. The logic of comprehension and of induction was, therefore, neglected or ignored, — the logic of extension and deduction exclusively culti- vated, as alone afibrding the rules by which we might evolve higher notions into their subordinate concepts. This may help to explain why, subsequently to Aris- totle, Logic was cultivated in so partial a manner ; but why, subsequently to Bacon, the logic of compre- hension should still have escaped observation and study, I am altogether at a loss to imagine. But the And why, .. , . -.in the case question, — why, when reasoning in general was viewed of the sori- only as in the quantity of extension, the minor form overlooked . ., ^ . ., 1 • 1 *'^® reason- 01 the Sorites should have been viewed as exclusively jng in ex- in that of comprehension, — may perhaps be explained by the following consideration : this form was not originally analysed and expounded by the acuteness of Aristotle. But it could not escape notice that there was a form of reasoning, of very frequent employment both by philosophers and rhetoricians, in which a single conclusion was drawn from a multiplicity of premises, and in which the predicate of the foregoing premise was usually the subject of the following. Cicero, for example, and Seneca, are full of such arguments ; and the natural and easy evolution of the reasoning is indeed peculiarly appropriate to demonstration. Thus, to prove that every body is movable, we have the following self-evident deduction. Every body is in space ; what is in space is in some one part of space ; what is in one part of space may be in another ; what may be in another part of space may change its space ; tension. XIX 382 LECTUUKS ON LOO TO. Lv.cT. what may change its space is movable ; therefore, every body is movable. When, therefore, Valla, or whoever else has the honour of first introducing the consideration of this form of reasoning into Logic, was struck with the cogency and clearness of this com- pendious argumentation, he did not attempt to reduce it to the conditions of the extensive syllogism ; and subsequent logicians, when the form was once intro- duced and recognised in their science, were, as usual, content to copy one from another, without subjecting their borrowed materials to any original or rigorous criticism. Ut nemo in sese tentat descendere ; — nemo ! Sed prsecedenti spectatur mantica tergo. " Accordingly, not one of them has noticed, that the Sorites of their systems proceeds in a different quantity from that of their syllogisms in general, — that their logic is thus at variance wdth itself; far less did any of them observe, that this and all other forms of reasoning are capable of being drawn in another quantity from that which they all exclusively contem- plated. And yet, had they applied their observation without prepossession to the matter, they would easily have seen that the Sorites could be cast in the quan- tity of extension, equally as common syllogisms, and that common syllogisms could be cast in the quantity of comprehension, equally as the Sorites. I have already shown that the same Sorites may be drawn either in comprehension or in extension ; and in both quantities proceed either by progression or by regres- sion. But the example given may perhaps be viewed as selected. Let us, therefore, take any other ; and a Persius, iv. 23.— Ed. LECTURES ON LOGIC. 383 the first that occurs to my recollection is the following lect. from Seneca," which I shall translate: — prehension and Exteu- He who is prudent is temperate ; He who is temperate is constant ; He who is constant is tmperturhed ; He who is unperturbed is without sorrow ; He loho is without sorro70 is happy; Therefore, the prudent man is happ)y. In this Sorites everything slides easily and smoothly from the whole to the parts of comprehension. But, though the process will be rather more by hitches, the descent under extension will, if not quite so pleasant, be equally rapid and certain. He who is without sorrow is happy ; He who is unperturbed is without sorrow ; He who is constant is unperturbed ; He who is temperate is constant ; He who is prudent is temperate ; Therefore, the p)rudent man is happy. I do not think it necessary to explicate these two reasonings, which you are fully competent, I am sure, to do without diflSculty for yourselves. What renders it still more wonderful that the logi- The GocIc- cians did not evolve the competency of this process in either quantity, and thus obtain a key to the opening up of the whole mystery of syllogistic reasoning, is this ; — that it is now above two centuries since the Inverse or Eegressive Sorites in comprehension was discovered and signalised by Eodolphus Goclenius, a celebrated philosopher of Marburg, in which university he occupied the chair of Logic and Metaphysics.^ a Epint. , 85. — Ed. Ed. [For tlie Goclenian Sorites be- fi Goclenii Isagoye in Organum fore Goclenius, see Pacius, Comtacut. Aristoldis, Francof,, 1598, p. 255. — in Anal. Prior., i. 25, p. 159.] 384 LiXTrm:s ox logic. 1 K< r. This Soritos has from him obtained the name of Goc- " lenian ; while the progressive Sorites has been called the common or Aristotelian. This latter denomina- tion is, as I have previously noticed, an error ; for Ai'istotle, though certainly not ignorant of the process of reasoning now called Sorites, does not enter upon its consideration, either under one form or another. This observation by Goclenius, of which none of our British logicians seem aware, was a step towards the explication of the whole process ; and we are, there- fore, left still more to marvel how this explication, so easy and manifest, should not have been made. Be- fore terminating this subject, I may mention that this form of syllogism has been sometimes styled by logi- cians not only Sorites, but also coacervatio, coiigeries, gradatio, climax, and de primo ad ultimum. The old name before Valla, which the process obtained among the Greek logicians of the Lower EmjDii-e, was the vague and general appellation of complex syllogism, — crvX\oyL(TiJ.oq avvdero^."' Epicheire- So much for the two forms of reasoning which may Sorites, as be regarded as composite or com^jlex, and which logi- gis^; com- cians have generally considered as redundant. But simple, aid hcrc it IS propcr to remark, that it m one point, that astic. is, as individual syllogisms, the Epicheirema and Sorites may be viewed as comparatively complex, in another, that is, as poly syllogisms, they may be viewed as comparatively simple. For resolve a Sorites into the various syllogisms afforded by its middle terms, and compare the multitude of propositions through which the conclusion is thus tediously evolved, with the short and rapid process of the chain-syllogism itself, and, instead of complexity, we should rather be a [Blemmidas, Epitome Logka, c. .31.] XIX. LECTURES ON LOGIC. 38i disposed to predicate of it extreme simplicity." In ljjct point of fact, we might arrange the Epicheirema and Sorites with far greater propriety under elliptical syllogisms, than, as is commonly done by logicians, under the pleonastic. This last classification is, indeed, altogether erroneous, for it is a great mistake to suppose that in either of these forms there is aught redundant. a [See Jjeibnitz, Nouveaiix Bssais, ed. E,aspe.] L. iv. c. xvii. § 4, pp. 445, 446, 448, VOL. I. 2 B 386 LECTURES ON LOGIC. LECTURE XX. STOICIIEIOLOGY. SECT. ir. — OF THE PRODUCTS OF THOUGHT. III. — DOCTRINE OF REASONINGS. SYLLOGISMS. THEIR DIVISIONS ACCORDING TO EXTERNAL FORM. B. DEFECTIVE, — ENTHYMEME. C. REGULAR AND IRREGULAR, — FIGURE AND MOOD. LECT. I PROCEED now to the Second Class of Syllogisms, — —^^ — those, to wit, whose External Form is defective. This gisaJdeiec- class I givc in conformity to the doctrine of modern ternaiFom. logicians, whose unanimous opinion on the subject I shall comprehend in the following paragTaph. Par. Lxxii. *^ LXXII. According to logicians in general, a meme. dcfective syllogism is a reasoning in which one only of the premises is actually enounced. It is therefore, they say, called an Enthymeme {evOv- fjir)fia), because there is, as it were, something held back in the mind {iu Ovfxco). But as it is possible to retain either the sumption or the subsumption, the Enthymeme is thus of two kinds : — an Enthy- meme of the First, and an Enthymeme of the Second, Order. The whole distinction is, how- ever, erroneous in principle, and even if not LECTURES ON LOGIC. 387 erroneous, it is incomplete ; for a Third Order of lect. Entliymemes is competent by the suppression of ^^' the conclusion. Such, as it is stated in the former part of the para- Expiica- graph, is the doctrine you will find maintained with The'com- singular unanimity by modern logicians ; and, with tTbe oTthe hardly an exception, this classification of syllogisms is fiuuennd ^ stated not only without a suspicion of its correctness, aSuted^ but as a division established on the authority of the *° '^"*'"'^®- great father of logic himself. In both assertions they are, however, wrong, for the classification itself is futile, and Aristotle afibrds it no countenance ; while, at the same time, if a distinction of syllogisms is to be taken from the ellipsis of their propositions, the subdivision of enthymemes is not complete, inas- much as a syllogism may exist with both premises expressed, and the conclusion understood. I shall, therefore, in the first place, show that the Enthymeme, as a syllogism of a defective enounce- ment, constitutes no special form of reasoning ; in the second, that Aristotle does not consider a syllogism of such a character as such a special form ; and, in the third, that, admitting the validity of the distinction, the restriction of the Enthymeme to a syllogism of one suppressed premise cannot competently be main- tained. ** L In regard then to the validity of the distinction, i. The En- This is disproved on the following grounds : First of non°s"!e- all, the discrimination of the Enthymeme, as a syllo- reLouiug" gism of one suppressed premise, from the ordinary syllogism, would involve a discrimination of the rea- soning of Logic from the reasoning in common use ; a Compare Discussions, p. 153 et seq. — Ed. 3SS LECTURES ON LOGIC. LECT. for, ill gi'iun-al ivn^soiiiiig, we riirt'ly express all the — '-^ — propositions dI" a syllogism, and it is almost only in the treatises on Abstract Logic, that we find examples of reasoning in which all the members are explicitly enounced. But Logic does not create new forms of syllogism, it merely expounds those which are already given ; and while it shows that in all reasoning there are, in the mental process, necessarily three judgments, the mere non-expression of any of these in language, no more constitutes in Logic a particular kind of syl- logism, than does the ellipsis of a term constitute in Grammar a particular kind of concord or government. But, secondly. Syllogism and Enth3^meme are not distinguished as respectively an intralogical and an extralogical form ; both are supposed equally logical. Those who defend the distinction are, therefore, neces- sarily compelled to maintain, that Logic regards the accident of the external expression, and not the essence of the internal thought, in holding that the Enthy- meme is really a defective reasoning. '^ It thus appears, that to constitute the Enthymeme as a species of reasoning distinct from Syllogisms Proper, by the difference of perfect and imperfect, is of all absurdities the greatest. — But is this absurd- ity the work of Aristotle 1 — and this leads us to the second head. II. The dis- IL Without entering upon a regular examination tw EnUiy- of the various passages of the Aristotelic treatises rela- ™8^ciai tive to this point, I may observe, in the first place, reining that Aristotlc expressly declares in general, that a Sis't^uc! ^ syllogism is considered by the logician, not in rela- tion to its expression (ov Trpo? top e^oi \6yov), but a [That Syllogism and Enthymeme reasoning, see Derodon, Lngica Resti- are not properly distinct species of tuta, Pars V. tract, i. c. 1, p. 602.] LECTURES ON LOGIC. 389 exclusively as a mental process (dXXa Trpo? tov iu rfj lect. ^vxj) Xoyoi^)." The distinction, therefore, of a class of — ^ — '- — syllogisms as founded on a verbal accident, he thus of course, implicitly and by anticipation, condemns. But Aristotle, in the second place, does distinguish the The Enthy- "i-,-, • ^ • -^ c ^^ ' i mcrae of Jiinthymeme as a certain kind oi syllogism, — as a syl- AristoUe,- logism of a peculiar matter, — as a syllogism from signs and likelihoods./^ Now if, having done this, it were held that Aristotle over and above distinguished the Enthymeme also as a syllogism with one suppressed premise, Aristotle must be supposed to define the Enthymeme by two differences, and by two differences which have no mutual analogy ; for a syllogism from signs and likelihoods does not more naturally fall into an elliptical form than a syllogism of any other matter. Yet this absurdity has been and is almost universally believed of the acutest of human intellects, and on grounds which, when examined, afford not the slight- est warrant for such a conclusion. On the criticism of these grounds it would be out of place here to enter. Suffice it to say, that the texts in the Organon and Rhetoric, which may be adduced in support of the vulgar opinion, will bear no such interpretation ; — that in one passage, where the word dreXr)^ {impei-- fect) is applied to the Enthymeme, this word, if genuine, need signify only that the reasoning from signs and probabilities affords not a perfect or neces- sary inference ; but that, in point of fact, the word areXT)? is there a manifest interpolation, made to accommodate the Aristotelic to the common doctrine of the Enthymeme, for it is not extant in the oldest manuscripts, and has, accordingly, without any refer- ence to the present question, been ejected from the a AnaL rost, i. 10, — Ed. /3 Anal. Prior., ii. 27 ; EluL, i. 2.— Ed. o'JO LECTUTvES ON LOGIC. LKCT. XX. A|>|>lir;t- tious of tlie tcnn Ku- (A 1/ menu. By Piony- (iug of Ilali caniassus. Author of HJutoric to A Ujca ndir. Sopator. Aulus Gcl- lius. Cicero. Quintilian. best rocoiisions, aiul, ;iim>ng others, from tlie recent edition o{ the works of Aristotle by the Academicians i>f r>eilin, — an edition founded on a collation of the principal manuscripts throughout Europe.*" It is not, however, to be denied that the term Enthijmeme was applied to a syllogism of some unexpressed part, in very ancient times ; but, along with tliis meaning, it was also employed by the Greek and Roman rheto- ricians for a thought in general, as by Dionysius the Halicarnassian,^ and the author of the Rhetoric to Alexander, attributed to Aristotle,*^ — for an acute dictum, as by Sopater^ and Aulus Gcllius,^ — for a reasoning from contraries or contradictories, as by Cicero.^ Quintilian gives three meanings of the term ; in one sense, signifying " omnia mente concej)ta," in another, " sententia cum ratione," in a third, " ar- gumenti conclusio, vel ex consequentihus rel ex repug- nantihiis.'"^ a For a fuller history of this inter- polation, see Discussmis, p. 154. — Ed. [For the correct doctrine of the Aristotelic Enthymeme, see Ma- riotte,] [Essai de Logique, P. ii. disc. iii. p. 163, Paris, 1678.— Ed.] )3 Epistola ad Cn. Pompeium clc prcecipuis Historicis, c. 5 : Ttjs fj.4vToi KaXMXoyias eKeivov Kal rod Tr\ovrov Twv iv6v^iifj.a.T(iiv Kara. iroKv vartpfi. The expression irXovros (vQvfxrifjLarwv is rendered by J. C. T. Ernesti, Ge- danken Fillle ; see his Lexicon Tccli- noIogicE Grcecorum PJietorkce, v. ivevfj.