START MASTER NEGA TIVE NO. 91-80002 MICROFILMED 1991 COLUMBIA UNIVERSITY LIBRARIES/NEW YORK as part of the "Foundations of Western Civilization Preservation Project Funded by the NATIONAL ENDOWMENT FOR THE HUMANITIES Reproductions may not be made without permission from Columbia University Library COPYRIGHT STATEMENT The copyright law of the United States - Title 17, United States Code - concerns the making of photocopies or other reproductions of copyrighted material... Columbia University Library reserves the right to refuse to accept a copy order if, in its judgement, fulfilhnent of the order would involve violation of the copyright law. AUTHOR: UEBERWEG, FRIEDRICH TITLE: SYSTEM OF LOGIC AND HISTORY OF LOGICAL.. PLACE: LONDON DA TE : 1871 COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DEPARTMENT Master Negative # BIBLIOGRAPHIG MICROFORM TARGET Original Material as Filmed - Existing Bibliographie Record Restrictions on Use: I. Ueberweg. ^^I^^'^'f^^'^, ,,^,^, doctrines. By Dr. System of logic and his^ry ot^og ^.^^^ ^^^ mans, Green, and co., 1871. XX, 590 p. diagrs. 22J«-. 1. Logic. I. Lindsay. Thomas Martin, 184a- tr. Library of Congress O BC16.U3 [SOfli ft— 32876 160 \ TECHNICAL MICROFORM DATA REDUCTION RATIO: FILM SIZE:___3,5or!NV> ' ^ IMAGE PLACEMENT: lA (fUA. .„ ..„ ^ ^ DATE FILMED: 4lif-fl INITIALS___il_£i.-_ FILMED BY: RESEARCH PUBLICATIONS. INC WOODBPJDGE. CT IB IIB Jh. hl Association for information and image Management 1100 Wayne Avenue, Suite 1100 Silver Spring Maryland 20910 301/587-8202 Centimeter 12 3 4 iUiliuiluiiiiuiiuii^^ TTT T I I 5 6 iliiiiliiiiliiii m 7 8 9 iiiliiiiliiiiliiiilimliii ^n J I I 10 11 12 13 iiliiiiliiiiliiii TTT TTT 14 15 mm iiliiiiliiiil Inches 1.0 I.I 1.25 M III 2A 1^ |ft3 ■ 80 m m lUbu 1.4 2.5 2.2 2.0 1.8 1.6 MRNUFnCTURED TO flllM STANDARDS BY APPLIED IMAGE, INC. »♦ I } i t ' / :Zä>KpdTOvs, rris 8e a\Tj0€tov TroAi; fiaWov, iäp fi4v ri vjuv OKTtTCtJ/aTC. Socrates npud Platonem. Tovrwv Sc TCI /Lie»/ iroXXol »cal iro\atoi \4yov(riv^ tÄ 5^ 0X170* ««^ epSo^oi ÄKSpes- ouSertpous Se toutojv cÜKpop Siafiaprdyuv rois '6\oi5, oAA' €v 7« Ti i) >cal tÄ TrXetffTa KOTOpQoVV. . . . , 1 Aristoteles. I- SYSTEM OF LOGIC AND HISTORY OF LOGICAL DOCTRINES. BY D^ FRIEDEICH ]LJfepEEWEG, PROFESSOR OP PHILOSOPHY IN THE UNIVERSITY OP KÖNIGSBERG. Intelligitur, quod, ars ilia, quae dividit genera m species et species in genera resolvit, quae 5ta\eKTt/c^ dicitur, non ab humanis machinationibus sit facta, sed in natura rerum ab auctore omnium artium, quae vere artes sunt, condita et a sapientibus invents et ad utili- tatem solerti rerum indagine usitata. Johannes Scotus {Erigend). Nam normae illae: experientia, principia, intellectus consequentiae, sunt revera vox divina. Philipptis Melanchthon. TRANSLATED FROM THE GERMAN, WITH NOTES AND APPENDICES, BY THOMAS M. LINDSAY, M.A., F.B.S.E., EXAMINER IN PHILOSOPHY TO THE UNIVERSITY OP EDINBURGH. n -sar:- SPOTTlSWOODi: ANÜ 1. I*.. SKW-STRK- ' - . .r; •»•^T »ittn • LONDON : LONGMANS, GEEEN, AND CO. 1871. ' 0523 AUTHORISED TRANSLATION, containing the LATEST ADDITIONS AND CORRECTIONS, AND REVISED BY THE AUTHOR. \^ iKbzx TO ALEXANDER CAMPBELL ERASER, M.A., LL.D., F.R.S.E., PROFESSOR OF LOGIC AND METAPHYSICS IN THE UNIVERSITY OP EDINBURGH, THIS ATTEMPT TO FOSTER THE HIGHER STUDY OF LOGIC BY THE TRANSLATION OF ONE OF THE BEST GERMAN MANUALS, IS DEDICATED BY AN OLD PUPIL. TRANSLATOR'S PREFACE. -•o*- PiiOFESsoR Ueberweg's ' System of Logic ' enjoys a popularity among German students which is shared by no other manual. It has already reached three editions, and will soon appear in a fourth. Acquaintance with these facts, personal experience of the value of the book, and the knowledge that there is no really good logical text-book for advanced students in our lan- guage, led me to undertake this Translation. While it is not especially intended for beginners, and while the student is recommended to make himself previously familiar with the outlines of Logic as given in such excellent little books as those of Fowler or Jevons some judicious ' skipping,' in the more difficult parts, will bring this manual down to the level required by those who begin it entirely ignorant of the science. This Translation is from the text of the third edition, published in 1868, and contains all the addi- tions and alterations which are to he inserted in the ( Vlll Translators Preface. next German edition. Although I am responsible for the translation, and liable to censure for its many faults and defects, it is but right to mention that anyone who compares it with the original will find numerous small omissions, additions, and alterations — indeed, there are few pages which do not differ in some particular from the text of the third edition,— all of which have been made by the author. Dr. Ueberweg has himself revised the sheets ; and, as he knows English well, this Translation may be held to give his opinions as he wishes them expressed in our language. In order to make the book more useful to students, the opinions of the more prominent EngHsh logicians on the points discussed have been from time to time inserted. Such passages are distinguished by the brackets [ ]. For these and for the first three Ap- pendices I am alone responsible ; but my friend Pro- fessor W. R. Smith has fiirnished the account of the late Professor Boole's logical opinions in Appendix A. Appendix D will appear in the fourth German edition, and has been added in deference to the author's wishes. It need only be added, that while agreeing in the main with the logical opinions of Professor Ueberweg, I must not be held responsible for every theory ad- vanced in the text-book, and must dissent from some Translator s Preface, IX of the statements regarding the Logic of Mathematics. The remarks made at page 577 in Appendix A seem almost as applicable to Dr. Ueberweg's views as to Mr. Mill's. Thomas M. Lindsay. 7 Great Stuart Street, Edinburgh June Istj 1871. Note. — Since writing these lines the sad and unexpected news of Dr. Ueberweg's death has reached me. These pages will have a mournful interest to his many friends, for their revisal was the last bit of work he was able to do. He had just finished them when death ended his labours. T. M. l. June Ibth. f( AUTHOE'S PEEFACE TO THE FIliST EDITION. ScHLEiERMACHER, whose philosophical significance has but too often been overlooked for his theological, in his Lectures upon * Dialektik ' (ed. by Jonas, Berlin, 1839), sought to explain the forms of thinking from science, which is the end and aim of thinking, and to make good his opinion by proving their parallelism with the forms of real existence. This appre- hension of the forms of thought holds a middle place between the sub- jectively-formal and the metaphysical Logics, and is at one with the fundamental view of Logic which Aristotle had. The subjectively-formal Logic — ^that promulgated by the schools of Kant and Herhart — puts the forms of thought out of all relation to the forms of existence. Meta- physical Logic, on the other hand, as Hegel constructed it, identifies the two kinds of forms, and thinks that it can recognise in the self-develop- ment of pure thought the self-production of existence. Aristotle^ equally far from both extremes, sees thinking to be the picture of existence, a picture which is different from its real correlate and yet related to it, which corresponds to it and yet is not identical with it. Hitter smd Vorländer^ have worked at Logic from the standpoint of Schleiermacher : the investigations into the theory of knowledge of most of our modern logicians, who do not belong to any definite school, lie more or less in the same direction. Trendelenburg j who has revived the true Aristotelian Logic, comes in contact in many ways with Schleiermacher 's Platonising theory of knowledge, without being dependent 2 upon him, and has a basis of metaphysical categories acquired independently in a polemic against Hegel and Herbart. The view of Lotze is more distantly related. It approaches nearer to Kant's, and represents that in the laws and forms of thought only the necessary metaphysical presuppositions of the human mind upon nature and the imiverse mirror themselves. Essentially accepting Schleiermacher's fundamental axioms concerning the relation of thouglit to perception » Now (1868) also George. (Added to the third edition.) ' At least without any direct dependence. Schleiermacher's Lectures on Dialectic, published in 1839, are only quoted here and there. But the influence of Bitter's Logw apparently shows itself in his doctrine of the notion and of the judgment. (Added to the second edition.) - ■ \}\ J Xll Author s Preface to the Second anct Third Editio7is. Xlll >/ and of perception to existence, BeneJce has proceeded to blend these with his psychological theory, partly constructed after Herbart's, into a new whole. This present work on Logic proceeds in the direction denoted by the labours of these men, while conscious of the right of complete independence in the mode of procedure. It sets before it both the scientific problem of aiding in developing Logic, and the didactic one of assisting to its study. In the ^rs^ reference, the Author hopes that he may succeed in the present work in answering the principal questions relating to the problem, sphere, and arrangement of Logic, and to the standpoint from which Logic is treated as a theory of knowledge, and in furnishing a not worthless contribution to the solution of many single problems. Polemic is used sharply enough where occasion demands, but only against those of whom I can say with truth — * verecunde ab illis dissentio.' That truth was the single interest, determining me in each case to agree with or contradict, need not require previous assurance, but will appear from the work itself On my side, I will welcome every thoroughgoing criticism as heartily as agreement. One thing I do not wish, and that is, that this independently thought-out work be laid aside by classing it under this or that general formula — Empiricism, Rationalism, Eclecticism. For this would falsely represent my work to be the mere exposition of a one-sided antiquated party standpoint, or, since it is essentially related to the whole of the philosophical tendencies, would accuse it, mistaking its leading lundamental thought, of want of principle. The Author would least of all object to have his system entitled an Ideal-Realism. In the didactic reference, I have striven to exhibit general Logic clearly, exactly, comprehensively, and so far completely, as a theory of knowledge, and to describe the chief moments in its historical develop- ment. What is universally recognised has been rendered in a precise and strictly systematic form. What is doubtful and debatable will be explained, not with the prolixity of the monograph, but with a sufficient consideration of the points which decide the question. A systematic representation of scientific Logic must, in so far as it is meant to serve as a text-book to those entering upon the study, presuppose genuine students of science, who do not mean to shirk difficulties, but to over- come them. Particular parts may always be passed over in a first study. Tliese will meet the want of those who, already familiar with the elements, may wish to extend their studies. The examples will show the importance of tlie logical laws in their application to all the sciences. Finally, by means of historico-literary examples and investigations, in which the Aristotelian point of view of thankful reference to all essential moments of development of scientific truth is preserved, this work strives to encourage the most many-sided study of Logic possible. Bonn : August, 1857. TO THE SECOND EDITION. I might recommend this work more especially to the attention of those engaged in the investigation of Nature as a thorough-going attempt at a comparatively objective theory of knowledge in opposition to Kant's subjective criticism. It may serve to give a philosophic basis to their more special methodic. The kernel of my opposition to Kant lies in the thoroughgoing proof of the way by which scientific insight is attained, an insight which mere experience in its immediate- ness does not warrant, which is not brought about by a priori forms of purely subjective origin, finding application only to phenomenal objects present in the consciousness of the subject (and has not, as Hegel and others desire, an ä priori, and yet objective validity), btit is reached by the combination of the facts of experience according to the [logical rules, which are conditioned by the objective order of things and whose observance ensures an objective validity for our knowledge. 'I seek more especially to show how arrangement, according to time space, and cause, on whose knowledge apodicticity rests, is not first of all imposed upon a chaotically given matter by the perceiving thinking subject, but is formed in the subjective consciousness in accordance with the (natural and spiritual) reality, in which it originally is, suc- cessively by experience and thinking TO THE THIRD EDITION. .... university education and its lectures, to bring forth good fruit, must presuppose a knowledge of the elements of Logic, and a tamiliarity with them such as is only to be got by school training. Philosophical propaedeutic is of value in the studies of the gymnasia, both as a very suitable conclusion to intellectual education, and more especially as a means in the teaching of one's own language and literature. ... I have I exerted myself in the present third edition of this book not only to in- I crease its scientific value by a more acute treatment of many problems, and by a thoroughgoing reconsideration of newly-risen difficulties, but,' more than hitherto, by the kind of explanations and the choice of ex- amples, to supply the needs of the teacher who gives preparatory mstruetion, and to meet the wants of the student for whom it is to serve as a solid foundation for philosophical instruction KÖNIGSBERO : September, 1868. F. Ueberweg. >!' CONTENTS -•o^ INTRODUCTION. Notion, Division, and General History/ of Logic. § 1. Definition of Logic '{ § 2. The forms of knowledge. Their double condition. Their rela- tion to the contents of knowledge 3 § 3. The end and aim of the activity of knowledge. Truth. Scientific knowledge g §4. The possibility of Logic as a science ]o § 5. The absolute and relative worth of Logic . . . .10 § 6. The place of Logic in the system of Philosophy . . . n § 7. The study of Logic as a propaedeutic for other philosophical studies 26 § 8. Division of Logic 16 § 9. The value of the history of Logic .... 19 § 10. The historical origin of Logic ! 19 § 11. The Ionic natural philosophers, the Pythagoreans, and tlie Eleatics «i § 12. The Sophists and Sokrates 25 § 13. The one-sided Sokratic Schools ... 26 § 14. Plato 27 § 15. The Platonists o^q § 16. Aristotle 30 § 17. The Peripatetics c^^ § 18. The Epikureans, Stoics, and Skeptics . . . 35 § 19. The Neo-Platonists . . '67 § 20. The Christian Fathers. The Study of Dialectic in the Schools among Christians, Arabians, and Jews . . . .37 § 21. The Schoolmen 30 § 22. The earlier times of the Reformation 42 § 23. Bacon of Verulam .... 49 §24. Des Cartes .*.'.!.* 44 § 25. Spinoza ^^ § 26. Locke ^ ^ ^ § 27. Leibniz and Wolft . . . . . . , . . 40 I 1 ^^ XVI Cojitents. § 28. Kant § 29. The Kantian School and allied tendencies. Fries. Herbart § 30. Fichte, Schelling, and their School § 31. Hegel § 32. The Hegelian School § 33. Schleiermacher § 34. The latest German logicians . § 35. Modern logicians beyond Germany PAGE 54 69 61 63 69 69 72 74 PART I. Perception in its relation to Objective Existence in Space and Time. § 3G. Definition of Perception A.— External or Sense-Perception. § 37. Arguments against the agreement of sense-perception with what actusdly exists without § 38. The incorrectness of the Kantian separation of the matter and form of perception • § 39. Upon the capacity to know the existence of objects affecting us grounded on sense-perception B.— Internal or Psychological Perception. § 40. The agreement of the inner perception with the perceived reality C— The Combination of Outer and Inner Perception. § 41. The knowledge of the plurality of animate existences § 42. The knowledge of the gradual series of existences— Science, Faith, Presentiment, Opinion, &c § 43. The reality of Matter and Power § 44. The reality of Space and Time PART II. The Individual Conception or Intuition in its relation to the Objective Individual Existence. § 45. Definition of individual Conception of Intuition. . 110 S 46 The distinction of individuals by means of individual con- ' 4.' Ill ceptions '^^'■ Contents. xvu PAQK § 47. The forms of individual conception and existence. The Cate- gories in the Aristotelian sense. The parallelism between the forms of individual existence, forms of conception, and the parts of speech 114 § 48. Clear and distinct conception 125 § 49. Attributes — The parts of a conception 125 § 50. The content of a conception. Its partition .... 126 77 ■ § ol. §52. §53. 79 ■ §54. § 55. 80 1 §56. §57. 83 1 «58. ^H §59. §60. 84 1 §61. § 62. 91 I § 63. 93 I §64. 97 I §65. 99 ■ %m. PART III. The Notion according to Content and Extent in its relation to the Objective Essence and the Genus. Attention and Abstraction. The General Conception . . 127 Determination .......... 130 Extent. Division. The relations of conceptions to each other according to extent and content ...... 130 The relation between content and extent ..... 135 The graduated series (pyramid) of conceptions . . ' . 138 Definition op the notion. The essence .... 139 The knowledge of the essential. The ä priori and ä posteriori elements in the formation of the notion .... 152 Class, Genus, Species, &c. Their reality and their knowability 156 The individual notion 159 Definition. Its elements — the notion of Genus and Specific Difference 160 The KINDS of definition 164 The most notable faults in definition ..... 172 Division. The ground of division. The members of division : Dichotomy, Trichotomy, «fee 177 Subdivision, and co-ordinate division 182 The most notable faults in division .... . , 183 The connection between the formation of notions and the other functions of cognitive thinking , 185 PART IV. The Judgment in its reference to the Objective Fundamental Combinations or Relations. § 67. The definition of the Judgment 187 § 68. Simple and complex judgments. The individual relations of the judgment, and their reference to the corresponding a '!l .^1 XVIII Confenis. Co7itents, XlX ^ -. PAGB relations of existence. The Catesortes of relation in the Kawtian sense . . . . , ^ ^ ^ jg^ § 69. QrALiTT and Modality of judgments 206 § 70. Quantity of judgments 214 f 71. Combination of divisions according to Quality and Quantity. The four forms of judgment A, E, I, and O . . . 216 5 72. Contradictory and contrary opposition between two judgments. Subaltemation .... oia S 73. The Matter and Form of judgments 221 $74. § 75. §76. §77. § 78. § 79. §80. §81. §82. §83. §84. §86. §86. §87. §88. §89. § 90. §91. §92. $93. §94 §96. PART V. Inference in its relation to the Objective Reign of Laic. Definition of Inference The principles of Inference in general . . . ! The axiom of Identity The axiom of Contradiction The axiom of Excluded Third or Middle between two judg- ments opposed as contradictories The combination of the axioms of Contradiction and Excluded Third in the principle of Contradictory Disjunction The relations between judgments whose predicates are opposed a« contraries. Dialectical Opposition. The axiom of the Third lying in the Middle between two contrary opposites. The axiom of the union of coincidence of opposites The axiom of sufficient reason The forms of immediate inference in general The analytical formation of the judgment. ' The* synthetic formation of a judgment Conversion in general. Its internal authorisation .' Conversion of the universal affirmative judgment . ' \ Conversion of the particular affirmative judgment Conversion of the universal negative judgment . ', ' The impossibility of the conversion of the particular negative judgment ° Contraposition in general. Its inner authorisation .' Contraposition of the universal affirmative judgment Contraposition of the universal negative judgment . Contraposition of the particular negative judgment '. The impossibility of the contraposition of the particular affirma- tive judgment Change of Relation ..'.'..'*' Subaltemation . . 225 22S 231 235 260 275 278 281 287 289 294 297 304 306 311 313 314 317 318 319 323 325 PAGB § 96. (Qualitative) ^quipollence 326 § 97. Opposition 328 § 98. Modal Consequence . . . . . . . . 331 § 99. Mediate Inference. Syllogism and Induction . . . 333 § 100. The simple and complex syllogism. The parts of the syllogism. Their relation ......... 335 § 101. Syllogism as a form of knowledge. Its relation to the real reign of law 337 § 102. The Simple Categorical sjllogism. Its three terms . . 350 § 103. The three chief classes (figures in the more comprehensive sense), or four divisions (figures in the narrower sense) of the simple categorical syllogism 352 § 104. The different forms of combination of the premises. The Moods 377 § 105. Comparison of spheres as a criterion of capability for inference 379 § 106. Ex mere negativis nihil sequitur. The forms of combination EE, OE, EO, 00, cut off 382 §- 107. Ex mere particularibus nihil sequitur. The forms of combina- tion II, 01, 10, cut off 385 § 108. The combination of a particular major premise with a negative minor does not give an inference. The form of combination IE cut off . .388 § 109. The First Figure in the stricter sense. The forms of combina- tion lA, OA, AE, AO, cut off 391 § 110. The First Mood of the First Figure :— Barbara . . .394 § 111. The other Moods of the First Figure : — Celarent, Darii, Ferio . 408 § 112. The Second Figure. The forms of combination lA, OA, A A, AI, cut off 411 § 113. The valid Moods of the Second Figure : — Cesare, Camestres, Festino, Baroco 413 § 114. The Third Figure. The forms of combination AE and AO cut off 420 § 115. The valid Moods of the Third Figure: — Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison 421 § 116. The Fourth Figure. The forms of combination OA, AO, AI, cut off 427 § 117. The valid Moods of the Fourth Figure, or of the second division of the First Figure in the wider sense : — Bamalip, Calemes, Diraatis, Fesapo, Fresison 429 § 118. Comparative view of the different Figures and Moods. The form of the conclusion. The Moods Barbari, Celaront ; Cesaro, Camestros; Calemos. The relative value of the different forms. The names of the whole of the Moods . 435 § 119. The Modality of the Syllogism 439 § 120. The Substitution of one notion for another in an objective or attributive relation. The syllogism from two simple It w XX Contents, § 121. § 122. § 123. § 124. § 125. § 126. § 127. § 128. § 129. § 130. § 131. § 132. § 133. § 134. § 135. § 136. § 137. PAGE categorical judgments reduced to the Principle of Substi- ^^^ tution ' • • • * * ' * • n i? The syllogism from subordinately complex and especially from ^^^ hypothetical premises . . • • - • . • * . * Mixedinferencesfroman hypothetical and a categorical premise, or the so- caUed Hypothetical Syllogism . . • - "^ Mixed inferences with co-ordinate opposed premises and espe- cially with a disjunctive premise. The Dilemma, Tnlemma, Polylemma, or the so-called Homed Syllogism . • • ^^'^ Complex Inferences. The chain of inference. The Prosyllo- ^ gism and Episyllogism . • • ' , .\ :! .' Simple and complex inferences expressed in an abridged form. The Enthymeme. The Epicheirema. The Chain Syl- ^^ logism, or Sorites ^^^ Paralogisms and Sophisms ^^^ Induction in general ^^^ Perfect Induction .^^ Imperfect Induction ^ The most notable errors in Induction . ... • • ^^^ Inference by Analogy Determination of degrees of probability . . • • ^u^ The Material truth of the premises and of the conclusions . 504 Hypothesis . . • ^^^ Proof . . • ' * ^, fjon Refutation. Investigation. Problem ^J'^ The most notable errors in Proof age 4, line Ö, >> » 16. note » 49, line „ 49, note „ 67, line » 72, >> » 76, note „ 196, line „ 225, >> „ 235, >» „ 274, )» „ 359, y> EEEATÄ. 5, for content read contents. 25, for Euklid read Euclid. * should be within brackets. 3, for Skepticism read Scepticism. », delete [Best edition by T. H. Greene, &c.] 8, for added by subject read added by the subject. 5, delete that. * should be within brackets. 11, delete the comma after • case.' 16, for give read gives. 9, for THE (avoidance of) read (the avoidance ot). 17, for popositions read propositions. 13, /or anology read analogy. PART VI. System in its relation to the Order of Objective Totality of Things. § 138. Definition of System. The law of thought of the totality . 5^ i 139. The Principle. Analysis and synthesis »4^ § 140. The analytic (or regressive) method ö4/ § 141. The synthetic (or constructive) method . . . • - ^^ Appendix A. Appendix B. Appendix C. Appendix D. On recent logical speculation in. England On the Quantification of the Predicate . On the doctrine of the Essence On the fundamental principles of Ethics 557 579 584 58<> SYSTEM OF LOGIC >;cec'psvo„ (TuyKuadai, lfiv,rrac Si 6 ivavr.'cos «X«"" V -r^ ■^paypara- . . . oi, y^p 8.Ä to v/^ao o};ech,, äXXk Savre, tovto iXvOevopev.* Tpimov Twä r, Mservance rests the realisation of the idea I of truth in the theoretical activity of man. In opposition to truth in the logical sense— the agreement of the tiioiight witli its object, and supplementary to it, is the ethical meaning of the word— the correspondence of the object with its idea or inner dstermination. The explanation of the so-called 'formal truth,' as 'the harmony of knowledge with itself ill coini)lete abstraction from all objects whatever and Knowledge. Truth. Sciertce. from all their differences, is insufficient." The explanation of the so-called transcendental truth, as the orderly arrange- mcnt of real objects, goes as far on the other s^de : ' Ven^s, quae transscendentalis appellatur et rebus ipsis messe intel- licrltur, est ordo eorum, quae enti conveniunt. , , . „ ^I„ so far as Logic seeks to determine whether and how far agLement betwee'n the content of knowledge and objecUv reality is attainable, it is a critique of knowledge. In so tar as U teaches the procedure by which the measure of agreement irle is aLally attained it is Logic ^r^^^l^^^^^l^^:;^ In the doctrine of perception the one side, and m the doctnne o? thought the other side of Logic is the prevalent. Without Iny inner contradiction, general criteria can be found accord- :J to which the agreement of a plan a picture, a notion a „TODOsition, &c. with its object can be decided. The refcr- ence X; the particular objects are in each case, first comes "SSl^td the CrUical PkHosopkg raise weighty' obiSrrgainst the possimtg of arriving at and being. ce r of material truth. In order to be assured of truth m Te absolute sense, we must be able to compare ou-ncg on with its object. But we never have (says the Critical i-liUo ol) the object otherwise than in our conception ; we never have t pure in itself. We only compare our conceptions '"th our'conceptions, never with the things -themselves Iltell truth in the relative sense succumbs to the difficu ^. whtl the old Skeptics expressed in the question: T. .p.u ro. Zra 6oeS>.^^ Formal validity, lastly, in the sense of i:rof con -diction, does not carry us beyond what we tZt implicitly, possess already. How then do.^ get atth first knowled<.e, and how can we advance m knowledge? To te e rneral difficulties are to be added particular ones bXngrng to single forms of knowledge, which will be men- 1 Kant, Log. ed. by Jasclie, p. 66. 8 Christian Wolff, Ontolog. § 495. 3 Arist. Metaph. iv. 6, p. 1011, a, 5. M i\ I 8 § 3- End and Aim of the Activity of Knowledge. Truth. Science. tioned afterwards. Their solution is the problem of the whole system of Logic, and cannot therefore be given in this place. ' It has been urged against the identification of Logic with the doctrine of the regulative laws of human knowledge, that the pnnciples of Logic would remain were there no thino-s and no tnowledge, and that thinking, e.g. a logical inference, can be (formally) correct when it is materially false (because false in the premisses).» But this exception in its first part amounts to a petitio prmcipii. Of course there are certain logical prin- ciples m which the relation of thought to things can be got rid of by abstraction. This is true of the law of Identity and Con- tradiction, which requires the harmony of thoughts with one another (the condition of their agreement with actual existence) as ^v^ll as of all other laws derived from it. Whoever limits Logic to these portions must maintain that logical principles are valid without reference to objective reality ; but he who assigns to Logic a more comprehensive sphere will not admit the correctness of that assertion in its universality. Whoever niaintains that Logic does not fulfil its task unless it pro- vides laws for the rigid construction of the scientific notion m Its distinction from the mere general conception, for natu- ral division, for the scientific form of Deduction, Induction and Analogy-whoever does not consider the principle of Logic to be the mere consistency of the thinking subject with Itself, but recognises truth to be the agreement with existence, and therefore no mere necessity of thou-^ht im- manent in the snlyective spirit, but rather a correspondence that the if •, 7 'i" .-tologieal categories, cannot assert that he logical laws, having reference to truth, would be quite as valid If there were neither things nor knowledge. Wilt is brought forward in the second part of the above objection feso aisl s'^sTÄ^ ''■ ''"' '''" "-'-' ^""'^"^ "'^- - ^<^-"-. *<=• ; ^ Uh-iei ; cf. Drobiscl,, X„,. 2nd ed. § 7, 3rd ed. § 5, and Pref p. xvm. According to D,obisch, in his introduction to Lo^ic only !o much IS to be taken from the doctrine of knowledge as is n edS o get at the data for the peculiar problems. far true that thinking may be conformable to single logical laws— to single laws of Logic even as the science of knowledge —without having material truth : but the agreement of the whole activity of knowledge with all these laws ensures material truth. He who has observed all the laws of percep- tion and of thinking cognition in a conclusion and m the structure of the premisses and in the foregoing operations, has arrived in the conclusion (be it immediately, or, as in indirect proof, mediately) at material truth. The Novel does not pro- ceed upon (historical) knowledge, and yet must follow logical laws : but it must follow them only in the combination of antecedents with consequences. If the poet constructed his antecedents from the contents of perception according to logical laws, as the historian and the judge do, he too would arrive throughout at material truth : if he follows logical laws m the combination of antecedents and consequences, he thus gams for this combination more than mere agreement with itself; he gains for it agreement with the laws of objective reality. The formal correctness of the mere conclusion, or generally of any definite part of the whole activity of knowledge, ensures material truth so far as it goes, i.e. it warrants that we, so far as we proceed from materially true antecedents (e.g. in con- cluding the return of a comet or the approach of an eclipse), will continue in material truth, and arrive at materially true results. And this is just what must be expected from the view that logical rules rest on the principle of material truth ; while it does not at all agree with the opposite view, which would understand logical rules in abstraction from material truth. According to this view material truth could be ensured neither absolutely nor partially (e.g. from premisses to conclusion) throuke. Heffel rightly remarks, so decidedly does he declare both against the first one-sided view,' and also against the second,^ that whatever is in itself of the most worth, importance, freedom, and independence, is also the most useful, and that Logic forms no exception to the rule. § 6. Logic is an integral part of the system of 'philo- sophy. Philosophy may be defined as the science of the universe, not according to its individual existences, but according to the principles which condition every individual, or the science of the principles of what is to be known in the special sciences. The principles are in the absolute or relative sense the first elements on which the series of other elements depend. In the system of Philosophy, metaphysics, including general rational theology (r^air,) ^i\o^o^ia, Arist.), makes the first great division, because it is the science of prin- ciples in general, in so far as they are common to all 1 WisB. (lei- Logik, ed. 1833-34, i. 13-17. ' ^n^jc/. § 19. 4 12 § 6. The Place of Logic in existence. The philosophy of Nature and the philoso- phy of Spiiit make the second and third divisions, because they are sciences of the special principles of the tAvo great spheres of existence, which are distinguished by the opposition of impersonality or of the absence of self-consciousness, and of personality or the capa- city for the thinking cognition of what actually exists, for perfection, and for ethical self-determination. / In the pliilosophy of Spirit three regulative sciences- Logic, Ethics, and Aesthetics, the sciences of the laws on the observation of which depends the realisation of the ideas of the true, the good, and the beauti- fu]_connect themselves with Psychology, the science of the essential nature and natural laws of the human soul. The true is knowledge which agrees with what actually exists. The good is what corresponds to its inner determination or idea, as the object of will and desire. The beautiful is what corresponds to its inner determination or idea, as the object of representation and feelinfr. To these sciences is further to be added, as both con- templative and regulative, Paedagogic, or the doctrine of training the capacities, determined by the genetic laws of the mental life, to develope themselves to their ideal ends, i.e. to the knowledge of the true, to will the Good, and to the sense of the Beautiful j and the Philo- sophy of History, or the science of the actual develop- ment of the human race, in so far as it proceeds in agreement or disagreement with the ideal rules of de- velopment. / It includes the philosophical consideration of the development of culture, religion, art, and science. the System of Philosophy. n The complete justification of this description of tlie notion and of the division of philosophy would lead us beyond the bounds of this Introduction. We therefore limit ourselves here to the following remarks. If we were to understand by -prin-^ ciple what is thought to be absolutely without antecedent, our discourse must needs be of one principle only ; but, accoixlmg to the definition of the notion given above, a plurahty of prm- ciples can be accepted, each of which in its own series is the ruling one, but when admitted into other series depend- incr upon other principles, can also subordinate itself to a higher principle from which it now derives its authority. In^^ thts sense the common principles of all existence are to be distino-uished from the particular principles of mdividual spheres. The science which treats of the earher evidently makes the first great division in any systematic arrangement. It bears the name of first philosophy » ever since Aristotle won for it an independent place, and is also called metaphysics from its position, after the physics in the system of the Aristotelian works. (This arrangement is not Aristotle's. It dates from a later time, and is due probably to Andronicus of Rhodes ; but it corresponds to Aristotle's didactic maxim, that what lies nearer the senses is the eariier for us in indue tive cognition, but the later in deductive cognition.) The divisions of philosophy which treat of the special principles of the individual spheres of being stand opposed to metaphysics. The division of these spheres into the two great groups of nature and of mind (Geist), of impersonal and personal exist- ence does not here require vindication, as it is commonly reco-nised by science. It follows from this presupposition that" the philosophy of nature and the philosophy of mmd must come after metaphysics, and make the second and third meat divisions of the system of philosophy. The division ot the philosophy of mind rests upon the law recognised by Aris- totle, that in the gradation of earthly existence every higher carries in itself the modified character of the lower, while raised above it by its higher characteristics. Thus, mmd 1 Arist. Phys. i. 4 ; Metaph. iv. 3; ibid. iv. 1. !! . J \ \ I i ' W N' 14 § 6. Place of Logic in the System of Philosophy. (Geist) has in itself the elements of nature and conformity to natural law ; and the series of the branch sciences of the philosophy of mind begins with the science of mental life from the side of nature and natural law — viz. with Psy- chology. The personal power of self-determination, by which mind is raised above nature, is conditioned by the consci- ousness of regulative laws or laws of what should be. Since these laws follow from the universal demand to realise ideas in life, each of the three chief tendencies of the life of the spirit— knowledge, will, and feeling— is governed by its special idea. Thus arise three sciences of ruling or ideal laws, co-ordinate to each other— viz. the sciences of the laws of truth, goodness, and beauty. Lastly, since the oppo- sition of the laws of nature and of the regulative laws points towards an adjustment in which the opposites become one (for, under the government of the divine spirit, what should be and what is are one and the same), the theory of Paedagogic and the philosophy of history must follow psy- chology and the regulative sciences, and 'close the series of the branch sciences of the philosophy of mind. The ideas of truth and beauty stand in essentially like relation to the idea of moral goodness. They can and should all be placed in relation to the divine spirit, for all eariier categories are destined to return as moments in the last and higher sphere ; but truth and beauty, as well as moral good- ness, must find their nearest scientific explanation from the essence of the finite spirit. We cannot, therefore, find (with Hegtd) the opposition to the ' subjective spirit ' yet linked with nature, and running through the first course of its self- liberation, in the ethical relations exclusively, but must assign aesthetic and logic, as well as ethics, to the second sphere. The doctrine of the regulative laws of thought forms part of the doctrine of the regulative laws of knowledge. It has no claim to the rank of an independent philosophical doctrine. The attempt to unite the doctrine of knowledge with meta- physics in one and the same ^d^ncQ—metaphifsical or onto- § 7. The Study of Logic, etc. 15 haical loqic-\^ untenable ; because it contradicts the funda- mental principles of any rational attempt at systematisation, by placing under the same notion with one of the branch sciences of the philosophy of spirit that philosophical ^cjence which has to do mth the most general principles. This difficulty would vanish, if we could (as Hegel does) explain the laws of knowledge to be the universal forms of all existence-ot things in nature as well as of spiritual existences. But this is a violent proceeding. Hegel's metaphysical logic treats not only of notion, judgment, and inference, but also of the analy- tic and synthetic methods, of definition, of division, of theorem, of construction, of proof, &c. All these forms must be ex- plained as metaphysical, and, consequently, as forms of nature and of spirit; but this is evidently incorrect. And even it this presupposition could be granted, the essential distinction would still exist, that those forms attain m the outer world only to an unconscious and limited, but in the knowing spin to a free conscious existence. This distinction is significant enoucrh to require a special consideration of these fornis as forms of spirit; and, in fact, with Hegel, the doctrine of the notion has three different positions in the system. It is ever coming forward in Logic, in the phenomenology of reason and in the psychology of the intelligence. Even if Hegel s presupposition, therefore, were true (which it is not), ve lould need a special theory of human knowledge besides metaphysics ; and of the two disciplines, the doctnne of know- ledge, both on verbal and historical grounds, has the bettei rioht to the name of Logic. & 7 In a system of philosophy divided according to purely scientific principles, Logic would not have the first place ; yet it is both lawful and suitable that the study of Logic should precede that of the other philo- sophical disciplines as a propaedeutic-Zaw)/»?, for its purposes are served when a few universal definitions, which are comprehensible and capable of a certain justi- I; I I N>, i6 § 8. Division of Logic. \ 8. Division of Logic. 17 fication outside of their own peculiar science, are taken out of the preceding disciplines, Metaphysics and Psy- chology; suitable for these reasons: (a) The study of Logic offers less difficulty than that of those philosophical disciplines which go before it in scientific arrangement, (b) Logic makes us conscious of the methods which find ajDplication in itself and in the other branches of philosophy, and the study of Logic is a valuable exer- cise of thinking. Li formal reference, therefore, it is convenient that Logic should be placed at the begin- ning of the whole study of philosophy, (c) The sci- entific representation of the system of Philosophy requires an introduction, in order to lead the conscious- ness to the stand-point of the philosophical treatment by means of the theory of the relations which exist between phenomena and Being ; and the task of this introduction is most completely and most scientifically accomplished by Logic as the criticaltheory of knowledge. Ilcf/el says, in his Letters to v. Räumer^ on philosophical pro- paedeutic, that it has to see to the education and exercise of thinking. It is able to do this by removing thinking entirely from the region of the phantastic, by means of the determinate - 11 ess of its notions and its consistent methodical procedure. It is able to do this in a higher measure than mathematics, because it has not the sensible content which mathematics has.^ § 8. The forms and laws of knowledge can be treated partly in their general character and partly in the par- ticular modifications which they take according to the * Werke, xvii. 355. ^Ut is tliis thought wliich is the grain of trutli in Sir W. Hamilton's ill-jiulged attiick on muthematics. Cf. Discussions, p. 282 ffl] different nature of the object- matter known (§ 2). The first is the problem of pure or general^ the second that of applied or particular Logic. Pure Logic teaches both the laws of immediate knowledge or perception, and those of mediate knowledge or thought. And since, speaking generally, knowledge mirrors the actual in its forms of existence, so more particularly — Perception mirrors the outer order of things or their existence in space and time, and represents or copies their real motion in an ideal way ; and — Thought mirrors their inner order, which is the foun- dation of the outer. The forms of thought separate into as many divisions as there are forms of existence in which the inner order of things exists, and correspond to them in the follow- ing way : — Intuition or individual conception, to the objective individual existence ; Notion^ with content and extent to the essence and genus or species ; Judgment., to the fundamental relations among things; Inference.^ to the objective reign of law ; and System., to the objective totality of things. The division of Applied or Particular Logic depends upon the sciences to which the logical doctrines find application. It treats of, for instance, the methods of mathematics or of the science of quantity and form, of the explanatory and descriptive sciences of nature, of the explanatory and descriptive sciences of spirit, and of philosophy or the science of princijJes. c i ' !3 : i8 S 8. Division of Logic. S The justification of this division in its particulars, so far as it rests on logical principles, remains to be considered below, of. §§ 36, 45, 56, 67, 74, 138; but in so far as it depends on metaphysical principles, cf. the first remark to § 2. The most common division of Logic since Kant's time has l)een— A. General Logic: 1. Pure General Logic: a. The doctrine of elements ; h. The doctrine of method. 2. Applied General Logic. B. Special Logic. Comparing this Avith our division, we remark : In so far as Applied Logic is understood to mean tlic doctrine of perception and of the relation of thought to perception, it belongs to our Pure Logic ; but in so far as it means the practical hints for the most suitable behaviour under the many subjective hindrances to thinking^ —[or as it is said to exhibit the laws of thought modified in their actual applications by certain general circumstances, external or internal, contingent in themselves, but by which human thought is always more or less influenced in its mani- festations *]— it cannot be allowed to form a special division of Logic, because it has more a didactic than a logical charac- ter (cf. § 5) ; and Applied Logic can only be understood in the same sense as we speak of applied mathematics, &c., viz. the application of its general rules to particular wider spheres in Avhich they hold good, and the consideration of the modifications under which they find application to each one of them. In this sense the notion of applied Logic docs not differ from that of special Logic, while, on the other hand. Pure Logic is identical with General Logic. The division of Pure Logic into the doctrine of Elements and doctrine of Method^ confuses its scientific interest with its didactic. Scientifically, notion, judgment, and inference are not merely elements of method. The notion is also an element in the judgment, and both are elements in inference. Besides, the notion, the doctrine of elements, is too relative to denote the opposite of Methodology. J Cf. Kant, Kritik der r. Venu Werke, ed. Hartenstein, iii. 84 ; Lor/il', viii. 18. 2 [Hamilton, Lcct. on Logic, i. 60.] ^ [Cf. Hamilton, iljid. i. 64.] > §9. Nisiory of Logic. \\o. Origin of Logic . 19 § 9. The History of Logic has worth and meaning in a double relation : (a) for its own sake, inasmuch as it brings clearly before us the ever-ongoing struggle of the human mind to obtain an understanding of the laws of its thinking and knowing; (b.) as a mean to under- stand the present position of Logic, since it informs us of the genesis both of the parts scientifically certain, and of the diverse opinions prevailing at present. Of the works winch treat of the general liistory of Logic, the most complete and thoroughgoing is the Geschichte der Logik im Abendlandc, by C. Prantl, 1st vol. (contammg the development of Logic among the ancients^ Leipzig, 1855, 2nd vol. (referring to the first half of the Middle Ages), do., 1861, 3rd vol., do., 1867, and 4th vol., do., 1870 (referring to the latter half of the Middle Ages). § 10. The foundation of Logic as a science is a work of "the Greek mind, which, equally removed from the hardness of the Northern and the softness of the Oriental, harmoniously united power and impressibility. For its general characteristic, cf. Plato ,''0^ Republ. iv. 435 E (ed. Steph.), and Arist. Polit. vii. 7. The impressible fancy/ of the Oriental has not the measure nor grip of strong thmk-(^ ing • it wants the mental power of the genuinely scientific ' mind. In its attempts to philosophise it is not ruled by the tendency to strict demonstration and to representation in a scientific form ; and where the art of strictly scientific thinking is absent, the theory can still less develope itself. Yet some true, deep fundamental thoughts appeared which, if they had been consistently followed out, would have served very well to be a foundation of a system of Logic. Thus the Chinese Men--tse, a disciple of Kon-fu-tse, says, 'The human mmd has in itsdf the possibility of knowing all things ; it must there- fore look to its own nature and essence, otherwise it errs. c 2 20 § lo. The Historical' Origm of Logic, §11. Tlie Ionic Natural Philosophers, etc, 21 Only the virtuous can fathom his own essence: he who has fathomed his own nature can also know that of other men, he can fathom the essence of things.' According to this writer the general original power of reason shows itself in man as the law of duty.^ Among the Hindoos we find, in the philosophies of the Sankhya and the Nyaya, an enumeration of the kinds and objects of knowledge. The three ways of obtaining knowledge, according to the Sankhya doctrine, are, (1) Perception ; (2) Con- clusion (from the cause to the effect and from the effect to the cause, and also by analogy); and (3) Tradition (by human testimony and Divine revelation): the Nyaya adds Comparison. The Nyaya, which perhaps first arose under Greek influence, recognises the syllogism Nyaya (from which the system takes its name) in the form of five propositions, which arise out of the three propositions by the repetition of the minor premise and conclusion, according to the following scheme : — Thesis — The hill is fiery. Keason — For it smokes. Proof — What smokes is fiery. Application — The hill smokes. Conclusion — It is fiery.^ It is very doubtful whether the Egyptians constructed a logical theory. Plato praises the antiquity of their knowledge, but by no means the elevation of their philosophy. The Greek thinkers, even if acquainted with Egyptian wisdom, had to find out for themselves both the fundamental doctrines of Logic and the ])roofs of the elementary propositions in Geometry. The Greeks have undoubtedly learned much of the material of their knowledge from the Egyptians, and from the Orientals generally. The Greek mind may have needed an impulse from without for its development, but it owes to its own inborn in- dependent power, not to foreigners, what is the more essential, its scientific and artistic form, however actively impressible it may have made their treasures its own. Cf. Hegel? ' From » Cf. Wuttke, Das Heklenthum (Breslau, 1853), ii. 102. 2 [C,Y. Colebrooke's 3Iisc. Essat/Sj i. 8, and the Aphorisms of the Nijaga Philos.. by Gautama, Allahabad, 1850.] 3 Fhilos,'iIcr Geschichte, 18o7, p. 21G. what they have naturally received the Greeks have created the spiritual.' The assertion of Lepsius agrees also with this:^ ' The Greeks of this great period (Thales, Pythagoras, &c.) collected the learning of the barbarians of all regions as ripe corn to the threshing-floor, to be new seed for their own fertile soil' § 11. The speculation of the older Ionic natural pJiilo- sophers (in the sixth century b.c.) — of Thales, Anaxi- mander, Anaximenes — was immediately directed to things only, not to the human knowledge of things. The later natural philosophers (in the fifth century b.c.) — Heraklitus, Anaxagoras, Leukippus, and Demokritus— showed that sense-perception as such was not trustworthy. It is the reason mingled with it, and going all through it, which decides what truth is. Empedocles taught that thino-s and man came from the same material and ideal elements, and that like is known by like. The Pytha- goreans held that the elements of number, limit and the limitless, are the elements of all objects. They seek therefore, by means of mathematical investigation and speculation on numbers, to get at all knowledge. Xeno- phanes of Colophon, the founder of the Eleatic philosophy, led on by his theological speculation, distinguished cer- tain knowledge from accidentally correct opinion. His immediate follower, Parmenides, the most developed of the Eleatic philosophers, in his polemic against the Hera- klitic doctrine of the universal flow of all things, and of the identity of contradictories, first reaches the theoretic consciousness of the axioms of identity and contradiction, although as yet in an incomplete form. Similarly, Par- menides taught the identity of thought with the exist- 1 Chronologie der Aegypfer, i. 55. .^! 22 §11. The Ionic Natural Philosophers, the Pythagoreans, and the Elcatics, 23 ence which is thought. He set in strict opposition to opinion about the multiplicity and change of what exists, resting on the deception of the senses, the knowledge of the One, which is truth, able to produce conviction, and attained by means of thinking. His young contem- porary, Zeno the Eleatic, was the first to use in its strict form the art of managing philosophical dialogue, especially the art of indirect proof. Hence Aristotle calls him the founder of Dialectic. Ileraklitus in Sext. Empir. adv. Math. vii. 126: Kavot /jLciprvpiS avSpcaTTOLCLV 6(i>ea\fio\ Ka\ coTa, ßopßopov fvxas f^o^Toy (according to the conjecture of Jac. Bernays; com- monly : ßapßdpov9 yp-vxas sxovtoov). In Diog. Laert. ix. 1 : UoXvfxaöUj voov ov Si^daKci' .... It/ to aocpoV i7riGTa(T6aL yvd)fivr, rjrs olaKL^sL (according to the conjecture of Bernays ; commonly: rjre ol syKvßspv-qasc, Schleiern. rfTS oltj Kvßspvrjazi) TTuvia hia TTavTcov, Yet the thinking through which wisdom is attained is, according to the view of Heraklitus, not so much an activity of the mind separable from sense-perception, and opposed to it, but rather the sense lying open and submit-, tino- itself to the universal all-ruling reason, while its isola- tion produces error.