-qfxa. The same sentence is repeated in nearly the same words by Dionysius, in his Veteinim Scrip- toruni Censura, iii. 2 Ed. 7 The author of the FJietorica ad Alcxandrum, c. 8, classes the enthy- meme among proofs (ttiVtsis), and, in c. 11, defines it as a proof drawn from any kind of oj>2)o.sition : 'Evdvfxri- jxara 5' icrXv oh fiovov ra r^ \6y(f Koi rij iTpa^ei ivavrLovp.eva, aWa koI ro7s &Wois anacriv. This work is attri- buted by Victorius to Anaximenes of Lampsacus, and this conjecture is adopted by the latest editor, Spengel. —Ed. 5 Sopatri Apamecnsis Prolego- mena hi Aristidcm. Aristidis Op. Omn., ed. Jebb, vol. i. f. d3: Kal rrj rcov (vQvfx.7tiJ.6.ru>v TzvKv6r7)ri ST]fiO(r- devi^ei. In Canter's Prolegomena this expression is rendered se??n.ios t ion, or the conclusion is suppressed.'* As examples of tlicse various Enthymemcs, the following may suf- fice : — The Explicit Syllogism. Every liar is a coioard ; Cuius is a liar ; Therefore, Caius is a coward. I. Enthymeme of the First Order — (the Sumptiou under- stood.) Caius is a liar ; Therefore, Caius is a cotcard. II. Enthymeme of the Second Order — (the Subsumptiun understood.) Every liar is a coioard ; Tlierefore, Caius is a coward. III. Enthymeme of the Third Order — (the Conclusion under- stood. ) Every liar is a coioard ; And Caius is a liar. Epigram- In thls last, you see, the suppression of the conclu- "mpTeTf sion is not only not violent, but its expression is even meme with morc supcrfluous than that of either of the premises, conciusfol. There occurs to me a clever epigram of the Greek An- tholoo-}-, in which there is a syllogism with the con- clusion suppressed. I shall not quote the original, o [That the Enthymeme is of three 1599), or rather of foiir orders, for orders is held by Victorinus, (in Cas- there may be an Enthymeme with siodonis, Opera, vol. ii. p. 536, ed. only one proposition enounced. See 1729 ; Rhetores Pithcei, p. 341, ed. Victorinus, as above.] LECTURES ON LOGIC. 393 but give you a Latin and English imitation, which lect will serve equally well to illustrate the point in ques- tion." The Latin imitation is by the learned printer Henricus Stephanus, and he applies his epigram to a certain Petrus, who, I make no doubt, was the Fran- ciscan, Petrus a Cornibus, whom Buchanan, Beza, Eabelais, and others have also satirised.^ It runs, as I recollect, thus : — " Sunt monaclii nequam ; nequam iion unus et alter : Prseter Petrum omnes : est sed et hie monaclivis." The English imitation was written by Porson upon Gottfried Hermann, (when this was written, con- fessedly the prince of Greek scholars,) who, when hardly twenty, had attacked Person's famous canons, in his work De Metris Grcecorum et Romanorum. The merit of the epigram does not certainly lie in its truth. " The Germans in Greek, Are sadly to seek ; Not five in five score, But ninety-five more ; All, save only Hermann, And Hermann's a German." In these epigrams, the conclusion of the syllogism is suppressed, yet its illative force is felt even in spite a The original is an epigram of mina. Excudehat H. Stephanus, ex Phocylides, preserved by Strabo, B. cujus etiam Ejjigrammatis Greeds tt X, p. 487, ed. Causaubon, 1620. Com- Latink aliquot ccetcris adjcda sunt, pare Anthologia Graca, i. p. 54, ed, 1569, p. 217. Brunck. Lips., 1794. Poetcc Minores Tlie parody by Porson is given in Grmci, ed. Gaisford, i. p. 444. A Short Account of the late Mr Rich- Kac ToSe *a)KvAi5eu)- Ae'pioi Kaxot- ovx 6 nrd Porson, 31. A., p. 14, London, fjikv, OS S' ov- 1808. The original Greek, with Por- Havres, nXr^v iipoKXeous- Kal iipoKAeyjs Son's imitation, is also given in I)r ^^p'-o'i- WeWesley's Antholorjia Polycjlotta, p. For the Latin imitation by Ste- 433. — Ed. phamis, see Theod. Bcza; Poemata, ^ See Buchanan, Franciscanus, 1. item ex Georgia Buchanano, alilsque 764; Beza, /*oe?/iato, p. 85, ed. 15C9; variis insirjnibus poetis cxccriHa car- Rabelais, L. iii. ch. 14. — Ed. XX. 30-1 LECTUKES ON LOGIC. LECT. of the oxpivss exception; nay, in really con([iu'iiiiL;- — l>v inii)lii'a(i()n tlu- apparent disclaimer, consists the whole })oint and elegance of the epigram. To put the former into a syllogistic shape : — Sumption — The monhs, one and all, arc good-for-nothing varlcts, excepting Peter ; Subsumption — But Peter is a vionk. Now, what is, what must be, understood to complete the sense I — Why, the conclusion, — Therefore, Peter is a good-for-nothing varlet like the rest. There is recorded, likewise, a dying deliverance of tlie philosopher Hegel, the wit of which depends upon the same ambiguous reasoning. " Of all my disciples," he said, " one only understands my philo- sophy ; and he does not." * But we may take this for an admission by the philosopher himself, that the doctrine of the Absolute transcends human compre- hension. What has now been said may suffice to show, not only that we may have enth3^memes with any of the three propositions understood, but that the distinction itself of the enthymeme, as a species of syllogism, is inept. I now go on to the Third Division of Syllogisms, under the head of their External or Accidental form, — I mean the division of syllogisms into Kegular and Irregular, — a distinction determined by the ordinary or extraordinary arrangement of their constituent parts. I commence this subject with the following paragraph : — a See DiiCKssions,]}. 788. — Ed. Par.LXXIII. LECTURES ON LOGIC. 395 If LXXIIL A syllogism is Irregular by rela- lect. tion, — 1°. To the transposed order of its Pro- positions ; 2°. To the transposed order of its S^d^of^ Terms ; and, 3°. To the transposed order of both syn^gSsms its Propositions and Terms. Of these in their order. 1°. A syllogism in extension is Kegular, in the order of its Propositions, when the subsumption follows the sumption, and the conclusion follows the subsumption. In this respect, therefore, (discounting the difference of the quantities of depth and breadth,) it admits of a fivefold irreg- ularity under three heads, — for either, 1°. The two premises may be transposed ; or, 2°. The conclusion may precede the premises, and here, either the sumption or the subsumption may stand last ; or, 3°. The conclusion may be placed be- tween the premises, and here either the sumption or the subsumption may stand first. Thus, re- presenting the sumption, subsumption, and con- clusion by the letters A, B, C, we have, besides the regular order, 1°. B, A, C,— 2°. C, A, B,— 3°. C, B, A,— 4°. A, C, B,— 5°. B, C, A. (This doc- trine of the logicians is, however, one-sided and erroneous.) 2°. A syllogism is Eegular or Irregular, in re- spect to the order of its Terms, according to the place which the middle term holds in the pre- mises. It is regular, in Comprehensive Quantity, when the middle term is the predicate of the sumption and the subject of the subsumption ; — in Extensive Quantity, when the middle term is the subject of the sumption and the predicate of the subsumption. From the regular order of oOG LECTUUKS ON LOGIC. i.KOT. tlio ti'iins tluMv aiv (liree possible clcviiitioiis, in -111— oitlicr i |iiaut ity. For the iiiidJle term may occur, 1. Twice lis predicate; lZ'\ Twice as subject; aiul, 3". In Comprehensive Quantity, it may in the sumption be subject, and in the subsumption predicate ; in Extensive Quantity, it may in the sumption be predicate, and in the subsumption subject. Taking the letter M to designate the middle term, and the letters S and P to designate the subject and predicate of the conclusion, the following scheme will represent all the possible positions of the middle term, both in its regular and irreo'ular arrano-ement. The Reoular con- stitutes the First Figure ; the Irregular order the other Three." A. — In Comprehension. I. S is M. M is P. S is P. II. S is M. P is M. S is P. III. M is S. M is P. S is P. IV. M is S. P is M. S ^6^ P. B.— In Extension. I, M is P. II. P is M. III. ]M is P. IV. P is M. S is M. S is M. M is S. M is S. S is P. S is P. S is P. S is P. These relative positions of the middle term in the premises, constitute, I repeat, what are called the Four Syllogistic Figures {crxqixara, figurw) ; and these positions I have comprised in the two following mnemonic lines : — a Cf. King, Logilc, % 104.— P:u. LECTURES ON LOGIC. 397 For Comprehension. LECT. Prce suh ; timi %)Tce prcm ; tumsuhsuh; denique sub prw. For Extension. Sub prce ; turn prce prce ; turn sub sub; denique prce sub."' Of these two kinds of irregularity in the exter- Expiica- nal form of syllogisms, the former, — that of proposi- irre^iar- tions, — is of far less importance than the latter, — that external of terms : and loo:icians have even thrown it alto- logism, aris- gether out of account, in their consideration of Syl- trausposi- logistic Figure. They are, however, equally wrong Proposi- ' in passing over the irregular consecution of the pro- positions of a syllogism, as a matter of absolutely no moment ; and in attributing an exaggerated import- ance to every variety in the arrangement of its terms. They ought at least to have made the student of Thatasyllo- T • i n • ^ • 1 Sism can be Logic aware, that a syllogism can be perspicuously perspicu- ./ o i X ousiy ex- expressed not only by the normal, but by any of the pressed by c • (• • • ' I'll" ^^y °^ '■'^^ five consecutions of its propositions which deviate five irregu- from the regular order. For example, take the fol- tions ofits . Proposi- lowmg syllogism : — tions. All virtue is praiseroorthy ; But sobriety is a virtue ; Therefore, sobriety is praiseworthy. This is the regular succession of sumption, sub- sumption, and conclusion, in a syllogism of extension • and as all that can be said, on the present question, of the one quantity, is applicable, mutatis TRUtandis, to the other, it w\\\ be needless to show articulately that a syllogism in comprehension is equally suscep- o This formnla for Extension is (jicct, t. i. c. iii. p. 169. The other taken from Purchot, Inst. Phil., Lo- line is the Author's own. — Ed. \x 30 S LECTURES ON LOGIC. i.EOT. tihle of ;i transposition of its propositions as a syllo- gism in extension. Keeping the same quantity, to wit, extension, let us first reverse the premises, leaving the conclusion in the last place (!>, A, C.) Si)hni'ti/ is a virtue ; But all virtue is praisetcorthy ; Therefore, sobriety is2)raiseworthy. This, it will be allowed, is sufficiently perspicuous. Let us now enounce the conclusion before the pre- mises ; and, under this head, let the premises be first taken in their natural order (C, A, B.) Sobriety is praiseworthy ; For all virtue is praiseworthy ; And sobriety is a virtue. Now let the premises be transposed (C, B, A.) Sobriety is praiseworthy ; For sobriety is a virtue ; And all virtue is praiseworthy. The regressive reasoning in both these cases is not less manifest than the progressive reasoning of the regular order. In the last place, let us interpolate the conclusion between the premises in their normal consecution (A, C, B.) All virtue is praiseworthy ; Therefore, sobriety is praiseworthy ; For sobriety is a virtue. Secondly, between the premises in their reversed order (B, C, A.) LECTURES ON LOGIC. 399 Sobriety is a virtue ; LECT, Therefore, sobriety is praiseivorthy ; • For all virtue is praiseworthy. a In these two cases the reasoning is not obscure, though perhaps the expression be inelegant ; for the judgment placed after the conclusion had probably been already supplied in thought on the enunciation of the conclusion, and, therefore, when subsequently expressed, it is felt as superfluous. But this is a cir- cumstance of no logical importance. It is thus manifest, that, though worthy of notice in a system of Logic, the transposition of the proposi- tions of a syllogism affords no modifications of form yielding more than a superficial character. Logicians, therefore, were not wrong in excluding the order of the propositions as a ground on which to constitute a difference of syllogistic form : but we shall see that they have not been consistent, or not sufficiently sharp-sighted, in this exclusion ; for several of their recognised varieties of form, — several of the moods of syllogistic figure, — consist in nothing but a rever- sal of the premises. In reality, however, there is no irregular order of Truedoc- ^ ,, . . . . • 1 • 1 trine of con- the syllogistic propositions, except m the single secution. case where the conclusion is placed between the premises. For a syllogism may be either called Syllogism Synthetic, in which case the premises come first, thetic or and the conclusion is last, (the case alone con- "'^ ^ ' ' templated by the logicians) ; or it may be called Analytic, the proposition styled the conclusion pre- ceding, the propositions called the premises following, as its reasons, (a case not contemplated by the a Cf. Krug, Locjlh, § 104, Anmcrk, i. — Ed. 400 LECTURES ON I.O(!Tr. LEt^. logicians). Tlie Analytic and Synthetic syllogisms — ^— ^ — may again be each considered as in the quantity of Exton.^ion, or as in the quantity of Comprehension ; in which cases we sliall have a counter-order of the premises, but of which orders, as indeed of such quantities, one alone has been considered by the loijicians. Ti.cna- I now, tliercforc, go on to the second and more turol and . i /> i ■ < i • i • transposed nuportaut ground oi regularity and irregularity — syUogistic the natural and transposed order of the Syllogistic Terms. The forms determined by the different posi- tion of the middle term by relation to the major and minor terms in the premises of a syllogism, are Figures of called Figures (cr^r^'/xara, jigurce), — a name given ) ogism, ^^ ^]jgjQ ]3y Aristotle.* Of these the first is, on the prevalent doctrine, not properly a figure at all, if by figure be meant in Logic, as in Grammar and Khetoric, a deviation from the natural and regular Three fig- form of cxprcssion. Of these figures the first three ^shed hy were distinguished by Aristotle, who developed their rules mth a tedious minuteness sometimes obscure, and not always in the best order, but altogether with an acuteness which, if ever equalled, has certainly Fourth never been surpassed. The fourth, which Whately, tributedto (at least in the former editions of his Elements,) on slender and othcr rccent Oxford logicians seem to sup- on y ^^^^ ^^ ^^^ ^^^^ ^^^ others, of Aristotelic origin, — we owe perhaps to the ingenuity of Galen. I say 2)erha2^s, for though in logical treatises attributed without hesitation to the great physician, as if a doctrine to be found in his works, this is altogether erroneous. There is, I am certain, no mention of the fourth figure in any writing of Galen -now extant, and a Anal. Prior., i. 4. — Ed. [Cf. Paciu3, Comment., pp. 118, 122.] LECTURES ON LOGIC. 401 no mention of Galen's addition of tliat figure, by lect XX. any Greek or Latin authority of an age approximat- ing to liis own. The first notice of this Galenic First as- Figure is by the Spanish Arabian, Averroes of Cor- oaien by 1 • 1 • 1 ^ a A Averroes. dova, m his commentary on the Organon. Aver- roes flourished above a thousand years posterior to Galen ; and from his report alone (as I have also ascertained) does the prevalent opinion take its rise, that we owe to Galen this amplification, (or corruption, as it may be,) of the Aristotelic doctrines of logical figure. There has been lately published from manu- script by Didot of Paris, a new logical treatise of Galen./^ In this work, in which the syllogistic figures are detailed, there is no mention of a fourth figure. Galen, therefore, as far as we know, afibrds no excep- tion to the other authors upon Logic. In these cir- cumstances, it is needless to observe how slender is the testimony in favour of the report ; and this is one of many others in which an idle story, once told and retailed, obtains universal credit as an established fact, in consequence of the prevalent ignorance of the futility of its foundation. Of the legitimacy of the Fourth Figure I shall speak, after having shown you the nature of its reasoning. Before proceeding further in the consideration of complex ,T T-i. I* n -\-\ • •• ' ^ modification the l^igure of Syllogism, it is, however, necessary of the to state a complex modification to which it is Syu^gism. subject, and which is contained in the following paragraph : — H LXXIV. The Figure of Syllogism is modi- par. lxxiv. fied by the Quantity and Quality of the proposi- Moodr'"' a Prior Analytics, [B. i. ch. 8. — ;3 Ta\r)vov Elaaywyil AiaXiKTiK^ — Ed.] eV Uapiirita au/xS' (1844). — Ed. vol. I. 2 c 402 LECTURES ON LOGIC. LEcrr. tioiis which constitute the reasoning. As tlic -^^— combination of (.Quantity and Quality affords four kinds of propositions, — Universal Aftirma- tivo (A), Universal Negative (E), Particular AlHrmative (I), Particular Negative (0) ; and as there are three propositions in each syllogism, there are consequently in all sixty-four arrange- ments possible of three propositions, differing in quantity and quality ; — arrangements which con- stitute what are called the Syllogistic Moods, (rpoTTOL, modi). I may interpolate the observa- tion : — The Greek logicians after Aristotle, look- ing merely to the two premises in combination, called these Syzycjies, (crv^vytat, jugationes, con- jugationes, combinationes). Aristotle himself never uses rpoTro^; for either mood or modality specially ; nor does he use (Tvt,vyia in any defi- nite sense. His only word for mood is the vague expression syllogism. The greater number of these moods are, how- ever, incompetent, as contradictory of the general rules of syllogism ; and there are in all only eleven which can possibly enter a legitimate syllogism. These eleven moods again are, for the same reason, not all admissible in every figure, but six only in each, that is, in all twenty-four ; and again of these twenty-four, five are useless, and, therefore, usually neglected, as having a particular conclusion where a universal is compe- tent. The nineteen useful moods admitted by logicians, may, however, by the quantification of the predicate, be still further simplified, by super- seding the significance of Figure. LECTURES ON LOGIC. 403 In enterinof on the consideration of the various lect. Moods of the Syllogistic Figures, it is necessary that you recall to memory the three laws I gave you of the ^o'^u.^'*'''" Categorical Syllogism, and in particular the two clauses of the second law, — That the sumption must be defi- nite, (general or singular), and the subsumption affir- mative, — clauses which are more vaguely expressed by the two laws of the logicians, — that no conclusion can be drawn from two ]3articular premises, — and that no conclusion can be drawn from two negative premises. This being premised ; you recollect that the four combinations of Quantity and Quality, com- petent to a proposition, were designated by the four letters, A, E, I, 0, — A denoting a universal affirma- tive ; — E, a universal negative ; — I, a particular affir- mative ; — 0, a particular negative. Asserit A ; negat E ; verum universaliter ambse : Asserit I ; negat ; sed particulariter ambo." A, it affirms of this, these, all ; As E denies of any : I, it affirms, as denies, Of some, or few, or many. Thus A affirms what E denies, And definitely either ; Thus I affirms what denies. But definitely neither.^ Now, as each syllogism has two premises, there are. The pos- sible con a See above, p. 255. — Ed. — Wilson, Eule of Reason, p. 27 a, j3 [The following are previous 155L English metrical versions of these » ^ ^^^^ ^^^ ^ ^^^;^^ . ^^^,^ ^^^^„y_ lines : j ^^y^ j^^^j q denies j both partial!)'." " A doeth affirme, E doeth denigh, which are bothe univcrsall: — Wallis, Institut'w Logicce, 16S6, L. I doeth affirme, O doeth denif,'h, ii. C. 4, p. 105.] whicho wee particular call." com- 404 LECTURES ON LOGIC. LKCT. consequently, sixteen dill'erent combinations possible -11 of premises ilitlering in quantity and quality, — viz. : bluutious of pmuiica. 1) A A. 2)EA. 3) I A. 4) O A. A E. E E. IE. O E. A 1. E I. II. I. A O. E 0. 10. 0. How many Now the question arises, — are all of these sixteen of ihoc lire ..^ ^ . . f -i- pc • ti syiiogisti- possible combinations oi dmerent premises valid to- wards a legitimate conclusion ? In answer to this, it is evident that a considerable number of these are c-illv valid. at once invalidated by the first clause of the second law of the categorical syllogism, in so far as recog- nised by logicians, by which all moods with two par- ticular premises are excluded, as in these there is no general rule. Of this class are the four moods, I I, 1 0, I, and 0. And the second clause of the same law, in so far as recognised by logicians, in- validates the moods of two negative premises, as in these there is no subordination. Of this class are the four moods, E E, E 0, E, and 0. FinaUy, by the two clauses of the second rule in conjunction, the mood I E is said to be excluded, because the particu- lar sumption contains no general rule, and the nega- tive subsumption no subordination. (This, I think, is incorrect.) These exclusions have been admitted to be valid for every Figure ; there, consequently, remain (say the logicians), as the possible modes of any legi- timate syllogism, the eight following — A A, A E, A I, A 0, E A, E I, I A, A ; " but some of these, as appar- ently contradictory of the second rule in its more de- finite assertions, — that the sumption must be general and the subsumption affirmative, — I shall, after stating a Cf. Bachinann, Locjlk, § 129. — Ed. LECTURES ON LOGIC. 405 to you the common doctrine of the logicians, show to lect be really no exceptions. XX. But whether each of the moods, though a r)riori whether each mood possible, affords a proper syllogism in all the figures, that is a — this depends on the definite relations of the middle sibie afifords 1 r> mi a proper syl- term to the two others in the several figures, ihese, logisminaii ••Tin ^^^^ figures. therefore, require a closer investigation, i shall con- sider them, with the logicians, principally in the quantity of extension, but, mutatis mutandis, all that is true in the one quantity is equally true in the other. Now if, in the first figure, we consider these eight First moods with reference to the general rules, we shall find that all do not in this figure afford correct syllogisms ; but only those which are constructed in conformity to the following particular rules, which are, however, in this figure, identical with those we have already given as general laws of every perfect and regular categori- cal syllogism. The symbol of the First Figure is,— ^ ^' !■ for Extension ; tt^V>' \ for Compreliension. The first rule is, — " The sumption must be univer- sal. Were it particular, and, consequently, the sub- sumption universal, as : — Some M are P ; But all S are M ; we could not know whether S were precisely the part of M which lies in P, and it might be altogether out of P. In that case, an universal negative conclusion would be the correct ; but this cannot be drawn, as there is no negative premise, and though accidentally 40G LECTURES OX LOGIC. LECT. XX. Legitimate moods of First Figure. Their sjin- bols. Perhaps tnio, still it i.s not a necessary consequence of the pivniisi's."" " The seconil rule is, — The subsumption must Ijc attirniative. Were it negative, and consequently the sumption atlirmativo, in that case S would be wholly excluded from the sphere of M ; and, consequently, the general rule under which M stands would not be applicable to S. Thus : — All ]\I are P ; No S is M ; No S is P. All colours are jyliysical plucnonicna ; No sound is a colour ; TJierefore, no sound is a physical phoenomenon. " Here the negative conclusion is false, but the affir- mative, which would be true, — all sounds are 2yhy steal phcenomeiia, — cannot be inferred from the premises, and, therefore, no inference is competent at all."'^ Thus, in this figure, of the eight moods generally admissible, I A and A are excluded by the first ; A E and A by the second rule. There remain, therefore, only four legitimate moods, A A, E A, A I, and E I. — The lower Greek logicians denoted them by the terms, — TpdfifjLaTa, ''Eypai/^e, Tpacpldi, Te)(^viK6s ; 7 the Latin schoolmen by the terms — Barbara, Celarent, Darii, and Ferio. a Bachmann, Lorjik, § 130, p. 203. — Ed. [So Hollmann, Phil. Ilaiion- alii, quce Logica wlgo dicitur, § 461, Gottingse, 1746 ; Lovanienses, Covi- mentaria in hay. Porphyrii et in omnes Libros Arist. de Dialectica, Anal. Prior., L. i. p. 215, Lovanii, 1547; Ulrich, Instit. Lofj. et Met, § 191, lense, 1785 ; Fonseca, histit. Dial, L. vi. c. 21, p. 363.] iS Bachmann, as above. — Ed. [Cf. Derodon, Logica Hestiivfa, P. iv. p. 618; Ulrich, as above; Lovanien- ses, as above ; Hollmann, Logica, § 462.] y For an account of these mnemo- nics, see Discussions, p. 671, second edition. — Ed. LECTURES ON LOGIC. 407 In the Latin symbols, which are far more ingenious and complete, and in regard to the history of which I shall say something in the sequel, the vowels are alone at present to be considered, and of these the first expresses the sumption, the second the subsump- tion, and the third the conclusion. The correctness of these is shown by the following examples and de- lineations. " The first mood of this figure : — LECT. XX. I. Barbara. All M are P ; All 8 are M ; Therefore, all S are P. All that is composite is dissoluble ; All material things are composite ; Therefore, all material things are dissoluble. 1. Barbara. II. Celarent. No M is P ; All S are M ; Therefore, no S is P. No fiyiite being is exempt from error ; All men are finite beings ; TJierefore, no man is exempt from error. III. Darii. All M are P ; Some S are M ; TJierefore, some S are P. All virtues are laudable Some habits are virtues ; Therefore, some habits are laudable. 2. Celarent. 3. Darii. " This diagram makes it manifest to the eye why 408 LEOTITKRS ON LOCK'. LECT. the conclusion can only be particular. As only a part — '-^— of the sphoro IS lies in the sphere M, this part must lie in the sphere P, as the whole of M lies therein ; but it is of this part only that any thing can be atlimied in the conclusion. The other part of S can either lie wholly out of P, or partly in P but out of M ; but as the premises aflirni nothing of this part, the conclusion cannot, therefore, include it. •*• ''<=^"'' IV. Ferio. No M is P ; Some S are M ; TJierefore, some S are not P. No virtue is repi'eliensihle ; Some habits are virtues ; Therefore, some habits are not reprehensible. " The conclusion in this case can only be particular, as only a part of S is placed in the sphere of M. The other part of S may lie out of P or in P. But of this the premises determine nothing."" Second The symbol of the Second Fisrure is — Figure. "^ ° Q, t^' i for Extension ; p X^^ > for Comprehension. Its rules. " This figurc is governed by the two following rules. Of these the first is — One premise must be negative.'^ For were there two affirmative premises, as : — o Bachmana, Lorjik, p. 204-206. — fi [See Derodon, Lorjica Rcstituta, Ed. p. iv. p. 637; Hollmanu, Loyica, §§ LECTURES ON LOGIC. 409 All P are M ; /- \ lect. XX. All S are M ; All metals are minerals ; All pelbles are minerals ; the conclusion would be — All pebbles are metals, whicli would be false. " The second rule is : — The sumption must be uni- versal." Were the sumption particular, the subsump- tion behoved to be universal ; for otherwise no con- clusion would be possible. But in that case the sump- tion, whether affirmative or negative, would afford only an absurd conclusion.'^ " If affirmative, as : — Some P are M ; No^isM; Therefore, some S are not P. Some animals lay eggs, i.e. are egg-laying things ; No horse lays eggs, i.e. is any egg-laying thing ; Therefore, some horses are not animals. " If negative, as :• — Some P are not M ; All S are M ; Therefore, some S a7-e not P. Some minerals are not precious stones ; All tojMzes ore precious stones ; Therefore, some to'pazes are not minerals. In both cases the conclusion is absurd. 463, 464; Lovanienses, Com. in a SeeHollmann, andLovanienses, Arist. Anal. Prior., L. i, p. 218; as cited above. — Ed. &cotyis,^[Qucestionesin Anal. Prior., $ [Cf. Fonseca, Instil. Dial, L. L. i. q. 20, f. 268.— Ed.] vi. c. 21, p. 363.] 410 LECTURES ON LOGIC. LECT. XX. "Tlioro tlius iviiKiiii," say the logiciiins, "only the iiuhhIs Ci'sarc, Camcstres, Festino, Baroco. 1. Cc^.VC 2. Canies- tres. I. Cesare. No P Is M ; All^ arc M ; Therefore, no S is P. NothiiKj material has free will; AH s/nrits have free willy Therefore, no spirit is material. II. Camestres. AUV are M ; No S is M ; Therefore, no S is P. All colours are visible s No sound is visible; Hierefore, no sound is a colour. 3. Festino. III. Festino. No P is M ; Some S are M ; Therefore, some S are not P. No vice is praiseworthy ; Some actions are praiseworthy ; Therefore, some act ions are not vices. " The diagram here is alternative, for as the con- clusion can only comprise a part of S, as it is only the consequence of a partial subordination of S to M, the other parts of S which are out of M may either lie within or without P. The conclusion can, therefore, only be particular. LECTURES ON LOGIC. 411 IV. Baroco. All P are M ; Some S are not M ; Therefore, some S arc not P. All birds are ovijjarous ; Some animals are not ovijmroiis ; Therefore, some animals are not birds.'^ " © LECT. XX. 4. Baroco. a Bachmann, Logik, as above. — Ed. 412 LEcrruRES on locic. LECTURE XXL STOICHEIOLOGY. SECTION IT. — OF THE PRODUCTS OF THOUGHT. III. — DOCTRINE OF REASONINGS. SYLLOGISMS, THEIR DIVISIONS ACCORDING TO EXTERNAL FORM. FIGURE THIRD AXD FOURTH. LECT. In our last Lecture, after terminatinsj the p^eneral XXI • — " consideration of the nature of Figure and Mood in Re^pituia- Categorical Syllogisms, we were engaged in a rapid survey of the nineteen legitimate and useful moods belono^ing to the four fiooires, accordinor to the received doctrine of logicians, (consequently, exclusively in Ex- tension) ; and I had displayed to you the laws and moods of the First and Second Figures. Before, there- fore, proceeding to any criticism of this doctrine, it behoves us to terminate the view of the two remain- ino; fioTires. Third To each of the first two figures, logicians attribute igure. £.^^^ moods ; to the third they concede six ; and to the fourth five. The scheme of the Third Figure, in Extension, is — M P, M S. Its rules. This figurc (always in extension) is governed by XXI. LECTURES ON LOGIC. 413 the two following laws : — the first is, " The subsump- lect tion must be afiirmative.'" Were the minor premise - a negative, as in the syllogism, — All M are P ; All fiddles are musical instruments ; NoM.is^; ' But no fiddle is a flute ; here the conclusion would be ridiculous, — Therefore, no S is P, — Therefore, no flute is a musical instru- raent. For M and S can both exclude each other, and yet both lie within the sphere of P. " The second law is, — The conclusion must be par- ticular, and particular although both premises are universal.'