* Anaxagoras in Sext. Emp. adv. Math. vii. 90 : viro ä(\>av' 0077)705 avTCJV {jcov al d'rr.pyd^era^. ^ In bext. Emp. adv. Math. vii. 92 : ' M rov ifioiov to ofiocov Kara- •KaaBüveirdai -ni^vKSV. —00/! X„.pA«n«in Sext. Emp. adv. Math. vu. 49 ; 110 ; viu. 326 : Kai TO piv olv Edited and commented on by Boeckh, Berlin, 1819. 2 Die angebliche Schriflstellerei des Philolaus und d,e Bruchstucke der ihm zugeschriebenen Bächer, Bonn, IHM. ,,,.,,„, ,„, 3 Melap''. i- 5. * See Boeckh, Piniol. 141. ' Hud. 191, 192. !i ; !• 11 24 § II- The Ionic Natural Philosophers, etc. S 12. The Sophists and Sokrates. 25 (äfptra ty of "dividual real essences. Herbart also attempts the pro- b emnot considered by Parmenides, to derive phüosoph^cally the ilusion of the changeable from the being of the chang - ess Parmenides further teaches that thought belongs to theOne. to the truly existing, which is thought of and ,s Identical with it. What exists, is itself thmkmg, the vov. Parm. Frag. vv. 94-97 : -rayvTOv 8' iarl voecv rs Kal oUsiciv hart vovfia'^ 0{,ryäp äviV TOV i6vT09, h d> nTiaTl t^oXvhjpvv jXevX"" i| i/jJdsv priöiina. Of Zeno the Eleatic, Diogenes Laertius informs us (ix 25): rLs. Zeno's dialectic art consisted essentially m this that by reasonin.. against the existence of the many ' and of motion he u dertook to bring forward indirect pi-oof for the truth rf Parmenides' doctrine of the One which was genuine H s dialogues appear, according to (Plato's?) Parrnemdesv. 127, to have contained regular courses of reasoning (X070V»). § 12 The Sophists elaborated the dialectic art, but often misapplied it to the purposes of subjective caprice. Sohrates (470-399 b.c.), who was animated by the idea of science, made it serve to aid the striving after that obiectively valid knowledge, which may be recognised by every thinking subject to be true in the same way, and 1 Si..pUc. in. Phjs. fol. 30 B. ' Arist. Ph,s. vi. 9. 3 Cf. (Plato's?) Farmen, p. I'i». -V w 26 § 13. T/i€ Onesided Sokratic Schools, necessarily. He sought by collecting and testing in- stances to recognise the general from the basis of indi- viduals. Wlien he had discovered the universal, he endeavoured to describe it by means of the definition of the notion. He is therefore the founder of Induction and Definition, but only in their application to ethical problems, and apart from any logical theory. Protagoras ap. Diog. 1. 9. 51: irdvTcov xpVH'<^Tcoi^ /lerpov avOpWlTOS^ TUV jJLSV 6v7(DV OOS Sail, TWV 8e OVK OVTWV Ot)S OVK S(7TIV, Ibidem : irpoyros ecjyrj Bvo \6yov9 stvat, irspX iravros Trpayuaros avT(Ksifisvov9 dWrjXois, {Arist?) de Melisso, Xenophane, Goi'firia, c. 5 : (0 Topyias) ovk elval (f)rjaLV ovBsv si Bs scttlp, ay- 2 (ocnov eIvul ' si Be Kal eaTL koX yvcoarov, aXV ov Br)\(OTov aWot9. Arist, Metaph. xiii. 4 : Bvo yap scttiv a tls dv diroBoLTj "^(ok pa- rs i BiKttLüys, TovsT^ irraKTiKOVS \6yovs Kal to opi^scrdaL KaOoXov * Tavra ydp scttiv aiJb<^(ii irspl dp')(r^v s7riaTri/jLr)9. Ar ist, Metaph. i. 6 : Xco/cpdTovs Bs irspl fxsv Ta rjOiKa 7rpay/jLaTSvofjJi/ov, irspl Bs TTJS 0\t]S (pVaSCaS Ovßsv, iu p,SVTOL TOVTOLS to Ka66\0V ^rjTOVlfTOS Kal TTSpl 6pia/jL0t)V sTTLGTrjaavTOS irpcoTov Tr]v Biavoiav,^ § 13. Of the one-sided Sohratic Schools,, the Cynic of Antisthenes, and the Cyrenaic or Hedonist of Aristippus, treat of ethical problems chiefly. Their contributions to Logic rest on their negative polemic against contem- porary systems. The Megaric School of Euklid, and Eretric School of Pliaedo and Menedemus allied to it, mix together the principles of Sokrates and the doc- trines of Parmenides. Since the Megarics, in order to defend the unity of existence, deny the truth of sense- phenomena, their dialectic became gradually more and more a mere Eristic, which takes special delight to find out numerous captious and sophistical arguments. * Cf. Xenoph. Memorah. iv. 5, 12; iv. 6, 1. V. § 14. Plato. 27 Antisthenes objected to the Platonic doctrine of idea. .-Tt could easily be said to what things were similar, but not what things were. Definitions of simple notions were a useless waste of words {iMKpos T^osY _ The Cyrenaics restricted science to the consciousness ot the sense-affections as such ; what the real object was which excited these, and whether it was in itself white or sweet, &c. could not be known.^ ^ • . ^ ^^ Euklid of Megara identified the One, ^^« t'«^«^!^*7^^°; the Eleatics, with the Good of Sokrates.' He vindicated hs doctrine, as Zeno did, by indirect argument, and sought to show the absurd consequences which flow from the opposUe yiew, which ascribes plurality and change to reality. For this purpose his followers, Eubulides, Diodorus fronus and Alex- inus, invented a number of captious arguments ; e.g. The Liar < The VeUed,' ' The Homed,' ' The Heap,' and The Bald- '"^The doctrine that no subject can be joined to a predicate which can be separated from it (e.g. man is wise), but that each must be predicated of itself only (e.g. ma« is man), is o be ascribed partly to the Megarics in general, but more eiccfally to l.7,<,!who„iixed up their doctrines with tho^ of the Cvnics,^ and also to Menedemus the Eretrian.« It is an immediate consequence from the doctrine of the oneness and unchangeableness of true existence. S 14 Proceeding froia the Sokratic method of Indue- tion and Definition, Plato (427-347 b.c.) developed the art of Logic in many ways— (a) He enriched it with the methods of Division and Deduction. . Simplic. in Arist. Categ. fol.54 B.; Arist. Metaph. viü.3,cf. Plat. Tlieaet. 201, Soph. 251. » Sext. Emp. adv. Math. tu. 191. 3 Diog. Laert. ii. 106 ; Cic. Acad. pr. ii. 42. . Z.. T , V, ten " Plut. adv. Col. 23. 4 Diog. Laert. u. H". « Simplic. in Phijs. 20 A. 28 14- Plato, i- (b) He removed its limitation to ethical inquiry, and extended it to the whole sphere of philosophical thought. (c) He used it with ingenious sagacity, scientific exactness, care, and depth ; and still more increased the value of these advantages by his masterly artistic repre- sentation. Plato also developed the theory of thinking in many relations — (a) He surveyed the art of philosophical thinking in the general, and comprehended it under a general notion (the notion oi Dialectic). (b) He strictly distinguished philosophical thinking, not only from sense-perception, as his predecessors had done, but from mathematical think in or. (c) He brought under observation also, and under- took to give an account of, the main operations of thought, more especially the formation of notions, De- finition, Division, and partly also Deduction. But Plato's logical theorems, showing throughout the traces of their origin from reflection upon ideo- logical thinking, want both a strict separation of the logical from the metaphysical elements, a scientific completeness, and representation in a systematic form. If Plato's lofty art of thinking and of representation rightly excites our admiration, his developments of logical theory have no less significance for the history of our science. Plato finds in existence the measure of thinking : Rep. v. 477 (of Cratyl. p. 385 b) : Xdyos, — Sr av ra ovra Xsy»? ft>y ss ettiv, 6 Bi ■'jrevBr)! erspa twv omwv, ra ft,r) ovra apa on ovra \syii). Plato theoretically assigns this double problem to 14. Plato. 29 the art of Dialectic, which he also seeks to explain in actual thinking— (1) to collect together into one form what appears scattered everywhere, in order to determine strictly each single one (Phaedr. p. 266, the mode of forming the notion by Abstrac- tion and Definition), and in this way by the same manner to ascend further to higher notions, until the very highest is reached;' (2) then to descend again from the higher notions to the lower, which are subordinate to it, ' to be able to distin- guish how each individual has grown by means of the notions ot the kinds' (Phaedrus, 1. \.-Dicision), and to examine what proceeds from the presuppositions laid down as a basis (Phaedon, \Q\-Dedvction), in order to follow it out to the last conse- quences. Real essences correspond to the notions, rightly constructed, by which they are known, the ideas, and these separate into the graduated series which the notions have from the lower up to the absolutely highest, the idea of the Good Mathematics proceeds from postulates which are not the highest. Dialectic uses these said postulates as the basis on which to rear its ideal principles. Mathematics takes the opposite course, and derives from its postulates individuals and particu- lars. For this reason, mathematical knowledge takes a position between pure thought and sense-perception, and the objects o Mathematics are intermediate existences between ideas and sensible things. Since Plato distinguished in sense-knowleage between the trust in sense-perception and mere conjecture and, in a corresponding way, in sensible objects between things perceived in sense and pictures or shadows, he arrives at the following division of ways of knowing :— and at the following analogous division of the whole of exist- ing objects: — 'OpaTov ysyos acofiara \ sUovss 1 Z)e7^i). vi. 511; cf. vii. 532 s(?^. 2 Ibid. p. 509. I 7^ 30 § 15. The Platonists, § 16. Aristotle, \ 16. Aristotle. 31 .« It is not only characteristic of Plato's method that he carries on toofether investi^cations into thinkinor and into what is thought about ; it is also the peculiarity of the content of his doctrine that he transfers the whole relation of his forms of thought to the objects thought about. With him the logical and the metaphysical stand in a very close relation, and almost in immediate unity. (Yet he does not proceed to identify them.) § 15. Plato's followers in the Academy felt the need of a stricter systematic form for the purpose of a con- nected exposition of doctrines. Hence Speusippus was induced to divide the sciences in general, and Xen ok rates the })hilosophical disciplines in particular. Xenokrates was the first to enunciate expressly the division of Philosophy into Physics, Ethics, and Dialectic. The second and third Academic Schools in the so-called Intermediate Academy^ founded by Arkesilaus and Kar- neades, inclined to scepticism; the fourth and fifth, founded by Philo and Antiochus of Askalon, inclined to dogmatism and syncretism. For Speusippus s. Diog. Laert. iv. 2 : ovtos irpwros sv tol? fxaOr^fiaaiv sOsdaaro to kolvov koX avp(pK£ico/t, Xtyerai. § 16. Aristotle, 33 name Analytic (rk ^i/aXurtm), i.e. the analysis of thought (not the doctrine of merely analytic thinking), and desires that every one will first make himself familiar with it before he proceeds to study the First Philosophy or Metaphysic.^ With regard to the single logical writings, the book De Categoriis, irspX KarrjyopLayp (whose authenticity is not quite undoubted ; perhaps caps, x.-xv. have been inserted by a stranger), treats of the forms of notions and of the corre- sponding forms of existence. The book De Interpretatione, iTEpl hpMvslas (whose authenticity was doubted by Andronikus of Rhodes), treats of the proposition and judgment. The two books Analytica Priora, avaXvTiica nrporspa, treat of inference. The two books Analytica Posteriora, ävaKvnKä varspa, treat of proof, definition and division, and the knowledge of principles. The eight books of the Topica, roiriKd, treat of dialectical or probable inferences. Lastly, the book De Elenchis Sophisticis, nspl ao(j>iaTiKcov kxiyx^v, treats of the deceptive inferences of the Sophists and of their solution. The best new collected edition of these writings is Aristotelis Orcranon, ed. Theod. Waltz,'' Trendelenburf/ s Elementa Lo- gices Aristoteleae is a very good help to the study of the chief doctrines of Aristotles Organon.^ For a wider and more thorough-going acquaintance, the student may be referred to the well-known historical work of PrantU Ge- schichte der Logik, and more especially to the representation of the Aristotelian philosophy given by Brandis m his Handbach der Geschichte der Griech.-Röm. Philos. 11., 2nd pt 1853. Biese (Die Philosophie des Arist. Logik und Metaphysik, 1835) may also be consulted. For the meaning of the expressions J;ia/yif/c and Dialectic m Aristotle, sec Trendelenburg, Elem. Arist., Int. and § 33 ; and Ckarles Thurot, Etudes sur Aristote, Paris, 1860, p. 118 ff. For the meaning of XoyiK^^, see Waitz ad Organon Arist. 82 B, 35 ; ScJmegler ad Arist Metaph. vii. 4; xi. 10; Prantl, Ge- schichte der Logik, i. 535 f. Aristotle refers the l^oyiK^s 1 Metaph. iv. 3; vii. 12. ^ Lips. 1844-46. 3 Berol. 1836, 5th ed. 1862. D ( 34 \j. The Peripatetics. 1 8. The Epikureans, Stoics, and Skeptics, 35 Z77TeZi;(in opposition to the ^vgik^gk^is) more particularly to Plato and the Platonists,^ partly with recognition of the superiority of their investigation into notions,^ partly and chiefly blaming them, because the merely logical treatment, the more it proceeds upon the general notion, the further it is from the particular qualities. He says : ' \^(d l\ XoytKtjv (rr)v aTToBsi^Lv) 8tä toOto, otl oVw KaOoXov fiaWov, iroppcoripo) iSiv oUeiwv icTTip apxoyv. In the time of Cicero Ko^lkti was in common use to denote the doctrine of knowledge and representation (especially whilst the influence of the Stoics lasted). He says, e.g. De Fin. i. 7 : in altera philo- sophiae parte, quae est quaerendi ac disserendi, quae Aors/iKi] dicitur. The expression rj XoyiKr) irpayfrnTsta is common with Alexander of Aphrodisia, the Interpreter of Aris- totle. Boethius says: logicen Peripatetici veteres appella- verunt. Seneca and Quintilian use the expression, rationalis philosophia, rationalis pars philosophiae. Thomas of Aquino rio-htly explains the sense of this in his Commentary on Arist. Anal. Post. : Katio de suo actu ratiocinari potest — et haec est ars logica, i.e. rationalis scientia, quae non solum rationalis ex hoc, quod est secundum rationem, quod est omni- bus artibus commune, sed etiam in hoc, quod est circa ipsam artem rationis sicut circa propriam materiam. Cf. Kanty* who says, * that it (Logic) is a science of the reason, not of its forms merely, but also of its matter, since its rules cannot be derived apart from experience, and since it has at the same time reason for its object.' § 17. The earlier Peripatetics^ giving their atten- tion to empirical investigation, developed the Logic of Aristotle in a few particulars only. The later Peri- patetics restricted themselves to the task of advancing the study of Aristotle's labours by commentaries. * Metaph. xii. 1, and elsewhere. ^ Ibid. xiii. 5. 3 De Generat. Animal, ii. 8, p. 747 b, 28. * Logik, Werke, viii. 14, Harten, ed. Leip. 1868. Theophrastus and Eudermis established the theory of Hypo- thetical and Disjunctive Inference. They developed the theory of the Categorical Syllogism by adding five new ones, moods of the first figure, to the fourteen Aristotelian moods. The so-called Fourth Figure was afterwards constructed out of these. For the particulars, see § 103. Of the Later Peripa- tetics, the most prominent were Andronihus of Rhodes, who classified the works of Aristotle, and Alexander of Aphrodisias, the Interpreter. The labours of Galen and of the Neo- Platonists are to be added to theirs. See Brandis upon the Greek expounders of the Organon of Aristotle in the Proceed- ino-s of the Berlin Academy of Sciences, 1833. § 18. Epikurus (341-270 b.c.) lowers the value of Loo-ic, which he calls Canonic. He places it exclusively at the service of his Hedonist Ethics, passes over the harder doctrines, and makes sense-perception and the conception proceeding from it the final judge of truth. The Stoics^ whose mode of thought owed its origin to Zeno of Cittium (circa 300 b.c.), and was built up into a system by Chrysippus (282-209 b.c.) chiefly, developed the Aristotelian doctrine of thought in parti- cular parts, by their elaboration of the doctrine of the hypothetical and disjunctive syllogism, and added to it the beginnings of a theory of perception and of its value for knowledge. From their investigations into the criterion of truth, their Logic, more distinctly than Aristotle's, acquired the character of a theory of know- ledge. They attribute to sense-perception, and in a higher degree to thinking, the capacity to become a true picture of actual existence. Some of the Stoics comprehended, under the name Logic, dialectical doc- trines (i.e. those of the theory of thinking and know- ing) and those of grammar and rhetoric. D 2 iS '.Ii ; I 36 § 1 8. The Epihireans, Stoics, and Skeptics. \\'i The Sle^ticH combated dogmatism in general, and especially that of the Stoics. The chief representatives of Skepticism are the followers of Pyrrho of Elis (circa 320 B.c.), and the Philosophers of the Intermediate Academy. For Efiliurus see Diog\ Laert x. 31 : h rolvvv rrS Kav6vL^ Xsyet 6 'EizUovpos, Kpiri^pia rns akr)deias ehac -rhs aladiftaeLS Kai -rrpoXvfsis fcal rä irdOn^ Cicero M tollit definitiones, nihil de dividendo ac partiendo docet; non quo modo efficiatur con- cludaturque ratio tradit; non qua via captiosa solvantur, ambigua distinguantur ostcndit ; iudicia rerum in sensibus ponit^ Some late.' Eplkurcans, Zeno (circa 100 B.c.) and his scholar Philodemus, following in the steps of Epikurus, have treated of tlie mode of concluding from signs {aritiua, (rvf^si- ovadai), ., ^ For the Stoical division of Logic see Diog. LaerL vn. 41 : to Se \o-fiKOV fispos (t>aaiv hioi sh Bvo hiaipfiadai sTnarri^as, eh pnrop- iKvu Kal ii9 SioKeKTiKr^P, cf. Senec, Ep. 89 ; upon the cf^avraaU KaraXv-fTTiK^ and the TrpSXvfis issuing from it, Dior/, L. vii. 46 ; Cic, Acad. Post. i. 11 : visis non omnibus adiungebant fidem, sed us solum, quae propriam quandam haberent declarationem earum rerum, quae viderentur— unde postea notiones rerum in animis imprimerentur.— 6'^oZ». Eclog. Eth. ii. 128: slvai Be Tr]v hnart still extant, evidence the studies of the Neo-Platonists. § 20. The Philosophy of the Church Fathers is essen- tially a philosophy of religion, and, grappling with the difficulty of the problems nearest it, takes only a secon- dary interest in the problems of Logic. The Platonic doctrine of ideas attracted their attention, but in a sense which departs essentially from the original one. Au- p-ustine, following Plotinus, makes the idea immanent in the divine mind. The chief doctrines of the Aris- totelian organon were incorporated in the text-books of the so-called seven liberal arts, and thus became an object of instruction in the Christian Schools from the sixth century. The Organon, as well as the Aristotelian ' t ./ \i. r 38 §21. T/ie Schoolmen. \2\. The Schoolmen. 39 works generally, was also diligently studied by the Arabian and Jewish literati. The relation of the Church Fathers to Greek Philosophy is a various one. Justin Martyr (circ. 150 A.D.) thus asserts h,8 conviction: o.^era A^ov ^.äv lcparv> >ca. iipa.Xuro J ol 'o^^oc airoU.^ Clement of Alexandria, Ortgen, and others are friends of the Greek Philosophy, and place it at the service of Christian Theology. Others, as Irenaeus, his dis- ciple Ilippolytus, and Tertullian, frightened ^7*6 Gnostic Syncretism, were afraid of danger from it to Christian doc- tie. Others, again, such as Augustine (354-430), ke p a middle course. The contact with Neo-Platonism was part y friendly, partly antagonistic. Augustine grounded the truth of knowledge in general on the truth of the knowledge of our inner life (cf. § 40). Ideas are for him : pnncipales formae ciuaedam vel rationes rerum stabiles atque «-— '"^-' quae in divina intelligentia continentur.» Boetluus (470-525 translated and commented on several treatises of Aristotle s Orcranon, and explained the Introduction of Porphyry. Marcianus Capella (circ. 430) and Cassiodorus (c.rc. 500), in their text-books of the seven liberal Arts (Grammar, Rhe- toric, Dialectic, Arithmetic, Geometry, Astronomy and Music), treat, among others, of Dialectic or Logic, following the course of Aristotle. Mdorus Hispalensis (circ. 600), Bede (circ. 700), Alcuin (736-804), follow in their footsteps. Amon- the Arabian Aristotelians, Avicenna (Ibn Sina, circ. 1000 A.D.) and Averroes (Ibn Roschd, circ 1175) were specially famed. The most noted of the Jewish Aristotelians vTthe contemporary of Averroes, Moses Maiorudes (Moses Ben Maimun, 1135-1204), ' the light of the Jews of the Middle Ages.' ^21 In the Middle Ages the Scholastic Philosophy developed itself partly under the influence of the Church Fathers, partly under that of the logical wnt- . lustin. Apolo^. i. 40, 83 c. ' De Div. qu. 46. inc^s of Aristotle, and later (about the beginning of the thtrteenth century) under that of his other works.' The essential characteristic of the Scholasticism of the Middle Ages is the application of the understanding, arranging°and inferring, to the formal outside of dog- matic, and of sciences whose contents have been tra- ditionally given. It has significance for Logic m a double reference : (a) by its subtle extensions of the Aristotelian Syllogistic ; and (b) by the struggle of Realism with Nominalism in the question about the real existence of universals. Realism acquired an almost unlimited sovereignty in the bloom-time of Scholasticism; Nominalism, asserting that the uni- versal was not something real, but only existed in the word, or at least in the conception (conceptualism), and thereby threatening to lower the value of Scholastic Art, appeared in the beginning of Scholasticism only in an isolated and transitory way, and in its last period more generally and victoriously. The universal tendency of Scholasticism is summed up in the maxim of Anselm of Canterbury (1033-1109), ; credo ut intelligam.' As was natural, this striving after a scientific rational insight, when it first came into power, busied itselt with a formal systematising of the given contents of the doc- trines of faith and of the sciences. The knowledge of the locrical works of Aristotle was, until the time ot Abelard (1079-1142 A.D.), limited to the Categories and the De Interpretatione, along with the Isagoge of Porphyry. I he contents of the other parts of the Organon were known throu-h the text-books of Boethius, the Principia Dialect, of Aucrustine, and the pseudo-Augustinian treatise on tlie ten Categories.' Soon after, about the middle, and even • According to the testimony of Abelard in Cousin, Oeuvres ined. ■ i 1 40 8 21. The ScJioolmen. §22. Earlier Times of the Reformation, 41 before the middle, of the twelfth century, the knowledge of both Analytics, of the Topics, and of the Soph. Elench. had gradually diffused itself, partly in the translations of Boethius, partlf in other new and more literal translations. John of Salisbury (d. 1180, Bishop of Chartres) knew the whole Organon. Partly perhaps in the course of the twelfth century, partly in the beginning of the thirteenth, Logic received an addition, which consisted essentially in the re- ception of grammatico-logical notions and doctrines. These new forms w^ere made popular by the Compendium of Petrus Hispanus (d. 1277, Pope John XXL), the Summulae Logicales, in which, among other things, the mnemonic words for the forms of the Syllogism are found. The logical doctrines were here expounded in six parts (tractatus) ; the first of which gives a summary of the contents of the book De Interpretatione. The second treats of the ' quinque voces ' of Porpyhry— Genus, Species, Difference, Property, and Accident ; the third, of the Categories ; the fourth of the Syllogism ; the fifth, of the Topics ; the sixth, of the Soph. Elench. A seventh part treats of De Terminorum Proprieta- tibus. It speaks of the use of substantives, and especially of their ' suppositio,' i.e. the representation of the more special by the more general, of proper nouns by common nouns, also of adjectives and verbs, and of the * syncategoremata,' i.e. the other several parts of speech. This seventh part is also called the Parva Logicalia, and is often published sepa- rately under this title. The part of the Aristotelian Logic which was the earlier known was called the Vetus Logica, and the part which became known about 1140, the Nova Logica. The representatives of Logic extended by the doc- trine 'de term, prop.' were called ' Moderni,' and the corre- sponding parts of the whole of Logic, ' Tractatus Modern • orum.' Occam, the revivor of Nominalism (circ. 1320), has « woven into the whole doctrine of Universals ' the pro- p. 228, cf. Prantl, Gesch. der Logik j ii. 100. Besides this, Abeliird perhaps knew indirectly single sentences which Aristotle had enunciated in otlier logical treatises. positions and terms of this part of Logic* It is better not to assume (as Prantl does) that this ' Modern Logic ' rests on a Byzantian influence. A Greek compend, which contains these additions, and quite in the same way as the Summulae of Hispanus, has been ascribed by some to Michael Psellus, who lived in the eleventh century. If this be true, it must have been copied by Hispanus and other later Logicians, but it is more correctly believed to be a translation of the text- book of Petrus Hispanus. The metaphysical and physical writings of Aristotle ^ were known in the West since the end of the twelfth and beginning of the thirteenth centuries ; for the Arabian and Hebrew translations were then translated into Latin. Soon after, also, the Greek texts were obtained from Constantinople, when once the taking of that city by the Crusaders (1204) had opened up this way. Kealism had among its followers Anselm, Albertus Magnus, Thomas of Aquino, Duns Scotus ; to Nominalism belonged Roscellinus, and also Abelard (with an approach to Conceptual- ism); and later, after the fourteenth century, William of Occam, Buridan, Peter of Ailly, Biel, and others. Melanch- thon was also a Nominalist. The chiefs of Scholasticism themselves, ^/Z»^r^M5 Magnus (\\^^-\2%0), Thomas oi Aquino (1225-1274), and Duns Scotus (d. 1308), did not disdain to write commentaries on the logical writings of Aristotle. Of the fantastic ' ars magna et ultima ' of Raymond Lulhj (1234-1315), a kind of combining topic. Des Cartes rightly judged when he said,^ that it served only ' ad copiose et sine iudicio de iis, quae nescimus garriendum.' § 22. The revival of the study of the old classical literature, and the great struggle for the reformation of the Church, made the questions disputed by Scholastics 1 According to Prantl, Sitzungsher. der Münchener Akad. 1864, ii. 1, p. 65. Cf. Geschichte der Log. iii. 334 fF. 2 Cf. A. Jourdain, Eecherches crit. sur Vage et Vorigine des Trad, iat. d'Äristote, Paris, 1819, 2nd ed. 1843. 3 Disc, de Methodo, ii. Ml II 42 2 3- Bacon of Verulam, §23. Bacon of Verulam, 43 lose all their interest. Yet in the universal break with traditionalism lay the germ of a new independent development of Logic, as well as of Philosophy in general. The study of Logic was retained and ad- vanced by the reformers. Text-books written by Melanchthon, and based upon the works of Aristotle, long served in Protestant schools to give the elements of loo-ical instruction. Ramus stood forth as the op- ponent not only of Scholastic but of Aristotelian Logic. Among the classically trained men of the time, Laurentius Valla (r41 5-1465), Agricola (1442-1485), and Ludooicus Vives (1492-1540) helped to purify Logic from Scholastic subtlety. Melanchthon{U97-\5ßOym his treatises— Dialectica, 1520; Erotemata Dialectices, 1547— placed the didactic side of Logic in the foreground, for he explained Dialectic to be the * Trs et via docendi.' His example and precept, ' carere monumentis Aristotelis non possumus,' restored again amongst Protestants the authority of Aristotle, which the assaults of Luther had at first threatened to overthrow. Feter Ramus (Pierre de Ja Ramee, 1515-1572)— in his Dla- lecticae Partitiones, 1543; Institutiones Dialect., 1547 ; Scholae Dialect., 1548— has done more to agitate than to positively advance the science. The Hke may be said of the tumultuous endeavours of the contemporary Natural Philosophers of Italy — Telesius, Campanella, Bruno, and Vanini, and also of the Natural Philosopher and physician Paracelsus, and others — who have, with all their fancifulness, done a lasting service, inasmuch as they founded their doctrine of nature, and their view of the universe, upon observation and mathematics. By his maxim ' to begin from experience, and by means of it to direct the reason,' Leonardo da Vinci (1452-1519) became a predecessor of Bacon. § 23. Bacon of Verulam (1561-1626), a champion of the anti-scholastic tendency of his time spending it- Llf on the investigation of Nature, brings into Logic an essentially new element by his theory of inductive knowledge. He wished Induction to ascend from the individuals which are the objects of experience, first to notions and propositions of mtermediate universality, then by degrees to knowledge of higher universality. Bacon holds that the syllogism is not valid as a means of scientific investigation, because it does not lead to principles, and in the descents from principles cannot increase the subtlety of Nature, and that it is only suitable for disputations. Bacon undervalued the worth of the deduction of the particular from the general, and the significance which the syllogism has for deductive and mediate, and also for inductive know- ledge. Bacon has stated his opinions in his treatise De Dignitate et Auo-mentis Scientiarum, and in the Novum Organum. He says : ^ Scientia nihil aliud est, quam veritatis imago ; nam Veritas essendi et Veritas cognoscendi idem sunt, nee plus a se invicem differunt, quam radius directus et radius reflexus. -- Syllocrismus ad principia scientiarum non adhibetur, ad media axioufata frustra adhibetur, quum sit subtihtati naturae longe impar. Assensum igitur constringit, non res. 3- Syllogismus ex propositionibus constat, propositiones e verbis, verba notionum tesserae sunt. Itaque si notiones ipsae, id quod basis rei est, confusae sint et temere a rebus abstractae, nihil in 11s quae su- perstruuntur est firmitudinis. Itaque spes una est m indue- iione vera. According to the Nov. Org.,^ Inductive Logic is not, like the common Logic, to be a standard for an intel- lectual activity only abiding in itself, but is to be a standard for the knowledge of things : ita mentem regimus, ut ad rerum 1 De Augm. i. 18. 8 Ibid. xiv. 2 Novum Org. i. aphor. xiii. y Ibid. i. 127. t ill 44 § 24- Des Cartes. naturam se applicare possit. This Logic boasts itself to be a key to every science, since it directs and strenprthens the thinking mind in its striving after knowledge : ^ Rationales scientiae reliquarum omnino claves sunt; atque queinad- modum manus instrumentum instrumentorum, anima forma formarum, ita et illae artes artium ponendae sunt. Neque solum dirigunt, sed et roborant, sicut sagittandi usus non tantum facit, ut melius quis collineet, sed ut arcum tendat fortiorem. In the Nov. Org.^ Bacon asserts that his induc- tive method is applicable to the intellectual and moral sciences, but does not proceed to apply it. This application was only ' a dark i)resentiment from afar ' (Beneke). Bacon has seldom g-iven the correct methods of investigation in particular cases, still seldomer reached good scientific results in his investiga- tions, and has not even recognised as valuable nor appropriated the best of the discoveries already made in his day by others (all which Lasson and Liehig have made manifest, while they were opposing the previously very widely-extended over- estimation of Bacon); but he did this service, he more strongly opposed than any of his predecessors the trivialities of Scholasticism, he firmly established universal laws of in- ductive investigation, and he gave a place in Logic to the new tendency, with its methods and principles. Cf. § 134, on Hypothesis and the ' Experimentum crucis.' § 24. If Bacon paid almost exclusive attention to sense-perception and outer nature, Des Cartes (1596- 1650), on the other hand, found in the inherent certainty of the thought of his own existence the one starting- point of philosophical knowledge which could with- stand every doubt. He made the subjective clearness and distinctness the criterion of objective truth, and found security for the validity of this criterion in the divine truthfulness, which could not allow a clear and * De Augm. v. 1. 2 Ibid. i. 127. §24. Des Carles. 45 distinct conception to be a deceptive one. Pes Cartes accordingly believes that by means of this criterion the human mind can truly know both its own thinking in the widest sense of the word, or its whole inner conscious activity, the divine nature, and, as the properties of extended things, extension in space and its modes. He calls immediate knowledge Intuition-, every mediate way of knowledge he comprehends under the general notion oi Deduction. In mediate knowledge Des Cartes occasionally distinguishes a double method of exhibiting his fundamental doctrines— the analytic and the syn- thetic : the former, which proceeds from what is imme- diately given to principles, serves for discovery; the latter, which proceeding from principles deduces single theorems, serves for strict demonstration. Des Cartes believes that in four general directions he exhausts all that can be said about method. The first rule demands evidence which is founded on perfect clearness ; the second, a division of the difficulties ; the third, an orderly ; and the fourth, a continuous advance in investigation. Every error is due to an abuse of the freedom of the will, leading to hasty judgment. Des Cartes enunciates ^ the following definition of Clear- ness and Distinctness:— Claram voco illam perceptionem, quae menti attendenti praesens et aperta est, distinctam autem illam, quae quum clara sit, ab omnibus aliis ita seiuncta est et praecisa, ut nihil plane aliud, quam quod darum est, in se contineat. The four rules of method (which are not so much logical laws as rules, which we must receive subjectively in order to be able to comply with the logical standard, and so escape errors) are to be found in 1 Princip. Ph'd. i. § 15. y ft. L 111 'II 1 46 § 24. Des Cartes. Discours de la Methode pour bien conduire sa raison et chercher la verite dans les Sciences, 1637,^ sec. part. Des Cartes says : * Thus, instead of the great number of precepts of .vhich Logic is made up, I thought that the four following would be suf- ficient, provided I firmly and constantly resolved not to tail even once in observing them. The first was, never to accept anything as true, unless I recognised it to be so evidently, i.e. to avoid carefully haste and anticipation, and to include nothing in my judgments but what should present itself so clearly and distinctly to my mind that I should have no occasion to doubt it The second was,'to divide each of the difficulties I had to examine into as many parts as would be requisite for better resolvino- them. The third was to arrange my thoughts m an orderly "fashion, beginning with the most simple objects, and those most easily understood, to ascend little by httle, by de-rees as it were, up to the knowledge of the most compound, and to imagine an order even between those which do not pre- cede each other naturally. And the last was, to make every- where such complete enunciations and such general reviews, that I should be certain I had omitted nothing.' In the same place, Des Cartes says of the Syllogism, and of most of the other doctrines of Logic, that they have more a didactic than a scientific value : ' As for Logic, its syllogisms and the majority of its other precepts are of avail rather in the commumcation of what we already know than in the investigation of the unknown.' Des Cartes touches upon the distinction between Analytic and Synthetic methods in his replies to objections against his Meditationes de Prima Philosophia, Kespons. ad secund. obiect. In the treatise, Regulae ad Directionem Ingenu (first published in his Opuscula Posthuma, Amstelod. 1701), Des Cartes distinguishes Intuition, or Knowledge immediately certain, by which we become conscious of principles, and Deduction, or the operation by which we deduce a knowledge, which is the necessary consequent of an other, and recog- nise it because of the other. The demands contained in the 1 Bimirms de Meihodo rede vtendi Batione, 1644. [Translated into Engli:^! by Prof. Vciicb, p. 61, Edin. 1863.] §25. Spinoza, 47 four directions for method in the Discours are further deve- loped by Des Cartes into rules when he applies them to single philosophical, and especially mathematical, problems. The most celebrated logical work which has proceeded from the School of Des Cartes is La Logique, ou I'art de penser, Paris, 1662,' in which the doctrines of Aristotle are combined with the principles of Des Cartes. It defines Logic to be the art of the right use of reason in the knowledge of things (Part de bien conduire sa raison dans la connaissance des choses, tant pour s'instruire soi-meme que pour en instruire les autres). This work is probably due to Antony Arnauld, assisted by Nicole and other Jansenists of the Port-Royal. Nicole Malebranche (1638-1715), the representative of the doctrine that we see all things in God, in his work, De la Recherche de la Verite, Paris, 1673, proceeds upon the funda- mental principles of Des Cartes. Among the opponents of Des Cartes, Gasseiidi (1592-1655) deserves special mention for his clear and well-arranged repre- sentation of Logic. § 25. Spinoza (1632-1677) traced false or inadequate knowledge to the influence of the imagination, true or adequate knowledge to thought. Truth is the agree- ment of the idea with its object. Truth makes clear both itself and error. The intuitive understanding recooiiises each individual from its causes, and the finite generally from the infinite. It attends, in the first place, to the idea of one substance whose essence includes in it existence, in order to know thought and existence as its attributes, and individual beings as their modes. The arrangement and connection of thoughts correspond to the arrangement and connec- tion of things. The philosophical method is identical with the mathematical. [I Translated into English by Prof. Baynes, 2nd cJ. 1851, Edin.] ' 111 n i'.iii r^M sill it n 48 § 26. Locke. §27. Leibniz and Wolff. 49 Of the works of Spinoza, the Tractatus do Intellectus Emendatione, in the Opera Posthuma, Amstelod. 1677, belongs more especially to our subject. Several passages in the Ethics are to be compared with it. The fundamental postulate of Sinnoza is : ' Ut mens nostra omnino referat naturae exem- plar, debet omnes suas ideas producere ab ea, quae relert originem et fontem totius naturae, ut ipsa etiam sit fons cete- rarum idearum.' He defines truth to be < convenient.am ideae cum suo ideato.' He distinguishes three kinds or grades ot knowledge : imaginatio {^v.aala), ratio (the H^^nM of Aristotle), and intellectus (the intuitive knowledge of prin- ciples, ahnost equivalent to the Aristotelian .-SirW. Hamilton, Discussions on Philosophy and Literature 1852 •>nd ed. 1869 ; Lectures on Logic, edited by H. L. Mansel and J. Veitch, Edinburgh, 1859, 2nd ed. 1869 ;-AC. Fräser, Rational Philosophy in History and System, Edin- ^The Logic of Chance- an Essay on the Foundations and Province of the Theory of Probability, mth especial reference to its Applications to Moral and Social Science, London and Cambridge, 1866. ^ . . . «• r,i„ The following profess a strict Empiricism :-Är John Herschel, A Preliminary Discourseon the Study of Natural Philosophy, London, 1831 ; cf. his review of the works oi Dr. \ ilil-i, I 76 § 35. Modern Logicians beyond Germany, Whewell in the Quarterly Review, June, 1841 ; — John Stuart Mill, A System of Logic, Rationative and Inductive, 7th ed. 1868, London, translated into German by J, Schiel^ 2nd ed. from the 5th ed. of the original, Braunschweig, 1862-63 ; ef. Die Methode der inductiven Forschung als die Methode der Naturforschung, in gedrängter Darstellung, hauptsäch- lich nach John Stuart Mill, by J. Schiel, Braunschweig, 1865.^ C, W, Opzoomer inclines to Empiricism in another sense. De Waarheid en hare Kenbronnen, 2nd ed., Leyden, 1863; Het Wezen der Kennis, een Leesboek der Logika, Amsterdam, 1863 ; cf. his Die Methode der Wissenschaft, ein Handbuch der Logik, from the Dutch by G. Schwindt, Utrecht, 1852. In France, * Positivism,' based on the investigation of nature and on Mathematics, is represented by A, Comte, Cours de Philosophie positive, Paris, 1830^2. The principal part of the contents of the work of E, Vacherot, La Metaphysique et la Science, Paris, 1858, 2nd ed. 1863, belongs to the theory of knowledge ; also J, TissoCs Essai de Logique objective, ou Theorie de la connaissance de la verite et de la certitude, Dijon, 1867. J, M, C, Duhamel treats of the doctrine of Method in his Des Methodes dans les sciences du raisonnement, Paris, 1865. Ch, Waddington, Essai de Logique ; Le9ons faites ä la Sorbonne de 1848 ä 1856, Paris, 1858 ; and Pellissier, Precis d'un cours elementaire de Logique d'apres les programmes officiels de 1857, 2nd ed., Paris, 1860. Logicians who, seeking a mean between Kant and Hegel, apprehend Logic to be the science of rules, which when followed enable one to attain to science, i.e. to knowledge con- formable to things, are represented by Joseph Delboeuf, Pro- legomenes philosophique de la Geometrie, Liege, 1860; and Essai de Logique seien tifique, Prolegomenes, Liege, 1865. His doctrines in many considerations approach the method pursued in this work. * jA fuller account of the recent history of Logic in England will be given in Appendix AA 36. Definition of Perception. 77 PART FIRST. PERCEPTION IN ITS RELATION TO OBJECTIVE EXISTENCE IN SPACE AND TIME, § 36. P£ÄC7:pr/o.v is the immediate knowledge of things ^ existing together and in succession. Outer or sense- perception has to do with the outer world, inner or psychological perception with the mental (psychic) life. Perception is the first and most immediate form of know- ledge, because in it the relation of subject to object rests on given natural relations. It thus presupposes no other forms of knowledge, but is the foundation of all others, and is con- ditioned only by the presence of its object. The mental (geistige) element in it is connected in the closest way with the definite constitution of nature, and this connection is the earlier form according to the universal law of the development of spirit. Yet the immediateness of knowledge in percep- tion is relative, since many influencing mental (geistige) operations are blended in it with the sense-activity, although only their collective product appears in consciousness, and not they themselves individually. [If this distinction had been as clearly stated by Hamilton, he might have escaped the charge of inconsistency which J. S. Mill and J. H. Stirlmg advanced against his doctrine of perception.»] Perception is distinguished from mere Sensation, which can [} Cf. Mill's Examination of Sir W. Hamilton's Philos. 3rd ed. Lond. 18G7, p. 17 ff.; Stirling's Philosophj of Perception, p. 2 ff.J ,1 I, i| \ 78 §36- Definition of Perception, 37. External or Sense-Perception, 79 be more particularly treated in Psychology, by this, that in sensation consciousness clings to the subjective occasion merely, while in perception it goes out upon something which has been perceived, and which therefore, whether it belongs tg the outer world or to the subject itself, opposes itself to the act of perception as something objective.* Its (relative) immediateness distinguishes -perception from thinking which produces mediate knowledge, separates perceptions into their elements, and re-combines them with each other. Thinking^ however, may be taken in a wider sense, and understood to mean the totality of the (theoretic) functions, which aim at the representation of any object in our consciousness. In this case perception itself may be called a kind of thinking. Perception is the object of Psychology in reference to the way it happens, but with regard to the agreement or want of asrreement of its contents with nature, it is the object of Lottie. The logical theory of perception is an integral part of Loo-ic, the doctrine of knowledge, and not a ' mere psycho- loo-ical introduction ' to the representation of the normative laws of the operations of thought. There is no contradiction in believing that the laws of percep- tion and thought are conditioned by things-in-themselves, and that our understanding of the laws of perception and thought is conditioned by our scientific knowledge of those things in themselves. The opinions of some writers [e.g. Prof. Bain] that there is such a contradiction arises from the erroneous sup- position that in order to know the thing-in-itself, it must be in our consciousness. The external thing-in-itself cannot be in us, but a knowledge of it on which we may depend can be in us. We get this knowledge by reflecting upon perception and upon thought itself, and in this way can reason back from the results to the cause. There is no contradiction in the asser- /tion that a true knowledge of what is outside my conscious- '. ness may be in my consciousness. \} Cf. Hamilton, Led. on Metaph. ii. 93 ; his edition of ReicVs Works^ p. 876 ff.] A. — External or Sense-Perception. § 37. The special question of Logic as the doctrine of knowledge, is, Whether in sense-perception things appear to us as they actually exist^ or as they are in themselves ? Skeptics assert the negative. Their arguments are : The agreement of thoudit with existence, even if there were such a thing, could never be known, for the sense- perception can only be compared with other perceptions, never with its object. The doubt is strengthened when we reflect upon the essential nature of sense-perception. The perception as an act of the mind (Seele) must either be of a purely subjective origin, or at least include a subjective element. In either case the assertion that the mind reflects undistortedly and exhaustively the peculiar real being of what is perceived, can only be supported by artificial hypotheses which are diflicult to be confirmed. The constitution of the world of phenomena is at least partly conditioned by the sub- jective nature of our sense. Sense may be different in other beings, and so may produce other kinds of worlds of sense-phenomena. What actually exists as such, as it is in itself independent of any way of apprehending it, or the thing-in-itself, is difi^erent from all of these. The uncertainty of sense-perception was maintained by tlie Eleatics, in a certain degree by Demokritus and other natural philosophers, then by Plato, and with new arguments by the earlier Skeptics, The Stoical criterion, the (jyavraala KaTdki^Tr- TLKijjwas a superfluous assertion, which could not overcome Skep- ticism. Among modern philosophers who take up the position that sense-perception cannot impart, at least, full material til 8o § 38. Incorrectness of the Kantian Separation truth, we may mention specially. Des Cartes^ Locke (with regard to the secondary qualities), Kant? Herhart? and Beneke,^ Jos. Delhceuf has discussed afresh the questions which belong to the inability to compare the conception with its object.^ He uses the formula : A—f (a, x) — that is, the real result. A, is not known as such, but must be brought about by a, that is, the object-phenomenon, and x, that is, the nature of our mind (Geist). l_8ir W, Hamilton's explanation is not unlike Delboeuf's — • * Suppose that the total object of consciousness in perception is = 12, and that the external reality contributes 6, the material sense 3, and the mind 3 : this may enable you to form some rude conjecture of the nature of the object of perception.'^] § 38. The Subjective element in sense-perception can- not be separated from the Objective in this way, that space and time can be referred to the subject only, and what ßlls space and tirne^ or its material (colour, sound, &c.), to external things aifecting our senses. For on this presupposition, although it would be neces- sary to apprehend the matter of sense-perception in any form of space and time, each particular matter would not be referred back to each particular form, and, consequently, might be perceived in another form from that in which it actually appears, without having un- dergone any real change. But in perception we feel ourselves actually confined to the union of definite forms with definite matters. Again, modern physics • 1 Meditat. mit, ^ Kritik der r. Vern. ; Elementarlehre^ Pt. I. ; Transcendentalen Aes~ thetik ; and Logik, ed. by Jäsche, p. 69 f. 3 Linl. ill die Philosophie, § 19 ff. ^ Metaphysik, pp. 91-119. « Log, pp. 35 ff., 71 if., 93 ff.; 105. * \_Lect. on Metapht/sics, ii. lect. xxv. p. 129.] 0/ the Matter and Form of Perception. 8 1 and physiology, because they trace sound, warmth, and colour back to the perception of vibrations of air and of aether, smell and taste to the perception of certain motions comiected with chemical occurrences, prove the dependence of the content of perception on motions, i.e. on changes belonging to the forms of space and time. It involves a contradiction therefore to admit that content rests on afi:ections which come from without, and to believe that these forms nevertheless are derived from tlie perceiving subject only, and are not conditi- oned by the external world affecting us. The view here combated is that which Kant enunciated (Kritik d. r. Vernunft, Part I., Transcendentale Aestlictik). The truth that a subjective and an objective element is to be distinguished in perception was aj)plied in a very unfor- tunate and misleading way, when Kant called the former element Xh^form and the latter the content or matter of per- ception, and still further defined the form to be intuition of space and time. ^Vccording to Kaiit, the qualities of sensation, such as blue, green, sweet, &c., as such, are only subjective, but rest on determinate outward affections, which determine the peculiar nature and character of each. This doctrine (which was afterwards developed by J oh. Müller into that of special sense-energies) is correct enough. Tlie form of intui- tion-in-space-and-time, on the other hand, is something pureltj subjective, because a priori ; but it is quite inadmissible not to attribute to intuition-in-space at least a measure of the objective conditionality, which is attributed to the sense- (jualities, which, as Physics show, depend upon distinct motions. Kant's doctrine of the forms of intuition-in-space-and-time wavers. For, on the one side (on the side on which our state- ment given above rests), these forms even in their particular determinations must originate in the subject onhj^ which can G i 82 S ^8. Incorrectness of the Kantian Separation, etc, t) ^ -^ only impose on a chaotic matter its li priori forms and laws ; and, on the other side, the particular determinate forms and the special natural laws must be given empirically, and their determinute nature and character cannot in each case (/row out of the suhject alone. They must depend ui)on the way in which the subject is each time affected from the side of ' thinc^s-in-themselves,' according to their own peculiar con- structionJ Fichte, seeing the separation to be untenable, explained both the matter and the form of perception to be merely subjective ; ScheUiny and Heyel made it at the same time subjective and objective. Ilerbart subjects the Kantian opinion to a very thorough criticism.^ [67r W. Hamilton and his School have devoted much labour to distinguish the formal from the emi)irical elements in sense- perception. The formal element is called the primary qualities of matter, the empirical the secondary. The primary qualities are attributes of body as body, are thought of as essential to body, and are conceived as modes of a not-self. The secondary are attributes of body as this or that kind of body. They are thought of as accidental, and are conceived as modes of self in relation to bodies. Hamilton has also 1 For a criticism of the Kantian doctrine, cf. my Grund, der Gesch. d. Phil. iii. § IG, 2na. ed. •^ Einl. in die Philosophie, § 127 ; Psychol, als Wissenschaß, in Herb. Sämmtlichen Werken, v. 504 ff. Upon the stimuli of sense us vibrations in matter, see especially Joh. Müller, Physiologie, 4th cd. i. ()G7 ff., ii. 249 ft". [English translation by Daly, i. 613 ff., ii. 1)03 ff., 1842 ; Carpenter, Principles of Human Physiology, 7th ed. ()r)3-722] ; cf George, Die Fünf Sinne, pp. 27-42 ; Maximilian Jacobi, iXatur- und Geistesleben, pp. 1-34 ; Lotze, Medicinische Psychologie, p. 174 tf., 1852; Mikrokosmus, i. 376, 1860; Helmholtz, Ueher die Natur der menschlichen Sinnesempßndungen, p. 20 ff., 1852 (where the distinction between the sensiitiolis and the relations of vibrations is emphasised, and the senses are 'thanked' very rightly for 'conjur- ing'' ' out of these vibrations, colours, sounds, &c., and ibr bringing us intelligence of the outer world by these sensations, as if by ' symbols ') ; Ueber das Sehen des Menschen, Leipzig, 1855. § 39. Insiifficiency of Sense-Perception. 83 secundo-primary qualities, which are intermediate between the other two.' Mr, Mill and his School ' do not think it necessary to ascribe to the mind (either in percei)tion or in any other cognitive faculty) certain innate forms, in which objects are, as it were, moulded into these appearances, but hold that Place, Exten- sion, Substance, Cause, and the rest, are conce[)tions put together out of ideas of sensation by the known laws of associ- tion.'^J § 31). Neither the })roportiou which the external reality contributes to the generation of perceptions, nor even the existence of the object affecting us^ can be known from the ground of sense-perception alone. Perceptions are acts of our mind, and as such do not carry us beyond ourselves. The conviction of the existence of external objects which affect us depends upon the presupposition of causal relations which do not belong to sense-perception only. The doctrine of Common Sense of the Scottish School (Reid, Stewart, Beattie, &c.), as well as the alUed doctrine of F, H, Jacobi, which asserts that a faith which cannot be scientifi- cally explained reveals to us the existence of an external world, is a fiction which has no foundation. The problem stated in this section can only be settled below (in §§41-44). [• Cf. Hamilton's ed. oi lie id's Works, Aj)pendix, Note D, pj. 825-75 ; cf. Rlansel's Metaphysics, p. 105 ff., 18G0; cf. also, for remarks upon the Siinie distinction in Racon's philosophy, the general Preface to his pliilosopliical works, by James Spedding and R. L. Ellis, i. 29. Cf. also Berkeley's Works, Fräsers Ed. i. pp. 122 ff., 160 ff., 249 ff., and j)asHim. 2 Cf Mill's Exam, of Sir W. Hamilton's Philos. pp. 219 ff., 258 ff., 3rd ed. 18C7 ; Bain's Senses and Intellect passim ; Deductive Logic, p. 10.] G 2 84 § 40- Agreement of the Inner Perception B.— Internal or Psychological Perception. § 40. Internal Perception, or the immediate hwwledije of mental {psychic) acts and constructions, can apprehend its objects as they are in themselves with material truth. For internal perception results when the individual pro- duction is apprehended by means of the process of Asso- ciation as an integral part of our whole mental produc- tion. It reaches its most developed form, blended with thought, when the mental production under considera- tion Ts placed under the notion to which it refers, and when at the same time the consciousness, which he who performs the internal perception has of himself, has reached the form expressed by ' Ego.' But : (a) The as- Bociation of a single act with others cannot change its con- tent and form. It remains what it is. We are conscious of our present conceptions, thoughts, feelings, desires, and in general of the elements of our mental (psychic) life, and of their mutual relations as they actually exist ; and they actually exist as we are conscious of them. In mental acts, consciousness and existence are one and the same, (b) In the recollection of earlier mental acts, their thought-pictures, remaining in unconsciousness, are again aroused. Earlier acts may be reproduced, with less intensity it is true, but in actual agree- ment with their orighial existence, (c) By the sub- sumption of individual acts and productions under the corresponding general notion, the strength of conscious- ness is directed to their common character, without the admixture of any foreign element. The consciousness attained by this of our mental acts, and productions with tlie Po^ceived Reality. 85 naturally harmonises with the real existence of these elements. But the possibility of error increases as we, in order to determine its notion, go beyond the act itself, and consider its genesis and relations (e.g. as in the ques- tion whether a certain conception be a perception or an illusion), (d) Self-consciousness in the strict sense, or consciousness of the Ego, developes itself in three mo- ments. The first moment is the unity of an individual capable of consciousness, by means of which every par- ticular in it must be viewed not as an independent existence, which together with others is found in an accidental aggregate, but as a member of a single whole organism. The second moment is the conscious- ness which the individual has of itself as one indivi- dual, or the coherent perception of single mental acts and productions in their mutual combinations, according to which they belong collectively to the same being. The third moment is the further perception, that that con- sciousness which the individual has of itself as an indi- vidual belongs again to the same being as the acts and productions to which it is directed, — in other words, the perception that the being conceived and conceiving, or the object and the subject of the conception, is one and the same. The first and second moments constitute the presuppositions or foundations ; the third constitutes the essence of the self-consciousness as consciousness of the Ego. This moment is only an inner perception become potential, and so does not introduce anything different from the actual existence. Accordingly, in every form of internal perception directed to one's own mental life, and in every form of thought combining \ 86 § 40. Agreement of the Inner Perception with it and working it up in internal experience, the phenomenon is in essential agreement with the mental actual existence. That mv pain appears to me as my pain, my sensation of colour as my sensation of colour, &c. is self-evident, and to wish to prove this were quite superfluous. But the psychological transcendentalist would distinguish from the pain, from the sensation of sound or of colour, (not only the essence and substance of the soul, and the inner conditions of individual mental occurrence, and not only the outer affections inducmg them, with all of which the present investigation has nothing to do— but also) an existence in-itself even of those psycho- loo-ical modifications in me, which appear to me as pain, sen- sation of colour, sound, &c. The present argument aims at proving the incorrectness of this distinction. I perceive by sense-perception a sound, a colour, &c. correctly, in the em- pirical sense, if I perceive it as it must be perceived by the normal sense-perception. I remember rightly when my me- mory-conception corresponds with this normal perception. Yet the question ever arises, whether this normal perception agrees with the fact as it took place in itself outside my con- sciousness, and, by working on my sense, gave rise to my per- ception. This question is, however, meaningless when it refers to the psychological apprehension of one of my sensations or of any of my mental productions. The distinsuon of truth in the ' empirical' and in the ' transcendentar sense which is valid of sense-perception can only be applied by a false analogy to in- ternal perception. There is meaning not only in seeking to know what are the external, but also what are the internal con- ditions of the origin of a mental act ; but when the mental image as such is the object of my apprehension, there is no meaning in seeking to distinguish its existence in my consciousness (in me) fronT its existence out of my consciousness (in itself)— for the object apprehended is, in this case, one which does not even exist, as the objects of external perception do, in itself outside my consciousness. It exists only within me. In the with the Perceived Reality, 87 external perception the sensation of the subject contains not only elements which correspond with objective existence, but also elements which differ from it ; and these last, the subjective elements, make a discrepancy between the image and the objective reality. In internal perception, on the other hand, so far as this has to do with my own acts immediately present in my consciousness (unless memory requires to come forward to introduce them), the subjective action, because it is itself the object of the apprehension, cannot, as purely sub- jective, contain elements which establish an inconsistency with the object to be apprehended. Every subject in thU self- apprehension is also object. AVe have not to distinguish be- tween two things which might or might not correspond with each other. There is only one thing identical with itself. The question of agreement, of course, enters into the conceptions of memory, and the subsumption of mental productions under psychological notions. The relation is no longer that of iden- tity ; but what apprehends can be homogeneous with what is to be apprehended, for both belong to the same animate exist- ence. It cannot be presumed to be so in sense-perception ; for there, what apprehends is mind, and what is apprehended belongs to the external world. To understand the nature of self-consciousnesa one must not confound the identity of the conceiving with the conceived essence, or the identity of the person with a supposed identity of the act of self-conception with the acts and productions to which the self-conception is directed. Nor must one, with Hegel, confound the identity of the person, as the concrete unity embracing in itself all acts, with the pretended identity of a supposed monad reduced to a simple quality w^hich remains over after the nhstraction of all actual acts. If we call the totality of these mental elements (conceptions, feelings, desires, &c.), to which the internal perception is directed. A, and the inner perception itself B, then B is not identical with A (how- ever much correspondent), it is only very closely associated. But the essence to which both belong, as integral parts, is identical, or one and the same essence. That b is only the 88 § 40. Agreonenl of the Inner Perception with the Perceived Reality. 89 consciousness of the singularity of itself as a person, which consciousness is expressed in language by naming one's proper name. Self-consciousness, however, as consciousness of the Eojo, C, is the consciousness of the co-existence of a and B in one and the same essence, the Ego, which includes in itself the totality of all my mental acts. The objection quoted in § 3, and § 37, against the possibility of truth and of the certainty of truth in the material sense, because a comparison of our concei)tions with existence is never possible, but only their comparison with other concep- tions, does not find application to what has been said about the internal perception of our mental acts and productions. We take to ourselves only an uncertain picture of material ex- ternal tilings. We picture within ourselves in a more adequate form the tliouglits, feelings, and volitions of others. Still more, memory may be true to my own earlier received thoughts, to my own feelings and volitions. The immediate apprehension of the mental images immediatelt/ presented to me is necessarily true. Error is possible only when they are subsumed under a general notion. In this sense, internal perception, more trust- worthy than external, is the foundation of all philosophical know- ledge. That we have a perception of our own inner mental (psychic) life, into which existence immediately enters, without the admixture of a foreign form, is the first stronghold of the theory of knowledge. Melissus the Eleatic asked : ' If nothing existed, how could men speak as of something?' The certainty of the existence of speech (and therefore also of thought) was to him the prius. The certainty of the thought of his own existence lies at the bottom of all the utterances oi Parmenides about thouirht. After the subjective individualism of Protagoras had iden- tified appearance and existence, Aristippus fnsisted upon the subjective truth of sensations. We only know that outer things which Avork upon us by the affections, exist, not how thev exist; but sensation itself is in our consciousness.* * ri) TTiiQüQ tj^lv ifTTi (pai}'6/.ierov, Aristippus in Sext. Enip. adv. Math. vii. 91. The Socratic study of Ethics and the church doctrine of Salvation made men look to the inner life. Augustine re- cognised that the conception which we have of external things may deceive us, but that the consciousness by the spirit of its own life, memory, thought, and volition, is free from de- ception. In this sense he puts forward the claim (De Vera Keligione, pp. 39,72) : ' Noli foras ire, in te redi, in inferiore homine habitat Veritas (et si animam mutabilem in veneris, trans- scende te ipsum).' Cf. contra Academicos, iii. 26 : noli plus assentiri, quam ut ita tibi apparere persuadeas, et nulla de- ceptio est. Soliloqu. ii. 1 : tu qui vis te nosse, scis esse te ? scio ; unde scis ? nescio ; simplicem te scis an multiplicem ? nescio ; moveri te scis ? nescio ; cogitare te scis ? scio. De Trinitate, x. 14: si dubitat, vivit; si dubitat, unde dubitet, meminit ; si dubitat, dubitare se intellegit ; si dubitat, certus esse vult ; si dubitat, cogitat ; si dubitat, seit se nescire ; si dubitat, iudicat non se teniere consentire oportere. Cf. de Civ. Dei, xi. 26. So also, in the Middle Ages, Occam the Nominalist taught that the propositions, such as, I know that I live, think, &c. are surer than sense-perceptions. Des Cartes, however, w^as the first to found a system of philosophy on this principle. Thought (cogitare) is to him the most certain of all things ; but * under thought,' he explains, * I include all that enters into our consciousness, so far as we are conscious of it, and so volitions, conceptions, and sensa- tions.'* Kant, on the other hand, disputes the truth of self-know- ledge also. Development in time belongs to our existence, not actually as it is in itself, but only as it is phenomenal ; and this development in time depends upon this, that the * internal sense ' is accompanied by the intuitional form of time. Our true being remains completely unknown to us. But if there were an inner sense of such a kind as Kant imagined, so that, when our being, in itself timeless, affected it, then the phenomenon of our conscious life in time resulted, this would yet be a result •* Medit. ii. ; Princ. phil. i. 9. I 90 § 40- Agreement of the Infier Perception, etc. which has actually happened. Consciousness and existence would still be identical in relation to our development in time, and the proposition would remain valid,— our mental (psychic) life in time exists in itself as we are conscious of it, and we are conscious of it as it exists. A stricter psychological treatment of the nature of internal perception makes it^'evi- dent that the Kantian hypothesis about our internal sense is untenable. We apprehend also our self-apprehension, which, according to Kant, exists in time. By what ' internal sense ' and by what form does this happen? Internal perception cannot bring time into what is in itself timeless, but can only recognise that what has already the attribute of time in itself, is in time. (It is a wholly different question, and one belonging not to the doctrine of knowledge but to metaphysics, to as\'— Has time any independent power or subsistence, or is it only an outflow of the essence of things, and in this sense merely phenomenal ? and if so, how far does each thing bear about in itself its own measure of time ? The confusion of the meta- phi/sical opposition between essential existence and what Is ovt- slile of essential existence, lohere the two sides belong to the peculiar nature of things, with the opposition In Logic or In the doctrine of knowledge between the peculiar existence of things or their existence In themselves, and the phenomenon which is only considered to be a true or untrue mirroring of things, has caused unspeakable confusion In these Investigations.) Hegel makes internal perception, as he makes external, the propaedeutical starting-point, not the scientific foundation, of philosophy, and allows truth to mental (psychic) processes' in so far as they make moments in the dialectical self-development of the Absolute.' Schleier ma eher rightly finds in self-consciousness the point where thought and being are originally identical : ' We exist thinking, and we think existino-.'^ Beneke, in agreement with Schleiermacher, teaches, ^ All ' Phän. des Gelsfes, and Enn/clopüdie, § 413 ff. 2 Dial. § 101 ff. p. 53, and Erlauf, p. 54 ff. ; cf Beil. D. xviii. xix. p. 452 ff., and Beil. E. xx.-xxiii. 488 ff. §41. Plurality of Animate Existences. 91 knowledge of our mental (psychic) activities is a knowledge of an existence in itself, i.e. the knowledge of an existence appears as it is in and for itself, or is independent of its being conceived,'* and makes this proposition the basis of his doctrine of Metaphysics (with him comprehending in itself the doctrine- of knowledge).^ [^Hamilton distinguishes carefully ^ between the data or deliverances of consciousness considered simply in themselves, as apprehended facts or actual manifestations, and those de- liverances considered as testimonies to the truth of facts beyond their own phenomenal existence ; ' but in so doing neither suffi- ciently distinguishes the state of the case in external perception from that in internal perception, nor sets clearly before himself the difference between the logical and metaphysical problems.^] C. — The Combination of Internal and External Perception. § 41. Tlie knowledge of the outer ivorld depends upon the combination of external with internal perception. Our corporeal eircumst«ances, sensibly perceived by ourselves, are in orderly coherence with circumstances belonging to our internal perception. In consequence of this co- herence, that association grows up within us, by means of which we presuppose, along with the sense-perception of corporeal circumstances analogous to our own, a mental {psychic) existence also analogous. This combina- tion, which is at first carried on instinctively, as it were, without any conscious reflection upon the mental laws * Neue Grundlefiung zur Mefaphysik, p. 10, 1822. 2 Sysfem der Metaphysik, pp. 68-75, 1840 ; Lehrbuch der Psychol. § 129, p. 121, 1845 ; cf. W. F. Volkmann, Grvndriss der Psychologie, Halle, p. 169, 1856. ^ 3 [Cf. Hamilton's ed. of Reld's Works, p. 743 ff. ; Lecf. i. 138 ; cf. Mill's Exam, of Sir W. Hamilfons Philosophy, 3rd ed. pp. 234-43.] H A 92 §41. Plurality 0/ Ajiimafe Existences. U of logical development, if logically developed, takes the form of a reasoning from analogy — as our corporeal phe- nomena are to our mental reality, so other corporeal phe- nomena are to a strange mental reality (here accord- ingly presupposed). As to the logical correctness of the presupposition of a plurality of personal essences after the analogy of our own existence, it is generally un- doubtedly certain, that, by this combination of the con- tent of external perception with that of internal, we make the first a moment, which belongs to reality, although it does not present itself in the external sense according to its nature. The proof for this lies partly in the consciousness, that the species and connection of external phenomena under consideration are not wholly conditioned by thb mere causality of our own individual mental (psychic) life, partly in the thorough-going positive confirmation which the presupposition has from experience. It does not belong to Logic to explain further the psycho- logical side of this matter. Logic has to do with what is psychological only in the form of an hypothesis to be established in some other place. On the other hand, it does belong to Logic to prove the logical right, or to decide upon the ques- tion, whether the assertion originally and necessarily formed according to psychological laws has truth, i.e. agreement with existence. This follows from the general notion of both sciences. See §§ 2, 6, and 36. Schleier ma eher was the first to recognise correctly that in the knowledge of existence external to us we first affirm a pluralitv of animate subjects. Betteke follows him in this, but expresses the psychological relation more definitely. He finds in it the essential foundation of Metaphysics.' > Grundleg. der Metaphiii. p. 23 ; Syst. der Mctaphys. pp. 76-90 ; § 42. The Gradual Series of Existences, etc. 93 § 42. Extending his consideration of the external world, man recognises the internal characters of other things., chiefly by means of the related sides of his OAvn^ inner existence. He copies in himself the existence of higher and lower objects ; for he partly raises, partly lowers, the corresponding moments of his own mind, and in this fashion gives a supplementary meaning to the content of the external j^erception of what appears at the time. By such a reproductive process, developed, trained, and fitted for a deeper self-knowledge, he imi- tatively seeks to recognise in gradually higher proportion the inner nature of other essences. The truth of these elements of knowledge modifies itself according to two relations: (1) in objective relation according to the distance of the then present objects of knowledge from our own existence ; (2) in subjective relation accord - inas Leben der Seele, ii. 28G; cf. § 101. Science, Faith, Presentiment, Opinion, etc, 95 and more adequate way, and faith become scientific knowledge or vision. Hence, within certain hmits, according to the diflPerent stages of mental development, the same content of knowledge, which is only an object of faith for the one, is for others an object of knowledge. But as often as knowledge completely annexes to itself one province, a higher jn-ovince of faith reveals itself. It must be noted, with regard to the sub- jective criterion or discrimination between nearer and further analogy, that the uneducated consciousness is at the same time liable to the two op})osite faults, of raising the lower too nearly u]) to, and of dragging the higher too nearly down to, its own peculiar nature. For, since our own peculiar existence is the only one immediately given to us, what first necessarily j)resents itself, until the phenomena refute this first hypothesis, is a multiplication of such existences. ' Man refers his own pecu- liar essence to Nature, and throws into the world of things the conception of human relations ' (Trendelenburg). The capa- bility both of fully idealising and of in the right way dividing and depotentialising our own nature is only attained gradually and amidst fluctuations hitherto by no means completely over- come even by the sciences. The tendency to anthropomorphism does not allow people living in a state of nature either to reach the pure ideal above, or the abstract categories of scientific l)hysics beneath. It ai)pears in numberless expressions of the l)oets and of the earlier ])hilosoj)hers. The well-known astro- nomical axiom of Heraclitus, the ancient equivalent of the modern theory of gravitation, belongs to this way of looking at things — ' The sun will not transgress its bounds, for if it did so the Furies, the servants of Dike, would find it.' Timoleon erected an altar to Automatia, to the personified might of acci- dent, moulding his notion to the very opposite of self-conscious personality. The exaltation of Christianity over Judaism aj)peared to the Gnostics to be the exaltation of the God of the Christians over the God of the Jews. Clement of Alex- andria thought that the Greek philosophy had been given by God to men by the lower angels. Up to the i)resent time this anthropomorphism continues to exercise its influence, not only m i 96 § 42. T/ie Gi^adiial Series of Existences, etc. in the thousand forms of popular superstition, down to spirit- raj)ping, but also in a way less evident perhaps, but all the more prejudicial because it checks the development of the sciences, in ' a course of symbolising myths, which were con- sidered real theories,'^ and in the hypostatlsing or quasi-per- sonification of the faculties of the soul, of the animal and vegetable powers, of the Ideas, and of the Categories, &c. Kepler's Pythagorean theory of heavenly harmony, which barred against him the way to Newton's great discoveries, since it did not let him know the actual powers, de[)ends upon this way of looking at things, as much as the Ancient and Aristotelian-Scholastic personification of the stars or their moving principles as gods or angels. Auguste Comte, the French philosopher, in his Philosophie positive, expresses this relation of personification, mere quasi- })ersonification, and adequate description, by the distinction of Theology, Metaphysics, and Positive Philosoi)hy ; for he be- lieves whole doctrines to embody the logical mistakes which explained lightning by an angry Jove, and fire by Phlogiston. On the other side, the polemic of science against these childish conceptions has not seldom mistaken the limits beyond which it becomes unscientific, when it denies the really existing analogy, and favours a false dualism. Into this error fell the Anaxagorean physics, and still more the Cartesian natural- l)hilosophy, which, seeking only pressure and resistance in nature, refused recognition to Gravitation and to the animal and vegetable powers. The same mistake of scientific endeavour induced Spinoza and many others to combat all Teleology, true or false. Final decision upon all these questions is only possible by the help of considerations which belong to the Positive Sciences. It belongs to Logic, however, to explain them so far as the grounds of determination lie in the essential nature of the human power of knowledge in general. A Logic which leaves this problem untouched, leaves its task unfulfilled in many essential relations. » Alex. V. Humboldt, Kosmos, ii. 399 ; cl'. i. Gß f. i * § 43. TAe Reality of Matter and Power. 97 That the same and the similar in things are recognised by the same and the similar in us is a doctrine agreed upon by the ancient Oriental, and by almost all the Greek Philosophers except Anaxagoras : of. Arist De Anima, i. 2, § 20. In modern times the same view comes back in the Leihnizian Monad- ology ; in the Kantian view, that the end and aim of Nature is the analogue of the moral law ; in the theory of Herhart, which traces back everything that has ' really ' happened, or every change of the inner circumstances of a simple real exist- ence (monad), to the analogy of conceptions, or of ' preserva- tions of self (Selbsterhaltungen), and to the relations of the conceptions of the human mind (Seele) ; in Schelling's Nature- philosophy ; and in the Hegelian doctrine of the identity of thinking and being. Schleiermacher taught that the powers of essences in nature were to be looked at as the lower ana- logues of the human will, and the whole of nature, as a fainter Ethic (Dial. p. 150). Man is a microcosm since he has in himself all grades of life, and hence constructs his conceptions of the external existence (Dial. p. 109). Schopenhauer forms his * panthelematism ' on the identification of the notions of power and will, but has not suflSciently noticed the distinction between a blind impetus and will consciously directed to an end. Gunther's ^dualism' arises from the thought that the analogy between the categories, according to which nature and mind (Geist) respectively develope themselves, is not to be understood as Identity, but as involving an essential Opposi- tion. He was fond of laying stress upon the opposition. Beneke has explained in the fullest and most satisfactory way ^ the problems of the theory of knowledge, which depend on this consideration. 2 § 43. In other phenomena, which cannot be looked on as merely subjective because of the consciousness ^ System der Metaph, und Religionsphil, especially pp. 102-5, 140-43, 495-511. 2 Cf. Trendelenburg, Log. Untersuch. 2nd ed. p. 460 ; 3rd ed. ii.49.S f.; Hist. Beiträge zw PInlos. ii. 123-24. H 98 § 43- 'The Reality of Matter and Power, 44. Reality of Space and Time, 99 I that they are not merely dependent on our own mental causality, the transference of the analogues of our own mental (psychic) life, by means of which we know with proximate truth the psychic life both of other men and of animals, does not seem to hold good. These phenomena lead to the admission of a material ( StofF), which we call Matter, remaining in itself in dead stillness, and capa- ble of change only by outer impulse. But the notion of matter so acquired cannot correspond with its actual existence. Every phenomenon objectively founded, as this very act of becoming a phenomenon itself testifies, and as the scientific investigation of the laws of nature makes evident, is to be traced back to some active power as its real basis. In all matter — and if there are atoms, in every atom — there must lie some internal conditions or qualities, which if they become mutually related in the immediate contact, or in the partial or total inter- penetration of matters (Stoffe), become 'powers by their opposition in reference to each other. The notions of Matter and Power denote two ways of comprehending things ; on the one side by sense-perception, on the other by the analogy of the internal perception of our own power of will. Helmholtz rightly says,* ' Matter and power are abstractions from the actual ; science calls the ob- jects of the outer world matter (substance) according to their mere existence there, without regard to their effects on other objects, or on our organs of sense, but we attribute power to them considered as acting.' What Herhart taught of the qualities of his supposititious point-essences, which he calls ' simple real essences,' holds true of the qualities of extended things : they act in contact as powers. I Erhaltung der Kraft, p. 4 f., Berlin, 1847. § 44. The co-existence and co-operation of a multi- plicity of powers necessarily involve some real order of coherence and succession, or some real existence in space and in time. This cannot be of a kind different from the space and time of sense ; for if the reality of development in time is recognised (§§ 40-43), then on the supposition that such a space of three dimensions as mathematics require really exists without our mind, and on it alone, the psychical-physiological facts which have place in our sense-affections are fully explained by natural law's. Therefore the order in space and time he- longing to real objects mirrors itself in the order in space and time of External and Internal Perception. Sense- qualities, however, colonics, sounds, ^'C. are, as such, sub- jective only. They are not copies of motions, but are regularly and connectedly related to determinate motions as their symbols (cf. § 38). From the truth of Internal Perception (§ 40) it follows that succession in time at least is not a mere phenomenon, but a reality.* The reality of extension in space in three dimensions follows from the reality of time, and must be ascribed to things- in-themselves, and not merely to our apprehension of things. For the order in time empirically given in us — the change of night and day, the change of the seasons, &c. — is embodied in > It follows not only that we apprehend the mental occurrence in the form of time, but that the mental occurrence itself goes on in us in time, and therefore also in other animate beings, and further by analogy that there is in real things a succession in time. A * fallacy ' occurs only in the unjustifiable transference of a ^ form of intuition' only mentally (psychically) real in us to the external reality ; for a sub- jective form of intuition could of course refer to * an order of things quite incomprehensible to us,' but succession in time is a mental reality in us, and inference from us to other essences is logically correct. H 2 lOO 44. Reality of Space and Time, 44. Reality of Space and Time, lOI i|M 1^ mathematico-physical laws, which, according to the principles of Mechanics, can only exist on the supposition of an external space which agrees with the space of sense-perception in all essential relations. For our senses are affected at certain times by certain things which exist in themselves outside of our con- sciousness. The succession of phenomena conditioned by their affections is to be explained not by the mere internal connection between acts of consciousness, but by the wider connection which comprehends both the subject and the things-in-them- selves which affect us. The natural laws which belong to this connection relate to a space of three dimensions. Newton's law in particular, according to which the intensity of gravity for unchanged masses is in inverse ratio to the square of the distance, necessarily presupposes a real space of three dimen- sions. For in a space of only two dimensions the intensity must be inversely proportional to the distance itself ; in a space of three dimensions, to the square of the distance ; and in every other space to another function of the distance. For since, on the hypothesis of two dimensions, the effect in any given dis- tance is distributed on the circumference of the circle whose radius is the distance, and since, on the hypothesis of three dimensions, the effect is distributed on the surface of the cor- responding sphere, and so on ; and as the circumferences are to each other as the radii, and the superficies of the spheres as the quadrates of the radii, therefore the part of the whole effect which belongs to every individual point is in each case in the inverse ratio.* In all physical phenomena, causes and effects are exactly commensurate as soon as they are reduced to motions in space, and a clear scientific insight into their real connection can be attained. And this justifies the fundamental thought of this paragraph, which makes the perception-picture in its position in space and time strictly parallel with the existence in space and time properly belonging to objective reality.^ J As Halley (1656-1742) has shown; cf. my treatise on the funda- mental contradiction in the Kantian view. Altpreuss. MonatscJuiftj 1869. 2 In the foregoing argument, a * brain really extended in three The relation of sense-qualities, such as sounds and colours (Locke's * secondary qualities '), to vibrations resembles tlwit dimensions ' has not been presupposed. What has been already proved in the preceding paragraphs — that there is a plurality of real essences, that many exist outside of the consciousness of one essence, and that these may stand in certain changing relations to each other — serves only as a starting-point. The connection among phenomena which are in the consciousness of the perceiving essence — e.g. among astronomical events, as they occur in the firmament — is not exclusively conditioned by the subjective manner in which they are perceived. It also depends upon the way — by no means chaotic, by no means presenting a matter (Sfoff) to be set in orderly arrangement ä priori by the subject alone in each particular — in which it is affected by things lying outside its con- sciousness. J£ now these latter are conformable to other laws which are to be understood from space knowable geometrically to the essence per- ceiving, this essence would be able to attain to a pure geometry har- monious with itself, but could never be able to attain to an applied geometry harmonious with itself, nor to a geometrico-p h?/sical explana- tion adapted to phenomena conditioned by sense-affections. By means of the projection of the external into the internal any arrangement held objective by the percipient subject would arise, on whose basis certain expectations finding confirmation in experience are created. But this orderly arrangement, in part conditioned by a conformability to law different from the form of the intuition of the subject, would not be able to be understood from the peculiar nature of this form of intuition, as the decrease of gravity in inverse ratio to the square of the distance is from the three dimensions of space. For example, in a projection firom an objective space which has w ± a dimensions into a subjective space of m dimensions, every relation of intensity of gravity to the distance understandable by the subject would vanish ; and the sub- ject confined to this form would construct deceptive laws, since it re- ceives as objective the course of nature intuitively perceived by it, but cannot fully explain it according to the nature of its phenomenal space. Physical phenomena find throughout their most complete explanation in the supposition, that things-in- themselves exist in a space of three dimensions as we know it. It is at least very doubtful that any other supposition could be so brought into agreement with the facts. We have, therefore, every ground for believing that our conception of substances extended in space in three dimensions does not in some way symbolise things which exist in themselves in quite another way. but truly repre- I02 § 44- Reality of Space and Time, i| of sounds to letters.* It is a constant relation (in the one case following by natural necessity, in the other arbitrary), and a sameness of combinations without similarity of elements. The sceptical thought (cf. § 37) which asserts that our know- ledge of the outer world is impossible, or at least unreliable, because it cannot be compared with its objects, is finally over- come by this, that the consideration of the causal relation gives a sufficient equivalent for the immediate comparison which is wanting (just as the mathematical reckoning of distances makes up for the want of direct measurement). Des Cartes' proof from the Veracite de Dieu, and Delboeufs ^ from the veracity of our thoughts, are expositions of our faith, not strict proofs.^ It has been already seen that the Kantian Dualism, which makes ' things-in-themselves ' affecting us the exclusive source of the material content of perception, and the subject the exclusive source of its form and intuition-in-time and-in- space, is untenable. But Pichte's assertion still remains possible, that matter and form have both a purely subjective origin. So does the intermediate assertion (which has found supporters quite lately) that an element is present in the sents tilings as they actually exist in three dimensions. Our conception of things and their motions is, therefore, the result of such ' an organisa- tion of the situation of our sensations ' as effects the harmony, not dis- crepancy of things and their phenomena as to size and form or as to the * primary qualities.' (Cf. my Grund, der Gesch. der Phil. iii. § 10.) From the impossibility that motion can change itself in consciousness«, follows the necessity of accepting a latent consciousness, which, aroused by definite motions, strengthened by combination and concentration, can arise out of its latency. » [Cf. Berkeley, Theory of Vision, Coll. Works, vol. i.,Fraser's Ed. ; cf. also Editor's preface to the Theory j and Eraser's Life and Philosophy of Berkeley, ch. x.] ' Log, pp. 73-78. . 3 [The same may be said of Sir \V. Hamilton's ai)peal to the veracity cf consciousness {Led, on Metaph. i. 264 ff.) ; edition of Beid's Works, note A, p* 773 if. ; cf. Mill's Exam, of Hamilton's Philos. 3rd ed. p. 72 f.l 44. Reality of Space and Time. \ox things-in-themselves which, when it aifects us, originates in us the forms of space and time, but that this element has ^ character essentially different from these forms. The possi- bility of such an assertion can be disproved, and the real truth of the forms of space and time can be proved, by reflect- ing upon internal perception and its co-operation with external. One must not presume to rise above the necessity of this scien- tific demonstration by a mere axiom, by which the agreement of our forms of intuition with those forms of existence is called something immediately certain — a postulate of reason, a neces- sity of thought, a something lying in the very notion of knowledge (since the validity of this notion, so understood, has first to be proved). Such dogmatic axioms, which make too comfortable pillows, will always lead back to scepticism and critical doctrines which they cannot confute. For example, in modern times, Schopenhauer, following Kant, says : ^ One must be forsaken by all the gods to imagine that this visible world there outside as it fills space in three dimensions, is com- pletely objectively real, and exists as it does without our co- operation.'^ This is true as regards colour, sound, &c., but as regards extension and space it is false. And since we do not want for arguments to support our position, we need not care much about being forsaken by Schopenhauer's gods. The assertions of students of Nature of the Kantian School that the investigation of Nature has to do always and above all with phenomena, are to be corrected by what we have said above. They are true so far as regards the results of the sense-affections, but false as regards their causes. These causes, the things-in-themselves, the metaphysical bases of phenomena, are themselves objects in space and time. The thesis — the world of phenomena accommodates itself to things- in-themselves ; and the antithesis, it accommodates itself to the organs of sense — are both one-sided and half-true. The world of phenomena is the common result of the two factors whose contributions can and must be adjusted. ^ Secondary qualities ' * Ueher die vierfache Wurzel des Satzes vom zureichenden Grunde, 2nd ed. § 21, p. 51. iii: I04 § 44- R^o^liiy of Space a^td Twte, 44. Reality of Space and Time* 105 (sound, colour, heat, &c.), as such, are purely subjective ; and they are symbols of motions. Time and space are both sub- jective and objective at the same time. Schleiermacher rightly teaches' — ^ Space and time are not only conceptions of ours, they are the kind and way in which things themselves exist.' ' Space is the-being-the-one-outside- the- other of existences, Time the-being-the-one-outside-the- other of actions.' Schleiermacher further held^ that if the contents of sense were conditioned by sense alone, there would result only a chaotic manifold of impressions. ' Organic func- tion,' as such, has to do only with the ' chaotic material,' or the formless boundless manifold of what fills space and time. Schleiermacher distinguishes' perception from organic function. He defines the perception to be the unity of the organic and in- tellectual function with a preponderance of the organic. In thought proper intellectual function prevails, and in intuition both functions have equal prominence. Schleiermacher, how- ever, has not made clear enough tchat the intellectual element is which enters into perception. If we hold that it is ' orderly arrangement in space and time,' we may make our theory agree with Schleiermacher's, and consider it to be its com- pletion and more definite statement; but we cannot admit that the activity of sense or the * organic function ' has not got this orderly arrangement. The senses seize upon all those forms of existence, as yet in unsettled unity and in ' chaotic ' com- mixture, on whose separation the different forms of thought rest (e.g. the essential and the non-essential, on whose separa- tion depends the formation of the notion ; substantiality and inherence, which are the basis of the subject and the pre- dicate of the judgment). They do not apprehend chaotically, but in distinct separation, those forms which make their special object, the relations of existence in space and time, or the external arrangement of things, in which the internal dis- tinctly expresses itself. The physiological consideration of the senses of Sight and Touch shows that the capability to ap- prehend distinct positions is established in their organisation. » Dial. p. 3o5 r. 2 ibi<^, ^^ iQg^ ;|ig^ 135^ 3 j^id. § US. The eye, it is time, does not see three dimensions ; but mere sensation suffices to distinguish positions on a superficies, 6n which distinction rests all further discrimination of the actual form of what is seen, and is so far by no means chaotic. If one believed (with Herhart and Lotze) that all separation in space of parts of the organic image of sight and of the affec- tions of the nervous vanishes in the spacelessness of the simple mental monads, in order to be reproduced in consciousness in a new way, out of the quality of sensation in general, or, accord- ing to Lotze, out of certain ' signs of place,' even on this hypo- thesis (which is not admissible from Schleiermacher's stand- point) it must be recognised that the production of every definite position of the picture conceived in space and time is conditioned by the position in space and time of each organic affection, and this again, on its side, by the position of the external thing affecting. The organic function even in this case would be by no means chaotic. Again, Schleiennacher's view of the nature of the sense- activity may be refuted directly from his own dialectical prin- ciples. For Schleiermacher distinguishes, in existence gene- rally, ^ Power ^ (Kraft) and 'Action^ and refers the former to existence-for-itself, and the latter to existence in connection with others. But the arrangement of real objects affecting our senses, and the organic function itself, fall under the notion of co-existence and co-operation or of ' Action.' The kind of this co-operation, however, can only be determined by the ' System of Poxcers^ and since, according to Schleiermacher, this is known to be undoubtedly conformable to reason, the co-operation must also be orderly. Hence organic function as ' The " Action " of things in us ' ' is not a chaotic but an orderly manifold of impressions. The same thing can also be proved indirectly. If the organic function, as such, produces a mere chaos of sensations, the function of reason could not stand in essential relation to it, but could only come after it, as something original and independent of it. Schleiermacher, in consequence of this opinion, ascribes to organic function this ' DiaL p. 56. io6 44. Reality of Space and Time, Sllltii !l II \s 4' significance only, that it excites the intellectual to self-activity. He thinks that ' the system of all notions constituting science is given in a timeless way in one reason dwelling in all.'^ These actual notions are always realised ' in connection with organic function ; '* but organic function is not a co-operating factor in the formation of notions, it is only an exciting element, on occasion of which the notions, lying in the universal reason in individuals and in races of men, develope themselves in con- sciousness more fully and more purely.^ Schleiermacher thus only allows organic function, as follows from the presup- position of its chaotic character, to influence the becoming conscious, not the formation and development of notions. But then he explains that ^ pure thought ' in the Hegelian sense, or the self-sufficiency of intellectual power wholly freed from any intermixture with organic function, is impossible. He is right, but scarcely consistent; for the impossibility of pure thought of any kind contradicts throughout Schleiermacher's presuppositions about organic function, and the system of notions. Why should pure thought be impossible if these pre- suppositions are true? The mere excitement of intellectual activity might as well have happened from some other side than that of sense-activity, — from the will or the resolve to keep itself thinking, and from the living power of delibera- tion. Schleiermacher says, because * the activity of the rea- son, w^hen it is set up, apart from all activity of the organisa- tion, is no longer thinking,' '* or, because ^ apart from all organic function no ground of partition can be found for the unity of existence.'^ But this only proves that no system of notions can ever be given in the human reason in itself, which only needs successive awakening to consciousness; for every system of notions presupposes a partition of indeter- minate abstract existence. If the doctrine of the impossibility of that pure thought, and the corresponding doctrine of the impossibility of partitioning the unity of existence into a plurality of distinct notions by means of mere intellectual 1 Dial p. 104. ^ Ibid. p. 105. ^ Ibid. p. 106 ff. § 177. 4 Ibid. § 109, p. 57. "^ Ibid. § 168, p. 96. 44. Reality of Space and Time, 107 function, be held correct, the view of the chaotic character of organic function, and the corresponding assertion that the sys- tem of notions is given in intellectual function, must be given up. The content of perception reached by means of organic affection must be recognised to be a co-operating factor in the process of the formation of notions. The notion is by no means reduced on this view to a ^ merely secondary product of the organic function ' — a doctrine Schleiermacher rightly op- poses ; — an essential part in the formation of notions is attributed to organic function. This part is to be more closely defined by this, that by it the external orderly arrangement in space and time is brought to consciousness. Then thinking led from the signs contained in it to the internal orderly arrange^ ment, makes it signify the moments constituting the essence of things. This is also the way in which the individual sciejices actually proceed in the construction of their notions and judg- ments. The system of notions is not given in a lasting way in the general subjective reason. It exists in the absolute reason which comprehends all mere subjectivity and adjusts it to objectivity. It is therefore as essentially requisite for the subject, in order to reach science, to advance by means of organic function, which is more powerful in relation to objectivity, as to verify its results by means of its own in- tellectual power, which works more independently in the service of the end and aim of knowledge. This also presupposes that organic function is not a ^ chaotic manifold of impressions,' but is orderly, the mirroring of the orderly arrangement in space and time which belongs to things, and can warrant a sure starting-point for thought. Schleier- macher himself almost expressly recognises this, when he makes the correspondence between thought and (external) existence to be brought about by the real relation in which the totality of existence stands to the organism ;^ for this presupposes that this higher significance belongs to organic function. The ascription of a chaotic character to organic function can only be viewed as a remaining part of the Kantian subjectivism not » Dial § 106. i 1 08 44. Reality of Space and Time, 44. Reality of Space and Time, 109 \ yet overcome, which supposes that all orderly arrangement originates in the spontaneity of the subject, and must con- sequently be quite different from organic affection. The op- posite expressions of Schleiermacher, on the other hand, rest on the deeper and truer thought of a conformability to law dwelling in the external reality, according to which organic affection, as the immediate action of things in us, or as ' our existence in so far as it is identical with the existence established without us,' ' must bear the character of an arrangement con- formable to. reason.' [The reality of Space and Time appears to be a necessary element in the Hamiltonian Philosophy of Common Sense, but we do not find Sir Wm, Hamilton giving thoroughly consistent utterances on this subject. He sometimes unreservedly assents to the Kantian doctrine ; at others he insists upon adding to the ä priori and subjective Space and Time of Kant an ä posteriori and objective Space and Time acquired in percep- tion;' while his doctrine of the primary qualities of matter 1 Dial, p. 56. ^ In connection with this whole paragraph, cf. the Author's tract, Zur logischen Theorie der Wahrnehmung und der zunächst an die Wahrnehmung geknüpflen Erkenntnissweisen, in Fichte's Zeitschrift für Phil, New Series (Halle, 1857), xxx. 191-225 (especially pp. 222-24, on the Reality of Space) ; — also my tract, Zur Theorie der Eichtung des Sehens, in Henle's and Pfeuffer's Zeitschr. für rationelle Medicin, 3rd Series, 1858, v. 268-82 (especially on the distinction of the objectively-real space from the space of the field of vision). Cf also my notes to my translation of Berkeley's Principles of Human Know- ledge, Berlin, 1869. The argument stated above for the extension of * things-in- themselves' in three dimensions, has been combated by Alb. Lange in his Ge- schichte des Materialismus, pp. 497-99, Iserlohn, 1866. I have answered it partly in my Grundr. der Geschichte der Philos. 1st ed. iii. 279, Berlin, 1866 ; p. 303, 2nd ed. 1868 ; and partly in this edition of my Logik, in the notes appended to this section. Cf. my tract Der Grund- gedanke des Kantischen Kriticismus nach seiner Entstehungszeit und seinem wissenschaftlichen Werth in the Altpreuss. Monatschriß, 1869, vi. pp. 215-24. 3 [Cf. Hamilton's edition of Eeid^s Works, p. 126, note ; Reid's implies that space is known ä priori and as objective. As the doctrine of the primary qualities is most essential to his system of philosophy, and most carefully elaborated by Hamilton, we may take it as his final deliverance. The primary qualities are all derivable from Space. They are, in fact, forms of Space. They are known as objective, and they are known a priori. Hence Hamilton must be held to believe in the ob- jective existence and ä priori nature of Space. He has not so explicitly expressed his opinion with regard to Time.^ Mr, Mill and his School deny the objective reality of Space and of Time. They are sensations worked up into permanent possibilities of sensation. All that they possess of reality, i.e. permanence, and objectivity, i.e. power to affect not one per- ceiving subject but several at the same time, they owe to the laws of association.