^ This may be shown both in affirmative and negative syllogisms. In the case of afiirmative syllogisms, as : — All M are P ; But all j\I are S ; here, you will observe, M lies in two different spheres — P and S, and these must in the conclusion be con- nected in a relation of subordination. But S and P may be disparate notions,'^ and, consequently, not to be so connected ; an absurd conclusion would, there- fore, be the result. For example, — All birds are animals toith feathers ; But all birds are animals with a heart ; Therefore, all animals with a heart are animals with feathers. *' Again," say the logicians, " in regard to negatives : — In these "only the sumption can be negative, as the a [See Aristotle, Anal. Prior., i. Prior., L. i. p. 220.] 6, §§ 8, 16; Hollmann, Logica, § y Disparate notions, i.e. co-ordi- 4G6; Lovanienses, In Anal, Prior., nate parts of the com[)rehensiou of L. i. p. 220.] their common subject M. See above, iS [But see Hollmann, Loijum, §§ p. 224.— Ed. .3.32, 458; Lovanienses, In Anal. 414 LECTURES ON LOOIC. LECT. subsumption, (hy the iir.st rule), must be afiirmativc. ''''^ Thus :— No M m'hisi()n can, in like inanuLT, only jiulgc of ;i part of S. or the otlior parts of S tliere is nothing onoiuu'oil in tho premises. The rchition between S and I' could likewise be as follows : — No M is P ; But all M are S ; or, No pigeon is a hawk ; But all pigeons are birds. " Here the conclusion could not be a universal nega- tive, — Therefore, no S is P — Therefore, no bird is a hcnvk — for the sphere of S {bird) is greater than that of either M {jngeon) or P {hawk) ; it may, however, be a particular negative — Therefore, some S are not P, (therefore, some birds are not hawks), — because the sumption has excluded M and P [pigeon and hawk) from each other's sphere, and, consequently, the part of S which is equal to M is different from the part of S which is equal to P. — But if this be the case when the subsumption has an universal expression, the same, a fortiori, is true when it is particular. " The third mood of this figure is : — 3. Disamis. III. Disamis. Some M are P ; But all M are S ; Therefore, some S are P ; or. Some acts of liomicide are laudahle ; But all acts of homicide are cruel ; Therefore, some cruel acts are laudahle. "LECTURES ON LOGIC. 417 The fourth mood of this figure is IV. Datisi. All M are P ; But some M are S ; Therefore, some S are P ; or, All acts of Iwmicide are cruel ; Some acts of homicide are laudable ; Therefore, some laudable acts are cruel. LECT. XXI. 4. Datisi. " This diao;ram makes it manifest that more than a single case is possible in this mood. As the subsump- tion is particular, the conclusion can only bring that part of S which is M into identity with P ; of the other parts of P there can be nothing determined, and these other parts, it is evident, may either lie wholly out of, or partly within, P. " The fifth mood of this figure is : — V. BOCARDO. Some M are not P ; But all M are S ; Therefore^ some S are not P ; or, Some syllogisms are not regular ; But all syllogisms are things important ; Tlierefore, some important things are not things rcgidar. 5. Bocardo " The sixth mood of this figure is : — VI. Ferison. No M is P j But some M are S ; Therefore, some S are not P ; G. Ferisou. VOL. I. 2 1) 418 LECTURKS ON LOOIC. LECT. <^r, ' No truth is irithout result ; ISituw truths are misumh'rstonil ; Thi'reforc, some thuKjs misuudcrstood are not without res>dt. " Here, as in the premises, only tliat part of S wliicli is M is excluded from P, consequently the other parts of S may either likewise lie wholly out of P, or par- tially in P."" So much for the moods of the third figure. Fourth " The formula of the Fourth Figure is : — Figure. '-' PM MS. Its laws. " This figure is regulated by three laws. " I. Of these the first is — If the sumption be affir- mative, the subsumption must be universal. The necessity of this law is easily seen. For if we had the premises — ^/Z P are M ; But some M are S ; in this case, M might, or might not, be a notion supe- rior to P. On the former alternative, if M be higher than P, and likewise higher than S, then the whole of S might be contained under P. — In this case, the proper conclusion would be a universal affirmative ; which, however, cannot follow from the premises, as o Bachmann, Logik, § 132, p. 211-218.— Ed. XXI. LECTURES ON LOGIC. 419 the subsumption, ex kyjyothesi, is particular. On the lect latter alternative, even if M were not superior to S, still since P is only a part of M, we could not know whether a part of S were contained under P or not. For example : — All men are animals ; But some animals are amj)hihiou8. From these premises no conclusion could be drawn. " II. The second rule by which this figure is governed is — If either premise be negative, the sumption must be universal. " Suppose we had the premises — Some P are not M ; But all M are S ; Tlierefore, some S are not P ; or, . Some animals are not feathered ; But cdl feathered animals are birds ; Therefore, some birds are not animals ; in this case, the whole of S lies within the sphere of P ; there cannot, therefore, follow a particular negative conclusion, and if not that, no conclusion at all. The same would happen were the sumption a particular affirmative, and the subsumption a univer- sal negative. " III. The third rule of the fourth figure is — If the subsumption be affirmative, the conclusion must be particular. This (the logicians say) is manifest. For in this figure S is higher than M, and higher than P, consequently only a part of S can be P. " If we test by these rules the eight possible moods, there are in this figure five found competent, which, among sundry other names, have obtained the fol- 420 LECTURES ON LOGIC. LEcn^ lowiiicj: Bramatitip, Camcncs, Dimaris, Fesafo, XXI. ., rrcsisou. 1. Bromau- tip. " Of tliesc moods the first is : — I. Bramantit, otherwise Bamalip, &c. All P are M ; AU M are S ; Therefore, some S ore P ; or, All greyhounds are dogs ; But all dogs are qvadrupeds ; Therefore, some quadrupeds are greyhounds. " The second mood is called : — 2. Camenes. II. CaMENES, CaLEMES, or CaLENTES, &C, AllV are M ; Biit no ]M is S ; / m Therefore, no S is P ; or, I ^ All ruminating animals have four ^v \,_y stomachs ; But no animal with four stomachs is carnivorous ; TJierefore, no carnivorous animal ruminates. " The third mood in the fourth figure is variously denominated : — Dimaris. III. DiMARIS, Or DiMATIS, Or DiBATIS, &C. So7ne P are M ; But all M are S ; Therefore, some S are P ; I p / /I m or, Some practically virtuous men are neces- sitarians ; All necessitarians speculatively subvert the distinction of vice and virtue ; Tlierefore, some who sj)ectdatively subvert the distinction of vice and virtue are practically virtuous men. LECTURES ON LOGIC. 421 '' Tlie fourth mood of this figure is : — lect. XXL 4. Fesaj)o. IV. Fesapo. NoF isM; All M are S ; Therefore, some S are not P ; or, No negro is a Hindoo ; But all Hindoos are blacks ; Therefore, some blacks are not negroes. or, " According to the first of these diagrams, all S is excluded from P, and thus the conclusion would seem warranted that — No S is P. This conclusion cannot, however, be inferred ; for it would violate the third rule of this figure. For while we, in the sumption, have only excluded M, that is, a part of S, from P, and as the other parts of S are not taken into account, we are, consequently, not entitled to deny these of P. The first diagram, therefore, which sensualises only a single case, is not coadequate with the logical formula, and it is necessary to add the second in order to ex- haust it. The second diagram is, therefore, likewise a sensible representation of Fesapo ; and that diagram makes it evident that the conclusion can only be a particular negative. " The fifth and last mood is : — V. FreSISON. 5. Fresison. No T isM.; But some M are S ; Therefore, some S are not P. 422 LECTURES ON LOGIC. i.wr. or, Mood auJ Figure iu Coniprc- hcusion. Xi> moral 2>f''»<^'il>^^' '•'' <^f^ atilinal impulse; Hut dome animal ijtqiulncs arc principles of action ; Therefore, some principles of action arc not moral principles. or, " The dcmoustration is here the same as in the former mood. Since the subsumption only phices a part of M in the sphere of S, the conclusion, whose quantity is determined by the subsumption, can only deny P of that part of S which is likewise a part of M." " Having thus concluded the exposition of the various Figures and Moods of Syllogisms, as recognised by logicians, in reference to Extensive Quantity, it will not be necessary to say more than a word in general, touching these figures and moods in reference to Com- prehensive Quantity. Whatever mood and figure is valid and regular in the one, is valid and regular in the other ; and every anomaly is equally an anomaly in both. The rules of the various figures which we have considered in regard to syllogisms in Extension, are all, without exception or qualification, applicable to syllogisms in Comprehension, with this single pro- viso, that, as the same proposition forms a different premise in the several quantities, all that is said of the sumption in extension, should be understood of the subsumption in comprehension, and all that is said of the sumption in comprehension, should be understood of the subsumption in extension. What, therefore, o Bachmanu, LorjiJc, § 133, p. 218-223.— Ed. LECTURES ON LOGIC. 423 lias liitherto been, or may hereafter be, stated of the lect. mood and figure of one quantity, is to be viewed as XXL applicable, mutatis mutandis, to the other. This being understood, I proceed, in the first place, to show you Criticism of that the complex series of logical forms which I have iug doctnuu enumerated, may be considerably diminished, and the forms. doctrine of syllogism, consequently, reduced to a higher simplicity. In doing this I shall consider, first, the Figures, and, secondly, their Moods. Now, as regards the number of the Figures, you are i-.The FififUTGS aware, from what I formerly stated, that Aristotle only contemplated the first three, and that the fourth. The Fourth. which is, by those who do not mistake it for an Aris- totelic form, referred with little probability to Galen, was wholly unnoticed until the end of the twelfth or the beginning of the thirteenth century, when it was incidentally communicated, as an innovation of the physician of Pergamus, by the celebrated Averroes, in his commentary on the Prior Analytics of Aristotle, but by Averroes himself rejected as an illegitimate novelty." The notice of this figure by the commen- tator was, however, enough ; and though repudiated by the great majority of the rigid Aristotelians, the authority of Scotus, by whom it was defended,^ secured for it at last, if not an universal approval, at least a a In Anal. Prior., i. 8. Opera nem non pervenit diversitas alicujus Aristotelis, t. i. f. 78, Veuetiis, 1560. prsemissse nee conclusionis : percon- — Ed. sequens nee diversitas figure." P This statement is marked as The Fourth Figure is, however, doubtful in the Author's Common- said by Ridiger, {De Scnsu Vcri et place Book, ^cotws {QucbsL in Anal. Falsi, \>. 337), to have been intro- Prior., i. q. 34) expressly rejects the dueed by Galen and Scotus. Hos- Fourth Figure. He says, "Solum pinianus (De Controvcrsiis Dialecti- tribus modis potest fieri debita ordi- cis, c. xix. ) attributes (erroneously) natioresjiectuextremorum secundum the invention of this figure to Scotus. subjectionem et prfedicationem ; igi- Compare also Noldius, Logica Eccog- tur tres erunt tigurai et non jilures nita, c. xiii. § 4, p. 277. — Ed. .... quia per solam transpositio- 424 LECTURES ON L0C1(\ LECT. very generixl tolenitioii, «is a legitimate though an — — — awkward form. The arguments indeed by which it Wiis attempted to evince the incompetency of this fio-ure, were not of a character calcuhited to enforce assent ; for its inference is not less valid than that of any other, — however tortuous and perverse it may be felt to be. In fact, the logicians, in consequence of their exclusive recognition of the reasoning in exten- sion, were not in possession of the means of showing, that this figure is a monster undeserving of toleration, far less of countenance and favour. I shall not, there- fore, trouble you with the inconclusive reasoning on the part either of those who have assailed, or of those who have defended this figure, but shall at once put you in possession of the ground on which alone, I think, its claim to recognition ought to be disallowed. Grounds ou lu thc first placc, thcu, you are aware that all rea- Fourth ^ soning is either in the quantity of comprehension, or oulht'to be in the quantity of extension. You are aware, in the disaUowed. gg^Qj^^i place, that these quantities are not only differ- ent, but, as existing in an inverse ratio of each other, opposed. Finally, in the third place, you are aware that, though opposed, so that the maximum of the one is the minimum of the other, yet the existence of each supposes the existence of the other ; accordingly, there can be no extension without some comprehen- sion, — no comprehension without some extension. A cross This being the case, it is evident that, besides the pSir definite reasoning from whole to part, and from parts iio™t?Com- to whole, within the several quantities and in their and'^S"" perpendicular lines, there is also competent an indefi- ''^''^'^' nite inference across from the one quantity to the other. For if the existence of the one quantity be only possible under the condition of the other, we may LECTURES ON LOGIC. 425 always, it is self-evident, in the first place, from the lect. affirmation of anything in extension, indefinitely affirm _ it in comprehension, as, reciprocally, from the affirma- tion of anything in comprehension, we may indefinitely affirm it in extension ; and, in the second place, from the negation of anything in extension, we may abso- lutely deny it in comprehension, as reciprocally, from the negation of anything in comprehension, we may absolutely deny it in extension. Now, what has not been observed, such is exclu- This the sively the inference in the Fourth Figure ; its two hfferenee iu last rules are in fact nothing but an enunciation of Figure""^ these two conditions of a cross inference from the one quantity to the other ; and the first rule will be hereafter shown to be only an error, the result of not observing that certain moods are only founded on the accident of a transposed order of the premises, and, therefore, constitute no subject for a logical legislation. To prove this statement of the nature of the infer- Proved and ence in the fourth figure, it is only necessary to look at its abstract formula. In extension this is : — FisM; S is P. Here in the premises P is contained under M, and M is contained under S ; that is, in the premises S is the greatest whole and P the smallest part. So far, this syllogism in extension is properly a syllogism in comprehension, in which the subject of the conclusion is the greatest whole, and its predicate the smallest part. From such premises we, therefore, expect, that the conclusion carrying out what was established in 426 LECTURES ON LOGIC. LECT. the antecedent, should affirm P as the part of S. — In -1— this, however, our expectation is disappointed ; for the reasoning suddenly turns round in the conclusion, and affirms S as a part of P. And how, it may be asked, is this evolution in the conclusion competent, seeing that it was not prepared, and no warrant given for it in the premises ? To this the answer is prompt and easy. The conclusion in this figure is solely legi- timated by the circumstance, that from an identity between the two terms in one quantity, we may always infer some identity between them in the other, and from a non-identity between them in one quantity, we can always infer a non-identity in the other. And that in this figure there is always a transition in the conclusion from the one quantity, is evident ; for that notion which in the premises was the greatest w^liole, becomes in the conclusion the smallest part ; and that notion which in the premises was the smallest part, becomes in the conclusion the greatest whole. Now how is this manoeuvre possible "? — how are we entitled to say that because A contains all B, therefore, B con- tains some A ? Only it is clear, because there is here a change from the containing of the one quantity to the containing of the other; and because, each quantity necessarily implying the indefinite existence of the other, we are consequently permitted to render this necessary implication the ground of a logical infer- ence. This hybrid It is mauifcst, however, in the first place, that such L Unnllu^ ^ cross and hybrid and indirect reasoning from the ^^^' one quantity to the other, in the fourth figure, is wholly of a diff"erent character and account from the reasoning in the other three figures, in which all inference, whether upwards or downwards, is equable LECTUEES ON LOGIC. 