^ Berkeley/ and Frof. Fräser, while they refuse to believe in any other Space and Time than Sensible Space and Sensible Time, recognise: (1) An externality to our present and transient experience in our own possible ex- perience past and future, and (2) An externality to our own conscious experience, in the contemporaneous, as well as in the past or future experience of other minds ; and therefore admit the reality of space and time as far as that is contended for in this section.'] Works, p. 841 ; Discussions, p. 273 ; Lect. on Metaph, i. 403 ; ii. 114, 166-70. ^ Cf. for a very severe criticism of Hamilton's theory. Dr. J. H. Stirling s Philosophy of Perception, pp. 69-87 and passim. 2 Cf J. S. Mill's Examination of Sir Wm, Hamilton's Philosophy, 3rd ed. pp. 258-304; Bain's Senses and Intellect, 2nd ed. pp. Ill, 197, 250, 370, 637. Cf for an analogous doctrine, Herbert Spencer, Psychology, pp. 52, 244, 309. 3 Cf. the Life and Letters, ^-c. of Bishop Berkeley, by Prof. Fräser, Oxford, Clarendon Press, 1871, ch. x.] no § 45. Individual Conception of Intuition. lii PART SECOND. THE INDIVIDUAL CONCEPTION OR INTUITION IN ITS RELATION TO THE OBJECTIVE INDIVIDUAL EX- ISTENCE. § 45. The individual conception or intuition (representatio or conceptus singularis) is the mental picture of the individual existence, which is (or at least is suppofiied to be) objective. External orderly arrangement, or that in Space and Time, which is represented by perception, is to be explained by the thought of the internal orderly arrangement, in which it is reflected. The first step towards the solution of the problem is naturally the discrimination of individuals by means of indi- vidual conceptions. The word conception is not used here to mean a perception reproduced, nor to mean a mental product generally. It means the mental picture of an individual existence, whether presented in perception or reproduced in memory. A conception may be either an individual conception or intuition, which has to do with one individual (or with what belongs to one individual), or a general conception, which refers to ä mutually-related group of individuals (or of what belongs to individuals), and forms the approximate mental (psychic; basis for the notion. In this section we shall explain what belongs equally to both kinds of conception. § 46. The Distinctio7i of Individuals^ etc. in § 46. Individual intuitions gradually arise out of the original blur of perception, when man first begins to recognise himself, an individual essence in opposition to the outer world. This form of individual existence or individuality is transferred to any external existence whose appearance betokens that it can be isolated or set over against other phenomena. The logical correctness of the application of this form of knowledge is to be tested by the same criteria as the truth (cf. § 42) of all those elements of knowledge which originate in our internal, and go to complete our sense-perception. For : (a) (cf. § 40) In reference to one's own person, self- consciousness directly warrants the reality of our in- dividual existence, (b) (cf. § 41) An existence analo- gous to our own must be attributed to all other persons, and therefore the form of existence as an indi\idual essence, (c) (cf. § 42) The analogy of things without us to our own essence decreases gradually, but never vanishes wholly at any point. Hence we may allow ourselves to believe that the parti- tion of the totality of impersonal existence into rela- tively independent individuals actually takes place, and is not brought by us by means of a merely subjective necessity. The sense -phenomena, however, taken along with the analogous gradations in the department of mental life, prove that the boundary, the individual de- terminate existence, and its development into a greater whole, becomes more indistinct and indefinite the lower any object stands on the gradual series of essences, (d) On the other side, the most complete individual independence, together with the widest «and most inti- iii'^üh m\= m 112 § 46. TAe Distinction of Individuals mate community of life and action, is to be found along with the greatest mental and moral height in the scale of being. The intuition, or the individual conception, like per- ception (§§41-42), is correctly formed in proportion as the gradations in question have been observed. The problems here treated often come up in the positive Bciences of Botany and Zoology in particular cases. Their full solution cannot be reached by the special means which these sciences have at their disposal, but only by reference to general considerations belonging to Logic or the theory of knowledge. Aristotle does not enter very deeply into these questions either in his physical or in his metaphysical and logical writings. He calls individual essences the first substances {irpHnTai ovGiai), without submitting to a stricter investigation the knowableness, essence, and limits of individuality. Ques- tions such as the following first arose in modern times, and received full attention as scientific problems: — Is the true indi- vidual the plant or the single shoot (eye, bud, &c. ; ^ gemmae totidem herbae,' Linnaeus ; cf. Roeper, Linnaea, p. 434, and other later botanical writings), the coral stem or the single coral insect ? How far is the life of the embryo individual and independent, and how far part of the life of the mother, &c. ? In natural science it has been seen that the individual cannot pretend to more reality than belongs to the genus, species and individual; that the individual is characterised not by unity of sensible appearance, but by unity in the course of development ; that the individual plant is far inferior to the individual animal in internal unity. Cf. Rud. Virchow, Atome und Individuen, a lecture delivered in 1859," where the individual is defined to be ^ a single community where all parts co-operate to a similar end or act according to a definite plan.' * Published in Vier lieden über Lehen und Kranlsein, pp. 35-76, Berlin, 1802. 6y means of Individual Conceptions. 1 1 3 In other provinces also the consciousness of the gradations of individuality is an essentially scientific demand, and a con- dition without which a solution of many important questions of debate cannot be reached. For example, the Homeric ques- tion between unitarians and separatists can only be got rid of by the scientific view (already attained by Aristotle) that the epic poem, because of its nature as an earlier and lower stage in the development of poetry, does not possess the strict comprehensive unity of the Drama, and yet does not exclude a certain poetic unity. The individual epic poet of that early age, belonging to an associated company of ipinstrels, had less independent individuality within his circle than the dramatist. The question to be asked is not, therefore, whether the poem is to be ascribed to one or to many, but what part of it is to be ascribed to the one and what to the many ? — or, more particu- larly, what is to be presupposed as the pre-Homeric foundation? what is to be considered as the work of one master, who, trained in intimacy with the smaller poems of the earlier minstrels who sung the history and tales of the people, seized on and realised the thought of the greater epic ? and what has been added by post-Homeric poets, and what praise or blame belongs to the rhapsodists, to the collectors, and, lastly, to the grammarians who arranged and made emendations and explan- ations ? The doctrine of Spinoza reduces all individuality to the same dead level of meaninglessness. The Leihnizian and Herbartian doctrine of monads, with equal incorrectness, transfers that full comprehensive individuality which belongs to the personal human spirit to the lowest bases of organic and inorganic life which they believe to be independent individual essences with- out extension in space. The Kantian critical philosophy believes that it has found the true mean between these two extremes, in the doctrine of the impossibility of settling the problem in question theoretically. It enumerates among the subjective elements of knowledge the categories of Unity, Plurality, and Totality, which, founded on the organisation of our means of knowing, are necessarily transferred by us to the world of I \ 114 § 47- Individual Conceptioti and Existence, The Categories in the Aristotelian Sense y etc. 115 phenomena, but find no application to real existences or to things-in-themselves. Schelling, Hegel, and Schleiermacher, on the other hand, believe that these forms have a real validity. But when they come to determine the different gradations of individuality, Schelling and Hegel approach very closely the doctrine of Unity founded by Spinoza, and Schleiermacher, in certain considerations, almost adopts the individualism of Leib- nix and Herbart. [In Mr. Mill's system of philosophy, where all independent and objective reality depends only on association, where all external and internal things are only congeries of possibilities of sensation, there seems no place for a theory of individuality. But the fact that, so far as regards mind, there always remains a final inexplicability unable to be resolved into a series of feelings affords a basis for our own existence as an individual. And Mr. Mill's theory of inseparable association, i.e. that when certain sensations have been thought of together in certain ways they cannot be thought as existing apart, combined with his theory of the chemical composition of causes, according to which a whole of association may have a character which is quite different from the sum of the characters of the associated parts, affords ground for the individual existence of things.^] § 47. As the individual conception corresponds gene- rally to the individual existence, so its different kinds or forms correspond to the different hinds or forms of individual existence. The individual existence is first recognised in independent objects. When the object of a conception makes up a whole, in which different parts, attributes, and relations may be distinguished, the dif- ferent elements of such a conception may be considered singly to be conceptions. We must distinguish two cases here. Either the form of objective independence [} Cf. Exam, of Sir Wm. Hamilton's Fhilos. pp. 234-43, 305-27; and Logic, 7th ed. 405-12.] is attributed to the objects of these conceptions, with the consciousness that this independence is only ima- gined not real, or these objects are absolutely perceived to be not independent. On these relations are based the forms of the substantially concrete^ the substantially abstract^ and the verbal^ attributive, and relative concep- tion. The forms of the individual conceptions and of their verbal expression, in their relation to the coitc- sponding forms of existence (and these last themselves metaphorically), are the Categories in the Ainstotelian sense of the word. , All these Categories are transferred from objectively valid conceptions to those whose objects are mere fictions (e.g. to mythical beings). As the {logical) forms of conception correspond to the {metaphysical) forms of individual existence, so the {gram- matical) forms or parts of speech correspond to the logical. A word is the expression in speech of a conception. The conception of an independently existing object is expressed by the concrete substantive, to which must be added the substantive pronoun, which denotes a person or thing in its relation to the speaker. The conception of that which does not exist independently, but is intuitively perceived under the borrowed form of individual existence, is denoted by the abstract substantive. The conception of that which does not exist independently, as such, whether an act, property (or quality), or relation, is expressed by the verb, the adjective with the adjective pronoun, and the adverb, and by the preposition with the forms of inflection. Numerals can only be understood on the basis of the formation of notions ; for they presuppose the subsumption of similar objects under the same notion. Conjunctions can only be comprehended on the basis of the formation of judg- ments and inferences; for they bind together sentences and parts of sentences, whose opposite references express the corre- I 2 'i. i > ii6 §47. Individiial Conception and Existence. sponding relations of conceptions to each other, which on their side ajxain must rest on relations between real combinations. {Prepositions, on the other hand, by means of the relations between single words and complexes of words, which express the corresponding relations between single conceptions, denote the relations of single things, actions, &c. to each other.) Interjections are not properly words, but only direct expres- sion of feelings not developed into conceptions or thoughts. ' The construction of all language proves that the oldest form was essentially that which is preserved in some lan- guages of the simplest construction (e.g. in the Chinese). All languages have started from significant sounds, simple ^unds picturing intuitions, conceptions, and notions, which do duty in every relation, i.e. as every grammatical form, without requiring for each function an audible expression — so to speak, an organ. In this earliest stage in the growth of languages neither verbs nor nouns, conjugation nor de- clension, are to be distinctively distinguished. The oldest form for the words which now sound deed, done, do, doer, doing, was, when the Indo-Germanic stem-language arose, dha-, for this dha (i.e. to set, to do — Old Indian dim. Old Bactrian dha, Greek ^e, Lithuanian and Slavonic de, Gothic da. High German ta) appears to be the common root of all these words. In a somewhat later stage of the develop- ment of the Indo-Germanic language, in order to express distinct references, they repeated the roots twice, not yet supposed to be words, along with another root, and linked them together into a word. In order, for example, to de- note the first person of the present, they said dha-dha-mi, from which, in the later stage of the growth of the language, by fusion of the elements into one whole, and by the con- sequent possibility of change, came the root dhadhämi (Old Indian dadhämi. Old Bactrian dadhämi, Greek ridrj/jii. Old High German torn, tuom; tetami, New High German thue). In that earliest form dha there lay, as yet unseparated and undeveloped, the different grammatical references, their whole verbal and nominal modifications ; and this can still be observed T/ie Categories in tlie Aristotelian Sense, etc, 117 in languages which have remained in the stage of simplest development. This example, selected by accident, represents all the words of the Indo-Germanic lansuao-e.' ^ The logical consciousness of the different forms of concep- tion originally developed itself with and in the grammatical consciousness of the different parts of speech, and with the meta- physical consciousness of the different forms of existence.* Plato recognises the grammatical opposition of the ovofjL% and pr)iia} The author of the dialogue Sophistes ^ refers them to the opposition between the corresponding forms of existence — Thing and Action— and refers these last to the more general opposition of Rest and Motion, which he imme- diately subserves together with that of Identity and Difference under the universal unity of Being. Aristotle developes the division of the parts of speech by adding the ovvIbcoir) aarjfi^os, e.g. fisv, rjToi, Bi],^ In the Poetics (c. xx.) the äp6poi; is also named ; but the reading is uncertain, and the genuineness of the passage doubtful. Aristotle calls single conceptions and words Tä äv£v avfiTrXoKrjf, ra Kara fin^sfiuip avfiirXoKrjv Xeyo- ^ Aug. Schleicher, Die Darwin'sche Theorie und die Sprachwissen- schaß, pp. 21-23, Weimar, 1863. 2 Cf. Classen, De (xramm. Graecae PrimorcUis, Bonn, 1829 ; L. Lersch Die Sprachphilosophie der Alten, Bonn, 1838-41 ; Bd. ii. {die Sprach- kategorien), Bonn, 1840 ; G. F. Schomann, Die Lehre von den Rede- theilen nach den Alten, Berlin, 1862; H. Steinthal, Geschichte der Sprachwiss. hei den Griechen und Römern (with special reference to Logic), Berlin, 1863. 3 Theaet, p. 206 d ; cf. Cratylus, p. 399 B. * P. 261 e sqq. •'* De Interp. c. ii. ff. ; Poet. c. xx. (cf. notes to my ed. and transl.). II M ii8 § 47. Individual Conception and Existence. y^zva^ i.e. the uncombined elements, into which the proposition or judgment (\070s) dissolves when analysed. Aristotle divides conceptions according to their formal points of differ- ence. In this division he proceeds on the fundamental thought that conceptions as elements of thought must corre- spond with the elements of what actually exists objectively, and their differences of form to the differences of form in what is conceived. Every conception, and so also its verbal expres- sion or word, must denote either : 1. a substance; 2. a quan- tity; 3. a quality; 4. a relation; 5. a where; 6. a when; 7. a position ; 8. a habit ; 9. an action ; or 10. a passion : — Twi/ Kara yjifizyjiav ovyan\oici)v Xe-^o^hwv sKaarov 7]toi ovguiv arjfjLaivsi tj iroaov rj ttoiov fj irpos tv rj ttov fj iroTS rj Kelaoai, rj s^stv rj TToislv rj irdaxstv (De Categ. iv. 1 B, 25). The Aristotelian examples are: 1. avOpayiros^ ittttos; 2. Bl7rr)xv, TpLirrp^y; 3. XsvKOVy ypafifuiTiKov ; 4. BiirXdaiov, Tjfiiav, fisl^ov; 5. iv AvKsio), SP aryopa ; 6. sxOh, mspvaiv ; 7. dvaKSirai^ KaOrjTat ; 8. dvaB^BsTai, &7r\tp4>'il or to tL rji/ slpai, or 17 kuto. \6oiv or to avvokov), Aristotle comprehends ^ the nine remaining kinds of concep- tion under the common name of ra avfjbßeßqKOTa, He some- times distinguishes^ three chief classes, ovo-ia, irddr), and irpos Tl/ ' Analt/t. Post. i. 22, 83 a, 25. 2 Mefaph. xiv. 2, 1089 b, 23. 3 It is not certain how tins doctrine of the Categories may have developed itself in the mind of Aristotle. Trendelenburg* believes that Aristotle had been led to it by the consideration of grammatical rela- tions — viz. of the parts of speech — whose characteristics were embodied in the terms {irTuxreti). The relationship of the doctrine of the Cate- gories to the grammatical doctrine of the parts of speech has been thoroughly, acutely, and evidently exhibited by Trendelenburg. But it is at least doubtful that the origin of the doctrine of the Categories was a consideration of the parts of speech and their distinction according to 7rra*/T£«c. The Aristotelian division of the parts of speech (see above) is too little developed to favour this assertion, ovo^ia and prifia corre- spond well enough to ovaia and avfißeßrjKocy but cannot supply a basis for the ten categories. Moreover, Aristotle adds to the 7rrw(T«t<,"|" forms of verbal inflection on which he has based no verbal categories (as the tenses uyiarep and vyiayt'i). When he further adduces a substantive (vaipoc) as an example of a logical irpoQ n, this is evidently independent of the distinction of the parts of speech, and rests on essentially dif- ferent grounds. Aristotle, as Trendelenburg himself recognises, has distinguished not so much parts of speech as parts of the sentence (subject and predicate, and different forms of the predicate). He defines : ofoiua kan (fKjjiq ariuavTiKi) Kara (rvr^tjicqy ayev ^fjoruv' — pfjfJio. ^i iffn to Trpoaarj^xairov XjOü»'ov,J but adjectives (such as o/icatoc, Xtvwc), as far as they are predicates with iotiv^ are considered to bep^/iara ;§ although elsewhere Xevkoq is called ovo^xa^ because it does not connote time. In the dis- tinction of ovofiara and piifiara^ and in the distinction of ra Kara firihi- ^iav (Tvijnr\()Kfiy Xeyo/icva, Aristotle seems to have kept to the empirically given forms of sentences, such as ' Socrates is wise, Socrates disputes, is * De Arist. Cnteg. 1833 ; Geschichte der Kategorienlehrej pp. 11-13, 1845. I De Interp. c. iii. 16 b, 16. J Ibid. c. i. and ii. § Ibid. c. i. and x. The Categories in the Aristotelian Sense ^ etc. 121 The Stoics reduced the ten Aristotelian Categories to four, which they call to. f^evLKODTara (the most universal kinds), and refuted,' &c. The distinction of oro/xara and pi'i^ara seems to have been the basis of that of ovtriai and xadq, and the distinction of the parts of speech seems to have been the basis of that of the nine kinds of ffVfißfßrjKora, Still Aristotle in his construction of the doctrine of the Categories may have been influenced by definite philosophical references, and especially by his polemic against the Platonic doctrine of ideas. Aris- totle sought to recognise the universal in the particular. He based his speculation on the empirical, and tested the truth of the doctrine of ideas in its relation to the actual existence presented to him. In this critical endeavour it could not have escaped his quick glance that all phenomena are not to be considered in the same way as pictures of ideas. Some contradicted this view in formal reference. When he came to account for this inconsistency, he must have found its cause in this, that Plato thought his ideas, and could only think them as ideas, under a single form of existence, the form of substantiality ; while what actu- ally exists is represented under different forms. The idea of the good, e. g. must be of substantial existence, and at the same time must be the common ideal for everything which actually appears good. But this latter is only in part something substantial, as God, the vovt: (thought substantial by Aristotle). It is partly something praedicative or accidental — an action, a property, a relation ; as, a good deed, the goods of the mind, the use- fulness of means to an end, &c. This formal difference contradicts the formal unity of the common ideal accepted by Plato.* The methodical and systematising mind of Aristotle, led to pay attention to the difference of the forms of existence by considerations of this kind, would soon attempt to draw up a comprehensive series of these. In his investi- gation into the Categories, he had positive points of connection with the investigations, carried on by Plato or a Platonist in the Sophistes, upon the Existent generally, about thing and action, resistance and motion, identity and difference, unity, indefinite greatness and smallness, and in the further discussions f upon relative notions, upon -rrou'ip and Traff^tii«, as kinds of yiveoic.i But these would assist him only in a small degree, because with Plato the question of the forms of the individual existence is entirely subordinated to the question of the relation of the * Arist. Eth. Nie. i. 4 ; Eth. End. i. 8 ; Metaph. i. 9, xiii. 4, xiv. 2. t As in De Rep. iv. 438. % ^^P^- P- -^^• •I II 122 § 47- Individual Conception and Existence, believe to be forms of objective reality. They are — 1. The Sub- strate (to vTTOKÜ^ivov) ; 2. The (essential) Property (to ttoiov) ; 3. The (unessential) Quality (to ttw* exov) ; 4. The Relation (to irpos Ti TTO)* e^ov).^ They subordinate all these Categories to the most universal of all notions, to that of 6v or (probably later) to that of ti. The Stoics also develope the doctrine of the parts of speech. They define the apBpov as a species of word, the article namely, and they afterwards add the adverb (TrapBsKTrjs or hripprjfia), and divide the ovopui into KvpLov and Trpoarjyopla.^ The inipprjfia serves for the extension of the predicate, and the avvhea-fios for the combination of the chief parts of discourse with each other. The doctrine of the eight parts of speech first arose in the Alexandrine era. The constituent parts of the thought, and therefore of speech, had been separated by philosophers from the logical point of view. The grammarians undertook to arrange the empirically given material of language. They joined to single definite parts of speech the terms used by philosophers in a wider sense, and they introduced new terms for the others. The avvhsap,os, which individual to the universal. The elaboration of the Categories is rather to be considered as the independent work of Aristotle. Cf. Bonitz, Sitzungsberichte der phiL-hist. Classe der Wiener Akad. der Wiss. Bd. x. pp. 591-645, 1853 ; Brandis, Gesch, der Gr.-Röm. Phil ii. 2 A, p. 375 ff. ; Prantl, Gesch. der Logik, i. p. 182 ff., 1855 ; Wilh. Schuppe, Die Aristotelischen Kategorien, im Jubiläums programm des Gleiwitzer Gymnasiums, Gleiwitz, 1866. [Cf. also Mansel, in his edition of Aldrich, Appendix, Note B, p. 175, where he follows Trendelenburg.] * These categories correspond to the three classes of categories placed together by Aristotle (Metaph, xiv. 2, 1089 b, 23) — rä ptp yap ohaiai, TO. 3c iraOrj, to. ^i irpog ri — the first and second to the first, the third to the second, and the fourth to the third. 2 Diog. Laert. vii. 57 ; Charis. ii. 175. Cf. Friscian, ii. 15, 16 : Pai-tes igitur orationis secundum dialecticos duae, nomen et verbum ; quia hae solae etiam per se conjunctae plenam faciunt orationem ; alias autem partes syncategoremata, hoc est consignificautia appellabant : secundum Stoicos vero quinque simt ejus partes — nomen, appellatio, verbum, pronomen sive articulus, conjunctio. TAe Categories in the Aristotelian Sense, etc. 123 had denoted both conjunction and preposition, from this time denoted the former only, and the preposition^ Avas called the irpodeais. The dvrayvv/jLia (the pronoun) was separated from the noun. The participle {p^eroxv) came in between the verb and the noun. Adjectives and numerals were added to the noun. The interjection was not reckoned an actual part of speech. Priscian, in his enumeration of the ' octo partes orationis,' followed in the footsteps of Apollonius Dys- colus. His theory remained the standard one for following times, while the Aristotelian doctrine of the Categories pre- vailed in the Middle Ages. The formal metaphysical notions of Des Cartes and Spinoza — substantia, attributum, modus ; those of Locke — substance, mode, relation; those of Wolff— ens, essentialia, attributa, modi, relationes extrinsecae — are related to the Stoical doctrine of the Categories. The Leibnizian five universal divisions of essence (cinq titres generaux des etres) — Substances, Quan- tities, Qualities, Action or Passion, and Relations — come nearer the Aristotelian division. ' The Kantian Categories, or ' pure stem-notions of the under- standing,' do not serve as the metaphysical basis of forms of conception, but of relations of judgments. Herhart considers the forms of common experience — Thing, Property, Relation, Negation; and the categories of the internal apperception — Sensation, Science, Volition, Action — to be the results of the psychological mechanism, and without metaphysical or logical significance. Hegel understands by the Categories, the universal, intelli- gible essentialities which enmesh all actuality. Schleiermacher founds his formal division of notions into * subject and predicate notions,' which he makes parallel with the grammatical division of words denoting notions into nouns and verbs, on the distinction of the forms of existence, of being set for itself, and of co-existence, or of things and actions. Abstract nouns are substantives which make the action sub- * Perhaps Aristotle's apBpoi> is the preposition and also the article ; cf. my transl. of the Poetics, Berl. 1869, note 95. \ il ; \\ «I 124 § 47' Individual Conception a7id Existence, etc. stantive in order to use it as a subject. Co-existence divides into activity and passivity, doing and suffering. The ad- jective which expresses the quality — i.e. the result of an activity already embodied in substantial existence, must be thought to arise by means of participles and other verbals out of the verbs (Dial. p. 197). Lotze * divides the manifold notions we find in our consci- ousness into three great groups of object-notions, predicative (i.e. verbal and adjectival) notions, and relation-notions. In each the peculiarity of the central point, as the point of dis- tribution of the attributes, conditions the whole configuration of the parts. {Hamilton thinks that the doctrine of the Categories belongs to Metaphysics, not to Logic. He regards the Categories of Aristotle as a classification of existences, and thinks them liable as such to many objections. He would substitute for them : 1. The Supreme Category Being (to oi/, ens). This is primarily divided into, 2. Being by itself (ens per se), and 3. Being by accident. Being by itself is the first Category of Aristotle. Being by accident includes his other nine.*^ J, S, Mill thinks the Categories of Aristotle an enumera- tion of nameable things, and as such ' a mere catalogue of the distinctions rudely marked out by the language of familiar life, with little or no attempt to penetrate, by philosophical analysis, to the rationale even of those common distinctions.' As ' a substitute for this abortive classification of existences ' Mr. Mill offers the following:—!. Feelings, or States of con- sciousness. 2. The Minds which experience these feelings. 3. The Bodies, or external objects, which excite certain of those feelings, together with the powers or properties whereby they excite them. 4. The Successions and Co-existences, the Likenesses and Unlikenesses, between feelings or states of consciousness.'] Cf. Trendelenburg, Gesch'. der Kategorieulehre, Berl. 1846. » Lo(/. p. 77 ; cf. pp. 42, 50. « [jr^^^ ^^ Metaph. i. 197-201. 3 Logic, 7th ed. i. 49-84.] §§ 48, /^(), Clearness a7id Distinctness. Attributes, 1 25 § 48. A conception is dear (notio clara in opposition to notio obscura) when it has sufficient strength of consciousness to enable us to distinguish its object from all other objects. It is distinct (notio distincta in opposition to notio ccnfusa) when its individual elements are also clear, and consequently when it suffices to distinguish the elements of its object from each other. The Cartesian criterion of truth (s. § 24) gave rise to a closer enquiry into the essential nature of clearness and dis- tinctness. The definitions given above are those of Leibniz (§ 27). They are to be found in all the Logics of the Wolffian and Kantian period, where a fundamental signi- ficance is often attached to them. Some of the later logi- cians, on the other hand, have undeservedly disregarded them. Clearness and distinctness were overrated in the seventeenth and eighteenth centuries, but were undervalued in the first half of the nineteenth. § 49. An Attribute (nota, rsxfjLrjpiov) of an object is everything in it, by which it is distinguished from other objects. The conception of an attribute is contained in the conception of the object as a part of its conception (representatio particularis). Attributes are attributes of things, of an o^Vc^ which is real (or conceived as if it were real). One can only speak cor- rectly of the attributes of a conception in so far as it is con- sidered to be something objective, i.e. as it is the object of thinking directed upon it. ^ To receive an attribute into a conception ' is a shorter expression for * to bring into con- sciousness the attribute of a thing by means of the correspond- ing part-conception, or to receive into the conception an element by means of which the attribute of the thing under consideration is conceived. \% W I ;. It Ill 126 § 50. Content of a Conception. Its Partition. § 50. The individual attributes of an object do not make a mere aggregate, but stand to each other and to tlie whole in definite relations, on which depend their grouping together, their peculiar character, and their very existence. This real relation must mirror itself in the relation of the part-conceptions to each other and to the whole conception. The sum total of the part- conceptions is the content (complexus) of a conception. The analysis of the content of a conception into part- conceptions, or the statement of the individual attri- butes of its object, is called 'partition. So far as the subjectively-formal Logic leaves unnoticed that real relation, it can only apprehend the combination of marks under the inexact scheme of a sum, or under the in- adequate, and still insufficient, picture of a product. If one of the numbers to be added is removed, this does not affect the other numbers to be added, and the sum is lessened only by the value of the number removed. If a factor is =0, then the whole product is =0. But the removal of an attribute ought neither to leave the other attributes undisturbed nor annihilate the whole. Both can happen in certain cases, but in general the other attributes are partly removed, partly modified by the removal (real, or thought to be real) of an attribute, and the whole is not removed with it. The expression Content has been formed after ivvirdp^^eiv.^ The expression mutual determination of attributes, which Lotze^ uses to designate the dependence of the attributes on each other, would be convenient if the term determination were not already used in another cognate sense (see below, § 52). ' Arist. AnaL Post. i. 4 : iivirapxeiy h rtp Xdy^ r^ ri eari Xiyoyn §51. Attention and Abstraction, etc, 127 or truvapyiiv ev tu> ti earw. Log. p. 58. PART THIRD. THE NOTION ACCORDING TO CONTENT AND EXTENT IN ITS RELATION TO THE OBJECTIVE ESSENCE AND TO THE GENUS. §51. When several objects agree in certain attri- butes and their conceptions in part of their content (§§ 49-50), there may result the general conception (allegemeine Vorstellung, Schema, notio sive represen- tatio communis, generalis, universalis). It arises by attention to the similar attributes and abstraction of the dissimilar, in consequence of the psychological law of the mutual arousing of similar mental (psychic) ele- ments and the reciprocal strengthening of the similar in consciousness. The more general conception arises in the same way from several general conceptions which agree in part of their content. The general conception (in opposition to the individual con- ception) is not to be confounded with the abstract (in opposi- tion to the concrete, s. § 47). The divisions cross each other. There are concrete aiid abstract individual conceptions, and concrete and abstract general conceptions. The usage of some logicians, which identifies abstract and general, is not to be recommended.^ Grammar distinctly distinguishes the two. [» Cf. Miirs Logic, 7th ed. i. 29.] ^ A 128 51. Attention and Abstraction, etc. Wolff's terminology agrees with the grammatical. He ^ defines the ' notio abstracta ' as that ^ quae aliquid, quod rei cuidam inest vel adest (scilicet rerum attributa, modos, relationes) re- praesentat absque ea re, cui inest vel adest ; ' but the ' notio universalis'^ as that 'qua ea repraesentantur, quae rebus pluribus communia sunt.' Aristotle noticed that one experience embracing them all together in it may arise from several similar perceptions if me- mory preserves them ; for the universal remains in the mind and as it were finds a resting-place there, and this universal is the one amongst the many, which dwells in the many as the same : — Yivovcq^ o alcdrjasdis lols ßsv t(üv ^coayv eYflvsTai, fiovt) tov aiaOijfjLaTos, roh 5* ovk syyivsrai. ''Oö"o^y fikv ovv fir) iyytvsTai, — ovK saTL T0VT019 yvwais lfa> TOV alaOdvsaOai. sv ols Be, eviariv aiaOofiivots (or, according to Trendelenburg's Conjecture, fir] aia6avofiivoL9, The Codices have mostly alodavofiivots without firj, one, D, Tf firj) s)(^siv hi h rfj yjrvxfj' — 'E/c fisv ovv aiadrjaseo^ yivsrai fivrjfirj, ek he fivrjfirfs ttoXXAkls tov avTOv >yivofisvr)s ifnrsipia^ ex 08 sfiTTSiplas 17 sk iravTos '^pefirjaapros tov Ka66\ov sv t§ '^vyrj, TOV evo9 irapd to. iroWd, o av sv äiraaiv ^v svfj skslvols to airro, T^x^^ o-PXV f^ol iTTioTTjßrjs.^ Aristotle calls Abstraction o^i- psaip6ai9 is irpoo-dsats.^ . The functions of Attention and Abstraction, which were ascribed by earlier writers for the most part to the ' understand- ing,' to a quasi-personifying general power, within the whole personality of the mind, have more recently by Herbart, Beneke \_Hamilton and MUT] been reduced to psychological laws.^ » Log. § 110. 2 Ibid. § 54. 3 Arist. Anal. Poster, ii. c. xix. 99 b, 36 ; De An. iii. 2, 425 b, 24. < Anal. Post. i. c. xviii. 81 b, 3 ; cf. De Anim. iii. 4, § 8, ibique comrn. Trendelenburg. * De Coelo, p. 299 a, 16 ; Anal. Poster, i. c. xxvii. 87 a, 34. Cf. Plato's Ä^/?. vii. 534 B : ano tCov aWutv Ttavrtav a6iKu)v rjjr tov ayaBuv i^inr, separating the idea of the good from all others. ^ Cf. Berkeley's remarks on Abstraction in the introduction to his Prin. ofHiim. Knowl, and note 5 to my translation. [Fraaer's edition of Berkeley's Collected Works, i. 140 f.] 51. Attention and Abstraction, etc. 129 Herbart also rightly remarks that a pure separation of the like elements from the unlike may be a logical ideal, which can easily be postulated by a definition, but can be actually realised only approximately by a process of abstraction. We determine to leave out of our consideration that kind of difference which is not connected with a certain course of thoughts, but it can never be quite rooted out of consciousness in the actual con- ception. The purest separation possible comes about when conscious scientific insight is superadded to the unconscious activity of the psychological law.^ Before Kant's time the grammatical rule in use was, — to abstract the common attributes. Thus, e.g. Lambert says,^ ' We abstract the common attributes from those which belong specially to each individual, in order to get at those which, when so abstracted, make a general or abstract notion.' Kant^ finds fault with this usage, and thinks the only valid expression is, — to abstract the dissimilar elements in the conception in order to attend to the similar. On his authority this latter rule has become the prevailing one, and cannot well be given up again. It is, however, open to the grammatical inconvenience that it does not agree with the procedure of the abstract participle, and to the actual defect that it lays too much stress on what is only an action of less importance. For (as Kant himself re- cognises) it is not the becoming unconscious of dissimilar ele- ments, but the concentration of consciousness on the similar, that is the essential thing in what is called the process of ab- straction. [Hamilton adopts the phraseology of Kant. He explains further that Attention and Abstraction are only the same process viewed in different relations— the positive and negative poles of the same act. He generalises the action of Attention and Abstraction into the rule, — Pluribus intentus minor est ad singula sensus. The points of resemblance among things are discovered by Comparison, and hy Attention constituted into * Cf. I. H. Fichte, Grundzüge zum St/stem der PhilosopJiie, 1. Abth. Das Erkennen als Selbsterkennen, § 86 ff. N. Org. i. § 17. 3 Log. ed. by Jäsclie, p. 140. » ' K l!l I30 § 52. Determination. § 53. Extent, Division. exclusive objects ; by the same act they are also reduced in consciousness from multitude to unity; for objects are the same to us when we are unable to distinguish their concep- tions. •] The process of Abstraction is reciprocally related to the designation of many similar objects by the same word. This sameness of designation is possible by the process of Abstrac- tion, and the result of this process is itself secured and made permanent by the sameness of designation. Extreme Nominal- ism is wrong, however, when it seeks to reduce the process of Abstraction to a mere identity of verbal relation.^ § 52. Determination {wpMstng) means the forma- tion of less general conceptions out of the more general. The content of these last is increased by the addition of new elements of conception appropriate to the object conceived, and what remained undetermined in the more general notion becomes more closely determined (determinatur). The formation of new valid con- ceptions implies an insight into the real relation of dependence among the attributes. Subjectively-formal logic, from the essential demand of its principles, is not able to lay down the rule, that, in the addition of new elements of content, reference must be had to the real relation of the characteristics to each other and to the whole. § 53. The EXTRNT (Ambitus, Sphaera, sometimes extensio) of a conception is the totality of those concep- tions whose similar elements of content (cf. § 50) make ' \_Lect on Logic, i. 123 if. ; cf. Led. on Metaph. i. ; cf. Mill. Exam of Sir Wm. Hamilton's Philos. 3rd ed. pp. 364 if. ; Mansel, Proleg. Log. 2nd ed. p. 65, where he distinguishes, as above, the unconscious psychological process from the conscious scientific procedure. 2 As Hobbes did; see Computatio sive Logica, c. ii. ; Leviathan, pt. i. ch. iv.] T/ie Relations of Conceptions to each other, etc. 1 3 1 up its content. The enumeration of the parts of the extent of a general conception is called Division (Di- visio). The general conception, in relation to those conceptions which fall within its extent, is the higher or superordinate ; they in relation to it are the lower^ or subordinate (Relation of Subordination). Conceptions which are subordinated to the same higher. one are co^ ordiiiate (Relation of Co-ordination). AequipoUent or Reciprocal (notiones aequipoUentes or reciprocae) con- ceptions are those whose spheres are identical with each other, without their content being exactly the same. Identical conceptions have the same extent and content. Those conceptions are opposed to each other as con- traries (notiones contrarie oppositae) which, within the extent of the same higher notion, are most different from each other, and furthest removed from each other when both have a positive content ; when one notion contains only the denial of the contents of the other, both are said to be opposed to each other as contradictories. A notion which merely denies is called notio negativa seu indefinita (ovo/xa aop/o-rov, p>)]M.a di^ivasi (cf. § 139). He uses the ex- pressions, irpoiTOS^ fiiaos, and saxaros opos^ of notions which stand in the relation of subordination, and says of the sub- ordinate notion, in reference to its extent, that it is wholly comprehended in the higher, or included in it {iu oXtp elvai TG) fisa(p, — tS irpcoT^, and so on). The representation of the relations of conceptions by means of circles is connected with these Aristotelian expressions. It was first applied in the Nucleus Log. Weisianae, 1712, written by J. Ch. Lange. Cf. § 85. For contrary/ opposition cf. (Plat. ?) Soph. p. 257 B, where ivavTiov and hspov are distinguished ; Aristotle, Metaph. x. 4, where the opposition is defined to be the fisyla-rrj hLaopd be- tween species of the same genus. The Aristotelian expres- sion,2 io-Tt tisv ravTO, to Be shac ov ravro, refers to conceptions of the same extent but different content. The expression disjunct is connected with the Aristotelian avTtSLrjprjfisvov,^ and more closely with the later term Blci^sv^ls (cf. § 123). IHamilton supplemented the list of relations of conceptions, in reference to their extent, by a list of their relations in reference to content. The great stress he laid upon the equal importance of content and extent in logical forms led him to make the two lists as far as possible parallel. The relations in content cannot be symbolised by figures. Hamilton's list is chiefly taken from the Logics of Esser and Krug.-*] § 54. The higher conception has a narrower mitent but a wider extent than the lower ; for it contahis only those elements of content which agree in several lower conceptions. The lower conception ha.s a fuller I content but a narrower extent. The extent, how- J ever, is by no means increased or lessened by ever]^ lessening or increase of a given content ; nor, on the » Anal. Ft. i. 1, 4. 2 Efh. Nie. v. 3, 1130 a, 12. ^ Top. vi. G. 4 [Cf. Lectures on Log. i. Icct. xii.] II ! ■ *< ?"' ß 13Ö § 54. Relation between Content and Extent, other hand, is the content increased or diminished with every decrease or increase of a given extent. Still less does the law of a strict inverse ratio [as Hamilton says] regulate those cases, in which the decrease of con- tent produces an increase of extent, and an increase of content a decrease of extent. {Hamilton asserts expressly—-^ these two quantities of com- prehension (content) and extension (extent) stand always in an inverse ratio to each other ; for the greater the comprehension of a concept the less is its extension, and greater its extension the less its comprehension.' *] Drohisch'^ seeks to express mathematically the relation, which exists between the increase of the content and the decrease of the extent. He proves that the content is not in the inverse ratio of the extent, but that other relations exist. He shows (to mention only the most important) that, under the simplest presupposition— i.e. when in the series of subordinations the number of conceptions, which are immediately subordinate to any one or are richer by one element of content, is always the same, and when, at the same time, the extent is mea- sured exclusively according to the number of the concep- tions of the lowest rank— the size of the extent decreases according to geometrical progression, while the size of the con- tent increases according to arithmetical progression. Drobisch further expresses this theorem by these two other assertions. On the above presupposition, the extent of a conception is inversely proportional to that power whose base is formed by the number of conceptions immediately subordinate to any one conception, and whose exponent is formed by the number of the elements of the contents of that notion. Under the same presupposition, the diiFerence between the greater number of elements of the content of one of the lowest conceptions, and the (lesser) number of the elements of the content of any » [Cf. for a thorough discussion of tlie matter, LecLon Logic, i. 146 ff 1 ^ Logik, 2nd ed. pp. 106-200. §54. Relation between Content and Extent, 137 conception, is directly proportional to the logarithm of the number which expresses the present size of the extent, ihe application of this investigation (which is valuable as a mathe- matico-logical speculation) is rendered useless in most cases by the circumstance that peculiar limitations, which cannot be brought under general rules, underlie the possibility ot attri- butes existing together. For example : (Rectilineal) Triangle equilat. acute isosc. seal. right-angled (equilat.) isosc. seal. obtuse (equilat.) isosc. scalene. Drobisch computes as follows : Triangle, cont. = a, ext. -9 - 3^ Acute triangle, cont. = a + 1, ext. = 3 = 3^ Equilat. tr., cont. = a + 2, ext. = 1 = 3°. But this computation is imagi- nary, because two of the nine combinations are not valid, according to the geometrical relations of dependence between the sides and angles of a triangle. Where conceptions refer to natural objects and relations of mental (geistige) life, the application of these laws is still more limited.^ The universal conception adjusts itself^ to the delineation, well marked in some fundamental features only, m which the outlinesdo not waver in the Whole; but in the individuals there is room for a freer play of the phantasy which fills m the out- lines The common picture within the fundamental outline which makes its limit, is elastic and can take a manifb d formation. If we calP this indeterminateness and elasticity a quantity of attributes or generalities of attributes, indefinite but able to be made definite, as numerous as those embraced 1 In the 3rd ed. of bis Logik (p. 211), Drobisch expressly says that the theory holds good only on the presupposition that every species of any order is to be determined by every specific diiFerence of the foUowmg order. It is true that this presupposition is sometimes realised but it •s realised completely in very few cases. Subjectively-formal logic, as such cannot take into consideration the limited validity of the presup- position, for that depends upon real relations of dependence. "^f Trendelenburg, Log. Unters. 2nd ed. ii. 220 ff. ; 3rd ed. n. 243 ff. 3 With Lotze, I^og. pp. 71 ff., 79. 1 « I Jp. 138 §55. Serüs of Conceptions. in the lower conception, definitely and simply; then, there stands opposed to the old doctrine, that the Wgher conception has the wdest extent and narrowest content, the new docti-ine, that the conten^of the higher conception does not come behind the content of the lower in number of attributes ; and this has a certain degree of correctness. But the terminology is artificial, and not to be justified. A richer content must manifest itself m reference to the extent;' but the way in which it mani- fests Itself 13 not by widening the extent, but by the de- veloping consolidation of thoughts around a definite object ; and this IS accomplished not by extending but by limit- ing the originally unsettled possibility. The sum total of individual conceptions is contained only potentially in the general conception. Their actual existence is accomplished by the entrance of other elements. There are in the nature of things, besides this or that specific connection of a common attnbute with a definite group of dissimilar attributes, other combinations, into which the common attribute can also enter The smallest number of (logical) elements of content and of (real) characteristics or attributes corresponds to the widest ex- tent, only potentially asserted ; the greater number, to a smaller (in the individual conception, to the smaUest) extent, actually asserted. The widest content possible has to do with actual existence only by combining the greatest number of elements of content m the whole of the individual conceptions. [Cf. also m this reference Mr. Mill's very valuable observations upon connotative and denotative names. Logic, i. 31 ff.] § 55. Since the relation of subordination and of super- ordination is repeated continuously by an abstraction which goes on until one simple content is reached, the sum total of all conceptions can be thought of, as ar- ranged according to the relations of extent and content in an organic gradual successwn. The summit or upper ' As Trendelenbiu-g demands, Log. Unters. 2nd ed. p. 226 ff. § 56. Definition of the Notion. The Essence. 139 limit is found by the most general conception ..m.«Ä%. Immediately mider it lie the categories. The basis, or under limit, is formed by the mfinite number of mdi- vidual conceptions. The gradual succession of conceptions may be compared to a pjlfä. But this picture is only apP-i-tely true Jec-e the subordination of conception is not carried on with strict IniforS The highest conception is not the conception of rSTsein), but of Somethino (Etwas), because Be^r^ under one of the Categories, viz. under that of Attributive ^ (predicative) Existence, and is opposed to 5.«, - suWUv • Son^etking, on the other hand, --P-^.^^^^^f ;^\^tfar" r«fPaories which are the highest formal divisions. They are SSd accoig to another%rinciple of division, and repeat themselves in every one of the Categories. S 56. The NOTION (Begriff, notio, conceptus) is that conception in which the sum total ^^ ^^X'^'T"^ ;^^. butes,or the essence (Wesen, essentia) of the object unde; consideration, is conceived. By the phrase-- attributes (Merkmale, notae) of the o^ect, we mc ude not only the outward signs by which it is known, but aU its parts properties, activities, and relations,.-m short r:Ler belongs' in any way to the dbject The — (essentialia) are those attributes which a contam th common and persistent basis for a multitude of otheis and on which (b) the subsistence of the object its worth L its meaning, depends. This meaning belongs to it partly because it is a means to something else, and partlj and principally to itself, as a final end u a ^ / 1 r. r.f nhipcts In a wider sense also, (rradual course ot objects, a" i< t V ' w i' 140 § 56. Definition of i/i£ Notion. The Essence. 141 these attributes are caUed essential, which are neces- sanly united to marks essential in the stricter sense and whose presence, therefore, indicate with certainty the presence of those others. The essential charac- teristics, in the strictest sense, are caJIed the funda- mentally essential (essentialia constitutiva) ; the others which are only essential in a lower sense, derivatively essential (essentialia consecutiva) or attributes in the stricter sense (attributa). The other characteristics of an object are called non-essential (accidentia, modi) The possibility of modi or the capability to take this or that modification must have its foundation in the essence of the object. Under the essential determina- tions are those which the notion has in common with notions super-ordinate and co-ordinate with it the common ones (essentialia communia), and those by which It 18 separated from these notions, the proper or peculiar (essentialia propria). The relations belong generally to the non-essential, but with relative notions they are essential attributes. In the proportion that the fundamentally essential characteristics are unknown the formation of the notion is ambiguous. With another grouping of the objects, other determinations may ap- pear to be common and essential, and the whole pro- cedure cannot raise itself above a relativity which rests on accidental subjective opinions. In proportion, how- ever, as the reaUy essential characteristics are known the conceptions acquire a scientific certainty and an objective universal validity. In perfect knowledge notions are valid only as they correspond to the types of the real groups of their (natural or mental) objects. When the formation of the notion is not made in the purely scilific interest, bnt is conditioned by any externa pujose (even were it the purpose of a superficial view of any part ot mfect^ that one which has for its aim the widest refer- t::^ti t be the most essential. Several difF.ent con structi^ns of a notion can exist alongside of each otW, eac of them being often relatively correct ; one only, however, is alily correct, that. viz. which constructs the no^u, purely according to objective laws, on the basis of what is most essential for the object in itself. . If er that Socrates had first shown that he -- -"-^ »^ the value of the notion in knowledge, Pfato sought to solve the testion of the real and peculiar object of notional knowledge. He defined it to be the Idea {ma or ^I8o.), aad stnctly distm- fulhed he real thing, which is known through the notion from the notion itself (the >^7o^), its corresponding subjective Sire in our minds.' We seek in vain throughout the whok extlt oTpiato's writings for one single passage where «80, or «t even partially denotes the subjective notion, or where rtns f Ilnl has not rather been introduced by interpreters. Plato riS^sought an objective correlative to the subjective notion. Äedb'ecause, instead of recognising this correlate in the Sence indwelling in things he ^ypostatised an objec^e Pxistence outside of things and separate from them , n other woXbecause he ascribed to the idea - e^Je- mdep^^^^^ dent and for itself. The Platonic doctrine of Ideas is the tore • De Eep v. 477, vi. 509 sqq, vü. 533 sqq. ; Tim. pp. 27 n, 29 c, ,7 „ n If ; Erf 5 14. The Farm. p. 132 b, was quoted in the f t'.d ol thU 'bol It represents very clearly the relation of the s^Sectt th"t of notion'al knowledge to ideal existence It cannot, subject to tne odj«. , ^^^ j^^ ^ ^^^^ however, serve as a proof of Plato s view , , ° ^^^^ the Parmenides is not genuine. Cf. Plat. ^"''~!^^/ pyi rt; rar«?' t:::— '^t ttr/»-i- Philol New Series, xviu. pp. 1-28, 1862 , ^ix.]>^ ^^> . Platonischen Schriften, Bonn, 1866, pp. 181-^^0;. « 142 56. Definition of the Notion, The Essence, 143 II shadowing of the logical metaphysical truth in a mythical form. Hence also Aristotle^ rightly compared the Platonic ideas to the anthropomorphic gods of Mythology.^ Aristotle battled against the Platonic x^^R^^stv of ideas, i.e. against the supposition that ideas exist in real separation from the individual existences as particular substances ; but he does not reject the doctrine of a real correlate to the subjective notion. He did not place the forms of thought outside of aU relation to the forms of being. He recognised a thorough-going parallelism between both (cf. § 16). According to Aristotle the essence corresponds to the notion, and is therefore called by him 97 fcaTu \6yov ovaia. The essence is immanent in the individual existence. Aristotle snys^—iiBrj jih ovv shat rj si^ tc irapa rcL iroWh ovx dvdyKrj^ slvai ^isvTOL %v Kara ttoXKmv aXrjdh elirecv dpdyKTj.*—ii; tols scSsa-t Toh alaOrjTois to, vorjrd sariv. This one in the many, this intelligible in the sensible, is called by Aristotle the form, the what is, and, with a ter- minology quite peculiar, the bein^ what a thing was—fiopcj^TJ, siBos, rj Kara \6yov ovcrla, to tI san, and to t/ tjv ehai. The expression to tI ^p slvat is explained by Aristotle himself to be the term for the matterless essence.^ to tl tjv slvat corre- 1 Met. iii. 2, 997 b, 10. 2 It is an apprehension historically true in the main, and agreeing with Plato's own declarations, especially in his later writings," and not, as some would have it (Ritter, Gesch. der Philos. iii. 120,°l'831) an open misrepresentation, when Aristotle thinks that ideas are hypo- statised by Plato, and made to exist separately from the sensible things. Aristotle has only defined, somewhat more dogmatically than it is in the conception of the poet-philosopher, the representation which in Plato vaciUates between figurative and real meaning. He has done it in strict accordance with Plato's own later constructions and with the doctrines of many Platonists. The desire to combine philosophy with poetry, which Schleiermacher with a too-sweeping generaHsation finds to be the cha- racteristic of the Hellenic Philosophy, is certainly the characteristic not only of Platonic representation, but also of Platonic thinking. Aristotle deserved commendation, not blame, when he in his own doctrines stript off this form, and thereby founded scientific Logic and Metaphysics. 3 Anal. Post. i. c. xi. ^ De Anima, iii. 8. ^ Metaph. vii. 7. .ponds, therefore, to the abstract fonn of the notion (and con- Jnuentlv to the substantivum abstractum). (Ci. m this Xence'the difference, explained by Plato - ü. ^^ogue Phaedo • of the inherent characteristic from the thing in fvh-ich h inheres.) It does not, however, amount to the me e tlit;TÄ wS' m'r e^tL into the definition) Ld includes' both the characteristics of the genus and the Icific difference. The .1 i<^^ of Aristotle is of wider and ess definite use. It can denote both the matter' and the matterleressence,' and, lastly and most commonly, the union rrt^ , L .^voK^ if -8- «al ÖX,./ In this last case i correspTnl to the concrete form of the notion (and so to the sls3^m concretum). The non-essential determmations tZ mere accidents i..,ß.ßn^lna), e. g. me.e <^^^^J^^^^ or Quantities (iroad), cannot serve as answers to the question . rr a least, not when, a. usually happens, the question is Ilout the «' i.rl of a thing. Aristotle recognises, that not only Xting (substances),'but also with Quantities Qua ities. Relatonslin short, in every category- the question r. ev o^u.. s.r,.^^ • ^n,'.TM9 Bv this remark the two meamngs of ovcui, Essence Z7 SuTsianUL placed in inward relation ^..each other^ Unfortunately, however, the number of the meanings of this wd which dUtes-now Substance in the sense of substrate rmaren'l basis of existence (xÄ W.^c or ^ SXr, sub- TecZ) ; now the essence corresponding to the notion (, Kara 1 Phaedo, p. 103 B. 3 E.g. Be Anima, p. 403 a, 30. 5 Ibid. vii. 4. 2 E.g. Metaph. viii. 3. 4 E.g. Metaph. viii. 2. 144 § 56. Definitioti of the Notion. The Essence. 145 % ll or what exists (to avvoXov, to if ayLtoti/, ens), and in this third case both the individual existence (toS^t^, individvum) and the sum total of the objects belonging to one genus, or to one species (to r^svos, to slhos, genus, species, materialiter sic dicta), — from then till now has been the cause of numberless cases of vagueness and error. A defect still more felt lies in this, that with Aristotle there are no criteria of Essentiality. The dif- ference often brought forward in the treatise on the Categories —that what belongs to the essence can be predicated of the subject, but cannot be in the subject, while the accident is in the subject (e.g. Socrates is man, but man is not in him; Socrates is wise, and wisdom is in him), is not sufficient.' It substitutes the opposition of substantive and adjective apprehension of the predicate notion for essentiality and non- essentiality. Now the two divisions are not parallel, but cross each other (e.g. Socrates is gifted with life and reason; Socrates is a wise man). Aristotle, not usually, nor yet in his logical writings, but now and then in single places, makes this criterion hold good for essentiality and non-essentiality : That is an essential part of the whole whose removal or altera- tion influences the whole.» But here, of course, the amount of influence on the totality of the remaining parts remains undefined. What lies in the definition belongs, in its totality, to the object of the definition only, or is peculiar to it ; but single parts of the definition may belong to other objects; 2 and besides the essence given in the definition, something else may be peculiar to the object of the definition. This is the Xhiov in the narrower sense.^ Predicates which follow neces- arily from the essence are called avixßsßrjKOja rals ovalais by » ÜtTTE liiTariBifxivov tlvoq fiipovQ Ti d(paipovfxivov liai^ipiaBai Kni KivtiaQai TO 6\oy, Poet. c. viii. 1451 a, 33 ; in the words following, o yitp irpotroy T/ fit) Trpoaiv finUv ttoie'i eTrihrjXor, fxriSep is the grammatical subject. Cf. my translation of the Poetics, Berlin, 1869, p. 102 • cf. Top. vi. 12 : iKaoTov yap to ßaKriaTOP tv rp ovaiq, paXiaTa. * Anal. Post. ii. 13. ' Top, i. c. iv. 101 B, 22 ; ibid. c. v. 102 a, 18. Aristotle,^ or (more commonly) avpßeßvKSra KaB ahro,^ These last were later called the consecutively essential or attributes. They too belong to the KaOhXov, for the ^a^oXou is everything 3 which belongs to what is denoted m the whole extent of its notion {^arä iravrhs and HaO' ahro or v avro), in distinction from what is common in any way {koivov), ihe KaObXov is a kovv6v, but every KOLvhv is not a KaOhXav.^ According to the doctrine of the Stoics, notions exist only as subjective creations in the mind. The «ot.o. X070. the reason of the universe separated into a plurahty ot XcWo., dwells in external things. But the Stoics do not ex- pressly make these \670t denote what is known by the sub- jective notion. 1 ^ -di + In the Middle Ages the Realists paid homage partly to Plato, and partly to Aristotle's opinions,- ' universalia ante rem,' and ' universalia in re.' The Nominalists allowed no other ex- istence to the ^universalia' (universal objects or universal predicates) than an existence in the word (strict Nominal- ists), or in the thinking mind also (Conceptuahsts)- Uni- versalia post rem.' The manifold defects in Platonic and Aristotelian Realism called forth Nominalism its extreme opposite, and gave a relative correctness to it Among modern philosophers Descartes, Leibniz, as well as Bacon and Locke, belong to Nominalism, or rather to Conceptualism. This logical and metaphysical problem, discussed by Scholasticism, w^ scarcely affected by the psychological question, chiefly discussed bv modern philosophers, about the origm of our notions, viz,- Are notions really innate ? Is development m common life limited to a gradual coming more and more dis- tinctly into consciousness? or, are all notions, m content and form, products of a mental development conditioned by outward influences? Kant and Herhart, like the earlier No- minalists, concede to notions a subjective meamng only. 1 De Anima, i. c. i. 402 b, 18. n» • ^ ^ > Metaph. V. c. xxx. 1025 a, 30 : Saa D/rapx" ^'^«^''y «^«ö avro ^ iv ovaiif. ovTa. 3 According to Anal. Post. i. 4. 146 56. Definition of the Notion, Herhart uses ^ universalia ' to denote all general and individual conceptions, so far as they are looked at, not on their psycho- logical side, but in reference to what is represented by them. Yet Herbart says,* in a passage where he is not expressly teaching Logic, but makes a logical remark accidentally — ' Definition becomes a significant expression of the result of this whole deliberation only after the first attempt to separate the essential from the accidentaV Now, since the notion is determined by what is essential, and not what is essential by the notion, there is here presupposed a difference of the essen- tial and accidental lying in the objective reality, and the dependence of the genuine formation and explanation of notions — i. e. a formation and explanation, which corresponds to scientific and didactic laws — upon this objective difference is recognised. Subjectively-formal Logic, which should identify the notion with the general conception, so far as it at all explains the cate- gory of essentiality, calls those attributes essential without which an object could not be what it is, nor remain what it is, nor be subsumed under the same notion. In other words, those attributes are essential which belong to the object in the whole extent of its notion or make up its content.* This ex- planation is unsatisfactory, for it argues in a circle. The notion is explained by the essence, and then the essence by the notion. If Logic' is to settle the normal laws of thought, it must answer the question, — according to what marks are ob- jects to be grouped together and their notions formed? For example, are plants to be grouped according to the shape and divisions of the corolla (Tournefort), or according to the number of their stamens and pistils (Linneus)? They are to be grouped according to their essential attributes. What attributes are essential? Those which belong to the object ' In his discourse at the opening of his Vorlesungen über Pädagogik^ 1803. Werke, Bd. xi. 63, Leipzig, 1851. * Cf. Drobisch, Log. 3rd ed. § 31. [Sir Wm. Hamilton's account is tlie same ; cf. Lect, on Logic, i. 217.] ' According to Drobipch, Logik, § 2. T/ie Essence. 147 in the whole extent of its notion, those which lie ^^ ;^^/^f ^jl' and to which the name belongs. If then we seek first the correct notion and name, how shall we d^^^™f ^^.^ the essential attributes. What are the essential? Those which lie in the notion ; and sic in infinitum. The consequence is, that the formation of the notion remains quite arbitrary. He who arranges plants according to the shape and divisions of the corolla, and thereby forms his botanical notions-for him the shape and divisions are essential. He who arranges them according to size-for him size is essential; and so on. At the best, the common use of words, as yet uncorrected by science, gives a starting-point; no way is pointed out; and we are left to the most elementary and wholly unscientific modes of forminc. notions.» When we once know what objec s, accord- ing to%heir nature, belong to each other, and make up the exlent of the one and the same notion, we can set ourselves rioht by this, in our search after the essentia properties. Bu how can we scientifically know that reciprocal dependence, and determine rightly the limits of the extent, so long as we are unable to distinguish the essential from the non-essential attri- butes? Does the whale belong to the extent of the notion fish V Is the Atomic philosophy within the sphere of the notion of Sophistic ? Does the mode of thought shown in the Pseudo- Clementine Homilies fall within the sphere of the notion of t Drobisch confesses this in the third edition of his Logic in a remark appended to § 119 (p. 137), inasmuch as he explains that his d IctionL only be fully justified and established when the refer.^^^^ is to the analytical definition of a notion which is given by its com- monly used designation, when we only seek the notion .^ich correspa.ds To a given nam^ But my assertion points to this, that subjectively- formal Logic, unless it goes beyond its principle, can only brmg forward ts laws for the solution of certain merely elementary and propaedeutic problems, and can only produce a small part of Je^-^^^^^^^^^^^ and not, as is promised in Drobisch's Logic (3rd ed. § 2 p 3) the norma laws of thought. The consideration of the 'synthetic forms ofTousht' can only be scientifically satisfactory when it is based fn Ätion to the forms of existence (e.g^of the ground of know- ledge to the causal relation, of the notion to the real essence). L 2 148 §56- Definition of the Notion. The Essence, 149 Gnosticism ? Does Joannes Scotus (Erigena) belong to the Scholastics ? Tiedraann says ' — ' Scholastic philosophy is that treatment of objects ä priori, where, after statement in syllo- gistic form of the greatest number of reasons for or against, decision is made from Aristotle, the Church Fathers, and the prevailing system of belief.' It follows from this definition of the notion that Scholasticism proper had its beginning at the commencement of the thirteenth century, after acquaintance with the metaphysics, physics, and ethics of Aristotle, which did not take place until the close of the twelfth century (before this the Logic only was known). Whether this de- finition of the notion is to be agreed to, can be settled only from a consideration of the essentiality of the attributes, inde- pendent of the previous settlement of the extent. Every ques- tion of this kind can only be settled scientifically, when, before and independently of the limitation of the extent, the essen- tiality, or degree of the essentiality, of the attributes has been settled. Now, icherein lie the criteria ? Subjectively -formal Logic, when it takes the forms of thought apart from their re- lation to forms of existence, and will not treat them as forms of knowledge, proves itself to be inadequate to give rules for that formation of notions which the positive sciences require. The somewhat common explanation of the essential attri- butes as the lasting and persistent properties is not more satis- factory.^ In its reference to the amount of time of duration, this definition does not prove a just one. The highest and most essential form, the most pre-eminent, is often the point of culmination of a life which swiftly passes away. If it only denotes inseparability from the object, so long as the object remains what it is, or while it is subsumed under the same notion, and can be called by the same name, the reasoning in a circle again results. The principle of grouping objects together according to the most important properties, or those which are of the greatest similarity or natural relationship (on which MilP would * Geist der spec. Phil. iv. 338. ' E.g. in Hitter's Logikj 2nd ed. p. 67. 2 Logic^ ii. 264. base the formation of notions), leaves the question undecided. For, What similarity or relationship is the greatest? A similarity in many, and even in most, determinations would by no means justify comprehension together and subsump- tion under the same notion, provided that the many were the least significant. A similarity in the significant, important, and essential would. But then we come back to the question, What are to be considered the essential ? H. Taines definition of the essential characters is to be cri- ticised in the same way i-.— 'The essential characteristic is a quality from which all the other, or at least most other quali- ties, derive according to a settled mutual interdependence.' The genetic consequence, without regarding the degree of value of each attribute, is scarcely sufficient for the determination of what is essential. Besides, one moment of an object ought not to come from another, but the sum total of the attributes from eariier original circumstances. The connection belong- ing-to-each-other, and the dependence, ought to be reciprocal and give no criterion to decide what attributes are essential among those which belong to each other. Schelling's Nature- Philosophy, while it seeks to blend the Platonic doctrine of ideas (modified in the Aristotelian sense) >vith Spinoza's doctrine of substance, finds the real antitype of the notion in the ideas, the creative types, or characters of genera, the media between the unity of substance and the end- less number of individual existences. Hegel does not seek a real antitype of the notion, but holds that the notion is as much the fundamental form of objective reality as of subjective thought. He defines the notion to be the hio-her unity and truth of being and essence, to be the sub- stantia power existing for itself, and therefore the freedom and truth of the substance.^ But the notion as a form of human thought is not sufficiently characterised by this. According to Ülrici,'' the logical notion is universality as 1 Philosophy of Art, p. 51, translated into English, 1867. 2 Logik, ii. 5 ff. in the ed. of 1834 ; Encycl. § 158 fF. 3 Log. p. 452. ISO 56. Deßmtion of the Notion. The Essence. 151 ill the category of separative thinking. But the mere category of universality will not sufficiently distinguish the notion from the general conception. Schleiermacher disrinoruishes the sensible and intellectual sides of the notion. The former is the Schema,^ or common picture, i.e. sense-picture of the individual object represented confusedly, and therefore become a general picture from which several particular pictures, co-ordinate to each other, could quite well arise. With respect to the intellectual side, Schleier- macher recognises^ in the system of notions, that creation of the thinking reason, or of the ' intellectual function,' to which the system of ^ substantial forms ' corresponds in real existence, or of powers and phenomena, in opposition to the system of judgments as the correlate of the system of ' actions.' This definition of Schleiermacher's, when it places the notion as a form of knowledge in relation to a form of existence, is the right mean between the mutually opposed one-sided views of the subjectively-formal and the metaphysical Logics. It labours tmder the defect that it does not distinguish sharply enough between substance meaning existence, thing, ens, and substance meaning essence, essentiality, essentia. This seems to be a consequence of the Aristotelian vagueness in the use of the word ovoia. Every conception of a thing is not a notion, nor does every notion rest vipon a thing. The conception is a notion when the essential is represented in it, whether it be of a thing, an action, a property, or a relation.' Schleiermacher makes the opposition of the higher and lower notion parallel with the opposition of power and phenomenon, or universal thing (Genus and Species), and individual existence ; so that (e. g.) the power of sight of the eye is to be thought of, in analogous relation to the single eye as a phenomenon of this power, as the universal notion of the eye is to the individual notion of the single eye. This theory has its root in the Aristotelian doctrine of the active power {sins\s')(sia^ as the essence, — 17 o^^is ovaia 6(j}0a\fjLov T] Kara TOP \6yov,* > Dial. §§110 if., 260 ff. 2 Ibid. § 175 if. ' Schleiermacher himself partly recognises this, Dial. pp. 197, 340, 545. ^ Arist. de Anima. ii. 1. Beneke' considers the notion or general conception to be a form of ' analytical thinking.' He incorrectly believes that its correspondence with the essence as the ' synthetical form is merely accidental. a„v,i^;o^ Ritter^s definition of the notion corresponds with Schleier- macher's :»-' the form of thinking, which represents the en- during basis of the phenomenon ;" « the existence which is re- presented in the notion is an enduring one, but one which can show itself in changing activities, now in one way, now in another-such an existence we call a llvmg thing or a sub- stance ;'* « when the understanding strives to think the in- dividual thing as the lasting foundation of many phenomena (or, according to p. Ö. as substance), its thought must take a form in which the meaning of many phenomena is compre- hended or conceived-every such thought we call a notion and when it comprehends this meamng m the thought of an individual, an individual notion;'^ 'the general notion/e- presents the totality of the particular essences with their activities. . ,^ n r Trendelenburg' understands by the notion, the forms o thinking which correspond to the real substance as its mental 'X a similar way Lotze^ calls a notion, that content which is thought of not merely as the conception m the mutually inter-dependent totality of its parts, but whose multiplicity is referred to a logical substance, which brings to it the method of combining its attributes. But the reference to a substance belongs to every substantive conception, and is not the disto- guishbg character of the notion. It cannot be granted tha Logic has nothing to do with the essenüal - not, at least, from the stand-point of Logic as the doctrme of know- ^^^IMiirs doctrine of the essence cannot be wholly summed up by 1 System der Log. i. 255 ff. ' Log. 2nd ed. p. 50. ä Ibid p 56 * Syst. der Logik und Metaphysik, ii. lö. ' Ibid', p. 297. ' ^S- Unters, ii. §§ U 15 7 Log. p. 177 ff. ' ^' ^'^^ '^'^^'' ^^- P- ^^- \ !.l 152 5 7- Knowledge of the Essential, etc. The ä Priori and ä Posteriori Ekments, etc, 153 i t • saying that objects have the same essence, or are to be sub- sumed under the same notion, which have similar properties, or are most naturally related to each other. He knows that the further question arises — What objects are naturally related, and so serve as the basis of the formation of a notion ? and would say that this latter question cannot be answered in a sentence, but is the one question of Inductive Logic. It is the business of induction to find out methods for discoveringr and testing the relations of properties, and so finding out whether they are so related that they can form the bases of notions. The inductive methods show what properties are essential. The portions of Mr. Mill's Logic which refer to this question in debate are the most instructive in the whole book; cf. especially, vol. i. pp. 131-170, and vol. ii. pp. 189-201, p. 216 fF., pp. 262-285. Essentiality, however, does not depend upon Induc- tive Methods ; Inductive Methods depend upon Essentiality ; and thus Mr. Mill fails to solve the problem of Essence.] § 57. We recognise and distinguish tlie essential — (a) In ourselves, immediately by feeling and medi- ately by ideas. Feeling is the immediate conscious- ness of the relation of our activities and conditions to the present existence and development of our whole life, of its single sides and organs, or of the life of other beings related to us. What aids is felt with pleasure ; what hinders, with uneasiness and pain. In the ethical feelings, more especially, the gradation of the worth of different developments reveals itself, according as they are sensible or mental, more passive or active, isolated or connected, limited to the individual or extended to a wider community, or consist in that relation on which the law of human will and action rests. The ethical ideas are developed (by abstraction) out of feelings. The knowledge of our own essence depends both on the consciousness of the ethical ideas, and on the amount of our actual existence in them. (b) By means of the knowledge of the essence in ourselves we recognise the essence of persons beyond us, more or less adequately, in proportion to their rela- tionship with ourselves. The relation between the knowledge of ourselves and of others is a reciprocal one. The clearness and depth of the knowledge of our own essence depend upon intercourse with others, upon living in connection with the whole mental de- velopment "^of the human race (just as one can say in theology, that the understanding of the revelation of God within us depends as much on the understanding of the historical revelation, as this does upon that). (c) The essence or the inner purpose of nature in animals and plants is the analogue of the ethical duty of man, and is to be known in the proportion of this analogy. The analogy is limited but not destroyed by a threefold opposition :— that the powers of the impersonal essence are of a very different and lower kind ; that they do not strive to win to their end by means of a free conscious activity, but by unconscious necessity actually realise the tendency indwelling in them ; and that the signi- ficance of their existence as ends in themselves is out; weighed by the significance of theu- existence for others, (d) With the inorganic objects of nature, existence as an end in itself, and self-determination, come after • existence as a mean for another, and the mechanically becoming determined by another. Hence the possibility of knowing their inner essence is thrown into the back- ground b>^the knowledge of their outward relations. ^54 § 5 7- Knowledge of the Essefittal, etc. § 58. Class, Genus, Species, etc. 155 /■ (e) The essence of what exists not in the form of independent existence or substantiality, and of what has only a factitious independence, the result of art, is known partly according to its analogy with the life of independently-existing individuals, partly and chiefly according to the significance which belongs to it as a mean to something else. Material truth is to be reached in our notional know- ledge of the ^essential from the same grounds, and undergoes the same limitations and gradations, as in the case of perception (§§ 41-42) and of the indi- vidual conception (§ 46). The essential relation of the activity of knowledge to the whole of the mental and ethical life depends upon this. The question whether human notions are present a priori (if the phrase, according to Kant's use, is applied to what is de- rived from the subject as such) in the mind (Geist) as innate possessions, or are raised up in it ä posteriori by means of the senses, by way of gradual development, may be decided in the following way. Every notion contains an * ä priori ' element, not only in the sense in which this is true of every conception , but, more particularly, because the knowledge of the essential in things can only be reached by means of a knowledge of the essential in us (though this knowledge is often not developed into full consciousness). Schleiermacher^ rightly places the development of the whole system of notions in relation to our self-consciousness. Man, as the microcosm, has in himself all the degrees of life, and thereon constructs his conceptions of outward existences. In this sense it may be rightly said that the system of all notions is originally contained in the reason or * intellectual function ;' only we must not make the mistake of supposing that the actual system of human notions is inde- pendent of the objective reaUty and quite different from it. » Dial § 178. When correctly constructed it represents the proper essence and arrangement of the objects. ,„ ti.p n„ter world But the formation of any notion refemng to the outer woria i. fond tioned by the outer or ' ä posteriori ' factor just as much as by the subjective or 'ä priori' element; for rf notional knowledge is i have truth, the completion of the contents °f perception by analogues of our essence must conform U, the phenomena, and can only be references of the outer phenomena of things to their inner essence. The ä priori element is only f priori a. regards the outer world, and is by no means in- dependent of inner experience.' it is impossible to admit the existence of notions, which although unknown, may have been present ««/?*>?"« ^"^"! ft m the beginning. On any acceptation, th.-d— would contradict the course of human development. And the end Sfwould induce us to make this „npsychological ad— the objective validity of notions apparently --« ^^^ in it^. s not satisfied by it. A pure subjectivism may -^^^^^J^^^™ the presupposition of an ä priori character ; a^d ^^^^'^^^^ Pritical nhilosophv has so connected itself, ihe trutn lyin^ ^t Zt£. of ?his doctrine is,^ that the human mind is able to reach a knowledge of objective reality. Cf. § 140. S 58 Those individuals which have the same essen- tial properties make a class, or genus, in the umversal sense. The genus is as much the real antitype of the extent as the essence is of the content of the notion. The essence has different degrees, and different circum: scribing groups of marks can serve as the basis of deter- mining the formation of the notion. In a ^müar way several classes or genera encircling each other can be distinguished, which are denoted successively by the 1 Cf ScUeiermacher's Ethik, ed. by A. Twesten, § 46 p. 55 . As XHoppe has rightly remarked in his Ge.am,nte LogA, .. § 54, p. 45, Paderborn, 1868. 156 §5^- Class y Genus, Species ^ etc. — \ % terms^ Kingdom (regnum)^ Sphere (orbis), Class (classisT), Order (ordo), Family (familia), Genus (genus), Specie^ (species). Group (coliors) is sometimes inserted be- tween Kingdom and Sphere ; Tribe (tribus) between Family and Genus ; Subdivision (sectio) between Genus and Species, and in other places ; and Subspecies and Variety (varietas) between the Species and Individual. The notion of Race is specially applied, in definite cases only, to the most general division of men in natural history. It might be referred to Subspecies. The opposition of Genus and Species is frequently used to denote the relation of any higher class to any lower, which is proximately subsumed under it without any intervening members. Objects are generically different when they belong to different genera ; specifically different when they be- long to different species of the same genus. They are gradually different when they differ only according to quantity or intensity. They are numerically different when they, although wholly similar in essence, are not identical, but are several objects. The characteristic of the species in natural history, main- tained by earlier investigators, was continuous fruitful pro- creation. Later research has made this criterion a relative one. But this characteristic, so far as it holds good, is to be looked at only as consecutively, not as constitutively essential ; for the possibility or impossibility of continuous fruitful procreation must depend upon the whole character of the organisation. The true characteristic attribute of the species is not procrea- tion, but the type. By type is to be understood, neither the mere outer form and figure, nor the peculiarity of any one given standard form, but the whole character of the organisa- tion — the Platonic idea, not in its historical but in its true tlieir Reality afid their Knozvability. 157 sense, the Aristotelian form, the Kantian ' Urbild der Erzeu- gungen,'» or« Uhe image which is afterwards realised.' The possibility of reproduction only serves as a mean to recognise the correspondence in the type. Formations belong to a kmd, if they, so far as their like stages of development are compared with each other, show correspondence in all essential attributes. Comparison is the function of the knowing subject only; essentiality of the marks compared is the objective moment which gives real meaning to the notion of species. Individuals which have been correctly arranged under a species (or any class) must agree with each other, not only in those marks which make up the content of the notion, but also in many secret relations. Hence it is seen that the notion of species (and every notion of class founded upon essentiality) is based upon the objective reality itself. George Henry Lewes^ says, * What is the aim of a zoological classification ? Is it not to group the animals in such a manner, that every class and genus may tell us the degree of complexity attained by its organisation, so that the outer form may explain the inner structure ?' But the degree of complexity on its part tells us the degree attained by every object in the scale of perfection. Cf. § 63. It is an inconsequence to recognise the real existence of the individual and then to deny the reality of species ; and it would be an inconsequence to recognise the natural reality of species, and then to deny the natural reality of genus, family, and other wider divisions in which the narrower are m- cluded. For the reality of species depends upon the reality of essentiality. Certain elements must be recognised, not only to be eminently useful as fulcra for the determination of notions, . but as eminently important and decisive for determining the existence and significance of real objects. If this be once allowed, the recognition of the graduation of essentiality, and with it the recognition of the reality of the graduated division ol » Krit. der TJitheilshrafi. 2 According to Spring, Ueher Gattung, Art und Abart. 3 Aristotle : a Chapter from the History of Science, ^c, p. 277, § 323, I8ra 158 58. Class, Genius, Species, etc. iii |!il III external existence, cannot be well denied. Braun says rightly' — 'As the individual appears to be a member of the species, so the species appears to be a member of the genus, the genus to be a member of the family, order, class, and kingdom.' The recognition of the organism of nature and its regular division, as objective facts witnessed to by nature herself, is an essential requisite for placing natural history in a higher position.^ Aristotle made species and genera Ssvrspat ova-lat, just as in- dividuals were ovaiai in the fullest sense of the word,^ and so recognised them to be real. He saw in the natural classes a graduated series of ascending perfection. Linneus rightly believed the classes and orders of artificial systems to be a make-shift for the natural until they are known, but considered the true species and genera, when known, to be objective works of nature. "* The knowledge of natural genera, families, and orders is always more uncertain than that of the species. The acceptation of an objective validity of natural division does not exclude the recognition of a certain relativity in the notion of species ; as little as the objective existence of the in- dividual excludes the partial indefiniteness of the limits of the individual. In a genetic view of nature (such as the Darwinian,* whose fundamental thought Kant had already expressed hypothetically in his Kritik der Urtheilskraft), which is founded on the supposition of a gradual origin and partial transformation of species, the objectivity of the species for the world as it now exists can still be accepted. For a realised tendency of nature to construct definite forms may be recognised, and objectivity does not mean absolute stability. On the basis of the Darwinian theory of species, inasmuch as its notion is referred to organisms existing contemporaneously at any given time, an objective validity in the full sense of the word can always be vindicated, because the systematic table of the classes of organisms rests on their genealogy, and * Verjüngung in der Natur, p. 343. ^ Cf. Rosenkranz, Logik, ii. 48 if. ^ Cat. v. * Philos. Botan. § 161 sqq. * Charles Darwin, On the Origin of Species, Lond. 1859. 59. The hidividtial Notion, 159 so unites the genetic point of view of common origin with the teleological point of view.» ' The difficulty of natural-history treatment does not now lie in the determination of the species, but in this, that every systematic category is considered to be a natural unity which represents the starting-point of a great historically developing movement. The genus and the higher notions (as much as the species) are not abstractions but con- crete things, complexes of connected forms which have a common origin.'^ As it is in the province of natural history, so is it in that of ethics. We must seek out the essential in the group- ing of the relations presented, and consequently in the forma- tion of the notion, which is thus not left to the subjective arbitrary choice, but is connected with objective law. The distinction of wider and narrower spheres rests throughout on the gradations of essentiality. § 59. In those cases where individuals which belong to the same species are separated from each other by essential peculiarities, they form individual notions. The individual notion is that individual conception, whose content contains in itself the whole of the essen- tial properties or attributes, common and proper, of an individual. A certain universality belongs to an individual notion also, inasmuch as it contains under it the different stages of the development of the indi- vidual. The conception of an individual Hving in time is not purely individual, unless it represents the indi-. vidual in a single moment of its existence. The schoolmen's question about the ' principium individu- ationis,' formed by the opposition of Aristotelianism and 1 Cf. for the logical treatment, Trendelenburg, Log. Unters. 2nd ed. ii. 225 ff., 3rd ed. ii. 248 ff. ; of. ii. 78 ff 2 Carl Nägeli, Entstehung und Begriff der natuvhist. Art, 2nd ed., München, 18H5, p. 34. h 1 60 § 60. Defifiition. Its Elements-^ Platonism,^ rests on the presupposition that the universal is not only a notional, but also a real prius of the individual. It loses significance, whenever it is seen, that to descend from the general to the particular can only be done by the thinking subject; and that, in objective reality, the essence cannot exist before the individual in any such way that the individual must form itself upon it. The Nominalists (who went too far on the other side) have recognised this when they explain that what exists is, as such, an individual. After them Leibniz and Wolff explain that to be individual which is determined on all sides (res omnimodo determinata, or ita determinata, ut ab aliis omnibus distingui possit), and assert that the universal, as such, exists only in abstraction. Individuality is constituted not by one determination (such as Matter, Space, Time), but by the sum total of all. This does not prevent the distinction of essential and unessential, and of de- grees of essentiality, from existing in the objective reality itself. So far as properties, which belong to this or that individual, have essential significance, there are individual notions. From § 46, it follows that individual notions are chiefly formed from the highest essences under the personal, § 60. The DEFINITION or determination of the notion (Definitio, opitr [xog) is the complete and orderly state- ment of its content (§ 50). All the essential elements of the content of the notion, or all the essential proper- ties of the objects (§ 49) of the notion, must be stated in the definition. It is the expression of the essence of the objects of the notion. The essential elements of content are, partly those shared by the notion to be defined along with co-ordinate notions and so form the content of the superordinate notion, and partly those by which the notion is distinguished from the co- ordinate and superordinate notions. But since (§ 58) » Cf. Arist. Metcfph. i. 6. tAe Notion of Genus and Specific Difference. 161 I- ' the opposition of genus to species serves to indicate, generally, the opposition of any higher class to any lower, in so far as the latter is immediately subordinated to the former, the essential elements of the content of the notion to be defined can be separated into generic and specific. On this rests the postulate— ^Aa^ the definition contain the superordinate or genus-notion and the specific difference or what makes the species distinct. The state- ment of the genus-notion serves also to determine the form or category of the notion to be defined (whether it be substantive or adjectival, &c.). Simple notions, in which the totality of attributes is reduced to one attri- bute only, cannot have a regular definition (cf. § 62). Plato finds in Definition (o/j/ffö-^a/) and in Division {hiaipuv, Kar* aihq BiarsfivsLv) the two chief moments of Dialectic,' but does not develope its theori/ more thoroughly. He does not expressly say that the Definition must contain the Genus and Specific Difference, but actually proceeds according to this axiom ; e.g. in the Gorgias,^ in the definition of Rhetoric ; in the Republic, in the definition of the co-ordinate virtues (Wisdom, Courage, Temperance, and Justice) ; for he adds to the statement of their generic character the specific peculiari- ties. In the Dialogue Euthyphro, the o66vo9 ^ as the \v7rrj ettI -rah riov (plXcov svirpa^i- In the Platonic Dialogue Theaetctus,* the hiajiopd or ais. StacfiopoTriS, or the arjfislov w twi' andvicov hLa(^spu no sprorrjOei is distinguished from the kolvov, as when, e.g. the rjkL09 is said to be to XaprnpoTarov t&u kut ovpaiou Iovtcov irtpi yqv. Plato combats the assertion, that a characteristic sufficient to » Phaedr. p. 265 sqq. 3 Xenophon's Memorab. iii. 0, 8. 2 Ibid. p. 462 ff. * Theaet. pp. 208, 200. M 102 § 6o. Definition, Its Elements — r distinguish science from mere (though correct) opinion is afforded by the consciousness of the hia^opL In the Philebus ^ generic identity is distinguished from the Bta(l>op6T7)9 of the fisprj (species); the latter may be increased up to the most complete opposition. The remark that simple notions do not admit of definition is introduced and examined in the Theaetetus : ^ — dEvvarov shai OTLOvv T(üv TrptoTcov pTjOrjiai X070), ov yap etvau avrw, aXK. rj ovofJid^saOai ^ovov, ovofia yap fioifov ^X^iv ' tcl hs ifc tovtcov rjBq ^vyKSLfisva wcnrep avrb, TrerrXsKTat^ ovTto Kal ra ovofiara ai- Twi/ ^vfnrXaKSvra \6yov ysyovevai. In the Dialogue Politicus ^ the term Biaijyopal signifies rather the species themselves, which are contained in the genus, and into which it can be divided, than the specific elements of content which must be added to the generic in the Definition of the species-notion. Definition is based on Division in the Dialogue Sophistes.'* In the Platonic Leges ^ are distinguished — 17 ovaCa^ rrjs ovaias 6 \6yo9y and to 6vop.a, By \cyos Plato here means both the notion and the definition of the notion, as, e.g. the Xayos of that which bears the name äpriov is dpiOfibs Biaipovfisvos ds tea Bvo fMsprj, Aristotle teaches,^ opiapLos ovaias tivos yvwpio-fios ' ^ opiafics icTL Xtyos TO tI riv slvat arjfialvayv ' ^ iv m apa fjLtf siiopd slBoTToios,^^ Later logicians " demand Mefinitio fiat per genus proximum et differentiam specificam.' It must also be pos- J Pp. 12, 13. 2 p, 202. 3 p. 285. * P. 219 sqq. » P. 895. ^ Analyt. Post. ii. 3. 7 Topic, vii. 5. ^ Metaph. vii. 4. ^ Top. i. 8. *^ Ibid. vi. 6 : iräaa yap tllioTroidg 3m0opa pera rov yevovg tt^oc iroiu. ^* Founding on Arist. lojy. vi. 5, p. 143 a, 15, where pi) vKeftßaiydi- Tu yii'1] is demanded. t/ie Notion of Genus and Specific Difiference. ^63 tulated that what can be said in few words should not be expressed in many. But the postulate cannot be universally applied. For example, the definition which would subsume the circle under the proximate genus conic section, would in the majority of cases be less useful and convenient than that which subsumes it under the more general notion of plane figure, and in elementary geometry would be quite inadmis- sible. Cases of this kind may be generally reduced to the foUowincr formula : — The notion to be defined. A, falls under the proximate genus-notion b, and both under the proximate genus- notion C. A differs from B by the Specific Difference a ; B from c by the Specific Difference b. Now. it may happen that the two differences {a and 6) cannot be easily defined by them- selves, but easily coalesce into one whole difference a, in which both are implicitly contained. When this happens, thö Definition by a remoter genus-notion is easier and simpler than the Definition which contains the proximate genus-notion, and is therefore to be preferred, save in single cases where the purpose requires the more difficult definition. Modern Dogmatic Philosophy since Des Cartes lays great stress upon Definition ; and Kant also, although he believed the knowledge of the essence of the thing to be unattainable, holds the stricter form of Definition to be important. Leibniz teaches that the genus and the diflference making the species are often interchangeable, for the difference may become the genus, and the genus the difference : this opinion, if, in accordance with Aristotle's view, a real relation is represented in the reciprocal relation of the elements of content, must be limited to the case where several definitions are equally essen- tial; as (e.g.), adulari can be as well defined to be mentiri lau- dando as laudare mentiendo, ut placeas laudato.* The Hegelian philosophy merges the Definition of the notion in its dialectical genesis. * Trendelenburg discusses the Element of Definition in the Leib- nizian Philosophy in the Monatsher. der Berl. Akad. d. Wis^. Juli 1860, repubhshed in his Hist. Beitr. zur Philos. iii. 48-62, Berl. 1867 ; cf. Log. Unters. 2nd ed. ii. 224 flf.; 3rd ed. ii. 217 iL M 2 ■'^^-^T-^'^^.T' ■" 164 61. The Kinds of Definition. 61. The Kinds of Definition. 165 [According to J. S. Mill, a Definition is a proposition declar- atory of the meaning of a word, and so must directly or indirectly include its whole content or connotation, or express the sum total of all the essential propositions which can be framed with that name for their subject. All names can be defined which have meaning. Even those whose meaning is summed up in a single abstract quality may be defined by their causes. Complete definition is not brief enough, and is, besides, too technical for common discourse. Hence arise incomplete definitions. Of these the most noteworthy is per genus et difFerentiam. Such definitions are useful abbreviations, but may be, and are con- tinually set aside in the progress of science.^] § 61. Definitions are divided according to various points of view. We distinguish — 1. Substantial and Genetic (Definitio substantialis and genetica sive causalis). The content of the notion to be defined is in the one case taken from the present existence, in the other from the origination of its object. 2. Nominal and Real Definitions (definitio nominalis et realis). The former defines what is to be understood by an expression. The Real Definition has to do with the internal possibility of the object denoted by the notion, and thus with the real validity of the notion ; for it either contains the proof of its real validity in the statement of the way in which the object originated, or was based upon such a proof. 3. The Essential Definition and the Distinctive Explanation^ or the Explanation of the Essence and Explanation by Derivative Determinations (Definitio essentialis ; Definitio attributiva vel accidentalis sive [1 Cf. Logic, i. 150-178.] declaratio distinguens). The one gives the constitu- tively essential marks; the other the secondary, and consequently the attributes or different possible modes, but in the number and connection in which they belong exclusively to all the objects falling under the notion to be defined, and therefore sufficient to distinguish these objects from all others. 4. Analytically-formed and Synthetically formed Defi- nitions (Definitio analytica and synthetica). The one is formed in conformity with the existing use of speech, or according to the way of conception at present in use among the sciences; the other is formed anew and freely, independent of any demand of agreement with present use and want. 5. Description (descriptio), Exposition (expositio), and Explication (explicatio) are less strict forms of explaining what belongs to the content of a notion, and so are related to Definition. These forms, along with Definition, may all be comprehended under the wider word Explanation (declaratio). Illustration (illustra- tio, exemplificatio), giving examples which are taken from the extent, is rather related to Division. There can only be one essence to the same object. Hence it might be expected that there can only be one definition to the same notion. Different definitions of the same notion are possible in as far as a reciprocal dependence of the constitu- tively and consecutively essential attributes exists; so that, when any one or any group of them is stated, the sum total of the others cannot be separated from it. For example, we might define the circle by the curve of the straight line which produces it, or by the equidistance of every point of the circumference from the centre, or by the section parallel to 1 66 § 6i. The Kinds of Definitmi. § 6i. The Kinds of Deünition. 167 the base of the right cone, or by the formulae of analytical geometry ready to our hand ; each of these attributes is so necessarily linked to the rest by mathematical laws, that the defined notion (of the circle) is the same in each. It is none the less undeniable, however, that only one definition fulfills the task of the definition in the fullest sense, viz. the definitio essentialis. Johannes Scotus (Erigena) said cor- rectly : ^ quamvis multae definitionum species quibusdam esse videantur, sola ac vere ipsa dicenda est definitio, quae a (Grraecis ovaLcoBrj?, a nostris vero essentialis vocari consuevit. — Sola ovauoBr)? id solum recipit ad definiendum, quod perfec- tionem naturae, quam definit, complet ac perficit. From the definitions given above several axioms may be derived about the relation which exists between the members of those different divisions. The substantial definition, at least when it stands alone by itself, is generally a nominal definition ; the genetic, unless where the pretended genesis is impossible, is always a real definition. The nominal definition seems to be related to the accidental, or to the distinctive explanation ; and the real definition to the essential. But it is by no means the case that every nominal definition is merely an accidental definition. A nominal definition may be an essential, and an essential a nominal. When, e.g. f^Volff defines truth to be the agreement of thought with the exist- ence which is thought, he himself correctly explains this defi- nition to be nominal, because it does not show the possibility of such a correspondence, and consequently does not warrant the real validity of the defined notion. Yet it is the essential definition of truth because it states its essence or fundamen- tally essential character. (If the essence were the ground of the thing, as some define it, every essential definition would at the same time be a genetic, and consequently also a real, definition ; but the essence is. only the ground of the other attributes of the thing, not the ground of the thing because it is not the ground of itself.) Every real definition is not at the same time an essential definition. It may also be an » De Divis. Nat. i. 43. accidental definition, and an accidental may be a real definition. (The possibility of the thing may be warranted in a more external way, perhaps, by reference to some genesis which does not follow from the essence itself: in this case we have a real definition which is not an essential definition.) The division of definitions into analytically- and synthetically-constructed definitions has no definite relation to the other divisions. The terms Nominal and Real Definition are not thoroughly expressive ; for every definition defines not the name, nor the thino-, but the notion, and with it the name and the thing so far as°this is possible. But so long as the real validity of the defined notion is not warranted, it is always possible that a notion may have been defined which is only apparently valid, and is in truth only a mere name or a feigned notion corresponding to nothing real. On the other hand, the dehni- tion of an objectively-valid notion serves at the same time to give a knowledge of the thing denoted by the notion. Con- sidered in this sense these terms justify themselves. Some logicians distinguish from the Real and Nommal Defi- nition a third kind, the Verbal Definition or explanation ot words, by which they mean the mere statement of the meaning of terms. This co-ordination of the so-called verbal definition with the other kinds is inadmissible. In the statement of the meaning of a word it is the object of the explanation, not the kind of explanation which is peculiar. The so-called verbal definition, if it be a definition at all, is either the Nominal or Real Definition of the notion of a word. Definitions formed synthetically are only admissible where science actually requires new notions. The intermixture of determinations, which are admitted into a synthetic definition of a notion according to the individual judgment, with the elements of the content of that notion, which, according to the universal use of language, bears the same name, has always been one of the most inexhaustible sources of errors and mis- takes Many of Spinoza's definitions serve as examples-his definition of Substance, for instance, of Love, &c. ; and not a few of Kant's, of knowledge ä priori for instance, and ot 1 68 § 6 1 . The Kmcis of Definition, the Idea, of Freedom ; the moral definitions of faith also, in their relation to its actual reference, which is also conformable to the use of language, to the acceptance as true of distinct propositions ; or, reciprocally, the definitions enunciated in this last sense, in their relation to another use of the word, in the sense of trust in God and Men, &c.