427 and liomogeneous within the same quantity. The lect. latter in short is natural and easy ; the former un- - natural and perverse. In the second place, the kind of reasoning com- 2. Usekss. petent in the fourth figure, is wholly useless. The change from the one quantity to the other in the course of a syllogism, is warranted by no necessity, by no expediency. The reasoning in each quantity is absolute and complete within itself, and all that can be accomplished in the one process can equally w^ell be accomplished in the other. The jumping, therefore, from extension to comprehension, or from compre- hension to extension, in the conclusion of the fourth figure, is a feat about as reasonable and useful in Logic, as the jumping from one horse to another would be reasonable and useful in the race-coui'se. Both are achievements possible; but, because possible, neither is, therefore, a legitimate exercise of skill. We may, therefore, on the ground that the fourth figure involves a useless transition from one quantity to another, reject it as a logical figure, and degrade it to a mere logical caprice. But, in the third place, there is a better ground ; 3. Logically the inference, though valid in itself, is logically, — is scientifically, invalid. For the inference is only legi- timated by the occult conversion of the one quantity into the other, which takes place in the mental process. There is thus a step taken in the reasoning, which is not overtly expressed. Were the whole process stated in language, as stated it logically ought to be, instead of a simple syllogism with one direct conclusion, we should have a complex reasoning with two conclusions; one conclusion direct and immediate, (the inference, to wit, of conversion), and from that immediate con- XXI 428 LECTUKES ON LOGIC. LECT. elusion another mediate and indirect, but wliicli, as it stands, appears as the one sole and exclusive conclu- sion from tlie premises. This ground, on which I thhik the fourth figure ought to be specially abolished, is stated with the requisite details in the Logical Appendix contained in the second edition of my Dis- cussions on Philosophy.'^ a p. GG3.— Ed. LECTURES ON LOGIC. 429 LECTURE XXII. STOICHEIOLOGY. SECTION II. OF THE PRODUCTS OF THOUGHT. III. DOCTRINE OF REASONINGS. SYLLOGISMS. THEIR DIVISIONS ACCORDING TO EXTERNAL FORM. C. REGULAR AND IRREGULAR. FIGURE — REDUCTION. In my last Lecture, after terminating tlie view of the lect. -" ^ XXII. nineteen Moods of the Four Syllogistic Figures, ac- cording to the doctrine of logicians, I entered on the Jon!''"'''^'' consideration, — how far their doctrine concerning the number and legitimacy of these various figures and moods was correct. In the conduct of this discus- sion, I proposed, first, to treat of the Figures, and, secondly, to treat of the Moods. Commencing, then, with the Figures, it is manifest that no exception can possibly be taken to the first, which is, in point of fact, no figure at all, but the one regular, — the one natural form of ratiocination. The other three fio^ures divide themselves into two classes. The one of these classes comprehends the fourth ; the other, the second and third figures. The fourth figure stands, on the common doctrine of the logicians, in a more unfavour- able situation than the second and third. It was not 430 LECTURES ON LOGIC. LECT. recognised by Aristotle ; it obtained admission into 11 L the science at a comparatively recent period ; it has never in fact been universally recognised ; and its ]>r(-»gress is manifestly more perverse, circuitons, and unnatural, than that of any other. In regard to this fourth figure, I stated that the controversy among logicians touching its legitimacy, had been without result ; its opponents failing to show that it ought to be rejected ; its defenders failing to show that it was deserving of recognition. I then stated that the logicians, in their one-sided view of the reasoning process, had let slip the one great prin- ciple on which the legitimacy of this figure was to be determined. I then explained to you that the pecu- liarity of the fourth figure consists in this, — that the premises are apparently the premises of a syllogism in one kind of quantity, while its conclusion is the converted conclusion of a syllogism in the other. It is thus in every point of view contorted and prepos- terous. Its premises are transposed, and the conclu- sion follows from these, not directly, but through the medium of a conversion. I showed how, and how far, this kind of reasoning was competent, and that though the inference in the fourth figure is valid, it is incon- venient and useless, and, therefore, that the form itself, though undoubtedly legitimate, is still only a legiti- mate monster. Herewith the Lecture terminated. General Now, looklug supcrficially at the matter, it might theSndf seem, from what has now been said, that the fourth FturtLFig. ought to be at once expunged from the series of '"^^' loffical figures. But a closer examination will show US that this decision would be rash. In point of fact, all figure properly so called, that is, eveiy figure, with the exception of the first, must be rejected equally LECTURES ON LOGIC. 431 with the fourth, and on the following ground, — that lect. they do not, in virtue of their own expressed pre- '- mises, accomplish their own inference, but that this is done by the mental interpolation of certain comple- mentary steps, without which no conclusion in these figures could be drawn. They are thus in fact reason- ings apparently simple, but in reality complex ; and when the whole mental process is expressed, they are found to be all only syllogisms in the first figure, with certain corollaries of the different propositions inter- mingled." This doctrine corresponds with that of the logicians, in so far as they, after Aristotle, have allowed that the three last figures are only valid as reducible to the first ; and, to accomplish this reduction, they have supplied us with a multitude of empirical rules, and lavished a world of ingenuity in rendering the working of these complex rules more easy. From Whately and the common books on Logic, you are of Latin and course acquainted with the import of the consonants mnemonics^ in the cabalistical verses, Barbara, Celarent, &c. ; ^ and ^thorl it must be confessed that, taking these verses on their own ground, there are few human inventions which display a higher ingenuity. Their history is appa- rently altogether unknown to logicians. They were, in so far as they relate to the three first or Aristotelic figures, the invention of Petrus Hispanus, who died in 1277 Pope John XXII. , (or as he is reckoned by some the XXL, and by others the XX). He was a native of Lisbon. It is curious that the corresponding Greek mnemonics were, so far as I can discover, the inven- tion of his contemporary Nicephorus Blemmidas, who o This doctrine of Figure, which vier syllogistischcn Flgvren, 1762; is developed in paragraph Ixxv., is WerTce, i. p. 55, ed. Rosenkranz and mainly taken from Kant. See his Schubert. — Ed. Essay Die falsche SpitzfmdirjkcU cler $ See Discussions, p. 6GG. — En. 432 LECTURES ON LOGIC. LECT. was dosigiia toil Patriarch of Constantinople." Between -11— _ them, these two logicians thus divided the two highest places in the Christian hierarchy ; but as the one had hardly begun to reign when he was killed by the downfall of his palace/ so the other never entered on his office, by accepting his nomination, at all. The several works of the Pope and the Patriarch were for many centuries the great text-books of Logic, — the one in the schools of the Greek, the other in the schools of the Latin church. The Greek The Crcck symbols are far less ingenious than the symbols less ^ . , i i i • , • • iu-enious Latiu, as they mark only the consecution, quantity, Latiu. "" and quality of the different propositions of the various moods of the three generally admitted figures, without showing to what mood of the first the moods of the other two figures are to be reduced, far less by what particular process this is to be done. All this is ac- complished by the symbols of the Roman Pontiff. As to the relative originality, or the priority in point of date, of these several inventions, I am unable to speak with certainty. It is probable, however, that the Blemmidas was the first, both because his verses are the simpler and ruder, and because it is not known that he was acquainted with the writings of the Western logicians ; whereas I find that the Summuloo of Hispanus are in a great measure taken, not indeed from the treatise of Blemmidas upon Dialectic, but from the Synopsis of the Organon of his somewhat earlier contemporary Michael Psellus."^ o But see Discussions, p. 672. — truer account ; the work which goes Ed. by the name of Psellus being in all /3 See Platina, [Historia de, Vitis probability a translation from His- Pontificum Eomanorum, p. 181, ed. panus, the mnemonics, with one ex- 1572. See sAsoBrvLcker, Hist. Phil., ception, being omitted. See ZHscus- vol. iii. p. 816.— Ed.] sims, p. 128.— Ed. 7 The reverse is probably the LECTURES ON LOGIC. 433 But the whole of the rules o-iven by loQ-icians for lect. . XXII. tlie Reduction of Syllogisms are unphilosophical, for they are merely the empirical statements of the opera- ofTo^cians tion of a principle in detail, which principle itself has auction ?f been overlooked, but which, when once rationally ex- u^phfio"'' plicated, supersedes the whole complex apparatus of '°^''"'''''" rules for its mechanical application. If I succeed, therefore, in ex^^laining to you how the The last three last Figures are only the mutilated expressions Figures of a complex mental process, I shall not only subvert mutilated their existence as forms of reasoning not virtually o'r a com- identical with the first figure, — I shall not only re- process, aurocess of redressing it, though equally easy, is some- what more complex. The formula is : — All? arc M ; But no S in M ; Therefore, no S is P. In reality Hcrc, iu thc first place, the premises are transposed, t\'lareiit. iii for you remember by the second general law oi syllo- gisms, the sumption must in extension be universal, and the subsumption affirmative. By a preliminary operation, their apparent consecution must, therefore, be accommodated to their real. The premises being restored to order, there is yet a further intricacy to unravel. The sumption and the conclusion are neither of them proximate ; for we depai-t from a conversive sumption, and primarily obtain a conclusion wdiich only gives us the ostensible conclusion, in the second instance, through an inference. Thus : — Ostensible Sumption, No S is M ; Proximate or Eeal Sumption, (Then, no M in S ;) Subsumption, All P ore M ; Proximate or Eeal Conclusion, {Therefore, vo P is S ;) Ostensible Conclusion, Tlierefore, no S is P. The concrete example given was : — All colours are visible ; But no sound is visible ; Therefore, no sound is a colour. a [That CcFarc and C'amestres are Opera Logica, Lc Quartn Fir/vrn the same syllogism with acciden- Sylloq., p. Ill, and authorities cited tal order of j)remisc3, see Zabarella, above, p. 414, note.] LECTURES ON LOGIC. 437 Reversing: the premises, we have : — lect. Apparent Sumption, JVo sound is visible ; Proximate or Eeal ^\!iVCi\)i\oi\,... {Then, nothing visible is a sound;) Subsumption, All colours are visible ; Proximate or Eeal Conclusion, ...(y/iere/bre, no colour is a sound ;) which gives, as a conversive inference, the Expressed Conclusion, Then, no sound is a colour. Thus it is evident that Camestres, in the second fig- ure, is only a modification of Celarent, in the first." The third mood of the Second Figure, Festino, pre- 3. Fcstino. sents no difiiculty. We have only to interpolate the real sumption, to which the subsumption and conclu- lu reality sion proximately refer. Thus : — Expressed Sumption, No P is M ; Eeal or Proximate Sumption,... (T/^ew, no IM is P ;) Subsumption, But some S are M ; Conclusion, Therefore, some S are not P. Our concrete example was : — Expressed Sumption, No vice is laudable; Some actions are laudable ; Therefore, some actions arc not vices. Here we have only to interpolate as the real sump- tion : — Nothing laudable is a vice. Festino, in the second figure, is thus only Ferio in the first, with its sumption converted. o Cf. Krug, Loii'ik, § 109, p. 3G8; glca Itcstit., Vars. iv.\>. GiS. lleusch, Mark Dimcan, Imtit. Loyicce, L. iv. Sydcma Loyicum, § 438, \>. Gl.'i]. c. 4, p. 229. — Ed. [Dcrodon, Lo- 438 LKcrrrvES on logic. i.F.cT. The t'ouitli mood, Baroco, is more troublesome. In — — — fact, this mood and Bocardo, in the third figure, have 4. Biiroco. [,^^^^l^ .^^i Q^^^.(3 tl^Q C7'tices and tlie opprobria of logicians. They have, indeed, succeeded in reducing these to the Ko.iiutio!».i first figure by what is called the rcductio ad impos- unpoisi I c. ^-j^^^j^^ ^YiqX> is, by circuitously showing that if you deny the conclusion in these syllogisms, the contradictory inference is absurd ; but as of two contradictories one or other must be true, it, therefore, remains that the original conclusion shall be admitted. This process is awkward and perplexing; it likewise only con- strains assent, but does not afford knowledge ; while at the same time we have here a syllogism with a negative subsumption, which, if legitimate, invalidates the universality of our second general rule. Now, on the principle I have proposed to you, there is no difficulty whatever in the reduction of this or of any other mood. Here, however, we do not, as in the other moods of the second figure, find that the syllogism proximately departs from an unexpressed sumption, but that the proximate subsumption and the proxi- mate conclusion have been replaced by two derivative In reality propositious. Tlic fomiula of Baroco is : — Darii. All P are M ; But some S are not M ; Therefore, some S are not P. But the following is the full mental process : — Sumption, AWP are M ; Real Subsumption, {Some wo/-M are S ;) which gives the j Then, some S are not-li ; Expressed Subsumption, | Qr^ gome S are not M ; Ileal Conclusion, ( Tlierefore, some not-F are S ;) LECTURES ON LOGIC. 