^ (The terms syn- thetic and analytic definition^ introduced by Kant, are parti- cularly useful to point out the distinct kind of quaternio ter- minorum, which rests on the confusion mentioned above. On the other hand, one must remember that the distinction denoted does not so much concern the character of the definition itself as the kind of its origin in the subject. It is rather a psychological than a logical distinction.) Aristotle teaches : 6 optCpyi^^vos BsiKwaiv rj rl so-tiv rj ri arj/juai- rsc Tovi^ofia,^ He calls the latter kind of Definition \6y09 6vofjiaTcoBrj9,^ the former is called by Aristotelians opos irpay- fjLaTü)Bi]9 (reali?) or of;o9 ovai(o3j]9 (essentialis). We can also give a definition of notions which have no real validity, as, for example, rpayi\aos. But we can only know the essence or the tL sail of what is, and of which we know that it is. Hence, e.g. we cannot know the essence of Tpa'ysKa(f>os, tl 8' sotI jpa- 'yi\xL Acta Erudit. p. 540, 1684. ^ ^o^^ § 191, 3 Log. § 192. The older logicians distinguished after Boethius the definitio secundum substantiam, quae proprio definitio dicitur and the definitio secundum accidens, quae descriptio nominatur. Cf. Abelard, Dial.j in Cousin, Oeuvr. ine'd. d'Ab. § 493 ; Job. Scotus, as above. * Log. ed. by Jiisclie, § 106. 170 tfie'^Kinds of Definition. Kant,* and have partly ^ referred the distinction of nominal and real definition to that distinction which Wolif expressed by the terms accidental and essential definition.» This termi- nology is, however, not advisable, partly because the mean- ino" of the words used refers more to the distinction between the subjectively arbitrary, and objectively or really valid, determination of the notion, than to the non- essential and essen- tial attributes ; and partly and chiefly because it is foreign to prevailing use and wont in mathematics and other sciences/ Those mathematical definitions, e.g. which are brought forward by Euclid to prove the construction of required figures, whether they contain constitutively essential or secondary attri- butes, are to be called Nominal definitions; but definitions which contain only secondary determinations, as, e.g. that of the straight line, as the shortest distance between two points (since the essence of straightness is rather continuous direc- tion), although it may prove its objective validity, are to be called Accidental or Attributive Definitions, or Distinctive » Ilerbart, Lehrh. zur Einl. in die Pliilos. § 42, following WolfE and Aristotle, finds the characteristic attribute of the real definition in the validity of the notion. 2 Schleiermacher, Dial. § 266 ; and Drobisch, Log. 2nd ed. § 109. 3 In the 3rd ed. of his Logic, in §§ 115, 116, which correspond to §§ 109, 110 of the 2nd ed., Drobisch uses the expressions, * distinctive explanation ' and ' definition,' in the sense of accidental and essential definition ; and in § 120 introduces as tlie common use and meaning of the term real definition, which he means to disregard, that explanation by which the possibility, or more correctly the validity, of a notion is made clear. * Drobisch has himself followed the use which he exclaims against in the 2nd ed. of his Logic, in his Empirische Psychologie, e.g. at p. 292, Avhere he says of the prevailing explanations of the mental iaculties, * they are only explanations of names which do not warrant the reality of their objects.' A discrepancy between the terminology in Lof'ic and in the other sciences is always a misfortune ; and should be the less admissible because it may be avoided without innovations, by a simple reference to definitions given by Wolff aller Aristotle and Leibniz. §61. The Kinds of Definition. 171 Explanations. When the penal code distinguishes felony and misdemeanour, and defines felony as ' a crime punished by forfeiture either of the fee or of the goods and chattels of the criminal,' this is an Attributive Explanation (Distinctive Explanation) ; but when ' trial ' is defined to be the proving of the resolve to commit a felony or misdemeanour, by deeds which contain a beginning of the procedure in this felony or misdemeanour, this is an essential explanation. Both explana- tions are equivalent, so far as the distinction between Nominal and Real Definitions goes. [J. S, Mill Teduces all definitions to Nominal Definitions. No definition is intended to explain the nature of a thing. All definitions are of names, and of names only. In some definitions, however, it is cleariy apparent that nothing is intended save to explain the meaning of a word; while in others, besides explaining the meaning of the word, it is in- tended to be implied that there exists a thing corresponding to the word. There is a real distinction between definitions of names and what are erroneously called definitions of things; but it is, that the latter, along with the meaning of a name, covertly asserts a matter of fact. This covert assertion is not a definition, but a postulate. On this doctrine of definition ]\Ir. Mill bases his hypothetical theory of demonstration, since the certainty of the so-called necessary sciences depends on the correctness of the hypothesis which connects their defi- nitions with real things. Definitions, however, are not arbi- trary, and though of names must be grounded on a knowledge of the corresponding things.* In tliis theory of Definition Mr. Mill seems to contradict the doctrine enforced with so much vigour when treating of jiropositions in general, that propositions express not a relation between two names,, but between matters of fact. Had Mr. Mill only applied this same doctrine to that class of propositions called definitions, he would have hesitated ere he reduced all definitions to defi- nitions of names, and might have been led to a theory of demonstration more consistent with fact, than that which makes [' Cf. Logical. lGO-178, ii. 21G-220. 172 62. Tfie most notable him say that there may be any number of sciences as necessary as geometry if only suitable nominal definitions are combined with a few real axioms. Mansel gives a very good resume of Aristotle's views upon Definition. He does not recognise Definition so far as it has to do with material truth or correctness, or so far as it gives information about the meaning of words we were previously ignorant of. Logical definition has to do only with the sub- jective distinctness of a notion.* Sir Wm. Hamilton gives the common division of definitions, but, refusing to introduce them into pure Logic, relegates the discussion to applied Logic* Aug, De Morgan divides Definitions into nominal and real. Nominal definitions substitute for a name other terms. A real definition so explains a word that it suflSces to separate the thing contained under that word from all others. ^J § 62. The most noteworthy faults of Definitions are: — (1) Too great w;zö?^Ä ov narrowness (definitio latior, angustior suo definito). The definition is of gi^eater or less extent than what is defined, and the rule is broken that the definition be adequate (definitio adae- quata), or that the definition and what is defined be reciprocal notions. (2) Redundancy (definitio abundans). Along with the fundamentally essential determinations are given derivative ones, which belong only to the development of the notion. (3) Tautology (idem per idem). The definition ex- plicitly or implicitly repeats the notion to be defined. > Cf. his ed. of Aldrich's Log. 4th ed., Appendix, pp. 181-197 2 Led. ii. 22-36. ^ Cf. Formal Logic; or, the Calculus of Inference, p. 36, 1817.] Faults in Definition. 173 (4) The Circle or Dialellon (circulus sive orbis in definiendo). A is defined by b, and b again by a; or A is defined by b, b by c, c by d, and d or any following member is again defined by A. This com- monly happens in consequence of an OVre.ov Trpor.pov, ie of an attempt to define a notion, whose scientific presuppositions are not known, by means of those notions which already presuppose it. (5) Definition hy figurative expression, by mere nega- tions, by co-ordinate and subordinate notions. The neo-ative definition is legitimate with negative notions, and in simple notions their mere separation from their state of confusedness among other notions, and ex- planation by means of the statement of their extent, is scientifically correct. The following- definition of the infinitely little (which is to be found in a recent text-book on the Differential Calculus) is an example of too great width : -^ A quantity which we think as a fraction, with the numerator always remammg the same, but the denominator continually increasing, we call the infinitely little.' The definiens has here a wider extent than the definiendum, for the denominator steadily increases when it advances in the following way :-10, 15, 17i, 18f . . .and yet the fraction is not in this case infinitely little. The limi- tation is needed-the series of fractions must also be of such a kind that whatever number be given, one member of the series can always be found, which is smaller than its whole value, or stands nearer zero ; in other words, the series must have zero as its limit of value. Cato's definition of an orator is too narrow, — ' Orator est vir bonus dicendi peritus ;' for individuals can be thought of which belong to the extent of the definiendum, and do not belong to the extent of the definiens. K. H. Becker s definition is also too narrow,—' Thought is that act of the mtel- livatv fvxv^ Kivrjais* where the meaning of ' motion' wavers between feel- » In his Versuch über die Geßlhle, i. 39. ^ jbid. p. 243. 3 Ibid. p. 244. -» Diog. Laert. vii. 110 ; cf. Cic. Tusc. iv. G : aversa a recta ratione contra natui*aui animi commotio. 176 § 62. The most notable Faults in Definition. ing and desire, is more indirect, and therefore more injurious in Science. The same fault of indirect figurativeness injures Wundt's explanation—^ Sensation is the inference which the mind draws from a series of signs lying in the nerve-processes.' Under the figure of inference the difficulty is concealed, whether and how a sensation can be the result of motions, and what kind of connection does actually exist. Euclid's definition—^ Parallel lines are straight lines in the same plane, which, produced infinitely, will never meet '—cha- racterises parallel lines by a determination merely negative, and only derivative, \iot fundamentally essential It leads to confusion, which does not occur in definitions formed upon the notion of direction (cf. § 1 10). The definition~7r5/9fcTToi/ {kaTi) TO ^lov(lhl fisi^op apriov — may be taken, with Aristotle, as an example of a faulty definition formed by means of co-ordinate notions. In formal reference it is alwa^-s more correct to define co- ordinate notions by means of the genus-notion and their specific differences. For example, the even number is a num- ber which is divisible by 2 without remainder; the odd is a number which, divided by 2, has a remainder of 1. It would, however, amount to a formal rigorism, if one were wholly to despise the shortness and comprehensiveness which can be reached, in many cases, by reference to a foregoing definition of a co-ordinate notion ; for example, after the definition of the even number has been granted, not to allow the definition,— the odd number is that which is distinguished from the even by unity. The enumeration of the members of the extent of a notion (e.g. the conic section is that mathematical figure which divides into these four forms— circle, ellipse, parabola, hyperbola) is useful to illustrate this notion, if it goes before or comes after definition. When it stands in the place of the latter, it be- comes the faulty definitio per divisionem or per disjuncta. Since simple notions, as has been already remarked (§ 60), admit of no proper definition, but can be brought into con- sciousness and distinctly distinguished from other notions only §63. Division. The Ground of Division, etc. 177 by abstraction and isolation, the highest scientific strictness possible in this case is reached by the form of the accidental definition. For example, the notion of the point is to be de- fined by a progressive series of limitations, which find scientific expression in the following accidental definitions — Space is what remains over from the sum total of sense-intuition, after the abstraction of matter (i.e. of what is unchanged in motion) ; ma- thematical body is a finite part of infinite space, or a limited space ; surface is the limit of body, the line of surface, and the point of the line. After that the simplest element has been reached in this way, the other constructions can be genetically reconstructed from them, and defined by the explanation of the essence. § 63. Division (divisio, hioLlpsa-ig) is the complete and orderly statement of the parts of the extent of a notion, or the separation of the genus into its species. The species-notions are distinguished from the genus- notions by this, that the more indistinct features of the genus-notion, by the addition of the specific differences, have actually taken the different forms or modifications of which they are capable. Hence, in the division of the genus-notion, the formation and arrangement of the species-notions must be founded on these modifications of the characteristics of the genus. Accordingly diflferent divisions are produced^ in any genus-notion, which unites in itself several characteristics able to be modified, when the species are distinguished according to the differentiations of the one or the other. That attribute of the genus, on whose modifications the formation and arrangement of the notions of species is based, is called the ground of division or principle of DIVISION (fundamentum sive principium divisionis) ; the N <>- f \^ 178 §63. Division, The Ground of Division, etc. species-notions themselves, the Members of Division (membra divisionis, less strictly membra dividentia). Division is Dichotomy, Trichotomy, Tetrachotomy, Poly- tomy, according to the number of the members in division. The formal postulates of Division are: — that the spheres of the members of division, taken together, exactly correspond to the sphere of the notion to be divided, and therefore fill it without hiatus ; — that they in no way overpass it ; and, — that they do not cross but completely exclude each other. In the arrangement of the members of division, those which are the most closely related to each other should be placed together. Division determined by the modifi- cations of a single attribute is called artificial division. It has scientific value in the proportion in which the presupposition is true, that by means of some causal connection the modifications of this attribute are linked to the corresponding modifications of the whole essential attributes. The most perfect Division founds itself on the essential modifications of the essentially constitutive attributes. It depends on the essential definition of the notion to be divided. It is called Natural Division in the same sense as the system which results from a continuous series of such divisions is to be called a natural system. Divisions of this kind cannot be formed in any way according to an external uniform scheme. It is incorrect to look for an equal number of members of division in all cases in divisions of this kind so far as they correspond to the ideal demand. A strict Dichotomy may always be attained by means of a nega- tive species-notion ; but then it labours under the Dichoto7ny^ Trichotomy, etc. 179 defect that the species classed under the negation are left indefinite. When there are several of them the dichotomy will show itself to be illusive, as soon a» they come to be specified according to their positive attributes. Such a division therefore can only serve as an introduc- tion in the formation and testing of divisions. Tri- chotomy usually finds application where a development occurs which is independent and rests on internal causes; because such a development is accomplished in the form of an opposition of two members and their fusion in a third. Mere trichotomy, however, not unfrequently falls short of the domain of actual existence ; for actual existence in its higher grades does not usually advance in simple series. The higher unity to be brought about often results from a great number of cross oppositions. By the natural method of division Cuvier means (Kegner animal. Introduction), ' An arrangement in which existences of the same kind will rather be neighbours of each other than of those of other kinds, kinds of the same order of each other than of those of other orders— and so on.' Cuvier explains this to be the ideal which natural history must aim after ; for it is * the exact and complete expression of the whole of nature.' Cf. § 58. The doctrine of Divisions, whose scientific value Plato had already recognised, formed with Aristotle an integral part of Analytic. Plato preferred Dichotomy. Every opposition has two members.^ The parts must be species (elBt)), i.e. formed according to essential difFerences,^ — Kar apdpd^ y irscpvKsv — els h Kul STTL iroWa Trgc^u/coVa opap.^ In his later period Plato was fond of adding to the two members of the opposition, as a third, TO if dfJL(t)oiv fiifcrov. He did not, however, recognise in »? I » Prot p. 332. ' PJiaedritSj 205. N 2 3 Cf. Poh't 262 sqq. i8o S 6^ Division, The Ground of Division, etc. Dichotomy, Trichotomy, etc. i8i this third member (as Hegel does) the highest but intermediate element.^ In the dialogue Sophistes^ dichotomy is traced back to the general point of view of ravrov and hspov,^ Tetracho- tomy results from the combination of two grounds of division. Aristotle treats of the doctrine of the grounds of division in Top. vi. 6, and De Part. Anim. i. 3, where he more especially notices the passing from one ground of division to another. He explains^ the advantages and disadvantages of dichotomy formed by negation. We do not find that he had the modern preference for a distinct number of positive members of divi- sion ; this is, for the most part, a consequence from the Kantian doctrine of the Categories. Kant believes that he can, according to his table of categories, which contains com- pletely and systematically all the elementary notions of the understanding, determine a priori every moment of every speculative science and their arrangement.^ Hence the scheme of the categories has served him, and still more his disciples, as a leading principle in the treatment and division of the varied scientific material. Goethe himself was once induced by Schiller to attempt the thankless task of dividing his doctrine of colours according to the Kantian Categories. One of the 'singular reflections' which Kant attached to his table of categories has proved very rich in consequences. He says that every other a priori division of notions must be a dichotomy (a is partly b, partly not b); but a trinity of Categories appears in every class, and in each case the third arises from the union of the first and second. This remark of Kant's has led to that scheme of thesis, antithesis, and synthesis, which, on all points, conditions the methodical course in Fichte' s con- structions, and still more in the Hegelian dialectic. These trichotomies are not purely arbitrary, but rest on a true insight into the essence of development. Yet they cannot be recog- » Sec Phileh. 23 ; Tim. 35 A ; cf. the author's article in the Rlmn, Mus. für Philologie, N. S. part ix. p. 64 ff., 1853. 2 P. 253. 3 Cf. Polit. 287. 4 Anal. Post. ii. 13 ; J)e Part. Anim. i. 2, 3. Ö Krit. der r. Vern. § 11. nised to be the only valid, and everywhere predominating, form of division ; not merely because now and then the phenomena of nature fall behind the notion, as Hegel says, and because dialectic thought is not yet thoroughly the lord of things ; but because the simple uniformity of trichotomy of itself is not enough to represent the fulness of the phenomena of natural and mental life. In many cases this fulness corresponds more to the intertwined double method of Schleier machers te- trachotomy, which starts from two cross dichotomies. Schleier- macher endeavours to prove the unity which is above the double opposition. (For example, he divides the sciences into the speculative and empirical knowledge of reason, and the speculative and empirical knowledge of naturc, or into ethics, science of history, physics, and natural science, according to the oppositions of reason and nature, force and phenomenon, and finds in Dialectic, which starts from their common principles, the vital point of unity.) But this fourfold or fivefold com- bination cannot be suitably applied to every matter, any more than the ninefold division of George^ which combines the prin- ciples of Hegel's and Schleiermacher's methods of division, or other schemes published by others. The only general rule which can be established is, — every natural division must be conformable to its objects.' The doctrine of Division owes to Herhart the remark, that, as the division of a notion depends upon the division of an attribute, which forms the ground of division, all divisions in the last resort return necessarily to certain fundamental divi- sions, in which only a single attribute of the notion to be divided is the ground of division ; but this notion is itself the ground of division, and the series of species or individuals must therefore be given immediately. For example, the series of colours, sounds, numbers, &c.^ * Cf. Trendelenburg, Log. Unters. 2nd ed. ii. 233 ; 3rd ed. ii. 256 ; cf. Johan. Scotus (Erigena) in Prantl, ii. 32, and PJato, Phaedr. p. 265. ^ See Herbart, Lehrbuch zur Einleitung in die Phil. § 43 ; cf. Dro- bisch, Logik, 3rd ed. § 123. I l82 64. Subdivision and Co-ordinate Division. § 65. The most notable Faults in Division. 183 § 64 When the single members of division are agam divided into tlieir subspecies, Subdivision results. When one and the same notion is divided according to two principles, Co-division arises. The same ground of divi- sion, on which a co-division of the genus-notion rests, can generally serve as a ground of division for the sub- division or partition of species into subspecies, under the limitations which result from the mutual relations of the dependence of the attributes.' Progressive divi- sion must proceed continuously by species and sub- species without hiatus (divisio fiat in membra proxima) It contradicts the laws of complete formal strictness if the subdivisions into which a co-ordinate species may be divided are placed directly beside the species, so that the subspecies may come in instead of whole species. It is a licence sometimes convenient however, m cases where the limit between the different ranks of species and subspecies is indistinct, and by no means to be rejected unconditionally, especially in a widely ramified division of a very comprehensive material. Only do not let the possibility of survey be lost, nor the divi- sion, in this reference, fail in its design. For example, it would be an unjustifiable rigorism not to admit the division of natural objects into Minerah, Plants ami Animals (instead of, I. Inorganic objects or minerals; U. Ui- ganic objects: a. Plants; b. Animals); more especially be- cause if the capacity of consciousness be the ground of the principal division, minerals and plants may be taken together as subspecies under the chief species-inanimate objects ol nature, and animals alone make up the second chief spec.es In the case of simple co-ordination the gradual sequence ot ' Cf. §§ 50, 54. internal value appears as a ground of division. When Epi- curus divides the desires in their ethical reference into three classes,— naturales et necessariae, naturales et non necessariae, nee naturales nee necessariae— the gradation in the proportion of its correctness forms the ground of division which may justify this kind of co-ordination. In any case the fault of superfluity is not justifiable which Cicero^ expresses against this division when he says, ' hoc est non dlvidere, sed frangere rem ; — contemnit disserendi elegantiam, confuse loquitur.' Cicero reproaches Epicurus with counting the species as a genus in this division (' vitiosum est enim in dividend© partem in o-enere numerare '), and on his side only admits the divi- sion— I. Naturales: a. Necessariae; b. Non necessariae ; If. Inanes. In this last division the naturales necessariae and the naturales non necessariae are only species, and the inanes, on the other hand, a genus. But this is not the case from the Epicurean point of view, which really makes the three classes co-ordinate with each other. Division can only descend to such groups as are not essen- tially separated from each other. Subdivisions are not formed for the sake of very small differences. Seneca warns against the extravagances which the usages of rhetorical arran<^ement seem to have introduced into the rhetorical schools of the ancients, in the words-' quidquid in mams crevit, facilius agnoscitur, si discessit In partes; quas vero innumerablles esse et minimas non oportet ; idem emm vita habet nimia, quod nulla divisio ; simile confuso est, quidquid usque in pulverem sectum est.'» Quintilian says the same of partitio : ' quum fecere mille particulas, in eandem mcidunt obscurltatem, contra quam partitio inventa est.' § 65. The most Important defects, in divisions are: — (1) loo ^esXwidthov narrowness. (The latter occurs chiefly by overlooking transition-forms.) ' De Fin. ii. c. ix. 2 Ei)ist. Ixxxix. Cv-. 184 § 65. The most notable Fatdts in Division. 66. Connection between Notions, etc, 185 (2) The placing side by side species-notions, which do not purely exclude each other, whose spheres fall wholly or partly within each other. (3) The confusion of different principles of division, (This fault is often connected with the others.) The defects in Division are nearly allied to those in Defi- nition (§ 62). In too great tcidth the spheres of the members of division, taken together, exceed the sphere of the notion to be divided (membra dividentia excedunt divisum ; divisio latior est suo diviso). The Stoical division of passions {iräBri) into four chief forms— laetitia, libido, aegritudo, and metus— is too wide, if, according to the definition recognised in that school, nrdOos is taken to mean opiirj -rrXsovd^ovcra.^ The member of division goes beyond the sphere of (positive and negative) desire, and embraces the feelings also. Divisions of men into good and evil, of systems into true and false, of actions into voluntary or not voluntary, or of temperaments into the four well-known fundamental forms, are too narrate, because they disregard the endless number of transition forms. The division of natural objects into simple and compound overlook the third possibility of organic unity, in which we can as little speak of a combination, which pre- supposes an original separation and an external conjunction, as we can of simple punctual unity. The same fault occurs often in disjunctions which are divisions of possibilities. A modern division of affections into self-love, affection for others, and mutual affection, may serve as an example of faulty division whose spheres do not thoroughly exclude each other. Mutual affections are those affections for others which are returned. They are a subdivision of the second, not a new third kind. A confusion of different principles of division exists in the division of the tenses of the verb into principal and historical tenses, used more especially in Greek grammar. The motive ' Appetitus veliementior, Cic. Tusc. iv. 6. for this illogical division lay, undoubtedly, in the well-founded dislike to call the historical tenses merely secondary tenses, which would have been actually false, and in the dislike, also well-grounded, to denote the one class, by a merely ne- gative designation, the non-historical tenses. The tendency, arising from a false love of system, to place on either side an equarnumber of classes of tenses, was unjustifiable. It should rather have been recognised that the one group of rules hold good for one class of tenses, for the historical, namely ; and the other group in an essentially similar way for two classes of tenses, viz. for the present and future tenses. These two classes', however, were not to be opposed to the historical under une positive notion, but were to be named in connection with each other. § 66. The formation of valid notions and of adequate definitions and divisions can only attain to scientific perfection in connection with all the other processes of knowledge. For the formation of general conceptions there is needed the combination of particular conceptions only, not of judgments, inferences, &c. the combination of the elements of the content of the conception does not need to be produced by judo-ments which include them ; it is already originally con- tained in the perceptions and intuitions. Nor does the separa- tion of the content need negative judgments. It results by means of the processes of attention and abstraction, which in no way presuppose the forms of the judgment. Those who mean by notion only a general conception, or a conception with an objective reference, are not correct if they make the struc- ture of the notion depend on a previous structure of judg- ments. The formation of the notion, however, in its fuller sense (as a knowledge of the essence) depends upon the for- mation of judgments. In order to decide what makes an essenUul, or what makes up the universal and lasting basis for the most, and the most important, attributes, one must as- certain on what conception the most universal, most exception- 1 86 66. Connection between Notions, etc. \ 67. The Definition of the Judgment. 187 less, and most scientific judgments are based. For example, the completion of grammatical notions depends upon an in- vestigation, requiring ever to be renewed, whether a consistent system of universal rules can rest upon the notions we already have. The dependence is reciprocal, however. The scien- tific judgment also presupposes the scientific notion. For example, it is impossible to reach a system of grammatical rules in any way satisfactory if a happy tact in forming gram- matical notions had not already prepared the way. The history of Grammar shows a gradual mutual development of notion and rule. In this sense Schleiermacher ' says rightly — the judgment presupposes the notion according to its essential existence, and the notion the judgment. The notion which, according to the measure of its form, agrees with the object, must have before it a whole system of judgments. The formation of the notion stands in like reciprocal relation to the syllogistic and inductive formation of inferences, to knowledge of principles, and to the formation of complete systems. Notions like Entelechies, Monads, Stages-ofdevelop- ment, Stages-of -culture, Differential and Integral, Gravitation, Chemical Affinity, and the like, presuppose whole scientific systems. They again, on their side, condition the develop- ment of the systems. We may say ^ — the notion must be the starting-point, and also the end and aim of all thinking, provided that it is not explained with a one-sided exaggera- tion, and with unjust disregard of the other function, and of their loo-ical analysis, to be ' the single product of the mind.' Any one function, in the degree of its own development, furthers the development of other functions, and is furthered by them. In science at least the mutual advancement of every member is no empty delusion. But the doctrine of the Notion as the simpler form must precede the doctrines of Judgments, Inferences, and Systems, without detriment to a real reciprocal relation, and must now be brought relatively to a close. » Dial. pp. 82, 83, 402. 2 With J. Hoppe, Die gesammte Logik, p. 20, Pudcrborii, 1868. PART FOURTH. THE JUDGMEST IN ITS KEFERENCE TO THE OBJECTIVE FUNDAMENTAL COMBINATIONS OR RELATIONS. S 67. The Judgment (iudicium, axo4;avo-is, as a part of the inference it is called propositio or xpoVao-zf) is the consciousness of the objective validity of a subjective union of conceptions, whose forms are different from, but belong to each other. It is the consciousness, whether or°not the analogous combination exists between the corresponding objective elements. As the individual conception corresponds to the individual existence, so the judgment in its various forms corresponds to and is the subjective copy of the various objective relations. A judgment expressed in words is an Assertion or Pro- position (enunciatio, äTo4>av(r«s). In the formation of judgments we advance from single con- ceptions and their elements to the combination of several. The progress here (as it is also in the combination of judg- ments and inferences) is synthetic, while the progress made from perception to the formation of individual conceptions and notions was analytic. The judgment is the first whole .vhich has been again reached by synthesis. Logical theory, how- ever, must not begin (as some logicians say) by attention to this (derivative) whole, but must first attend to the imme- diately given (primitive) whole, i.e. to the perception. t I f m 1 88 § 67. The Definition of the Judgment, Neither single notions (absolute or relative), nor mere com- binations of notions, are judgments. Conviction conceiving the happening or not happening of what is thought, is Judg- ment. The Judgment is distinguished from the merely sub- jective combination of conceptions by a conscious reference to what actually exists, or, at least, to the objective phenomena. The reference of thought to actual existence gives the judg- ment its character of a logical function. Where the conscious- ness of the objective validity is wanting there is no judgment ; where it is erroneous the judgment \^ false. The formation of a combination of conceptions, and of the consciousness of its validity, can be contemporaneous ; but the combination of conceptions (e.g. of the conception of this criminal with the conception of the deed laid to his charge, and of his unlawful intention, which makes him guilty) may be ac- companied for a time by the consciousness of the uncertainty of its objective validity, until sufficient grounds of decision present themselves, which lead to the consciousness of its correspondence or non-correspondence with objective reality, i.e. to the (affirmative or negative) judgment. In mathematical judgments the reference to objectivity is never wanting. Our conception of space corresponds to objective existence in space, and the geometric judgment is the consciousness of the accordance of a (subjective) assertion with an (objective) relation of a construction in space. The true axiom in actual construction, whether this is realised in us or in nature, must prove itself to be objectively valid, in each case, in proportion as it is the more exactly constructed. The notion of a number, also, although number does not exist without our consciousness, has its basis on objective reality, viz. on the quantity of the objects, and on the existence of genus and species, which compel the subsumption of many objects under one notion. The true arithmetical axiom must accord with the objective relation of quantity, that when the presupposition (hypothesis) is realised the assertion (thesis) is realised also. If I take 30/. from 100/., and then add 20/., 90/. must remain in the cash-box ; for in the abstract the §67. The Definition of the ftidgment, 189 equation is 100 — 30 + 20 = 90 ; and the validity of the equa- tion is its applicability to all numerical objects possible. Numbers can be detached by abstraction from this reference, and can be raised to be themselves objects of thought, but in this way they attain only a relative independence. The assertion made [by Hamilton, Mansel, and others] that thouo"ht is to be called /o?'ma/ only in so far as it can be con- sidered from the side of its form, without reference to the matter, is not correct. It is not the thinking, which is considered from the side of its form, that is formal, but the logical treatment which has to do with the form of the thinking, just as it is not language grammatically considered, but its grammatical con- sideration that is formal. Thinking in Logic itself is some- thing formal, i.e. it is thinking which has to do with the form of thinking. Thinking considered and legislated for by Logic, is logical thinking when it is logically correct or in accordance with the logical laws. It is not a special kind of thinking co- ordinate with other kinds. Every operation of thought is loo-ically or formally correct when it corresponds with the locrical laws. Now, in so far as the logical postulate, Avhicli has to do with the judgment, is concerned — that it may be true — formal correctness and material truth coincide in the individual judgment. The former can also be limited to the mere correctness of the structure (of the conjunction of sub- ject and predicate) ; but it is a proceeding of very little value to do so, and to say, for example, that the materially false proposition, ' all trees have leaves,' is formally correct. So far as the derivation of a judgment from data (which are pos- sibly false) corresponds to the logical laws which are valid for it, this derivation is formally correct ; and the derived judg- ment has then been derived with formal correctness, though it may not be materially true. The logical correctness of the sum total of all the operations of external and internal percep- tion aiming at knowledge, though not identical with the material truth (which is the result aimed at by it), is necessarily con- nected with the material truth (whether in the fullest or in a limited sense of the word). Logic, as such, cannot decide upon \ \ 1 iQO § 67. The Definition of the Judgment. the truth of a judgment, because it only enunciates rules, and does not itself carry out their application. Its problem is legislative only. Logic, as such, has ' no exception to take ' against the judgment, ' all trees have leaves.' But it is a mistake when this is understood to mean,' that the proposition is recognised to be ' a judgment logically correct according to form.' Logic takes no exception to it, because it has not to do with this judgment any more than with any other. The application of the logical postulate, that it must have a subject and predicate, is to be put into execution by means of a merely logical knowledge, but the logical postulate, that it must be true, by means of knowledge of natural science, which.forces the falsehood to appear. ' Formal correctness ' is limited to ' free- dom from contradiction ' only when the logical rules aim solely at this absence of contradiction. ^ But even in this case Logic, as the legislative science, would not decide upon the correct- ness (in this sense not at all involving the material truth) of any one given judgment, nor expose the single contradictions, but would only enunciate the rules for this judicial function. As the forms of conception weire originally recognised in and by kinds of words, so judgments are in and by proposi- tions. Plato explains the \670s to be the revelation of thought (hidvoui) by the voice ((/jwi//)) by means of ptjfjuaTa and opofxara; for thought is, as it were, coined into the sounds which stream from the mouth.' In the Dialogue Sophistes (more probably 1 By Dr. Cal, in his Lehrb. der propäcl. Log.:, § 8, Vienna, 1865 [and Mansel, in his Proleg. Log. p. 258 ; Rudimenta, 4th ed. pref. 69]. Against these statements, cf. J. Hoppe, Die gesammte Logik, § 29, Paderborn, 1868. Hoppe believes thinking to be the function of translating the objective reality into subjective conceptions. His o^vn opposition between 'notional' and 'formal' thinking is defective. Thinkinf^, in Logic, is both ' formal ' because it considers the forms of thoiifrht, and ' notional ' because it attains to notions about them. « Cf § 3. ' 3 Theaet. p. 206 D : to ttiv uvtov diavoiay Ifiipaifj woiely ^la (ptovfiQ uera prjfiartjy re icai oi'o/iarwv, üauep tic Karoirrpov f/ vlu)p rnv ^o^av Itn-vTTuvfjisi'ov elg rqv ^la. tuv arofjiaTOQ poiiv. Shorter and less strictly, p. 202 B : ovopaTtjjy yap ^v^iTrXoK^v tlyai Xoyov ovaiay. § 67. The Defi?iition of the J'tidgment, 191 the work of an early Platonist than of Plato ^) the proposition (\6yos), which is the verbal expression of the thought {Sidvoia) ^ in its simplest fundamental form (e.g. avOpoiiros ^avhdvsi), explains the combination of substantive and verb as that which corresponds to the combination of thing and action (^^vfiTrXoKT) or ^vvdeais ex re prjfiaTcov ryiyvofjisyTj /cal ovopaTcop, — ^vPTvOsvaL irpayfjua irpd^si Sc' opoparos koI prfparos), Aristotle ^ defines the Judgment (aTr6(f>apais or \6yos äiro- apTiK6s) to be a combination cf conceptions in w^hich there is truth or falsehood {avfOeais vorjp^drwp, ip y to dXTjdsvsip rj yfrevBeadaL vTrdp'^si), or, with reference to the verbal expression, as an assertion about existence or non-existence : * sarip rj aTrXrj dTT6(f>ai(n9 (Jxopt) arfpuPTiKT) irepl tov virdp^UP rf firj vTrdpxsLv. Aristotle,* agreeing with Plato, makes the opopia Koi prjfjua the elements of the simple judgment. In accordance with the Platonic and Aristotelian defini- tions, Wolff defines a judgment as ^ ' actus iste mentis, quo aliquid a re quadam diversum eidem tribuimus vel ab ea removemus, indicium appellatur.' The judgment is formed by means of the union or separation of conceptions.^ The proposition or assertion (enunciatio sive propositio) is the combination of words, corresponding to the conceptions, which are the elements of the judgment denoting the union and separation of the conceptions and what belongs or does not belong to the thing. ^ Wolff, accordingly, demands, as Plato and Aristotle had done, three series parallel to each other — the combination in things is to correspond with the union of conceptions, and this last with the expression. Several logicians after Wolff, in order to get rid of the dis- junction, * combination or separation,' in the definition of the » Theaet. p. 262 e ; 263 d, e. ^ Soph. 263, E. A not very happy abbreviation of Plpto's defini- tions in the Theaet. : to airo ttjq ^laroiag ptvpa ^la tov (TTOfjiaTog toy paTa it)ir}g yiyvoptyog. 3 De Interp. c. iv. '* Ibid. c. v. * Ibid. c. v. x. « Log. § 39. 7 Ibid. § 40. « Ibid. § 41. m 'I ¥> T92 ^67. Tlie Defi7iition of the Judgment \ 67. The Definition of the Judgment, t93 judgment, use the expression, The judgment is the conception of a relation between two notions. Kant defines the judgment ^ to be the conception of the unity of the consciousness of different conceptions, or the conception of their relation so far as they make up one notion, or, more definitely ,2 the way to bring given cognitions to the objective unity of the apperception. By objective unity Kant understands the mutual connection of cognitions according to those categories which the Ego evolves from itself by the orio-inal activity of its own spontaneity, and by which, as ä priori forms of thought, the Ego fashions the whole content of perception. Objectivity in this sense evidently does not denote a reference to a real external world, but only to a kind of activity of the ego. Hence this doctrine of judgments, in spite of the expression of objectivity which it contains, re- veals throup-hout the subjective character of the Kantian philosophy. The view which regards the judgment as merely a process of subsuming the special under the universal is very prevalent among logicians influenced by Kant. In this sense Fries teaches,' the judgment is the knowledge of an object by notions, since the notion is added to the object as a cha- racteristic, and the object is thereby rendered able to be un- derstood. Herhart* believes the judgment to be the deciding upon the capability of uniting given notions. Hegel ^ understands by the judgment, the determination given to the notion by itself, or the notion making itself par- ticular, or the original self-division of the notion into its moments, with distinguishing reference of the individual to the universal and the subsumption of the former under the latter, not as a mere operation of subjective thought, but as a univer- sal form of all things. Here again, as in the notion, refer- ence to reality is taken to be identity with reality. Hegel dis- tino-uishes judgments from propositions which do not refer I j^og. § 17. ^ Kritik der r. Vern. § 19. 3 Syst. der Logik, § 28. * Lehrbuch zur Einl. in die Phil. § 52. « Logik, ii. 65 ff. ; Encf/cf. § 166 ff. the subject to a universal predicate, but only express a circumstance, a single action, &c. But in fact every (asser- tory) proposition must express a logical judgment. Beneke ^ distinguishes the logical judgment, as the analytic act of the subsumption of the particular under the universal, from the synthetic bases of the judgment or the combinations of conceptions by which knowledge is advanced, which are accompanied by those analyses. In common life we generally have to do with the syntheses only, which precede the judg- ment proper; the logical element is the analytic subsump- tion of the less general subject-notion (or subject-conception) under the more general predicate notion. For examjJe, in the judgment, A is a coward, the combination of the notion of A with the notion of his deeds is the basis of the judgment ; its subsumption under the notion of cowardice is the judgment proper. Ulrici in a similar way teaches that the judgment in the logical sense is the subsumption of the particular under the general,^ and distinguishes from it the grammatical proposition as the mere expression of a perception or a remark.' But the reference to objectivity is, however, essential to every judg- ment. It is true or false, according to this reference, but not according to a merely subjective subsumption. How the view of the subsumption can be united with this, cf. 68. Schleiermacher explains the judgment tu be that product of the intellectual function or of the thinking reason, which corresponds to the community of existence or the system of the reciprocal influences of things, i.e. of their co-existence, their actions and passions. Subject and predicate are related as noun and verb. The one corresponds to the permanent existence or to an existence contained in itself; the other expresses a circumstance, deed, or suffering — an existence contained in another. The notion of the predicate is con- tained in the subject only in judgments improperly so called. The judgment proper proceeds upon a fact, and asserts some- thing which is contained only potentially in the notion of the ^ System der Log. i. 156 ff., ^60 ff. 2 Log. p. 482 ff. ' Ibid. p. 487. 11 i I ■ V.I t: I fl 'I m 194 § ^7- The Definition of the Judgment, ■11- subject. The primitive judgment asserts mere action ; the incomplete mere reference to the acting subject ; the complete a reference also to the object of the action under considera- tion. ^ Schleiermacher's definition makes justly prominent the relation of the subjective element to the objectively real. It is defective in this only that it keeps in view too exclusively the predicative and the objective relation. The definition of judgment, without being vague, i.e. without effacing the limits between the judgment and other forms, must be wide enough to embrace all the forms of judgment. The same may be said of the opinions of Trendelenburg and Lotze, Trendelenburg'^ recognises the judgment to be the logical form, to which action corresponds as the analogous form of existence. In the incomplete judgment the action alone is originally considered. In the complete judgment, however, the subject represents the substance, and the predicate the action or the property which carries the fundamental notion of the action. Lotze^ also gives in the same way a too narrow explanation of the judgment, when he calls it a conjunction of conceptions, whose material is worked up in the logical forms, which cor- respond to the metaphysical presuppositions concerning Sub- stance, Accident, and Inherence. [J. S, Mill asserts that a proposition is not the mere ex- pression of a relation between two ideas, nor of a relation between the meanings of two names, nor the referring or excludino" something from a class. It is the assertion of a matter of fact that the set of attributes connoted by the predi- cate constantlg accompany the set of attributes connoted by the subject. But as sets of attributes may be classed under heads, the proposition really asserts or denies a sequence, a co-existence, a simple existence, a causation, or a resemblance. Propositions whose terms are abstract are no exception. The abstract terms stand for attributes which really exist, 1 Dial p. 304 ff. 2 Log. Untersuch, ii. 208, 2nd ed. ; 231, 3rd. ed. ^ x^^, p. 36. § 68. Simple and Complex yudgments, etc. 195 and the real ground of the proposition is that when the real states connoted by the subject are found, they are always accompanied by the real states connoted by the predicate. Co-existence and immediate succession, not subsistence and inherence, are, according to Mr. Mill, the real analogues of the relation of the subject and predicate in the judgment.* Boole^ divides propositions into primary and secondary. The primary express relations among things, the secondary among propositions. The former are also called ' concrete,' — The sun shines; and the latter ' abstract,' — It is true that the sun shines. The difference between the two kinds is one of interpretation, not form, and therefore they require different methods of expression.] § 68. Judgments are both simple and complex. In simple judgm,enfs the following relations are to be dis- tinguished : — (1) The predicative^ or the relation of subject and predicate, i.e. the subjective representation of the real relation of Subsistence and Inherence. It comprehends under it the following : — (a) The relation of the thing to the action or to the passion. - (b) The relation of the thing to the property, which is, as it w^ere, an action become per- manent (with this must be reckoned the rda- tlon of the thing to the sum total of those attributes which make the content of the super- ordinate notion), (c) The relation of the action or property (thought as subject) to its nearer detennination. [» Cf. Logic, i. 96-118, especially pp. 107-110, 115-118. 2 Laws of Thought, 1854 ed., p. 32 ff.] o 2 96 § 68. Simple and Complex Judgments, etc. Categories of Relation in the Kantian Sense, 197 In the so-called judgments without subjects (which are expressed by sentences with 'impersonal' verbs) the sum total of the existence surrounding us, thought of indefinitely, or an indefinite part of it, takes the place of the subject. In the substantial judgments the being conceived as inhering, or the existence, takes the place of the predicate. ' (The verhol designation of the predicative relation is the grammatical congruence between the subject and predicate in the inflection of noun and verb, In the case^ (a) the grammatical subject is a substantivum concretum and the predicate a verb; (b) the subject is again a substantivum concretum, and the predicate either an adjective or a substantive, with the auxiliary verb to he ; (c) the subject is a substantivum abstractui?i, and the predicate is either a verb, adjective, or substan- tive, with the auxiliary verb. The copula in every case hes in the form of inflection. The auxiliary verb to be belongs to the predicate, and is not, as usually but erroneously happens, to be considered as itself the grammatical copula. The grammatical agreement of its inflection with the inflection of the subject, by means of which the forms is, are, &c. come from the infinitive to he, is the copula, or the expression of the relation of inherence between the predicate and subject.) (2) The object-relation of the predicate to its object, i.e. the representation of the real relation of the action to the objects towards which it is directed. The change of reference to others is contained immediately in the essence of the action as the proper change of the sub- ject. (Here also the real relation is expressed in the logical, and the logical in the grammatical.) The object t\the,v completes or makes more determinate. The object which completes the predicate corresponds to the imme- diate object of the action, the object which makes more determinate or is adverbial corresponds to an object which stands in some mediate relation to the action. These relations are those of space, time, modality, causality, conditional and concessive, instrumental, con- secutive, and final. (The oblique cases are the verbal expression of the various fundamental forms of the object- relation. The accusative, as it appears, originally denoted distance, and so the whither or aim of the action ; the genitive, the whence, and the wherefrom, or the starting-point of the action ; and the dative, the where, wherein, and whereby, or the place, determination, and means of an action. The causal relation was thus originally con- fused with the local, just as in the formation of indi- vidual conceptions, notions, &c., and in all logical operations generally, the elements which arise from internal perception are confused with the time- and space-form. Some other cases, and prepositions joining themselves to the cases, serve to denote the manifold modifications of those fundamental forms.) (3) The attributive relation. It is a repetition of the predicate, and mediately also often a repetition of the object-relation as a mere member of a judgment whose predicate is another member. (The grammatical agreement in the inflection of nouns and verbs is the verbal expression of this relation. When the object-relation is added, the use of cases and preposi- \vM iq8 § 68. Simple and Complex judgments, etc, tions must be combined with this agreement. Some- times the cases and prepositions alone (e.g. the Gene- tivus possessivus) serve to express the relation; for the participial determination added in thought — arising, being, &c. — is not to be expressed.) The multiple or complex ]\xAg\nQni arises from simple judgments (as complex propositions from simple pro- positions), which are co-ordinate or subordinate to each other. Co-ordination belongs both to complete judgments (and propositions) and to simple parts of a judgment (and proposition). It may be copulative, divisive, and disjunctive, comparative, adversative, and restrictive, concessive, causal, and conclusive. Subordination rests on this, that a judgment (and proposition) is joined to another judgment (or proposition) either as a whole or with one of its parts. The subordinate judgment is : (a) according as it enters into its superordinate, either as a whole or with only one of its elements, either an infinitive or relative judgment (and accordingly its verbal expression, the subordinate proposition, is either an infinitive or relative proposition ; the 'conjunctional proposition' is logically classed with the former, and the ' pronominal proposition' with the latter) ; (b) ac- cording to the place which it or the part of it entering into the whole judgment (proposition) takes, it is a judgment (or proposition) either subjective, predicative, attributive, objectively completing or objectively deter- mining. The objectively determining or adverbial judgments (and propositions) divide again into local, temporal, comparative, causal, conditional (or hypo- thetical), concessive, consecutive, and final. Several Categories of Relation in the Kantian Sense, 1 99 . judgments (propositions) which are subordinated to the same principal judgment (or sentence) may be co- ordinate or subordinate to each other, and may be formed (e.g.) copulatively-hypothetical, disjunctively-hypothe- tical judgments (propositions), &c. (Language denotes the relations, co-ordinate and sub- ordinate sentences, partly by conjunctions and relative pronouns, partly by peculiar syntactical forms.) Logic has hitherto paid attention to a few cases only out of the great number of these relations, while Grammar, more accustomed to correct itself by the consideration of indi- vidual cases, has recognised them for a long time in greater completeness, and (by means of the researches of Karl F. Becker) has learned to know them more thoroughly.» False explanation and a one-sided exaggeration of the logical charac- ter of language are always to be rejected. But, to deny the assertion of a logical basis of grammatical relation itself, is a perverseness which cannot be logically justified, however easily it may be psychologically explained. Strenuous batthng against one extreme easily impels us to the opposite. Aristotle discussed the so-called (by later logicians) cate- gorical judgments exclusively (he himself understood by the categorical judgment the affirmative). The earlier Penjoa- tetics and Stoics soon brought " hypothetical and disjunctive judgments within the circle of their logical investigations. Kant^ based the division of judgments into categorical, hypothetical, and disjunctive, on the Category of Relation— Subsistence and Inherence, Causality and Dependence, Com- munity or Reciprocity. But this division is by no means « Although many points of Becker's doctrine are seen to be false from the stand-point of the historical investigation of the development of language, the doctrine itself is very serviceable for the logical under- standing of language, and is especially useful for that of the structure of sentences » Kritik der r. Vern. §§ 9-11 ; Froleg. 2 ; Metaph. § 21 ; Loff. § 23. H n It ; 1i ' 200 § 68. Simple a^id Complex Juclgnients, etc, complete, and referring the disjunctive to real reciprocity is a mistake. Besides, the Kantian Categories of Relation may be naturally compared with the Aristotelian Categories. For the latter proceed upon the formal kinds of individual exist- ence, and the former on the formal kinds of relations which arise between the different forms of individual existence and groups of similar individual existences. The compari- son extends similarly to their application to Logic. The Aristotelian Categories denote forms of conception, but the Kantian Categories of relation establish forms of judgments. The defects of the Kantian division have been partly, but not sufficiently, recognised and avoided by later logicians. The logical meaning of the grammatical relations of the sentence has seldom been rightly appreciated.^ Schleiermacher gives some hints about the mutual dependence of relations in simple judgments worthy of consideration. The existence which corresponds to the judgment is, according to him, the co-existence of things, by means of which every one thing is in every other, and acts and is acted on by it.' The first moment of judging, or the 'primitive judgment, asserts mere action without reference to a subject which acts, or to an object which endures. The place of the subject is occupied by the chaotically established sum total of existence. The pri- mitive judgment is verbally expressed by the impersonal verb.' The advancing construction of the judgment is a passing over from the more indefinite to the more definite. If reference to * We may say * Logic means by predicate the verb together with its objective relations, if such are present. For example, in the proposi- tion, A strikes B, it is not the mere striking, but the striking b, that is the logical predicate. But we must, in the predicate so defined, distinguish the purely predicative from the objective relation, and give to the latter a particular consideration ; which consideration belongs to Logic and not to Grammar, because it depends upon a special real fundamental relation ; mere grammar has to do with the mere form of the verbal expression. 2 Dial § 139. 3 Ibid. § 304. * With Trendelenburg, Log. Unt, 2nd ed., ii. 253. Categories of Relation in the Kantian Sense. 201 the acting subject merely is affirmed the primitive judgment passes over to the incomplete : if, further, the fact can be traced back to its two co-operating factors, the complete judg- ment results, which must, besides the predicative, include also the objective-relation.* An absolute judgment is developed from the sum of all complete judgments, whose subject is the world, or the orderly whole of existence.* The Adjective as Epitheton (or Attribute) is the result of an earlier judgment, which is already contained as an element in the subject- notion.' The division of Judgments * into Judgments of Content and of Extent presupposes that the judgment, as if it were a depen- dent form, is to be estimated only according to its relation to the forms of tHe notion (though Trendelenburg himself attributes to it a peculiar ' antitype in the actual ' — the action of the substance). This estimation does not wholly include the essence of the judgment, and the division falls short of its multiplicity of its relations. The judgment, with its flexible form, may be of service in the formation of notions ; but this is not its whole significance. The so-called ^judgments of con- tent^ denote as categorical judgments a relation of inherence^ and the designation is convenient when the inherence of the essential marks is under consideration. Every relation of inherence is not to be thought of as a relation of content (e.g. the inherence of mere modi and relations is not). As hypo- thetical judgments they depend upon a relation of causality, whether they denote the connection of a cause with its eflfect, or the connection of several efiects with the same cause, or the connection founded on the real causal relations of several 1 Dial. § 305. « Ibid. §§ 306-7. ^ i^id. § 250, p. 197 ff. * Cf. Trendelenburg, Log, Unt. 2nd ed., ii. 237 ff". ; 3rd ed., ii. 261 fi*. Categorical and Hypothetical Judgments are called * judgments of con- tent' by Trendelenburg ; and Disjunctive Judgments, * judgments of extent.' For example, the proposition : Conic sections are regular curves, is a judgment of content; but the proposition: Conic sections are either circles or ellipses or parabolas or hyperbolas, is a judgment of extent. rif I II' li i * f m- 202 § 68. Simple and Complex Judgmmts, etc. objects of knowledge. In any case they correspond to special relations of existence, and their meaning does not merely express the relation of content. The so-called judgments of extent may be reduced to the 'judgments of content,' and are recognised to be designations of the relation of what subsists to what inheres ; provided only that the true predicate is not sought for in the predicate substantive, but (as must happen) in the connection of this substantive with existence, and the copula not in the auxiliary verb, but in the logical connection of subject and predicate and its verbal expression in the gram- matical form of inflection. (The so-called 'judgment of extent,'—' Every man is by race either a Caucasian, Mongolian, Ethiopian, American, or Malay '—is equivalent to the judgment, < Every man has either the sum total of marks which charac- terise the Caucasian, or &c.' The true predicate is being a Caucasian. The expression of the copula lies in the inflection only, according to which the form ' is ' has resulted from the form ' to he:) This reduction exempts us from the necessity either of comprehending under the one notion, or at least under the one name of judgment, operations of thought which are quite distinct, or with Fries, Hegel, Ulrici, and others, of considering subsumption to be the only valid form of judg- ment, and so taking this relation out of its natural connection with the rest. [Sir W. Hamilton, starting from the thought that judgment is the subsuming one class under another, and that the pre- dicate and subject are respectively greater as the notions are taken in their extent and content, divides judgments into two classes, according to the relation of Subject and Predicate, as reciprocally whole and part. If the subject, or determined notion, be viewed as the containing whole, we have an Inten- sive or Comprehensive Judgment : if the Predicate notion be viewed as the containing whole, we have an Extensive Judg- ment, On this distinction the Comprehensive and Extensive forms of Syllogism are afterwards based. ^ J. S. Mill, who proceeds upon the thought that the most [^ Led. on Logic ^ i. 231. Categories of Relation in the Kantian Sense. 203 important relation of the notion is its connotation of a set of attributes, bases on this his attributive theory of propositional forms. All propositions express an actual relation between two sets of attributes, so that when the one is present the other is present or absent. The attributes, e.g. connoted by the word 'man,' are always accompanied by the attributes which are connoted by the word ' mortal,' and so we say ' all men are mortal.' Mr. Mill's attributive theory of propositional forms agrees to some extent with the comprehensive judg- ments of Hamilton ; though it has an entirely different point of view. It is more nearly related to Trendelenburg's Judg- ments of content as modified by Ueberweg. Mr. Mill has noticed the ambiguity which results when the copula is taken to be the auxiliary verb ' is,' and tries to get rid of it by distinguishing between ' is ' when a mere sign of predication, and when it signifies existence. In the proposition, ' Socrates is just,' the word ' is ' may mean either that the quality just may be affirmed of Socrates, or that Socrates is, that is to say, exists. But the difficulty is better got rid of while the thought that the relation of subject and predicate in the judgment actually mirrors a corresponding relation in real things, and in turn is mirrored by the verbal relation in the proposition, is better expressed by saying that the real copula is not * is,' but the form of inflection which changes 'to be ' into ' is.' For example, in ' man is mortal ' the real copula is that form of inflection which changes the ' to be ' into ' is,' so that, in- stead of the unconnected notions, * man ' and ' to be mortal,' we can say ' man is mortal.' ^] The question of debate between Localists and Causalists, in reference to the original meaning of the cases, might be decided in this way, that the unity of the causal relation with that of space (and that of time analogous to it) must be held to be the original, and that the stricter separation of the mean- ings is later. This principle of the original unity of the causal relation with the local is not contradicted but established by the historical proof that the nominative in the Indogermanic » Cf. Logic, i. 85-87, 107-10.] 204 § 68. Simple and Complex Jtidgments, etc. Categ-ories of Relation in the Kantian Sense. I 205 languages was probably originally formed by an s = sa = this (or here) added to the stem; and the accusative by an m = amu = yon (or there) (which was dropped in neuters); so that, e.g. Rex donum dat is = This here king gives that there gift.» "rhe 'predicate proposition has been named among the sub- ordinate complex propositions. They are such sentences as— Nonnulli philosophi sunt qui dicant, and the like. That the relative proposition hav^—qui dicant, is, according to its logical nature, a predicative sentence, is clear from the transposition— multi sunt dicentes, and is especially apparent in cases where a proposition of the same kind as a co-ordinate member comes in beside a simple predicate, e. g.^ Est hie— animus lucis con- temptor et istum qui vita bene credat emi— honorem. It is here as certain that qui credat is the predicate sentence, as that contemptor is the predicate to the corresponding proposition. It is only the copula as the expression of the connection between subject and predicate, not the predicate, ih^t cannot be changed in a subordinate proposition. A judgment (and proposition) can never altogether want a subject. There may be no distinct subjective conception, and in its stead a mere something (it) may enter. Cf. vu and Zeuy v£i. The indefinite conception of the subject may have been the earlier form. The view, that hypothetical and categorical judgments are opposed to each other as conditioned and unconditioned is combated by some logicians.^ Judgments such as — God is just, the soul is immortal, do not, they say, involve the asser- tion, there is a God or a soul. But- it is a fact that he who does not accept the presupposition must add clauses to these propositions, which will make them hypothetical; — if there be a (one or several, personal) God, if there be a (substantial) soul. A proposition such as— True friends are 1 Cf. the Dissertation of G. Curtius, Ueher die localistische Casus- theoriCj to the Philological Association of Meissen, 1863. « Virgil's Aen. ix. 205 sqq. 3 Herbart, Eint, in die Phil. § 53 ; Drobisch, Log. 3rd ed. p. 59 f. ; Beneke, Log. i. 165. to be esteemed, rests on the supposition that there are true friends. This presupposition is contained in the indicative. Lano"uages have created other forms for expressing its doubt and denial (the Greek, the fullest and strictest). Such a clause is superfluous, only when the connection of the whole (as in a novel) or the well-known sense of the word (as Zeus, Sphinx, chimera) refers to an actual existence merely imaginary. Cf § 85 and § 94. The grammatical question, concerning the meaning of a categoncal proposition spoken in the indicative, is to be strictly distinguished from the logical question about the meaning of the categorical judgment. Affirmative judgments and such negative ones as only take away a distinct predi- cate from the subject (as — this criminal is not guilty) are not co-ordinate with (formal or only actually) negative judg- ments of such a kind, that the subject-notion is itself thereby abolished (as— An absolutely greatest number is impossible). The stricter expression for judgments which deny the sub- ject itself would be the negation of the objective validity of the conceptions and words under consideration (e.g. the word magic is an empty sound), or some turn of expression such as— there is no absolutely greatest number. The presupposi- tion of the reality of the subject is already contained (with the above exception) in the categorical expression, and the affirma- tion of mere existence in the predicate would amount to a tautology. This affiraiation can only come in expressly to oppose a doubting or denial of the existence of the subject (as when it is said— God is, the soul exists). It would then, how- ever, be an artificial form quite different from the common use of lano-uage. The natural mode of expression, when existence is to be asserted, prefers other forms— as, e.g. There is a God, equi- valent to Es (i.e. etwas, something) ist ein Gott - where the indis- tinctly conceived totality of existence, or an indefinite part of it, comes in as subject (just as in the sentences it rains, it snows, &c.); or where we affirm of the existing subject, its existence as something (sunt aliquid Manes), or its existence there, its entrance into our neighbourhood, or within the sphere of our observation, and more than its mere existence in general. For this last is itself implicitly asserted by positing the subject. ! 2o6 ^ § 69. Quality and Modality of Jtidgments, 69. Quality and Modality of Judgments. 207 r. ; Hi! i § 69. The kind of reference of the combination of judgment to actual existence furnishes a basis for the dwision of judgments according to quality and modality. We must be conscious in the judgment, as we have defined it, whether or not the combination of concep- tions corresponds with the reality. The Quality of the Judgment rests on the result of the decision, the Modality on the degree and kind of its certainty. According to ^wa/%, judgments are affiraiative or nega- tive. The notion or idea of affirmation is the conscious- ness of the agreement of the combination of conceptions with actual existence ; the notion of negation the con- sciousness of the want of agreement of the combination of conceptions with actual existence. According to modality., the judgment is problematic, assertory, or apodictic. Its problematic character lies in the uncer- tainty of coming to a decision upon the agreement of the combination of conceptions with actual existence. Its assertory character lies in the immediate (based on one's own or another's perception) certainty; and its apodictic character in the mediately acquired (based on demonstration, oLirohi^ig) certainty of coming to such decision. (Negative particles form the verbal expression of the negation ; the moods of verbs and corresponding par- ticles, e.g. perhaps, certainly, &c., which all belong to the copula, not to the predicate, express modality.) Aristotle divides^ the Simple Judgment {äTr6(\)ava(jLs) and Negation (a7ro<^a(Tty). A co- existence is predicated in affirmation, a separate existence in * De Int. c. v., vi. negation (^KaTd(f>aaL9 saTLv d'Tr6(f>ava Cf. Trendelenburg, Log. Tint. ii. 137. 2 Waitz says {Ad Arist. Org. i. 376) to Ivvardv is the physically possible, TO ivltx^iitrov the logically possible, the problematical. This definition, so far as it refers to Iwaröv, is correct, but not strict as regards kvlix^y^erov. Waitz himself admits that it does not quite bar- raonise with Aristotle's actual usage when he thinks that Aristotle ^ saepius alterum cum altero confundit.' Our definition given above may correspond better. Cf. Arist. Anal. Pr. i. 13, p. 32 A, 18 : Xiya, Ik irlixttjQai KOi to iylEx6fievor, oh /i^ ovtoq dvayKaiov Ti- eiyTOi U hir^px^LV, ohUy ttTTat Bm to'vt' d^vraTor. The ^vyaadat denotes the presence of the internal reason, the hhixifrdat the presence of the external conditions and the absence of hindrances. physical powers of air, earth, and light— the (external) condi- tions. When the reason is present alone, or the conditions alone, possibility arises ; where both are present together, there is necessity in the objective sense. In this sense the possibility (or capability) of the existence of the oak is contained in the acorn. The historical genesis depends on the advance from an objective possibility (potentia) to actuality. It is pos- sibility in the objective sense that Buhle speaks of, e.g. when he* explains the opinion to be erroneous, that acquaintance with the pure Platonic and Aristotelian philosophy was again brought about by learned Greeks crossing over into Italy and by their literary activity, and says, ' They only brought about its possihilitg because they brought with them the tcorks of Plato and Aristotle, and taught people to understand them in the onginal language, so that sooner or later an un- prejudiced person who studied them could remark the diflfer- ence between the kind of philosophy taught in each and the kind which had been formed from them.' Again, it is the re- establishment of the conditions and the objective possibility, not a ' perhaps ' (subjective uncertainty), that is meant when we say to a boy — I know that it is possible to solve this problem ; you can solve it (you have the ability to solve it). The assertion that possibility is something objectively real does not contain the contradiction that the same thing is called both merely possible and also actual. For the occurrence is possible ; but its possibility actually exists in the object of our thinking as a real complex of causal moments, which is objectively separated from the others whose presence makes the occurrence neces- sary. This real possibility, however, as such, is not expressed in a problematic, but most commonly in an assertory judgment, by means of the verbs — can, is capable, &c. ; just as the real necessity in an assertory judgment is expressed by means of the verbs — must, is necessary, &c. (which then belong to the predicate, and not, like the ' perhaps,' to the copula). But a problematic judgment may be based upon our know- * Gesch. der neuern Philos. seit der Epoche der Wiederherstellung der H'j>.N\ ii. 123, Gcitt. 1800. p 2 Ii ^;f si I 212 § 69. Quality and Modality of Jtidgments, § 69. Quality and Modality of Judgments, 2 1 3 ledge of an objective possibility, and an apodictic judgment upon our knowledge of an objective necessity ; for what is pos- sible may perhaps occur, and what is necessary will certainly occur. A negative judgment is most conformable to nature when it is based on an objective negation in the sense given above, or on a tendency which is never realised ; but it is not confined to this relation. In the same way the problematic judgment is most conformable to nature where the subjective uncertainty about any occurrence, property, &c., rests on a known objective possibility— i.e. when the subjective separation of the part of the total cause known and of that unknown to us (or of what is kept in view by us and of what has not, at first at least, been brought into consideration) corresponds strictly with the objective separation of the internal cause and the conditions. Wherever we know assertorically that the occurrence can happen or has objective possibility, we naturally use the problematic judgment about the occurrence, that it perhaps will happen. The application of the pro- blematic judgment, however, is not limited to this one relation, but occurs wherever we have any ground of probability and no absolute hindrance, i.e. know no cause of impossibility. In the same way, the apodictic judgment is most complete, and yields the highest satisfaction to the mind in its search after know- ledgcj'when it rests on an insight into the real genesis from the internal cause and the external conditions. Wherever we know the presence of this objective necessity of an occur- rence, we ought to express the subjective necessity, that it will happen, in an apodictic judgment. The application of the apo- dictic judgment goes beyond this one relation, however, and embraces all subjective mediate certainty, even when it has been reached in another way (e.g. by indirect proof). The assertion of an objective possibility, or of an objective necessity, belongs to the matter or content of the judgment because it belongs to the predicate, but the problematic or apodictic character belongs to the form of the judgment. Aristotle, in his De Interpreta- tione and in his Analytics, treats of such ' modal ' modifications of judgments as really belonging to their matter or content, and do not concern the logical theory of judgments. The modal difference, however, of problematic, assertoric, and apodictic form does concern logical doctrine. In a monograph of Gustav Knauer ^ Aflfirmation and Nega- tion are traced to Modality. Both are, in fact, to be regarded from the same point of view. They have not to do, as Relation has, with the diflPerent objective relations which are mirrored in the judgment, but with the various relations of the subject to the object. Accordingly, Knauer calls negation in a nega- tive judgment * modal negation,' and distinguishes it from ' qualitative negation,' which rests on the opposition— not of reality and negation, but— of the positive and the negative con- trarily opposed to it, as black to white, vice to virtue. (This distinction corresponds to that of Trendelenburg, between * logical negation ' and ' real opposition.') In a similar way, Knauer understood by the ' limited judgment,' one in which the predicate is saddled with a limiting determination, which can be expressed either by a positive adverbial addition (as in ' bright red, dark red, half right), or by a * qualitative not,' strictly to be distinguished, however, from the 'modal not.' But Knauer has overlooked this, that the logical division of judgments has to do with differences which belong to the form of the judgment, as such, and not \^dth differences belonging to any form whatever of notions entering into the judgment. Whether man or not-man, red or bright-red, &c., is the pre- dicate of a judgment, makes a difference in the form of the notions under consideration, and in the content of the judg- ment. It makes no diflference in the form of the judgment with which the logical division of judgments has alone to do. Accordingly, the rectification of the Kantian Table of Categories attempted by Knauer— the substitution of Positive and Negative for Reality and Negation — contradicts the general point of view, according to which the Categories con- Conträr und contradictorisch, nebst convergirenden Lehrstücken, festgestellt und Kant's Kategorientafel berichtet, Halle, 1868. Well worthy of attention, although making some mistakes in what is new, and often erroneously believing a correct statement to be new. ' ! ;t ) 'i Nl :ii I 214 § 70. Quantity. 70. Quantity. 215 1 dition the various functions of judgment. Reality and Nega- tion are not, of course, like Substantiality and the other Cate- gories of Relation, valid as forms of actual existence. They only denote a relation between our thoughts and actual exist- ence. This, however, only justifies the attack upon the Kantian table of Categories, not Knauer's own doctrine. On the other hand, the axiom of Knauer's is correct (in which he recogmses the ' master of Stagira ' as his ally, but which is not a new doctrine, even in the sense that it had been lost sight of since Aristotle, and was first brought to light again by Knauer), that necessary contradiction exists only between aflftrmation and negation of the same thing, and not between judgments whose predicates are opposed contradictorily. See §§ 77-80. [5/r W. Hamilton, vfiih Hansel and T/iom/^^ow, refuse to recognise the modality of judgments as any part of their logical treatment. The mode, they say, belongs to the matter, and must be determined by a consideration of the matter, and therefore is extralogical.^j § 70. Quantity is the extent in which the predicate is affirmed or denied in the sphere of the subject-notion. Some logicians divide judgments according to Quantity into Universal, Particular, and Singular. Singular judg- ments are to be subsumed imder the other two classes : under the first when the subject is definite and indivi- dually designated (e.g. Caesar, or this man) ; under the second when the subject is indefinite and designated only by a general notion (e.g. a man, or a great general). For in the first case the predicate is affirmed or denied of the whole sphere of the subject (which in this case is reduced to an individual), and in the other case of an indefinite part of the sphere of the subject-notion. [» Cf. Hamilton's Lect. on Log. i. 257 ; Hansel's Aldrich's Etidi- menta, 4th ed. p. 46 n. ; Proleg. Log. 2nd ed. Note H.] Aristotle distinguishes Universal, Particular, and Indefinite Judgments: irporaais — rj KaOoKov, 7) h fiipsi, rj aBtopKnos.^ The Judgment Indefinite according to quality, which Aris- totle makes co-ordinate with the Universal and Particular, is not properly a third kind, but an incomplete, or incompletely expressed, judgment. 2 Kant recognised three kinds — Singular, Particular or Plurative, and Universal Judgments — and traces them to the three Categories of Quantity — Unity, Plurality, and Universality. He teaches that singular judgments belong to the same class as the universal.^ Herhart says, that individual judgments are only to be reckoned along with universal ones when they have a distinct subject. When the meaning of a general expression is limited by the indefinite article to any individual not more definitely designated, those judgments are to be reckoned with the parti- cular. "* This manner of reduction shows itself to be the correct one, partly in itself, because it does not depend upon the absolute number of subject-individuals, but on the relation of this num- ber to the number of individuals falling under the subject- notion generally; partly in its application to the forms of inference.^ The subject of the particular judgment is any part of the sphere of the subject-notion, and at least any single individual falling under this notion. Its limits may be enlarged up to coincidence with the whole sphere, so that the particular judg- ment does not exclude, but comprehends, the possibility of the universal. The rule that the judgment, indesignate in reference to quantity, is universal if affirmative, and particular if negative, is more grammatical than logical, and not unconditionally valid. ^ Anal. Pri. i. 1. * [Cf. Hamilton's Lect. on Log. i. 243.] 3 Krit. d. r. Vern. §§ 9-11 ; Proleg. § 20 ; Logik, § 21. ^ Lehrbuch zur Eint, in die Phil. § Q2. * Cf. below, § 107. 1 Uli' M 11 |1 1 „ ^^1 2 1 6 §71. Combination of Divisions, etc. § 71. By combination of the divisions of judgments according to quality and quantity four kinds arise :— 1. Universal Affirmative of the form— All S are P. 2. Universal Negative of the form— No S is P. 3. Particular Negative of the form— Some S are P. 4. Particular Negative of the form — Some S are not P. Logicians have been accustomed to denote these forms by the letters a, e, i, o (of which a and i are taken from affirmo, e and o from nego). It will be seen from a comparison of spheres, that in every universal judgment the subject is posited universally, and particularly in every particular judgment ; but the predicate is posited particularly in every affirmative judgment, or, if uni- versally, only by accident (for, according to the form of the judgment, both in a and i its sphere can lie partly outside of the subject), and universally in every nega- tive judgment (for in e the sum total of S, and in o the part of S concerned, must always be thought as separated from the whole sphere of the predicate). The judgments of the form a (S aP— All S are P) can be represented in a scheme by the combination of the two follow- ing figures : — a, 1. e, 2. The following scheme is for judgments of the fonn e (S 6 P ■No Sis P):— e. T/ie Four Forms of Judgment, A, E, I, and O. 217 Judgments of the form i (S i P — At least a part of S is P) require the combination of the four following figures (of which 1 and 2 are peculiar to the form i, but 3 and 4 repeat the schema of the form a) : — i.1. i, 2. i, 3. i,4. Judgments of the form O (S O P — At least one or some S are not P) are to be represented by the combination of the three following figures (of which 1 and 2 are peculiar to the form O, while 3 repeats the schema of the form e : — O, 1. 0,2. O, 3. If the definite be denoted by a continuous, and the indefinite by a dotted line, the symbol of judgments of the form a may be reduced to the one figure : — \V til 1 '- 2l8 71. Combination 0/ Divistons y etc ■I' The Symbol for the judgments of the form i under the same presupposition : — P \ And for judgments of the form O : **• ••*' The use of these Schemata is not confined to that ap- prehension of the judgment which finds it to be only a sub- sumption of the lower subject-notion or conception under the higher predicate-notion, and which, therefore, requires that the predicate-notion be made substantive in cases where this is actually unsuitable. If the predicate-notion is the proper genus-notion of the subject, it is quite natural to take it for substantive, but not when it denotes a propertij or action. This last case does not require to be reduced to the first for the sake of a comparison of spheres. It is not necessary (although in many cases very convenient) to attach such a meaning to the circle P as to make it embrace the objects which fall under the substantive predicate-notion. The sphere of an adjective or verbal conception can be also under- stood by the sphere P. It may mean the sum total of the cases in which the corresponding property or action occurs, while S may denote the sphere of a substantive conception — the sum total of the objects in which the corresponding pro- perty or action occurs. On this presupposition the coincidence of the circles or parts of the circles is not to be taken to be the symbol of the identity of objects, but as the symbol of the co-existence of what subsists and what inheres. Cf. § 105. In a, 1 all S are only a part of P, but in a, 2 all S are all P ; in i, 1 some S are some P, &c. The Quantißcation of the Predicate consists in paying attention to these relations. It § y2. Contradictory afid Contrary Opposition, etc. 219 has been carried out by Hamilton on the basis of assertions of Aristotle,^ and according to partial precedents in the Logique ou I'Art de penser,^ and in Beneke,^ Cf. § 120. For the use of these Schemata as aids in the demonstration of the theorems which have to do with inference, cf. § 85 and § 105 ff. ; cf. also § 53. § 72. Two judgments^ of which the one precisely affirms the very thing which the other denies, are con- tradictory to each other, or are contradictorily opposed (indicia repugnantia sive contradictorie opposita). Con- tradiction is the affirmation and denial of the same thing. Judgments are opposed to each other diame- trically., or as CONTRARIES (contrarie opposita), which, in reference to affirmation and negation, are as different as possible from each other, and, as it were, stand furthest apart. Judgments should be called subcontraries, the one of which particularly affirms what the other, agree- ing with it in other respects, particularly denies. Judg- ments are subaltern (indicia subalterna), the one of which, affirmatively or negatively, refers a predicate to the whole sphere of the subject-notion, while the other refers the same predicate in the same way to an inde- finite part of the same sphere. The former is called the subalternant (indicium subalternans), the latter the subalternate judgment (indicium subalternatum). Aristotle defines ^ — saio) ävTlaaTiKa)S dvTOKilaOai,' rj avTCKSi^ievr) d7r6(pai/ai,s) from * De Interp. c. vii. ^ p^^, 1664. ^ Cf. upon this Trendelenburg, Log. Unters. 2nd ed. ii. 304-307, and Appendix B. ^ De Interp. c. vi. Ii- 1 1 I ! 1 1 • III f r 1 I 'il k ; it^H 220 § 72. Contradictory and Contrary Opposition, etc. contrary {ivamlcos avTiKslaOat ' tj havrla aTr6avais). Judg- ments with the same content of the forms a and O (S a P and S O P) stand to each other in the relation of contradictory opposition, and so do judgments of the forms e and i (Se P and S i P). Judgments of the form a and e (S a P and S P) stand in the relation of diametrical or contrary opposition. The relation between the forms of judgment i and O (S i P and S O P) Aristotle calls only apparently analogous,* Kara rrjv \s^iv avTiKcladau fiovov. Later logicians call such judgments TrpoTaasLf vTrevavrlas, indicia subcontraria. Aristotle arranged the four forms of judgment,^ iras eartv avSpwrros BUaios (a), ov iras sa-Tiv avOptoiros hUaios (o), iras eariv avOponros ov SiKaios (e), ov TTCLs saTiv ävOpiOTTos OV BUutos (i), according to the an- nexed scheme : — The judgments a and e, which stand furthest apart from each other, according to their mutual relations, and in the same way the judgments i and O, are thus set at the opposite ends of the diagonal or 8idfjL£Tpo9. In this scheme all the above-mentioned relations of judgments are thus arranged: — a opposit. contradict. O CD a- Xi vN.^^ h^ o^-^ SP ^^^ ^°«* 'S OD %:. opposit. contradict. e Modern Logicians represent these relations in the following scheme (which is found in Bo'ethius, and, with some difference ' Anal. Pi\ ii. 15. De Interp. x. 19 b, 32-36. § 73. The Matter and Form of Judgments. 221 of terminology, but with the same position of the forms of judgment, in Apuleius) : — a opposit. contraria 6 OD cr %o.. •-cN* 0« o^^ ''i. fß" ..0«^^ °«Ä VC* }>' 03 p 4q^ '^t. i opposit. subcontrar. O This is less convenient because contraries do not lie at the opposite ends of the diameter, but in another view is better. § 73. The matter or content of our judgments is obtained immediately through external and internal perception, mediately by inference. In the act of judg- ment the/ör7W5, which are designated by the Categories of relation^ are imposed upon this matter. We recog- nise these forms : — (a) First and immediately in ourselves by means of internal perception. For example, the relation of what inheres to what subsists is recognised in the rela- tion of the individual perception or individual feeling or volition to the totality of our existence or to our ego, the relation of causality to dependence in the relation of our will to its expression, &c, (b) In the personal and impersonal essences without us, on the ground of its analogy to our own internal existence. The notional apprehension of these forms, in their separation from the content, with which they are com- bined, comes afterwards, by means of abstraction. i 4i M- ! 1:5 ;, I 1 k.\ ii t 1 ' Ik 222 § 73. The Matter and Form of Jtidgments. The objective validity of these forms is warranted by the same moments, and lies under the same limitations and gradations, as the truth of internal perception and its analogues (§ 41 fF.), as the truth of the conception of individuals (§46), and as the notional knowledge of the essential (§ 57). Kant beheved these forms to be ä priori, or originally inher- ent in the human understanding ( StammbegrifFe des Ver- standes). Before his time knowledge a priori meant, agree- ably to the Aristotelian idea, knoicledge from causes which are the prius natura {irporepov <\)vasi), and knowledge ä pos- teriori, knowledge from effects which are the posterius natura {vaTSpov ^vaei), and therefore knowledge from immediate expe- rience and by testimony (for this knowledge is a kind of know- ledge from effects). Leibniz identifies ' connaitre ä priori and par les causes. He calls ^ ratio ä priori that reason which is the cause not merely of our knowledge, but of the truth of things themselves. He distinguishes ' prouver ä priori par des demonstrations' (which, of course, is sufficient only when * demonstrations ' mean syllogistic deductions from known real reasons), and * ä posteriori par les experiences.' He recoo-nises the Axiom of Identity and Contradiction (the element ä priori) to be the only ^principe primitif' for all knowledge co-ordinate with experience (the ä posteriori element) ; ^ but later adds the Principle of Sufficient Reason.* The same use of the terms is also found in Leibniz, ap- plied to mathematics, in a very instructive passage of his Epistola ad Jacobum Thomasium,^ in Leibniz's edition of the work of Nizolius, De veris principiis et vera ratione philoso- ])handi : ^ 'Si rem cogitemus curatius, apparebit demonstrare earn (sc. geometriam) ex causis, Demonstrat enim figuram ' Theod. i. § 44, e.g. * Nouv. Ess. ii. 17. • 3 Reflexions sur V Essai de Locken 1696. * Theod.'i. § 44, 1710; Monad. § 32, 1714. s Published in 1669. ^ Opera Phil. Leib., ed. Erdman, p. 51. § 73. T/ie Matter and Form of ^udg^nents. 223 ex motu, e.g. ex motu puncti oritur linea, ex motu lineae superficies, ex motu superficiei corpus. Ex motu rectae super recta oritur rectilineum. Ex motu rectae circa punctum im- motum oritur circulus, &c. Constructiones figurarum sunt motus ; iam ex constructionibus affectiones de figuris demon- strantur. Ergo ex motu, et per consequens ä priori et ex causa,'' Wolff says, very insufficiently : * utimur in veritate proprio Marte eruenda vel solo sensu; vel ex aliis cognitis ratioci- nando elicimus nondum cognita : in priori casu dicimur veri- tatem eruere a posteriori, in posteriori autem a priori. He adds that experience has to do with the individual only, but yet supplies us with the principles from which those indi- vidual cognitions, which are not to be reached by immedi- ate experience, must be derived a priori. Only by such a ' connubium rationis et experientiae ' can the trifling Scholas- tic formulae be avoided, and be taught ' non ex proprio ino-enio conficta, sed naturae rerum consentanea.' Kant'^ holds that knowledge which has been reached by a general rule, if this rule be itself derived from empirical sources, is only relatively to be considered knowledge ä priori. He, for his part, will ' not understand such knowledge to be ä priori which is independent of this or of that experience, but only knowledge which is absolutely independent of all experi- ence. Opposed to it is every kind of empirical knowledge, or knowledge possible only ä posteriori, i.e. by experience.' Kant has narrowed the notion a posteriori in its relation to the Aristotelian knowledge from effects, or from the {jarspov (J)v Theaet. 186 d; cf. Phileb. 41 c. 3 Ibid. ii. 23. 2 AnalPri. i. 1,24 b, 18. 4 Ibid. 74. Definition of Inference, 227 to mediate inference only, defines it:* est ratiocinatio operatic mentis, qua ex duabus propositionibus terminum communem habeatibus formatur tertia, combinando terminos in utraque diversos; Syllogismus est oratio, qua ratiocinium (seu dis- cursus) distincte proponitur. Kant'^ defines inference to be the derivation of one judgment from another. This happens either without an intermediate judgment (indicium intermedium), or with the help of such. On this is based the division of immediate and mediate inference. Kant calls the former inferences of the under- standing, and the latter inferences of the reason. HegeP sees in inference the re-establishment of the notion in the judgment, the unity and truth of the notion and judgment, the simple identity into which the formal distinctions of the judg- ment have returned, the end and aim towards which the judcr- ment in its various kinds advances gradually, the universal which by means of particularity has coalesced with individual- ity. He thinks inference the essential basis of all truth, the intellectual and all intellectual, the return upon itself of the mean of the moments of the notion of the actual. Hegel here also identifies the logical and metaphysical relation, or the form of knowledge and existence. Schleiermacher* defines inference to be the derivation of one judgment from another by means of a middle premise. He does not recognise inference to be an independent third form, co-ordinate with notion and judgment, and denies that it has a real correlate of its own. He therefore does not believe that it has any scientific value for the production of knowledge ; but thinks its worth didactic only, for the transmission of knowledge already existing. We believe this view to be erroneous, and will seek to show (§ 101) the real correlative of inference, and its significance as a form of knowledge. \J. S, MilP defines inference to be the setting out from known truths to arrive at others really distinct. He refuses the name to the so-called ' immediate inferences,' because in ' Log. §§ 50, 332. 2 Xritik der r. Vern. p. 360; Log. § 41 fF. 3 Log/u. 118 ff; Encycl. § 181. * Dial. p. 268. ^ [Log, i. 185.] Q 2 r % .1 r^i i y\-- !? t^-i in v L ''I •28 § 75- 'T^^ Principles of hiference in general 75. Tlu Prificiples of Inference in general 229 them the progression from one truth to another is only apparent, not real, the logical consequent being a mere repeti- tion of the logical antecedent. He divides inference into three kinds, from generals to particulars, from particulars to gene- rals, and from particulars to particulars. The third kmd, thouo-h not generally recognised by logicians, is not only valid, but il the foundation of both of the others. It is the inference of every-day life, and in its finer forms corresponds to the hdiGiios of Aristotle, which plays such an important part in the formation of our judgments in matters of taste and morality— the delicate imperceptible ingathering of instances gradually settling and concreting into opinions. It is the recognition and discussion of this third kind of inference in all its manifold forms, but more especially in its formation of religious beliefs, which gives so much logical value to J, H. Newman's Grammar of Assent, 2nd ed., Lond. 1870.] § 75. The PRINCIPLES of inference are the axioms of identity and correspondence, of contradictory disjunc- tion (or of Contradiction and Excluded Third) and of sufficient reason. The derivation of a judgment from a notion rests on the first, the derivation of a judgment from a judgment on the first and second, and the deri- vation of a judgment from several judgments on the first, second, and third. Logic considers these principles as rules of our thinking (which is also an act of knowing). It leaves to psychology to discuss in how far these laws are, or are not, so simple and evident in their appUcation that they cannot be altered in clear thinking, and in this sense attain the character of natural laivs for our thinking. Aristotle does not place these axioms at the head of Logic, but discusses them, in so far as he enunciates them in scientific form at all, partly and occasionally as laws of the formation of inferences, and partly and more particularly in the Meta- physics,^ where he holds the axiom of Contradiction to be waceop ßsßaioTaTrj ap'^rj, Leibniz'^ holds them to be the principles of our inferences (raisonnements) ; Wolff does as Aristotle. Daries and Reimarus were the first to find the principle of Logic in some or other of those axioms. Reimarus places^ the essence of reason in the power to reflect upon conceived thino-s according to the two rules of consistency and contradiction, and holds that by the right use of reason the knowledge of truth is to be attained. He defines the ' doctrine of Eeason 'to be a science of the right use of reason in the knowledge of truth,* and truth in thinking to be the agreement of our thoughts with the things we think about.^ He seeks to prove the proposi- tion, ' When we think according to these laws of consistency and contradiction, our thoughts must also correspond to the things themselves, and so be true ;' ' these laws are sufficient to give truth and correctness to all our thoughts.'^ Kanty on the other hand, reduces formal Logic to the doctrine of the laws which flow from the principles of Identity and Con- tradiction, in this sense, that by their observance the agree- ment of thought with itself, or the absence of contradiction, will be attained. He does not believe possible an agreement of the contents of thought with actual existence or with things in themselves. Fries remarks^ that these axioms should not be placed at the head of Logic, since they can only be understood in their true meaning when one has learned to know the notion and the relation of subject and predicate in the judgment. This remark is correct, for these axioms express the relation of several judgments to each other, and so have their first distinct influence upon the doctrine of inference. Delboeuf^ places at the head of the whole of Logic three axioms which partly take the place of those given above. These » Met. iv. 3. 2 Monad. § 31. 3 Vemunßlehre, § 15. -* Ibid. § 3. » Ibid. § 17. ^ Ibid. § 17ff. 7 System der Logik, § 41. ^ Log. pp. 91 sqq., 104 sqq., 113 sqq., and 130 sqq. . 1 I 230 § 75- Tlu Prifuiples of Infer ence in general. axioms are-1. We must conclude from the representation of phenomena to phenomena themselves; 2. We must posit the results as identical by abstraction of the differences; 3 The logical concatenation of ideas corresponds to the real concatenation of things. He derives them from the ' first postulate of the reason '-' that certainty is possible, by the following argument. If certainty is to be given, truth must be given; if truth be given, our conceptions must be able to be true; if they can be true then-1. The mind must be able to conceive phenomena as they are. 2. The causes which produce them must remain identical with themselves in the various combinations into which they enter. 3. The logical power of deduction must also correspond to actual objective existence, the mental analysis be a true (though converse) picture of the real synthesis. By means of the first prmciple we advance, says Delboeuf, from the conception to the actual existence,- by means of the second from conceived identity to actual identity, by means of the third from conceived connec- tion to actual connection. Delboeuf finds the warrant for the agreement of a thought with what actually exists in a thorough-going logical harmony in the operations.-observa. tion, conjecture, and verification (p. 85). Understood in this sense-that the agreement of thought with objective existence is attainable by man and guaranteed by the observation of the sum total of the logical laws (s. § 3)-the first of those three principles coincides with the principles of this system of Logic and of every Logic which is a doctrine of know- ledge The second principle has chiefly to do with the process of abstraction (s. § 5 1 ). Delboeuf recognises the third principle to lie at the foundation of inferences (raisonnements) (cf § 81). He calls these three principles ' principes reeU; and makes the first two correspond to the principle of Identity, and the last to that of Sufficient Reason. He places beside them as ' principes formels ' the axioms of Contradiction and Excluded Third." [Hamilton, Mansel, Thompson, and that school of formal logicians make Logic the science of these laws of thought and ' Log. p. 165 flf. 76. TAe Axiom of Identity. 