439 whicli gives the . 2^;^^^^ ..^^^ g ^^^ ^^t-F ; LECT. Expressed Conclusion, | Qr, some S are not P. ^^"- Or, to take our concrete example : — All birds are oviparous ; But some animals are not oviparous ; Therefore, some animals are not birds. Of this the explicated process will stand as follows : — Sumption, All birds are oviparous ; Eeal SiiT.="r-r.f,-nT. f ('^^^'^^ ^^^^'^^^ '^^^ oviparous are ci V ■• [ (So7ne things bUDsumption, J ^ \ ( animals ;) wliich gives the ( Then, some animals are not-ovi- Expressed Subsumption, •^ parous ; y Or, are not oviparous ; T> , -r^ . , ^ , . { (Therefore, some things not birds Keal or Proximate Conclusion, \ . , \ ( are animals ;) which gives the /• Then, some animals are not- Expressed Conclusion, <| birds ; \ Or, are not birds. Now, in this analysis of the process in Baroco, we not only resolve the whole problem in a direct and natural and instructive way ; but we get rid of the exception which Baroco apparently affords to the general rule, that the subsumption of a categorical must be affirmative. Here you see how the real sub- sumption is affirmative, and how, from having a negative determination in its subject, it by conversion assumes the appearance of a negative proposition, the affirmative proposition, — some things not-hirds are animals, being legitimately converted, first into, — some animals are not-hirds, and this again being legi- timately converted into, — some animals are not birds. You recollect that, in the doctrine of Propositions," I showed you how every affirmative proposition could a See above, p. 253. — Ed. 440 LECTrKES; 0\ LOGIC, LEtT. XXII. Third Fig- ure. 1)0 adequately expressed in a negative, and every negative in an allirmative form ; and the utility of that observation you now see, as it enables us sinii)ly to solve the problem of the reduction of Baroco, and, as we shall also see, of Uocardo. Jjaroco is thus directly reduced to Darii of the first figure, and not, as by the indirect process of logicians in general, to iKirbara." On this doctrine the name Baroco is also improper, and another, expressive of its genuine affin- ity, should be imposed. We proceed now to the Third Figure. You will observe that, as in the Second Figure, with the ex- a There seems to be an enor in the text here. The syllogism, as finally reduced, is not in Darii, nor in any legitimate mood; and its na- tural reduction, according to the me- thod adopted by the Author, is not to Darii, but to Ferio, by means of an unexpressed sumption. Thus : — All P are M; Tken no »w<-M are P ; Some S are not-M ; Therefore, some S are not P. This is the method adopted by the following logicians, referred to by the Author in his Common-Place Book, viz. : — Noldius, who calls Baroco, Facrono, Logica Recognita, cap. xii. § 12, p. 300, 1666 ; Keusch, (who follows Noldius), Si/st^ma Lo- gicum, § 539, p. 611, 2d ed., 1741; Wolf, Phil. I'Mtionalis, § 384 ; Bach- mann, Logih, § 133, Anm., L p. 224. Before any of the alx)ve-mentioned WTiters, Mark Duncan gives the re- duction of Camestres to Celarent, and of Baroco to Ferio, by counter- position. He adds, with special re- ference to the reduction of Earoco to Ferio by this method, — " Hanc re- ductionis speciem exLstimo a scholas- ticis perspectam fuisse : sed despcc- tam ; quia in prima figura propositio minor affirmans attributi infmiti, quam primo intuitu videatur esse negans, formse evidentiam obscurat : atqui syllogismorum reductio com- parata est non ad formse bonitatem obscurandam, sed illustrandam." Institntioncs Logica, L. iv. c. 3, § 4, p. 230. Salmurii, 1612. The syllogism of the text may also be exhibited more circuitously, as Darii, by retaining the affirmative quality in the converted proposition. Thas :— A II '/K)<-M are not-P ; SojJie S are not-'M ; Therefore, some S are not-V. This is the method of reduction employed by Derodon, who, in the same way, would reduce Camestres to Barbara, Logica Ilest'duta, P. iv. tract, i. c. 2, art. 6, p. 648. The error here noticed seems to have ori- ginated in a momentary confusion of the reduction of Baroco with that of Bocardo ; which, however, could not be rectified without greater al- terations in the text than the Edi- tors consider themselves justified in making. — Kd. LECTURES ON LOGIC. 441 ception of Baroco, it was the sumption of the two lect. XXII premises which was affected by the conversion, so in '— the third it is the subsumption. For in Camestres of the second, and in Disamis and Bocardo of the third, figure, the premises are transposed. This understood subsumption is a conversive inference from the ex- pressed one, and it is the proximate antecedent from which the real conclusion is immediately inferred. In the first mood of this figure, Darapti, the sub- 1. Darapti. sumption is an universal affirmative ; its conversion is, therefore, into a particular affirmative. Its for- in reality - . I)aiii. mula IS — Sumption, All M are P; Exjiressed Subsumption, But all M are S ; which gives the Eeally Proximate Subsumption, ...(7'7ssod Sumption, All M are S ; The Keal Subsumptiou, (Then, some S are M;) from which The Conchision, Therefore, some S are not P. Our example was — Sumption, Noth ing material is a free agent ; Expressed Subsumptiou, i ^«^ everything material is ex- \ tended ; Of which the Real Subsumptiou ) (T/iCH, something extended is is the converse, J material ;) From which the Conclusion, ... / ^'^re/ore, something extended is \ not a free agent. Felapton, in the third Figure, is thus only a modifi- cation of Ferio in the first. 3. Disamis. Thc third mood in this figure is Disamis. Its for- mula — Some M are P ; But all M are S ; Therefore, some S are P. In reality Here the premises are transposed. Their order being rectified : — Sumption, Alllsl are ^ ; Expressed Subsumptiou, But some M are P ; Which, by conversive infer- \ ence, gives the Proximate \{Tlien, some P are M ;) Subsumption, j From which proceeds the Pical ) /^, . ^^ ^ , p , . > {Therefore, some P are S ;) Which, by conversion, gives the ) ^^^^^ ^^^^^ g ^^^ ^ Expressed Conclusion, J Our example was (the reversal of the premises being rectified) : — Sumption, All acts of liomicide are cruel ; T^ J o i_ L- i But some acts of homicide are Expressed Subsumption, \ , ,,, '' K laudable; LECTUHES ON LOGIC. 443 Which gives, as a conversive in- ) ,777 , LECT. r. .1 T1 • i 01 V I (Then, some laudable acts are yytt lerence, the Proximate Sub- V^ ' . ., x aah. ,. i ads of honiicide ;) sumption, ) •' ' -c ii,- -T) • i. n 1 • { (Therefore, some laudable acts Jbrom this Proximate Con elusion, < ^ x ( are cruel ;) Which again gives, as its converse, ) Therefore, some cruel acts are the Expressed Conclusion,. ... J laudable ; Thus Disamis in the third, is only Darii in the first figure. The fourth mood of the Third Figure is Datisi, which 4. Datisi. is only Disamis, the premises not being reversed, and the conclusion not a conversive inference. It re- in reality quires, therefore, only to interpolate the proximate subsumption. Thus — Sumption, AWK are P; Expressed Subsumption, But some M are S ; Giving by conversion, {Then, some S are M ;) From which last the Conclusion, Therefore, some S are P. Sumption, All acts of homicide are cruel; T7, JOT, i.- f But some acts of homicide are Expressed Subsumption, < •' ( laudable ; Which gives, by conversion, the J (Tlien, some laudable acts are Proximate Subsumption, 1 acts of homicide ;) -c T, • T, i.1- /^ 1 • f Therefore, some laudable acts are r rom which the Conclusion, .... \ •' ' I cruel. Thus, Datisi likewise is only a distorted Darii. The fifth mood of the Third Figure is the famous 5. Bocardo. mood Bocardo, which, as I have mentioned, with Baroco, but far more than Baroco, was the opprobrium of the scholastic system of reduction. So intricate, in fact, was this mood considered, that it was looked upon as a trap, into which if you once got, it was no easy matter to find an exit. Bocardo was, during the middle ages, tlie name given in Oxford to the Aca- 444 LECTURES ON LOGIC. LK(T. demieal -lail or Can-cr, — a iiainc wliicli still ivmains as — L a reliqiie of the ancient logical glory of that vener- able seminary. Ixcjecting, then, the perplexed and un- satisfactory reduction by the logicians of Bocardo to Uarbara by an apagogical exposition, I commence by stating, that Bocardo is only Disamis under the form of a negative aflirmative ; its premises, therefore, are transposed. Eemoving the transposition, its formula is- — All M are S ; But some M are not P ; Therefore, some S are not P. which is thus explicated, like Baroco : — Sumption, AWM. are S ; Expressed Subsumption, Some M are not P ; AVTiich gives, by conversive in- ) -. ( (Then, some not-V are M ;) ference, ) ^ ' . " From thisEealSubsumption pro- \ ceeds the Proximate Conclu- ATJierefore, some not-F are Sj) sion, ) AVbicbao;ainfnves,by conversion, l „„ ^ ^ -r. ° , ' , . } Then, some S are not-V ; the Expressed Conclusion, J Whence again, Some S are not P ; Our concrete example was (the order of the pre- mises being redressed) : — Sumption, All syllogisms are important ; T, TOT i.- f Bid some syllonisms are not Expressed Subsumption, < -^ "^ ( regular ; From which, by conversive in- \{Then, some things not regular ference, J are syllogisms ;) And from this Proximate Sub- "^ . . J i-u -n • ( Tlierefore, some things not reou- sumption proceeds the Proxi- )■ , y^ 1 . \ lar are important : mate Conclusion, ; -^ From whence, by conversion, the ) Tlien, some important things are Expressed Conclusion, J not-^regular ; ,„. I Whence, some important things \ are not regular ; LECTURES ON LOGIC. 445 Bocardo is thus only a perverted and perplexed lect Darii.'^ ^^"- The last mood of the Third Figure is Ferison, which 6. Ferison. is without difficulty, — it only being required to inter- polate the real subsumption, from which the conclusion in reality is derived. Its formula is — Sumption, No M is V ; Expressed Subsumptionj Bnt some M are S ; Which gives, by conversive infer- ) ence, the Subsumption, | ^^'^'^' ^^"'^ S are M • From which immediately flows ) ^, ^ r, , -r. . _, , . '' > llicrefore, some S are not P. the Oonclusion, J Sumption, No truth is ivitho7it result ; Expressed Subsumption, i ^"^ ''''''' ^'''*^'' ''''^ misunder- I stood ; The Conversive Inference from 1 Then, some things misunderstood Avhich is, / are truths ; And from this Implied Subsump- •j tion immediately proceeds the i Therefore, some things misunder- Conclusion 1 ^t'J^^'^ ^-^^^ ''^ot without result. Ferison'^ is thus only Ferio, fringed with an accident of conversion. The Fourth Figure is distinguished from the two Fourth former in this, — that in the Second and Third Figures '^'^^' one or other, but only one or other, of the premises requires the interpolation of the mental inference ; whereas, in the Fourth Figure, either both the pre- mises require this, or neither, but only the conclusion. The three first moods, (Bamalip, Calemes, Dimatis,) need no conversion of the premises ; the two last, Fesapo and Fresison, require the conversion of both. The result of the foregoing discussion is that, in a [See Noldiui?, Log. Eec, c. xii. /3 [Scotus says that Ferison, I'o- § 12, p. 30L Bocardo is called Do- cardo, and Fclapton, are useless, as camroc by Noldius. Cf. Ilcusch, concluding indirectly. QvoMiovcs, Syst. Lvij., % 539, p. Gil.] hi Anal. I'/'ior., L. i. q. 24.] 4U) LECTURES ON LOGIC. LEri\ rigkl tnith, no figure is entitled to tlie dignity of a. simple iind independent form of reasoning, except xxii Syllogisms. The First ^\y^^i wliicli liHs improperly been termed the First ; h ij^ro tho . only simple ^]^q three hitter iioures bein^]: only imperfect or au.l imle- , ° ° • r- r'"*'«^''t elliptical expressions of a complex process of infer- roasoning. encc, wliicli, whcn fully enounced, is manifestly only a reasoning in the first figure. There is thus but one figure, or, more properly, but one pro- cess of categorical reasoning ; for the term figure is abusively applied to that which is of a character regular, simple, and essential. Figure of Having, therefore, concluded the treatment of figure Ilvpntlicti- . „_^ •icoso of doceivinpj otliers. The term Fallmnj may 1)0 applied iiuliHereiitly in either sense. These distinctions are, however, frequently confounded ; nor, in a logical relation, arc they of account. False Syllogisms are, again, vicious, either in respect of their form or of their matter, or in respect of both form and matter." Kspiicn- In regard to the first distinction contained in this paragraph, — of Syllogisms into Correct or True and Logical and Incorrcct or False, — it is requisite to say a few words. truth iiis- It is necessary to distinguish logical truth, that is, the criminated. i i • i t • • • r ±.^ truth which Logic guarantees m a reasoning, irom the absolute truth of the several judgments of which a reasoning is composed. I have frequently inculcated that Logic does not warrant the truth of its premises, except in so far as these may be the formal conclu- sions of anterior reasonings, — it only warrants (on the hypothesis that the premises are truly assumed) the truth of the inference. In this view^ the conclu- sion may, as a separate proposition, be true, but if this truth be not a necessary consequence from the pre- mises, it is a false conclusion, that is, in fact no con- clusion at all. Now on this point there is a doctrine prevalent among logicians, which is not only erroneous, but, if admitted, subversive of the distinction of Logic as a purely formal science. The doctrine in question is in its result this, — that if the conclusion of a syllogism be true, the premises may be either true or false, but that if the conclusion be false, one or both of the premises must be false ; in other words, that it is possible to infer true from false, but not a Krug, Loyik, § 115.— Ed. LECTURES ON LOGIC. 451 XXIII. false from true. As an example of this I have seen lect given the following syllogism : — Aristotle is a Roman; A Roman is a European ; Therefore, Aristotle is a European. The inference, in so far as expressed, is true ; but I would remark that the whole inference which the premises necessitate, and which the conclusion, there- fore, virtually contains, is not true, — is false. For the premises of the preceding syllogism gave not only the conclusion, Aristotle is a European, but also the con- clusion, Aristotle is not a G7xeh ; for it not merely follows from the premises, that Aristotle is conceived under the universal notion of which the concept i^oman forms a particular sphere, but likewise that he is con- ceived as excluded from all the other particular spheres which are contained under that universal notion. The consideration of the truth of the premise, Aristotle is a Roman, is, however, more properly to be regard- ed as extralogical ; but if so, then the consideration of the conclusion, Aristotle is a European, on any other view than a mere formal inference from certain given antecedents, is, likewise, extralogical. Logic is only concerned with the formal truth, — the technical validity, — of its syllogisms, and anything beyond the legitimacy of the consequence drawn from certain hypothetical antecedents, it does not profess to vindi- cate. Logical truth and falsehood are thus contained in the correctness and incorrectness of loojical in- ference ; and it was, therefore, with no imjiropriety that we made a true or correct, and a false or in- correct syllogism convertible expressions." a Cf. Esser, Lo(jilc, § 109.— Ed. 452 LECTURES ON I,0(^1(\ i.FCT. In rocranl to tho distinction of Incorrect Syllocjisms XX 111. . . . — — '- into Paralogi-snis and Sophisms, notliing need l)e said. tUmoHu-' 'A'li^ moro statonicnt is sullieiently manifest ; and, at K'ilinw^into t^li^ same time, it is not of a logical import. For wTsc'r*'"* liOgic does not regard tlie intention with which rea- S'loXni"' -^onings are employed, but considers exclusively their import. internal legitimacy. But wliile the distinction is one, in other respects, proper to be noticed, it must be owned that it is not altogether without a logical value. For it behoves us to discriminate those artificial sophisms, the criticism of which requires a certain acquaintance with logical forms, and which, as a play of ingenuity and an exercise of acuteness, are not without their interest, from those paralogisms which, though not so artificial, are on that account only the more frequent causes of error and delusion. Formal and Thc last distluction is, however, logically more im- Faiiacics. portaut, viz., of reasonings, 1°, Lito such as are mate- rially fallacious, that is, through the object-matter of their propositions ; 2°, Into such as are formally falla- cious, that is, through the manner or form in which these propositions are connected ; and, 3°, Into such as are at once materially and formally fallacious. Material Fallacies lie beyond the jurisdiction of Logic. Formal Fallacies can only be judged of by an application of those rules in the exposition of which w^e have hither- to been engaged. Ancient The appHcatiou of these rules will afford the oppor- so^hisms. tunity of adducing and resolving some of the more capital of those Sophisms, which owe their origin to the ingenuity of the ancient Greeks. " Many of these sophisms appear to us in the light of a mere play of wit and acuteness, and we are left to marvel at the interest which they originally excited, at the celebrity LECTURES ON LOGIC. 453 wliicli they obtained, and at the importance attached lect. to them by some of the most distinguished thinkers - of antiquity. The marvel will, however, be in some degree abated, if we take the following circumstances into consideration. " In the first place, in the earlier ages of Greece the method of science was in its infancy, and the laws of thought were not yet investigated with the accuracy and minuteness requisite to render the detection of these fallacies a very easy matter. Howbeit, there- fore, men had an obscure consciousness of their fal- lacy, they could not at once point out the place in which the error lay ; they were thus taken aback, confounded, and constrained to silence. " In the second place, the treatment of scientific subjects was more oral and social than with us ; and the form of instruction principally that of dialogue and conversation. In antiquity, men did not isolate themselves so much in the retirement of their homes ; and they read far less than is now necessary in the modern world : consequently, with those who had a taste for science, the necessity of social communication was greater and more uro-ent. In their converse on CD O matters of scientific interest, acuteness and pro- fundity were perhaps less conducive to distinction than vivacity, wit, dexterity in questioning and in the discovery of objections, self-possession, and a confident and uncompromising defence of bold, half- true, or even erroneous assertions. Through such means a very superficial intellect can frequently, even with us, puzzle and put to silence another far acuter and more profound. But, among the Greeks, the Sophists and Megaric philosophers were accomplished masters in these arts. ir.i MicrriJKs ON lAicic. LF.CT. XXIII. '* 111 tho third place, as we know from Aristotle and l)ioiroues l.aertius " it was the rule in their dialoiiical disputations, that every question behoved to be an- swered by a yes or a no, and thus tlic interrogator had it in his power to constrain his adversary always to move in a foreseen, and, consccjucntly, a deter- minate, direction. Thus the Sophisms were somewhat similar to a game at forfeits, or like the passes of a conjuror, which amuse and astonish for a little, but the marvel of which vanishes the moment we under- stand the principle on which they are performed."^ As the various fallacies arise from secret violation of the logical laws by which the different classes of syllogisms are governed, and as syllogisms are Cate- gorical, or Hypothetical, or Disjunctive, or Hypothe- tico-disjunctive, we may properly consider Fallacies under these four heads, as transgressions of the syl- logistic laws in their special application to the several kinds of syllogism. Par. LXXVFI. Fallacies, — their divi- sion and classifica- tiuu. II LXXVII. The Syllogistic Laws determine, in reference to all the classes of Syllogism, the three following principles ; and all Fallacies are viola- tions of one or other of these principles, in rela- tion to one or other class of syllogism. I. If both the Logical Form and the Matter of a syllogism be correct, then is the Conclusion true. IL If the syllogism be Materially Correct, but Formally Incorrect, then the Conclusion is not (or only accidentally) true. a Arist. Soph. Eh/ich.,c. 17; La- /3 Bachmann, Lofjik, § 381, p. ertiu3, L. ii. c. 18, § 135. The refer- 513. ences are given by Baclimaun. — Ed. LECTURES ON LOGIC. 455 III. If the syllogism be Formally Correct, but lect. Materially Incorrect, tlien the Conclusion is not — L (or only accidentally) true. Fallacies, as violations of these principles in more immediate reference to one or other of the Four Classes of Syllogism, must again be vicious in reference either to the form, or to the matter, or to both the form and matter of a syllogism. Fallacies are thus a^ain divided into Formal and Material, under which classes we shall primarily arrange them. IF LXXVIII. Of Formal Fallacies, the Catego- Par. lxxviii rical are the most frequent, and of these, those Fallacies I .,..,. f. . I p,i Categorical. whose vice lies m having lour m place oi three terms {quateimione terminorum) ; for this, in consequence of the ambiguity of its expression, does not immediately betray itself. Under this genus are comprised three species, which are severally known under the names of, \°,Fallacia sensus compositi et divisi ; 2°, Fallacia a dicto secundum quid ad dictum simpliciter, et vice versa ; 3°, Fallacia figures dictionis. " That in a categorical syllogism only three terms ExpUca- are admissible, has been already shown. A categori- Faifacies cal syllogism with four capital notions has no con- Tqiuu^^o nection ; and is called, by way of jest, the logical omm. quadruped {animal quadrupes logicum). This vice usually occurs when the notions are in reality differ- ent, but when their difference is cloaked by the ver- bal identity of the terms ; for, otherwise, it would be too transparent to deceive either the rcasoncr himself or any one else. This vice may, however, be of various 456 LECTURES ON LOGIC. i.ix'T. kinds, ami of tlicse there are, as stated, tlirec principal will. . ' i i species. this Fallacy. 1. FaNacia "Tlic fu'st is the FctUacia sensus compositi at divisi, — StHSHs com- , 71 77 ^•y-y • • 7 t^ ■ • • a mi • f>i>fUui the raiUwij oj Comj^osition and JJii'ision. ihis arises when, in the same syllogism, we employ words now collectively, now distributively, so that what is true in connection, we infer must be also true in separa- tion, and vice versa ; as, for example : — All must sin ; Caius sins ; therefore, Cuius must sin." ^ Here we argue, from the unavoidable liability in man to sin, that this particular sin is necessary, and for this indi- Moiics of vidual sinner. " This fallacy may arise in different ways. 1°, It may arise when the predicate is joined with the subject in a simple and in a modal relation. For example, — Wliite can he (i.e. become) black, tlierefo7'e ivliite can be black. — 2°, It may arise from the confusion of a copulative and disjunctive combin- ation. Thus, — 9 consists or is made up of 7 + 2, which a?'e odd and even numbers, therefore 9 is odd and even. — 3°, It may arise, if words connected in the pre- mises are disjoined in the conclusion. Thus, — Socrates is dead, therefore Socrates is." '^ An example of the first of these contingencies, — that which is the most frequent and dangerous, — occurs when, from its universality, a proposition must be interpreted with restriction. Thus, when our Saviour says. The blind shall see, — The deaf shall hear^ he does not mean that the blind, as blind, shall see, — a [See Fonseca, Inst it. Dial., L. de Idcis, de Vcr'itate, ac de Vita Dei, viii. c. V. p. 106, Ingolstadii, 1G04.] Disp. xxxiii. p. 261 et seq. Alvarez, /3 Krug, Lofjik, § 116, p. 420. — in Gale, Philosophia GencraUs, L. Ed. [On the distinction of Sensus iii. c. iii. sect. 2, § S, p. 466.] Camposiii ct Divisi, so famous in the y [Denzinger,] [Die Logik als question of foreknowledge and lib- Wissenschaft der Dcnkkunst, dar- erty, see its history in Iluiz, Com- gestcllt, § 558, Bamberg, 1836. — iiicntarii (cc Disinitationcs, de Scicntia, Ed. ] LECTURES ON LOGIC. 457 that the deaf, as deaf, shall hear, but only that those l^^^- who had been blind and deaf should recover the use of these senses. To argue the opposite would be to incur the fallacy in question. The second fallacy is that A dicto secundum quid ad 2. Faiiada dictum simpliciter, and its converse,^! dicto simpliciter cundum -,-,.-,. quid ad dre- ad dictum secundum quid. The former of these, — the ^«"i simpii- fallacy^ dicto secundum quid ad dictum simplicite7\ — converse arises when from what is true only under certain modi- fications and relations, we infer it to be true absolutely. Thus, if from the fact that some Catholics hold the infallibility of the Pope, we should conclude that the infallibility of the Pope is a tenet of the Catholic Church in general. The latter, the fallacy a dicto simpliciter ad dictum secundum quid, is the opposite sophism, where from what is true absolutely we con- clude what is true only in certain modifications and relations, — as, for example, when from the premise that Man is a living organism, we infer that A painted or sculptured man is a living organism."" The third fallacy, — the SojjhismaJigurcB dictionis, — arises when we merely play with the ambiguity of a word. The well-known syllogism, Mus syllaha est ; Mus caseum rodit ; Ergo, syllaha caseum rodit,^ is an example ; or, Herod is a fox; A fox is a quadruped ; Therefore, Herod is a quadruped. To this fallacy may be reduced what are called the Sophisma equivocationis, the Sophisma amphiholice, and the Sophisma accentus^ which are only con- temptible modifications of this contemptible fallacy. oCf. 'Deu'z,ingeT,Logik, §564. — Ed. 7 On these fallacies, see Denzinger, )3 Seueca, Epiit., 4S.— Ed. Lojik, §§ 559, 500, 5GL— Eu. 458 LiiCTUKES ON LOGIC. y.KCT. H LXXIX. Of Materia] Fallacies, tliose are of — — 1- the most frequent occiUTeucc, where from a pre- Psu. LXXIX. j^jis^. xvliich is not in reality universal, we conclude Fallacies. universally ; or from a notion which is not in reality a middle term, we infer a conclusion. Under this genus there are various species of fallacies, of which the most remarkable are, 1°, the Soj^hisma cum hoc {vel j^ost hoc), ergo proi)- ter hoc ; 2°, Sophisma ingvum, or ignava ratio ; 3°, Sophisma polyzcteseos ; and 4°, Sophisma het- erozeteseos."' Expiica- In this paragraph you will observe that there arc FaUacies of given two gcucra of Material Fallacies, — those of Univcre^- an Um-eal Universality (sophismata Jlctce universali- ai'iuusive tatis), aud those of an Illusive Reason [sophismata eaion. j^^^igi Q-jiedH, OT 710)1 causcB ut causcB). I must first explain the nature of these, considered apart ; then show that they both fall together, the one being- only the categorical, the other only the hypothetical expression of the same vice ; and, finally, consider the various species into which the generic fallacy is subdi^dded. 1. Of an " Our decisions concerning individual objects, in so Unreal Uni- p , , i . -, ^ versaiity. far as thcy belong to certain classes, are very ire- quently fallacies of the former kind ; that is, conclu- sions from premises of an unreal universality. For example: — The Jeius are rogues — The Carthaginians, faithless — The Cretans, liars — The French, braga- docios — The Germans, mystics — The rich, purse- proud — The noble, haughty — Women, frivolous — The learned, pedants. — These and similar judgments, which in general are true only of many, — at best only a Cf. Krug, Luijik, § 117. — Ed. LECTURES ON LOGIC. 459 of the majority, of the subjects of a class, often con- lect. stitute, however, the grounds of the opinions we form — — '- of individuals; so that these opinions, with their grounds, when expressed as conclusion and premises, are nothing else than fallacies of an unreal generality, — sophismata Jictce universalitatis. It is impossible, however, to decide by logical rules, whether a proposi- tion, such as those above stated, is or is not universally valid ; in this, experience alone can instruct us. Logic requires only, in general, that every sumption should be universally valid, and leaves it to the several sciences to pronounce whether this or that particular sumption does or does not fulfil this indispensable condition." " The sopliisma fictce universalitatis is thus a fallacious syllogism of the class of categoricals. But the second kind of material fallacies, the2.ofUnrea sophisms of Unreal Middle, are not less frequent than those of unreal universality. When, for example, it is argued, (as was done by ancient philosophers), that the magnet is animated, because it moves another body, or that the stars are animated, because they move themselves ; — here there is assumed not a true, but merely an apparent, reason, there is, consequently, no real mediation, and the sophisma falsi medii is committed. For, in these cases, the conclusion in the one depends on the sumption, — If a body moves an- other body, it is animated ; in the other, on the sump- tion, — If a body moves itself, it is animated, but as the antecedent and consequent in neither of these sumptions are really connected as reason and conse- quent, — or as cause and effect, — there is, therefore, no valid inference of the conclusion./^ The sophisma a Krug, Logllc, § 117, Anm., p. /Q Cf. Krug, Locjik, p. 423. — 422.— Ei>. Ei>. 460 LECTITKKS ON LO(;iC. i-KCT. itoii causa itt causw is thus an hyi)otlictical sylldoisin ; — — '- but, as it may be categorically enounced, this fallacy T1.0 nuhuies Qf unreal reason will coincide with the cate<]jorical fal- IfTuroT' ^'^^^^y ^^^ ^^i^i*^''il universality. Thus, the second example i-niver- abovc alloood — sulitv CO- ~ // the stars move themselves, thcij are an'unated ; But the stars do move themselves ; Therefore, the stars are animated ; is thus expressed by a categorical equivalent : — All bodies that move themselves are animated ; But the stars move themselves; Therefore, the stars are animated. In the one case, the sumption ostensibly contains the subsumption and conclusion, as the correlative parts of a causal whole ; in tlie other, as the correlative parts of an extensive whole, or, had the categorical syllogism been so cast, of an intensive whole. The two genera of sophisms may, therefore, it is evident, be considered as one, — taking, however, in their par- ticular manifestation, either a categorical or an hypo- thetical form. Fallacy of I may notice that the sophism of Unreal Generality Reason as or Unreal Keason, is hardly more dangerous in its posi- in uTne"4. tlve than in its negative relation. For we are not itspositWe more disposed lightly to assume as absolutely uni- versal, what is universal in relation to our experience, than lightly to deny as real, what comes as an excep- tion to our factitious general law. Thus it is that men having once generalised their knowledge into a compact system of laws, are found uniformly to deny the reality of all phsenomena which cannot be compre- hended under these. They not only pronounce the laws they have generalised as veritable laws of nature, LECTURES ON LOGIC. 4G1 wliicli, haply, they may be, but they pronounce that lrct. there are no higher laws ; so that all which does not 1 at once find its place within their systems, they scout without examination as visionary and fictitious. So much for this ground of fallacy in general ; we now proceed to the species. Now, as unreal reasons may be conceived infinite Specios of m number, the mmor species oi this class oi sophisms of umeai cannot be enumerated ; I shall, therefore, only take notice of the more remarkable, of those which, in conse- quence of their greater notoriety, have been honoured with distinctive appellations. The first is the Sophisma cum hoc {vel post hoc), a. sopMs- ergo propter hoc. ihis fallacy arises, when, iYom{vdpost the contingent consecution of certain phsenomena jwo^to-Toc. in the order of time, we infer their mutual dependence as cause and efiect. When, for example, among the ancient Romans, a general, without carefully consult- ing the augurs, engaged the enemy, and sufii'ered a defeat ; it was inferred that the cause of the disaster was the unfavourable character of the auspices. In like manner, to this sophism belongs the conclusion, so long prevalent in the world, that the appearance of a comet was the harbinger of famine, pestilence, and war. In fact, the greater number of the hypotheses which constitute the history of physics and philosophy, are only so many examples of this fallacy. But no science has exhibited, and exhibits, so many flagrant instances of the sophism cum hoc, ergo propter hoc, as that of medicine ; for, in proportion as the connec- tion of cause and effect is peculiarly obscure in physic, physicians have only been the bolder in assuming that the recoveries which followed after their doses, were not concomitants Imt effects. This sophism is, in 462 LECTURES OX LOO TO. LRCT. practice, of great influence and very frequent occur- JJ L rence ; it is, liowcver, in theory, too perspicuous to require illustration, b. /<^K«m The second fallacy is that which has obtained the name of Ignava ra t io, or Soj^hisma lyigvum, — in Greek , apyo<; \6yo<;.'^ The excogitation of this argument is commonly attributed to the Stoics, by whom it was employed as sul^sidiary to their doctrine of fate. " It is an argument by which a man endeavours to vindi- cate his inactivity in some particular relation, by the necessity of the consequence. It is an hypothetico- Exanipie. disjuuctivc syllogisui, and, when fully expressed, is as follows : — Sumption, J/ 1 ought to exert myself to effect a certain event, this event either must take place or it must not; Subsumption, If it miist take place, my exertion is superfluous ; if it miist not take place, my exertion is of no avail ; Conclusion, Tlierefore, on either alternative, my exertion is iiseless"^ Cicero, in the twelfth chapter of his book, De Fato, thus states it : — If it be fated that you recover from your -present disease, whether you call in a doctor or not, you mill recover ; again, if it he fated that you do not recover from your present disease, whether you call in a doctor or not, you will not recover ; But one or other of the contradictories is fated ; Tlierefore, to call in a doctor is of no consequence. Others have enounced the sumption in various forms, for example : — If it he impossible hut that you recover a See Menage on Diogenes Laer- t. i. De Log. Orig. et Var., L. i. c. tins, L. ii. p. 123. — Ed. [Facciolati, G, p. 51.] Acroai^es, v. p. 55. Gassendi, Opera, $ Krug, Lofjil-,% 117, p. 424. — Ed. LECTURES ON LOGIC. 463 from the present disease, &c., — or — If it he true that lect you will recover from this disease, — or — Ifithedecreed xxin. Its various gna- hy God that you will not die of this disease, and so 1^2 likewise in different manners, according to which like- '"'''*• wise the question itself has obtained various titles as Argument De Fato — De Possihilihus — De Lihero Arhitrio — De Providentia — De Divinis Decretis — De Faturis C outing entihus — De Physica P^'cedeter- minatione, &c. No controversy is more ancient, none more universal, none has more keenly agitated the minds of men, none has excited a greater in- fluence upon religion and morals ; it has not only divided schools, but nations, and has so modified not only their opinions but their practice, that whilst the Turks, as converts to the doctrine of Fate, take not the slightest precaution in the midst of pestilence, other nations, on the contrary, who admit the contin- gency of second causes, carry their precautionary policy to an opposite excess. The common doctrine, that this argument is an its history. invention of the Stoics, and a ground on which they rested their doctrine of the physical necessitation of human action, is, however, erroneous, if we may accord credit to the testimony of Diogenes Laertius, w^ho relates, in the Life of Zeno, the founder of this sect, that he bestowed a sum of two hundred minse on a certain dialectician, from whom he had learned seven species of the argumeiit called the \6yo^ Oepi- l,oiv, metens, or reaj^er, — which differs little, if at all, from the ignava ratio. '^ For how this sophism is con- structed, and with what intent, I find recorded in the commentary of Ammonius on the book of Aristotle a See Laertius, vii. 25. The ob- ciolati, Acroases, v. p. 57, ed. 1750. servation in the text is from Fac- — Ed. •104 LKOTURES ON LOOTC. LF.(T. llept 'EpuTnueiaq.^ Of the same character, likewise, — — '- is the argument called the Xoyo? Kvpievoiv, the ratio dominant, or controlling reason, tlie process of which Arrian describes under the nineteenth chapter of the second book of tlie sayings of E]:»ictetus.^ The lazy reason, — the reaper, — and the controlling reason, are thus only various names for the same process. Tlie virc In regard to the vice of this sophism, " it is mani- ^opi.isin. fest that it lies in the sumption, in which the disjunct members are imperfectly enounced. It ought to have been thus conceived — If I ought to exert myself to effect a certain event, whicli I cannot, however, of myself effect, this event must either take place from other causes, or it must not take place at all. It is only under such a condition that my exertion can on either alternative be useless, and not if the event depend wholly or in part for its accomplishment on my exertion itself, as the co7iditio sine qua non."'^ It is plain, however, that the refutation of this sophism does not at all affect the doctrine of necessity ; for this doctrine, except in its very absurdest form, — the Fatum Turcicum, — makes no use of such a rea- soning, c. Sophis- " The third fallacy is the Sophisma loolyzeteseos leie^'s! or qucestionis diiplicis, — the sop)hism of continuous questioning, which attempts, from the impossibility of assigning the limit of a relative notion, to show by continued interrogation the impossibility of its deter- mination at all. There are certain notions which are a F. 91 b, cd. Aid. Venet. , 154G. not explained, by Lucian, Vil. Avct. — Ed. c. 22; Plutarch, Sympos., i. 1, 5; /3 The purpose of this sophism Gellius, N.A., i. 2. Compare Fac- may be gathered from Arrian, but ciolati, Acroascs, v. p. 57. — Ed. not the nature of the argument it- y Knig, Lo(jik, p. 424. — Ed. self. It is also mentioned, though LECTURES ON LOGIC. 465 only conceived as relative, — as proportional, and whose lect, limits we cannot, therefore, assign by the gradual '- addition or detraction of one determination. But there is no consequence in the proposition, that, if a notion cannot be determined in this manner, it is incapable of all determination, and, therefore, abso- lutely inconceivable and null." " Such is the Sorites, its various the nature of which I have already explained to you. tions. This reasoning, as applied to various objects, obtained various names, as, besides the Sorites or Acervus, we have the crescens,^ — the ^aXaAcpog or calvus,"^ — the vTrepOeTLKos, superpositus or siq^erlativus,^ — the 170-1;- Xccl'ajv or quiescens, &c. &c.^ The Sorites is well de- fined by Ulpian,^ a sophism in which, by very small degrees, the disputant is brought from the evidently true to the evidently false. For example, I ask. Does one grain of corn make up a heap of grain 1 My op- ponent answers, — No. I then go on asking the same question of two, three, four, and so on ad injinitum, nor can the respondent find the number at which the grains begin to constitute a heap. On the other hand, if we depart from the answer, — that a thousand grains make a heap, the interrogation may be continued downward to unity, and the answerer be unable to determine the limit where the grains cease to make up a heap. The same process may be performed, it is a Krug, Logih, § 117. — Ed. e Cicero, Acad., ii. 29. Epictetus, /3 Wyttenbach, ^(Z PZzttarc/i. De i>mer<., ii. 18, 18.— Ed. Sera Num. Vinci., p. 559; Prcece2}ta ( Ler/e, 177. De Verb. Sif/ni/. : Phil. Log., p. iii. c. 9, § 4. — Ed. " Natura cavillationis, qiiam Grteci 7 Diog. Laert., ii. 108. Cf. Gas- o-wpeiTTj^ appellarunt, hrec est, ut ab sendi, De Log. Grig. , c. 3. — Ed. ea ab evidenter veris per brevissimas 5 Epictetus, i)mer<., iii. 2, 2. As mutationes disputatio ad ea qua; interpreted by Gassendi, De Log. evidentur falsa sunt perducatur." Orlg., c. 6. But the true reading is (Quoted by Gassendi, De Log. Orig. probably vTroOeTiKovs. See Schweig- el Var., c. .3, (Jiiera, t. i. p. 41, and bieuser's note. — Ed. by Menage, Ad. Litert. ii. 108. — Ed. VOL. I. 2 G 466 LECTURES ON LOGIC. LKCT. XXIU. A. Sophis- ■iui luteio- Its various names. lu charac- ter. manifest, upon all the notions of proportion, in space and time and degree, both in continuous and discrete quantity/ The fourth and last fallacy of this class is the sojyhisma heterozeteseos, or so2)hism of coimter-ques- tionincjj^ and, as applied to various objects, it obtained, among the ancients, the names of the Dilemma,'^ — the CoDiutus,^ — the Litigiosus, — the Achilles,^ — the Men- tienSy^ — theFallensJ' — theElectraf — theOhvelatus,' — the Reciprocus,^ — the Crocodilinus,>< — the ovtl^s,'^ — the Inductio imperfecta ;" and to this should also be re- ferred the Ass of Buridanus.i " It is a hypothetico- disjunctive reasoning, which rests on a certain suppo- sition, and which, through a reticence of this supposi- tion, deduces a fallacious inference. To take, for an example of this fallacy, the /ceparti^os or Cornutus : — it is asked ; — Have you cast your horns ? — If you answer, I have ; it is rejoined. Then you have had horns : if you answer, I have not, it is rejoined, Then you have them still." — To this question, and to the inferences from it, the disjunctive proposition is sup- posed, — A certain subject has either had horns or has them still. This disjunction is, however, only correct a Krug, Logik, § 117.— Ed. /3 [See Gassendi, Ojycra, t. i. De Log. Orig. et Var., c. 6, p. 51.] 7 Hermogenes, De Invent., L. iv., and Proleg. ad. Etrinogc'iiem. See Walz's Rlietores Grceci, vol. iii. p. 167, iv. p. 14— Ed. 5 Seneca, Epist.,4iO. Menage, ^o? Diog. Laert., L. ii. 108.— Ed. e Diog. Laert., L. ix. 23. Aris- totle, Phys., vi. 9. (S'qpA. Ele7ich., 24.— Ed. ( Menage, Ad Diog. Laert., L. ii. 108. Cicero, Acad., ii. 29.— Ed. 7j Diog. Laert., ii. 108. — Ed. e Lucian, Vit. Auct., § 22. Cf. Menage, Ad Diog. Laert., L. Li. 108. —Ed. 1 Menage, ibid. — Ed. K Aulua Gellius, N.A., L. v. c. 10, 11.— Ed. A. Lucian, I. c. QuintiUan, Inst. Orat., L 10, 5. Cf. Menage, Ad Diog. Laxrt., L. ii. 108. — Ed. IX Ammonius, Ad Arist. Catcg., f. 58. Cf. Menage, loc. cit. — Ed. v Cicero, De Inventkme, L. i. c. 31.— Ed. ^ See Denzinger, LogiTc, % 571, from whom these designations are taken. RckVs Works, p. 238. — Ed. Diog. Laert., vii. 187. — Ed. LECTUEES ON LOGIC. 467 if the question is concerning a subject to which horns lect. previously belonged. If I do not suppose this, the '- disjunction is false ; it must, consequently, thus run : — a certain subject has either had or not had horns. In the latter case they could not of course be cast. The alternative inferences {then you have had them, or the7i you have them still) have no longer ground or plausibility." " To take another instance in the Liti- tiic LUigio- giosus or Reciprocus. Of the history of this famous dilemma there are two accounts, the Greek and the Roman. The Roman account is given us by Aulus Gellius,^ and is there told in relation to an action between Protagoras, the prince of the Sophists, and The case of Euathlus, a young man, his disciple. The disciple had aud St- covenanted to give his master a large sum to accom- plish him as a legal rhetorician ; the one half of the sum was paid down, and the other was to be paid on the day when Euathlus should plead and gain his first cause. But when the scholar, after the due course of preparatory instruction, was not in the same hurry to commence pleader, as the master to obtain the remainder of his fee, Protagoras brought Euathlus into court, and addressed his opponent in the follow- ing reasoning : — Learn, most foolish of young men, that however matters may turn up, — (whether the decision to-day be in your favour or against you), — pay me my demand you must. For if the judgment be against you, I shall obtain the fee by decree of the court, and if in your favour, I shall obtain it in terms of the compact, by which it became due on the very day you gained your first cause. You thus must fail, either by judgment or by stipulation. To this Euathlus rejoined : — Most sapient of masters, learn a Krug, Locjik, p, 425. — Ed. j3 L. v. c. 10. 4C8 LECTURES DN LOOIO. LECT. iVom your own argnineiit, that Avliatevcr may be the ^^"'' liiuliiii;- oi' thi> court, absolved I must be from any Tis chiim by you. For if the decision be favourable, I pay nothing by the sentence of the judges, but if unfavourable, I pay nothing in virtue of the compact, because, though pleading, I shall not have gained my cause. The judges, says Gellius, unable to find a ratio decidendi, adjourned the case to an indefinite day, and ultimately left it undetermined. I find a Paniiioi parallel story told, among the Greek writers, by Arsen- Conix aud ius, by the Scholiast of Hermogenes, and by Suidas," of the rhetorician Corax (anf/Iice Crow) and his scholar Tisias. In this case the judges got off by delivering a joke against both parties, instead of a decision in favour of either. We have here, they said, the plaguy egg of a plaguy crow, and from this circumstance is said to have originated the Greek proverb, KaKov Kopa- KOS KaKOV OiOV. Herewith we terminate the First Great Division of Pure Logic, — Stoicheiology or the Doctrine of Ele- ments. a [Prolegomena to Hermogenes, 314 ; quoted by Sigwait, Locjik, § in Wak's Rhetorcs Greed, torn. iv. 333, p. 211, 3d edit. Suidas, quoted pp. 13, 14. Arsenii Violetiim, edit, by Schottufi, Aday'm Gracorum, p. Walz, Stuttgard, 1S32, pp. 313, 450, 1G12.] END OF THE FIEST VOLUME. PRINTED By V/ILLIAM BLACKWOOD AND SONS, EDINBUKOH. A A 001 412 391 ■i^tf ^^VTi^>^r ■; , :^:.-v^Av ^v.., v..