231 their application. They push Kant's doctrines to an extreme which he himself would have scarcely contemplated. But Hamilton, on the side of metaphysics, asserts that the three laws of Identity, Non-contradiction (as he calls it), and Excluded Middle are ' laws of things ' as well as ' laws of thought,' and hold good of things-in-themselves. * They reject the law of Sufficient Reason because it either has to do with the matter, not the form of thought, or else is no law of thought, but only the statement that every act of thought must be governed by some law or other.^ Mansel has tried to show how Logic should be merely a statement of these three fundamental laws — the laws of the thinkable — the deduction from them of the laws of thinking in the stricter sense — viz. those of concep- tion, judgment, and reasoning, and their thorough-going ap- plication to produce in thinking, consistency with itself.^ J, S, Mill refuses to place these laws at the head of Logic, and considers them of little or no value in the science. He severely criticises the views of Mansel and Hamilton in his Exam, of Sir Wm. Hamilton's Phil.'*] § 76. The Axiom of Identity (principium identitatis) should be thus expressed: A is A, i.e. everything is what it is^ or — omne subiectum est praedicatum sui. The axiom of consistency (principium convenientiae), which is allied with it, should be thus expressed: a which is B, is B ; i. e. every attribute which belongs to the subject-notion may serve as a predicate to the same. The reason of the truth of the axiom lies in this, that the attribute conceived in the content of the notion [^ Cf. Lect. on Logic, i. 98. ^ Cf. Mansel, Proleg. Log. p. 214, and Hamilton, Disc, 2nd ed., Appendix. 3 Prolegomena Logica, 2nd ed. p. 190 ff. Cf. also Hamilton's Lect. ii. 244 for an elaborate list of authorities. * 3rd ed. pp. 430-480.] (. !l t 232 ^ y6. The Axiom of Identity. §76. Tlte Axiom of Identity. 233 inheres in the object conceived through the notion, and this relation of inherence is represented by the predicate. The sentence — Not-A is Not-A, is only an application of the axiom of Identity to a negative notion. It is not a new axiom. In the same way : A, which is Not-B, is Not-B, is only an application of the axiom of consistency. The latter formula furnishes a basis for the application of this thought to negative judgments in the axiom of negation (principium negationis) — A, which is not b, is not b. In a wider sense the axiom of Identity may apply to the agreement of all knowledge with itself, as the (necessary though insufficient) condition of its agree- ment with, actual existence. The axiom of Identity was not, as some think, discovered by a Schoolman (perhaps the Scotist Antonius Andreae, quoted by Polz, and after him by Bachmann and others, who enun- ciated the formula — ens est ens). Still less is it due to modern logicians. Parmenides, the Eleatic, is its author. He ex- presses it in its simplest form — lo-rt;^ further, ')(prj to Xsystv re VOÜV t'* hov sfifjbsvat* oportet hoc dicere et cogitare: id quod sit, esse^ and sgtl yap slvat^ (cf. § 11). Heraclitus thought that anything is and is not, at the same time, and that all fleets. Parmenides thought that only Being exists ; Not-Being is not ; everything lasts. Plato seeks to overcome this opposition by his distinction between the in- variable world of Being or Ideas, whose every essence is always like to itself, tale, quale est, asi Kara raina 6v (Tim. p. 27, and elsewhere), and the changeable world of Becoming or of sensible things. Science or true knowledge has to do with existence, and consists in this, that what exists is known as ^ Pan«., Fragm. ed. Miiliach, vs. 35, 58. 2 Ibid. 1». 13. 3 ji^id. existing* — ovkovv iTTKmjfir) fi€V sttI toJ ovti 7rsVKS yp&vac (Ls saTi TO 6p;^ S7ri(m]ur/ fisp yi irov snl tw oi^Tt {TT£(f>vKe) to ov yva>vac 0)9 sxst,,^ — \6yos — bs av ra oma Xsyy d)5 sariv^ aXrjOrjs, 09 8' av 0)9 ov/c ea-Ti, 'sjrivBi]9. The admission, that a mere agree- ment of conceptions with each other is a criterion of their truth, is expressly rejected by Plato.* Aristotle defines^ to fisp yap Xsyscv, to ov fxrj elvai rj to firj ov Eivai, 'fev8o9' TO 8s, to ov elvai Kal to firj ov firf sJvai, aXrjOh,^ aXrjdsvsL fisv 6 to Btyprjfisvov ol6/j.ivo9 haipeiaOat, Kal to avyKuiMSvov avyKsladar syjrsvaTac 8s 6 svavTL(09 sx^v rj to, irpdyfjuaTa. When he^ requires from truth thorough-going agreement with itself— 8slyhp Trav to dXrjOh avTo savTo) 6/j,o\oyovfievov slvat iravTrj — this does not amount to the mere tautological oneness, which the axiom of Identity in its stricter sense requires, it also means the agreement of the consequences with the reasons.« Leibniz ^ enunciates as the first aflirmative truth of reason, or as the first identical truth, the sentence ' everything is that which it is,' or A is A. In a similar way fFolf^^ considers the most universal iden- tical judgment to be the axiom— idem est illud ipsum ens, quod est, seu omne A est A. The Wolffian Baumgarten^^ used the formula: omne pos- sible A est A, seu quidquid est, illud est, seu omne subiectum est praedicatum sui, and calls this axiom ' principium positionis seu identitatis.' Schelling^^ declares the axiom inadmissible in scientific Logic, and very properly draws attention to this, that proposi- tions sounding identical do not belong, according to their sense, to the merely analytical principle, A is A. HegeU^ makes the correct remark against the axiom of Identity in the form A is A, that no consciousness thinks, » Rep. v. 477 b. 2 ibj^. p. 473 a. 3 cf. Cratyl 385 B. * Ibid. p. 436. 6 Metaph. iv. 7, § 2. 6 Ibid. ix. 10, § 1. 7 Anal. Pri, i. 32 ; cf. Eth. Nicom. i. 8. « Cf. De Interpret, c. xi. 9 Nouv. Essais, iv. 2, § 1. '« Log. § 270. 11 Metaph. § 11, 1739. '2 Phil. Sehr. i. 407. '3 j^^g. i. 2, 32 ff; Encj/cl. § 115. i !li 234 76. The Axiom of Identity, §77. The Axiom of Contradiction, 235 1.1 nor conceives, nor speaks according to this law. Speech conducted according to it would be absurd:- A plant is-a plant ; the planet is— the planet. Schleiermacher^ thinks that the axiom, in order not to be an empty formula, must either express the identity of the subject as the condition of science, or the identity of thought and existence as the form of science. Some more recent logicians' make the axiom express the sure and self-identical nature of human knowledge, especially notional knowledge, and make the principle of Contradiction its ne-ative form. But this is too far removed from the mean- in- and application which has been given to these axioms in Locicand especially in the doctrine of Inference and Proof, since the time of Aristotle. The doctrine of the notion has also another metaphysical principle, in the doctrine of Essence, whose significance is by no means exhausted by mere necessary identity with itself (cf. § ^Q). When men proceed to say that the axiom must contain the principle of all Logic, a corre- sponding meaning must be given to it. It must assert the pos- tulate, that knowledge in general be true, i.e. consistent with existence. But why should not this postulate be signified distinctly, by means of the adequate expression. Idea ofjruth, rather than concealed under the ambiguous formula, A - A. Delboeuf recognises the axiom of Identity, interpreted either by the postulate that every judgment be true, i.e. in agreement with actual existence (which meaning was given m the first edition of this work), or by the first or second of his three logical principles (cf. § 75). \ Hamilton and Mansel say that the law of Identity expresses the fact thai every object of thought, as such, is conceived by limitation and difference, as having definite characteristics, by which it is marked off and distinguished from all others; as being, 1 Dial. § 112. ^ ^ _, 2 Weisse, üeher die philos. Bedeutung des Grundsatzes der Men- tität in Fiehte's Zeitschrifl für Philosophie u, spec, Theol. iv. 1, 1 ff' 1839; I. H. Fichte, De principiorum contradictionis, identitatis, exclusi tertii in logicis dignitate et ordine dissertatio, pp. 10 ff., 26, 1840. in short, itself w^d. no other ; and that an object is in any other way inconceivable. It is the law of logical Affirmation and Definition.» J, S, Mill' expresses the law of Identity thus-, ^ Whatever is true in one form of words is true in every other form of words which express the same meaning.' He calls it an indispensable postulate in all thinking, and says that it is of value in Logic,— providing for (e.g.) the whole of Kant's ' Inferences of the Understanding.'] § 77. The Axiom OF(ihe(avoidance of) Contradic- tion (principium contradictionis) i^— Judgments op-' posed contradictorily to each other (as— a is b, and a is not b) cannot both be true. The one or the other must be false. From the truth of the one follows the false- hood of the other. The double answer, Yes and No, to one and the same question, in the same sense, is inad- missible. The proof of this axiom comes from the definitions of truth (§ 3), of the judgment (§ 67), and of affirmation and negation (§ 69). According to these definitions, the truth of the affirmation is equivalent to the agreement of the combination of conceptions with actual existence, and consequently to the falsehood of the negation. The truth of the negation is equivalent to the absence of agreement between the combination of conceptions and actual existence, and consequently with the falsehood of the affirmation. Hence, when the affirmation is true the negation is false, and when the negation is true the affirmation is false— which was to be proved. The axiom of Contradiction may be applied to an [} Cf. Mansers Pro%. Log, pp. 195-96, 2nd ed.; Hamilton's Led, on Log. i. 81. - Exam, of Sir Wm. IIamilto?i's Philos, 3rd ed. p. 466.] ■I I! U I If 236 77- TJie Axiom of Contradiction. §77. The Axiom of Contradiction, 237 individual notion (notio contradictionem involvens sive implicans), to the combination of a notion with a single attribute (contradictio in adiecto), and further to the repugnance (repugnantia), i.e. to the mediate contra- diction which first appears by inference in corollaries, in so far as these forms can be resolved into two judge- ments opposed contradictorily to each other. Although the axiom of contradiction is so simple and obvious in itself, many questions and discussions have clustered round it in the course of the centuries during which it has been con- sidered to be the first principle in Logic and Metaphysics, and require to be strictly examined. These have to do chiefly with its expression and signification, its capability for proof, its validity, and the sphere of its application. Its Expression. — The formula most commonly used is, — J udgments opposed contradictorily cannot be true at the same time. This must be rejected as inexact. It leaves it uncertain whether the relation of time which lies in the ' at the same time ' refers to the judgments themselves as acts of thought, or to their content If the former (which the verbal sense of the formula implies), then, because of the relation of time, the law says too little. It does not suffice for the avoidance of the contradiction that its one member is thought now, and the oth(ir then. Can it have been true in the eighteenth century that the works of Homer proceeded from one poet, while it is true in the nineteenth that they have several authors ? If, how- ever, the formula bears the second meaning — Judgments opposed contradictorily cannot both be true so far as their content has reference to one and the same time — then (1) the words of the formula strictly taken do not mention this, and the expression, which must be as strict as possible in formulas of this kind, suffers from grammatical inexactness, and (2) the law is burdened by a superfluous addition. One judgment which agrees with another in other things, but differs in the determi- nation of time (although this difference does not enter into the verbal expression, but only lies impHcitly in the reference to the presence of the person who judges at a particular time), is no longer the same judgment. Hence its denial does not make the contradictory opposite of the other judgment. Hence the law of Contradiction, which has only to do with judgments contradictorily opposed, cannot be applied to judgments of that kind, and it is not necessary, in order to state this inapplica- bility, that the formula should contain a determination of time. The determination of time has no more right to admission than a determination of place, and than all other adverbial determina- tions, none of which require particular mention for the same rea- son, that judgments in which they differ cannot stand opposed to each other in contradictory opposition. If the ' at the same time ' does not denote a relation of time {simul), but the being true together, or community of truth {una), it is better to avoid the double sense which has led so many not insignificant logicians astray by the expression,— They cannot both be true. Its MEANING.—Perfect sameness of sense, both in the single terms of the two judgments and in their affirmation and negation, is the condition without which no contradictory opposition can take place. Hence, in given judgments, which according to sound appear to be opposed contradictorily, the relation of thought is to be strictly tested in these references. When judgments contradict each other in words only, and not in sense, or when they appear to be logical judgments, but are really, because of the indefiniteness of their sense, mere rudimentary thoughts, yes and no very often can, and must rightly, be answered to the same question. For example, it can be both aflSrmed and denied, without any real contradic- tion existing between the answers apparently contradictorily opposed, that Logic is part of Psychology, if the word psycho- logy, in the affirmative answer, be used in its widest sense (as equivalent to mental science), and in the negative answer in a narrower sense (as, e.g. that given in § 6). The logical demand, that a choice be made between yes and no, interposes m force after that the possibihty of a simple answer Has been established by the strict statement of the ambiguous sense of a f^ I f u i ■A^ 238 77. The Axiom of Contradiction. ^77. Tlie Axiom of Contradiction. 239 I! question and the correction of its somewhat erroneous presup- positions. Not a few empty disputed questions, and not a few obstinate mistakes and deceptive sophisms, have been con- nected with the neglect of this precaution. The possibility of a different sense in the way in which the affirmation and negation is to be understood rests on this, that the combination of conceptions contained in the judgment may be compared, either with existence in the absolute sense or with the mere objective phenomenon (as it is conditioned by the normal function of the senses), and with this latter in various ways. For example, the question whether the sun moves on in space must be affirmed, denied, and again affirmed, as it refers to the first sensible phenomenon, to the system of the sun and the planets revolving round it (looked at from the distance 01 their centre from the centre of Gravity), or to the relation of the sun to the system of the fixed stars. Finally, he who (with Kant) believes that all existence in space is merely phenomenal, conditioned by the peculiar nature of man's sense- intuition, and refers the question to the sun as ' a thing-in- itself,' or to the transcendental object, which, since it affects us, causes the appearance of the sun in space, must give a denial to the question, from this critical stand-point. Its Proof. — The possibility and necessity of proving the axiom of Contradiction may be disputed, because it is a first principle, and so cannot be derived from another. At the most it can only be proved in the indirect way, that no thinker can avoid recognising its validity in any individual case. But it is doubtful whether this axiom is absolutely first and underiv- able. It has been often denied by Sceptics, Empiricists, and Dogmatists. And we ourselves believe that the highest logical principle is not the axiom of Contradiction, but rather the idea of truth, i.e. the consistency of the content of percep- tion and thinking with existence (cf. §§ 3, 6). The desirability of a proof can scarcely be denied now, when there are so many discussions of its correct formula, validity, presupposition, and the probable limits of its application. These can never find a settlement which will be generally recognised without some proof which will make clear the true meaning of the axiom. The fact that in some treatises the very truth of the axiom is seriously questioned contradicts in the most forcible way the vague assertion of its innateness, which would by anticipation prevent every philosophical investigation and recommend blind submission to the incomprehensible authority of the axiom. The possibility of proof rests on sufficient definitions of truth, of the judgment, and of affirmation and negation. If these are premised, then it is (as an analytically-formed proposition) deduced without difficulty from the mere analysis of the notions. Accordingly, the proposition correctly bears the name o^ fundamental proposition (axiom) only in so far as it has a fundamental significance for a series of other propositions, those, viz. in the doctrine of inference and proof, but not in the sense that it is itself underivable. Several objections of course arise against the general possi- bility of proving the axioms of contradiction, and against the special deduction given above. The deduction, it may be said, presupposes the validity of the axiom. To deduce it from the definitions is only possible on the presupposition that the contradictory cannot be true. But this objection proves too much or nothing at all. The same thing may be said of all logical laws — the thinking which deduces them rests upon them. If on this account demonstrations become fallacious reasonings in a circle, all scientific representation of Logic must be abandoned. ^But it is not so. For though these laws carry with them their own validity, and they are (at first unconsciously to us) [actually present[m our actual thinking even in that which deduces them, yet this deduction does not rest upon a scientific knotcledge of these laws ; and this know- ledge is to be carefully distinguished from their actual validity! (cf. § 4). The deduction of the axiom of Contradiction, as of any other logical law, would be a reasoning in a circle, if the proposition to be proved is itself, explicitly or implicitly, presupposed as known, and as one of the means of proof, as a premiss-, but this does not happen in the above deduction. This fallacy does not occur because the thinking, which makes 4 11 J 240 77. The Axiom of Contradiction, ^77, TIu Axiom of Co7itradiction. 241 II !.{' the deduction, is correct, i.e. by its being conformable to the law to be derived as well as to the other logical laws.^ It may be objected to our proof and to the validity of the axiom, that the deduction given above presupposes real existence to he the steady standard of thinMng. This, however (one may say), can only happen upon the metaphysical presupposition of the unchangeable persistency of all actual existence. Under the opposite metaphysical presupposition, and in reference to the objective phenomenal world, that very standard of change may be brought under the influence of time and become itself changeable. And in this way the necessary truth of the axiom is destroyed, or at least narrowed to a very limited sphere. We do not accept the metaphysical presupposition, however, for we (§ 40) have recognised the realty of change in time independent of human comprehension. 0istory shows that most famous thinkers of the past and of the present, Parmenides and Herhart, and in a certain reference Plato himself and Aristotle, have held the validity of this logical principle to be connected jointly and separately with that of the metaphysical doctrine! and that, on the other hand, Heraclitus and Hegel, who cpjK^e reality to Becoming and Change, also allow the axiom of Contradiction to disappear in the vortex of the universal flux; Nevertheless, we maintain our two theses equally firmly. Motion and Change have reality ; but this does not exclude the universal validity of the proposition that judgments opposed contradictorily to each other cannot both be true. The appearance that one of these theses excludes > This conformability appears to me to exist only in the division of the possible relations of thought to actual existence, into agreement} and want of agreement (cf. § 69), on which division the above proof rests (p. 235). This division is a dichotomy, because, in constructing the notions of Negation and Falsehood^ we comprehend whatever is noi; agreement under one other notion. If we believed (as Delboeuf, Log, p. 61 ff. does) that the principle of Contradiction enters into the pre- misses of the proof given above, and that it is therefore not valid au an actual proof, the discussion would still have significance because showing the relation of that principle to the fimdamental definitions (and so Delboeuf accepts it). the other is due to that one-sided view of the judgment which sees in the subject and predicate its only essential constituent parts, while all the diflferent parts of the proposition which grammar distinguishes have a logical significance, and cor- respond to just as many parts in the judgment (§ 68). The determination of time does not belong to the formula of the law, but to thejudgments to which the law finds application, if these refer to something which belongs to a section of time. If the objective existence with which the judgment has to do is a changing one, it is postulated that the same change enters into the combination of conceptions, and that it may come into consciousness along with the contained element of time. To this section of time the conception generally must be referred, and the simple elements of the conception to those points of time which are within this section. In this way, in spite of the continuous change, the conception of what has happened finds its steady, i.e. sure, standard in what has actually hap- pened. An historical fact, e.g. the assassination of Caesar, belongs as a whole to a definite section of time, and in every moment during its occurrence must bear the character of that which continuously happens. Nevertheless, the law of truth, excluding the contradictory opposite, for the judgment which relates to it, is : — The judgment is true if the real motion in the occurrence is truly mirrored by the corresponding ideal motion in the combination of conceptions, so that our concep- tion of the occurrence takes its place in our conception of tho universal connection of historical occurrences in our conscious- ness, just as the occurrence has its place in this connection in actual existence ; and the conception of each of its elements is arranged in the conception of its whole course, as each element is arranged in the actual and real course of the event. His- torical judgments affirming and denying the same about an occurrence in time, e.g. Socrates was bom 469 b.c., and Socrates was not born 469 B.c. (but 470 or 471), are as strictly opposed to each other as contradictories, and can as little be both true as the mathematical judgments which refer to unchangeable existence — the sum of the angles of any rec- R il' II I' I.' ii in Ai^ 242 ^77- T^^^^ Axiom of Contradiction. §77. T/ie Axiom of Cofiiradiction. 243 ^11 tilineal triangle is, and is not, equal to two right angles. Hegel and Herhart assert that motion and change are in them- selves contradictory, and Hegel teaches that motion is THE existing contradiction. Every moment of passing over from the one circumstance into the other (e.g. the beginnmg of day) unites in itself predicates which are opposed as contridictories to each other. Hegel asserts that these contradictory judg- ments are both true in reference to the same moment; but Herhart thinks that that is impossible according to the irre- frao-able law of Contradiction, and that the passing over mto, and the becoming another, have no reality.^ Both opinions are false. The semblance of contradiction results from the indefiniteness of the sense, and disappears as soon as every individual expression is referred to distinct notions. 13y means of strict definition of notions secure points of limitation are at once reached. For example, if the beginning of day be defined to be the moment in which the centre of the sun s disc appears above the horizon, the time of passing over into, which unites in itself the predicates opposed as contradictories, must now signify either a finite or an infinitely small section of time, or none at all. If the first be the case, the parts cf the finite section of time lie either on the negative or on the positive, or upon different sides of the boundary. In the first case (when the time of dawn is called the passing over of mght into day, or the beginning of day), the negative judgment, and it only, is true. The time of the passing over into, or the beginning, in this sense, is not the present existence (the dawn is not d^y). In the second case, when all parts lie on the positive side (when the first time after the passing over into is called the beginning of day), the affirmative judgment, and it only, is true. The beginning, in this sense, belongs to the time of present existence (to the day). In the third case, where the parts of the section of time, which forms the passing over into, fall on diiferent sides (e.g. when the time between the » Hegel, Wiss. der Logik, i. 2, p. G9, ed. 1834; cf. i. 1, p. 78 C; Encycl. § 88, p. lOG, 3rd ed. 1830 ; Herbart, Einl. in die Phil. § 117 : Metaph. ii. p. 301 ff. transit of the upper, and the transit of the under edge of the sun's disc is considered as the time of passing over into, or as the beginning of day), the difference holds good of the different parts of the subject, and the two judgments now stand as co-ordinate to each other. The one part of the begin- ning in this sense belongs to the time of the present existence (to the day), and the other does not. But no contradiction exists in this any more than in the co-ordination in space of different attributes in one subject. With reference to the undivided subject, however, the negative judgment, and it alone, is true (the time of the passing over into, in this third sense, considered as a whole, is not a part of the day). This does not prevent it, that the affirmative judgment, and it alone, is true of one part of the subject. If an infinitely small section of time be taken to denote the passing over into and begin- ning of, it must either fall on the one side, or on the other side of the boundary point, or divide itself on either side. In all these three cases, however, and for the same reasons, there is no more contradiction than in the supposition that the passing over into and the beginning of, is denoted by a finite section of time. Lastly, no contradictory judgments arise under the third supposition, that the boundary point itself, without any reference to extension in time, denotes the pass- ing over into. For this boundary point is a nothing of time. Its extension in time is supposed to be equal to zero. There are, therefore, no positive predicates at all* which can be predicated of it. In actuality, present existence is joined to non-existence immediately, i.e. without any intervening (finite or infinitely little) time. (For example, the ended transit of the centre of the sun's disc through the horizon to the time anterior to the transit.) The boundary point, so far as it is represented as something existing, or as a real intervening time which is also a nothing of time, is a mere fiction, which for mathematical purposes cannot be dispensed with, but which is destroyed in logical reference by the contradiction which it bears in it.* If this non-existent be feigned to exist, * This fiction rests on the abstraction, which holds fast and modifies s 2 i 1 i; 244 § 77. The Axiom of Contradiction, and be made the subject of a positive assertion (the point of time of the beginning belongs to the time of present existence —the point of the beginning of day belongs to day), this assertion is false, and what is opposed to it as contradictory is true ; not in the sense that this feigned point of time belongs to the time of what is about to exist, but in the sense that it does not belong to time at all. It is no part of time, neither finite nor infinitely little. It is a nothing of time. We may say of this judgment what Aristotle said of the judgment— rpaysXs^S? aarv \svk69. It is false, and its denial true ; not in the sense that the stag-goat had another colour, but because there is no such existence, and its conception is a mere fiction. We cannot, therefore, agree with Trendelenburg, who says that a contradiction is present in motion,' and yet allows that motion has reality, because the axiom of contradiction, although of irrefragable validity within its own limits, cannot be ap- plied to motion, which only conditions and creates the objects to which it applies.2 The axiom of contradiction may be applied to the notion of motion if we do not confine our attention to the proposition which is without difficulty—^ Motion is motion ;' but analyse the notion and go back to the elements which are fused too-ether in it, as Trendelenburg himself has done in the statements given above, that 'motion (why not rather that which moves itself?) is and is not at the same point at the same time.' According to our previous explanations, this the second of two really inseparable predicates— to be extended, and to occupy a place— while it completely sets aside the first. The Leib- nizian monadology, and the Herbartian assertion of simple real essences, involve the mistake of taking for real the separability of the two predicates, which exist only in abstraction, and of hypostatising the existence of a point. 1 Log. Unters. 2nd ed. i. 187 ; 3rd ed. i. 189 : ' Motion, which by means. of its notion is and is not at the same point at the same time, is the living contradiction of dead identity ; ' 2nd ed. i. 271 ; 3rd ed. i. 276 : ' The point first carries that contradiction which was present in motion aa soon as the elements contained in it were separated.' 2 Ibid. 2nd ed. ii. 154 ; 3rd ed. ii. 175. I 77. The Axiom of Contradiction. 245 being and not being, at the same point at the same time, is a mere fiction. Motion is not impossible because it is not con- tradictory. Yet it would appear as if the axiom of Contradiction, at least in one special case, admits of an exception, which is not excluded, but confirmed by the above argument. The actual existence to which the judgment refers, and in which it finds its measure of truth, whether it be external or internal (mental, psychic), is in both cases generally opposed to the judgment itself as another thing. The truth of the judgment depends uj)on it, but it, on its side, is not dependent upon the truth of the judgment. Now, there is one case in which the dependence is mutual. The actual existence to which it refers becomes another thing by the judgment (and that not me- diately by an action connected with the judgment, but imme- diately by the judgment become a thought). Hence the judgment appears able to become false because of its own truth. It is evident that this case happens when, and only when, the truth of the judgment is itself the object of the judgment, or belongs to the object of the judgment. The ancients have empirically discovered this case, without (so far as we know) giving an account of its logical nature. What is called ' The Liar ' represents it. Epimenides, the Cretan, says, all the Cretans are liars (K/a^Tfy au ^jreva-Tat), No logical difficulty exists if the invariable practice of lying refers only to the majority of cases, or rather to a prevailing inclination to lie; and this is the meaning of the sentence spoken by anyone who wishes to depict the Cretan character. It is also un- doubted that the assertion, if the invariable habit of lying be stiictly understood, is actually false, and false only. It may be granted, however, that apart from this assertion of the Cretan Epimenides, the proposition — All Cretans are always in all things liars— is true in all cases without exception. This assertion, although actually inadmissible, contains no internal contradiction, and in this sense is not iinpossible. But now it may be asked whether, on this presupposition, the axiom of contradiction has or has not validity when ai)plied f l\ I T w!f M* ii U. I 246 § 77. 7"/^^ Axiom of Contradiction. TJ. The Axiom of Contradiction, 247 to the assertion of Epimenides, and whether this assertion, together with its contradictory opposite, can or cannot be true ? Here is a logical problem which must be solved scien- tifically, and must not, as too commonly happens with modern logicians (the ancients, at least, tried earnestly to solve it), be evaded by one or other way of escape, least of all by an appeal to the pretended innateness and absolute character of the axiom. If, on the above presupposition, the assertion of Epime- nides universally comes to pass, and is true ; then if a stranger had asserted it, its contradictory (Cretans are not always in all they say liars, but sometimes speak the truth) would be, and remain, false. But since Epimenides, who has made this true assertion about the Cretans, is himself a Cretan, there is this one true assertion spoken by a Cretan. Hence the proposition that Cretans always lie about everything has become false by its own truth ; and its contradictory opposite is just as . true as itself. This may also be put thus :— If the general statement about the Cretans is true, it must also be true of Epimenides the Cretan, and of his assertion. He must in this statement have told a falsehood. The statement has proved itself false by its own truth, and its contradictory must be true. The two propositions then— This expression is true, and It is not true, are both true, contrary to the principle of contradiction. (Our first consideration had for its basis the truth of the assertion of Epimenides as its logical predicate. This must help to serve to constitute the objective matter of fact, and we infer from this matter of fact to its untruth in its content. The second proceeds from the meaning of the truth of the assertion in its content, and infers, back from it to a matter of fact to which it belongs, that the attribute to be untrue belongs to its assertion.) If we first take the expres- sion to be false, we find ourselves equally compelled to con- clude that it must also be true. For all other assertions of the Cretans, according to the above presupposition, are false- hoods. If this assertion of Epimenides be untrue, they are all absolutely untrue. But then, because of this matter of fact, the assertion is true that all Cretans are always liars ; the pro- position has become true by its untruth. The same may be shown in the following way : — If the assertion is untrue that all Cretans are always liars, then, that at least one ex- ample must be given where a Cretan speaks the truth. But according to the above presupposition, all their other assertions are untrue, and the assertion of Epimenides cannot be untrue, but must form a single exception, and be true ; and so has given us the statement of its truth from its untruth. The propositions, This expression is not true, and It is true, are again both true. (In this statement, as in our previous one, our first consideration has for its basis the untruth of the assertion of Epimenides as its logical attribute. Let this now be taken along with the matter of fact, and from the matter of fact, the truth of the assertion, in its content, follows. The second, on the other hand, proceeds from the meaning of the untruth of the statement in its content, and infers from it back to the matter of fact to which it belongs, that to-be-true belongs as a predicate to the same assertion.) But yet, in spite of this apparent confirmation, it would be too hasty a decision to grant that there is here an actual exception to the axiom of Contradiction. Under the simple grammatical ex- pression two different logical judgments are comprehended, the second of which cannot at all be thought, nor can exist as an actual judgment, unless the first has been previously thought. The first judgment has to do with all other asser- tions of the Cretans. It is true, and only true, on the pre- supposition on which we have here gone, that they are all of them untrue. Its contradictory is false, and false only. The second can only be formed with reference to this first jud«*- ment. In the second a similarly sounding statement is made with such universality that it also refers to the first judgment and its truth. But since the true assertion lies in the first judgment, the proposition in this enlarged sense is not more generally true, but false, and false only. Its denial or con- tradictory is true, and true only. If that complete strictness of thought and of expression of thought prevails, without which all these investigations are useless, we cannot assert that the 248 § 77- The Axiom of Contradiction. §77. The Axiom of Contradiction. 249 i same judgment, by the truth belonging to it, may change the matter of fact with which it has to do, and thereby become false. We must correct our statement in this way— By the truth of the first judgment the second becomes false, whose ideal presupposition is formed by the first. Hence the axiom of contradiction, in spite of this very deceptive appearance of an exception, asserts its exceptionless validity. To absolutely shun contradiction is a task demanding so harmonious a thorough construction of thought, and at the same time such a purity and freedom of intention, that to fulfil it remains an ideal which is ever to be reached proximately only. Not merely gaps in our investigation, but every kind of ethical naiTOwmindedness, the tenacity of national, religious, political, and social prejudices, lead to contradictions. The difficulty of overcoming contradictions reveals itself in anti- thetic propositions. Cf. § 136. Its History.*— We make the following remarks on the history of the axiom. Parmenides, the Eleatic, placed the positive axiom, eo-Ttv, or hov i^ifisiai, or Icrrt 7^^ slvai, by the side of the negative, ou/c fo-Tt M e'^'«*'" o^' 0^^^ "f^P "^""^ ^°^ ^'^'^''^ ^^' ^"^ ^^^ "^^^7 f^^f^ vo7)t6v saiLif OTTcos ovK scTt,,'' or, ov yap firjiroTS tovto 7 srj {^avfi ?) £LvaL firj eovra.^ In these expressions, and especially in the last,^ lies the germ of the axiom of Contradiction. They decline to assert that, what is, is not ; and they deny the co- existence of the truth of the judgments— This is and This is not.^ These expressions in Parmenides, however, have rather a metaphysical than a logical meaning. 1 Cf. the Articles of Weisse and I. H. Fichte referred to in § 76. 2 Pann. Fragm. ed. MuUach. vs. 35. 3 Vs. 106. ^ Vs. 64-65. * Vs. 52. 6 The forms given above partly depend upon conjectures in the (Plat.?) Sophist, p. 237. Bergk supposes toZt oh Aäv 7] ; cf. my Hist. o/Philos., translated by G. S. Morris, New York, 1871 (-Ith Germ. ed. 1871), i. § 19. 7 The axiom did not originate, as Weisse thinks, m the opposition of Aristotle to the Stoics, nor yet, as I. II. Fichte (cf. as above, p. 17) siii)poses, in the Flatonic Doctrine of Ideas. Socrates saysi^ os av ßovXofisvos Td\7)6rj X^ynv fiTj^siroTS ra avra irspl tcov avTcov 'SJyrj, a\X' 686v re pd^wv ttjv avTrjv tots fisv irpos lo), TOTfi Bs irpos iairspau (t>pd^y, . . . BrjXos on, ovk olBsv. Plato, when he is engaged with the metaphysical problem of establishing the relation between Bein^ and Becomino-, distin- guishes intelligible and sensible things. Every sensible thing unites in itself the oppositions, — what is large is at the same time little, what is beautiful is at the same time ugly, &c. We can- not establish the thought that it is what it is, nor yet that it may be the opposite, or is not, for all sensible things are in continual change. Hence, they have not existence, but vacil- late between existence and non-existence : dfia 6u te koi firj 6u — sKslvo TO äfi(f>0TEpo)V jjLETsxov Tov slval T£ KOI fiTj elvai. On the other hand, the axiom of Parmenides about Being is true of the Idea, It is asl kutci ravra (haavTcos s^ovaa.'^ In the Phaedo Plato mentions, besides ideas and sensible things, a third class, viz. the qualities which inhere in sensible things. He there does not attribute persistent sameness to ideas only, but asserts of the qualities of sensible things also, that they, so long as thc}^ remain that which they are, can never become nor be at the same time the opposite:^ ov fiovop amo to ^sysOos ovBsttot sBsKhv a/jua fisya Kal afxixpov ehai, dXXd xal to sv rj/xlv /jtsyeOos ovBeiroTS irpoaBix^ea-OaL to a^nKpov ovB' idsXsiv vTTSpsxscrdai, dXXa Bvoiv to sTSpov, rj (jysvysiv Kal vireKxcopsiv—rj — d-TroXcoXEmL.* ovk sdsXsL — ovBhv tS>v EvavTLwv STL ov OTTsp Yjv cLfia TovvavTLov yiyvE- aOal TE fcal shai.^ avTo to havTiov savTo^ svavTiov ovk av ttote ysvoiTO^ 0VT6 TO sv r]fuv, ovTE to ev T§ (f>vaEL.^ ivvwfioXoyrjKafjLEv dpa — /üLTjBsTroTS svavrlov savTw to svavTiov sasaOai, Plato says of sensible things, however, the opposite always comes from the opposite, and that opposite qualities are in them at the same time:^ ovrcoal yiyvsTat Trdvra, ovk dXXodsv rj i/c t61)p svavTLODV Ta svavTLa,^ ek tov svavTiov Trpdr/fjuaTos to svavrlov irpdyua * In Xenophon Memorah. iy. 2, 21. * Plat, de Rep. v. 478 sqq. 4 Ibid. p. 102 E. Ibid. p. 70 1). ^ Phaedon, p. 102 d. 5 Ibid. p. 103 B. 6 Ibid. p. 103 c. ^ Ibid. p. 103 B. lA ;' ...... \ 250 § 77. T/ie Axiom of Contradiction. §77. The Axiom of Contradiction. - 251 I fs^'u^v^aQai} V ov—XsySLS tot alvai h to, l^tfifila äfi6Tepa, Kai ^^ys6o9 Kai afjLLKpSTVTa ; h^^' ^f. the words in an already quoted passage of the Rep. p. 479 b: avdyKfj—Kal KaXa ircos avTk alaxpa avi]iai Kal oaa aXKa ipcoTas'—asl EKaaTOV äfi4>o- Tspwv s^STac. In another passage i^ ov/covv sifyafiev t« avT^ äfia irspl Taxnh havTia ho%aK^iv aUvaTov elvac ;— from which it is proved that the XoyiaTiKov whose spyov it is to measure,^ &c. is different from the lower parts of the mind : to tta/)«^ to, fihpa apa ^o^d^ov ttjs f W* '^^ '^^'^^ "^^ f^^'^P^ ^^'^ ^^ ^'"^ '^'^^J^'' —the union of different parts of the contradiction in the object is not taken into consideration, but the existence of the contra- diction in the thinking subject is. This copious quotation is needed to make clear in how far it is an incorrect expression to say (as is often done) that Plato has enunciated the axiom of Contradiction (particularly in the words,^ firjBsTroTS kvavTiov kavTw TO havTLov 'ecTsadat). The axiom of Contradiction has . to do with contradictory opposition exclusively ; the passage quoted from the Phaedo refers, in the first instance at least, to predicates opposed as contraries. The difference between Con- trary and Contradictory Opposition was not enunciated by Plato with the distinctness which is a necessary condition of the pure apprehension of the axiom. Thus he believes that, when he finds contraries combined in things, he must ascribe to them Contradictory Opposition. The chan(/e of predicate —the same thing has now, and then has not now, the same predicate— seems to him rather a contradiction in things. (The thought that, because the second point of time is another one, and therefore the second judgment in the affirm- ative a new judgment, and its negative form not the contradic- tory of the first, would have solved the difficulty, but lies beyond Platonism.) Accordingly, Plato excludes sensible things from the domain of this axiom (in both senses) because they are, what is and at the same time is not. He places under its authority the slXiKpucos ov, that which is uniform and un- chano-eable— Ideas and Mathematical objects. The axiom least » PhaedoTij p. 102 b. 3 Phaedon, p. 103 c. Plat. Rep. 603 a. entangled in ideological relations, and approaching most closely to the logical form in Aristotle, is stated in the Euthydemus,* where it is said to be impossible that any existing thing may not be what it is (tI tüv ovtwv tovto, o Tvy-^dvst. 6v, avTo tovto firj slvai), Aristotle, developing Plato's doctrines, expresses the axiom of Contradiction as a metaphi/sical axiom in the folio win o- care- fully circumscribed formula,— It is impossible that the same can and cannot belong to the same in the same reference : ^ to avTo äfm imdpxscv ts Kal /htj inrdp^eiv dSvvaTOP tw avTM Kal KaTä TO avTo,^ In a parallel passage^ he makes the ex- pression of contemporaneousness iv tS avrm XP^^V co-ordinate with the afia ovtco Kal ovx ovToys. By adding to the sio-ni- ficance of the TavTo, Aristotle expresses the same axiom in the shorter formula, — The same cannot be and not be:^ to avTO dfia ehac ts Kal ovk ehai — dBvpaTov,^ dBvi^aTov dfjua alvai Kal fiTj sivai.'^ Aristotle joins to this the corresponding lo(/ical axiom, — It is not to be asserted that the same is and is not ; Contradictory expressions cannot both be true : ^ ßsßaioTdTij Sofa Tracrwv to fir) slvai dXrjdsh äfia tcis dpTiKSi/jtsi^as (pdasc?.^ dBvvaTov Trjv dvTLaaLv dXrjOevsaOai dfia KaTa tov avTov.^^ dvTi- (fidasLS — ovx ^^^^ '^^ «/^« dXrjMs slvai. QV^ Kal s(tt(o dvTLa- hi- 12 ^T] £V CIS TOVTO' KaTd^aais Kal d7r6aai9 at dvTiKslfisvai. XScOai dfjLa (j)dvac Kal diro(f>dvai.^^ d^vvaTov ovtlvovv Tamov vTToXafißdvsLv slvai koi jirj slvai. We can recognise the influence of the Platonic thought in Aristotle's statement, that nothing can be true if all things are in motion ; '^ and that in order » P. 293 B. 2 Metap)h. iv. 3, § 13 Schw. ^ The statement of the axiom reminds us of the passage quoted in another sense from Plato, Rep. iv. 436 : IfjXov, on ravrdy rdvavTia TTüiely 11 Tra(X')(Eiv Kara Tuvroy ye Kai irpoQ ravroy ovk idiXt/tTet ä/xa. ^ In the Metaphysics, iv. 5, § 39. ^ ^^^^1. Pri. ii. 2^ 53 b, 15. 6 Metaph. iii. 2, § 12. ^ Cf. Ibid. iv. 4, § 1. 8 Ibid. iv. 6, § 12. 9 Ibid. § 13. 10 Ibid. p. 8, § 3. ^1 De Interpr. p. 6. »2 ^^^i p^^^ j jj 13 Metaph. iv. 3, § 14. Metaph. iv. 8, § 10 : ct he ivuvTa Kirtirai, ovdey ecrTai dXrjBic, TraiTU fiiiu x^evcf} : cf. iv. 5, § 27, and ix. 10, § 4. I 252 § 77. The Axiom of Contradiction. to completely secure the validity of the axiom of Contra- diction, Aristotle thinks he must state that there is an exist- ence unchangeable throughout.» But he does not, like Plato, hold the axiom to be absolutely invalid with reference to the changeable. By means of his distinction between Ivva^Lis and %Tikkx^ia or IvB^^iua, he more correctly shows that the same object may at the same time possess the capacity or possibility for opposites, but cannot contain the^ opposites m actuality or in their developed existenca:^ Ivxa^^i hhix^rai äfm Tamo ehat rä ivavria, ivreXex^la 8' oiJ.^ This last pro- position, however, has to do with contraries rather than with contradictories. Besides, Aristotle does not hold the axiom oi' Contradiction (as modern Formal Logic does) to be a sufficient foundation for a whole logical system. So far from this, he makes mention of it only occasionally in his logical writmgs, aud considers it to be a principle of Demonstration only ; and this not without the distinction that the axiom of Excluded Middle has a more intimate connection with indirect than the axiom of Contradiction has with direct Demonstration.* Aristotle sought to deduce the logical form of the axiom from the metaphysical (by a course of reasoning which is not stringently correct) f and, conversely, from the supposed truth of th'e logical to prove the truth of the metaphysical.« He thus placed the two in the strictest reciprocal relation. But he explains that it is impossible to deduce its truth from a higher principle by direct proof, for the reason that the axiom (in its metaphysical form) is itself the highest and most certain of all principles : ^ (pvasi jap apxh '^^t '^^^ a\\(ov a^Ko^aTav avTTj {rj .Bo^a) Trdvreov, ßsßaLordTT)^ avrrj tcov apxtov Traawv. The validity of the axiom itself can only be proved indirectl)', viz. by showing that no one can help recognising it in actual thinking and acting, and that were it destroyed' all distinctions of thought and existence would perish with it.^ According to » Metaph. v. §§ 10, 33. ^ jbid. iv. 5, § 9. 3 Cf. Ibid. ix. 9, § 2. * Anal. Post. i. 11. * Metaph. iv. 3, § J -3. 6 Ibid. iv. 6, §§ 13-11. ^ Ibid. iv. 3, § 16. 8 Ibid. p. 4, § 2. ' Ibid. iv. \. § 77. The Axiom of Contradiction. 253 the statements we have given above, a direct proof is impossible only when distinct definitions are wanting. The proof of the axiom in its metaphysical form may be put thus : — If the thought, or whatever is defined to be a copy (picture) of actual existence, differs from its real original, then the notions of untruth and non-existence find application, conformably to the definitions enunciated above. The notion of untruth is to be referred to the supposed image or picture. The notion of Exist- ing-but-not-in-this-manner is applied to what the copy was defined to correspond to ; and the notion of Non-Existence is applied to what was falsely thought to be the real correlate to the elements which do not acrree with it. Truth and falsehood, like affirmation and negation, are only in the image in so far as the image can be referred to the thing, and are in the domain of actual existence only in so far as images exist in it. The notion of the Existence exists independently of that of the image (while, on the other hand, the notion of reality implies that the existence has become known by means of an act of thought different from it, and may be applied to thinking itself, only in so far as this thinking has itself become the object of thought to another act of thinking reflect- ing upon it). Non-Existence is neither in the image (although it may be in its denial) nor in the object (although the exist- ence of the object in a judgment, which is therefore false, may be denied), but simply does not exist. The notion of non- existence, however, is primarily in the negative judgment in which we think the discrepancy between image and actuality. It can always be used to denote what does not exist, but is falsely conceived to exist; never to denote what does exist. In other words — It is not true, that the same thing which is, also is not ; or (as Aristotle says) — It is impossible that the same thing is and also is not.* The Aristotelian doctrine, in spite of many attacks, remains the prevailing one in antiquity, in the middle ages, and in modern times. * Cf. Trendelenburg, Log. Unters, ii. § 11 : Die Verneinung. M 1J t il I i ri 254 ^77- The Axiom of Contradiction, §77. The Axiom of Contradiction, 255 i In Antiquity.-T\i^ axiom of Contradiction was attacked by the Sceptics, who believed that the one of the two contradictory opposites was not truer {ovhlv ^aXXov), or at least not more able to be proved true, than the other. Epicurus also attacked it He did not wish to abolish it absolutely, but only to make it as indefinite as some things themselves are. The bat (.v/cr.pts), e.g is a bird and yet is not a bird. The stem of the broom (vaparj^) is and yet is not wood, &c.^ (Plato had said the same thing m reference to the world of sense.^) But this exception is false In such intermediate forms, which according to the notions ot natural science do not belong to a definite class, the negative and this only, is true. If a more extended notion is enunciated which includes it, then the affirmative is true. But then the iudcrment (in spite of the identity of words) has matenally become another, and this affirmation is not the contradictory of the former negation. . In the Middle Ages.-The Thomists followed Aristotle un- conditionally ; but in the School of the Scotists, doubt began to attack, not the axiom itself, which Aristotle, the highest authority in philosophical matters, had declared to be most certain, but its outworks. The question was raised, whether the axiom had the originality of a highest principle. The Scotist Antonius Andreae appears to have been the first who denied its originality and the impossibility of its direct proof. He souo-ht to derive the axiom of Contradiction from the axiom ens est" ens, which he thought was the positive and earlier. Somewhat later the Thomist Suarez defended the Aristotelian doctrine, and discussed the formula, ens est ens, in order to show that it could not, because of its emptiness and barrenness, be the highest principle and ground of metaphysics.^ In Modern Times,— T\iQ axiom has experienced bolder attacks. Locked despised it as a meaningless abstraction, an artificial 1 loann. Sic, schal, ad. Hennog. vi. 201, ed. Walz, republished by Prantl, Gesch, der Log, i. 360 ; cf. Cic. De Nat, Deorum, i. 25. 2 De Rep, v. 479. ^ Cf. Polz, Comm, Metoph. pp. 13, 21, 61 sqq. * Essay, iv. 7. construction of the Schools yielding no food for actual thought. But the reputation of the axiom was more firmly established after that Leibniz undertook to vindicate it, and combated Locke's objections. Leibniz held it to be an innate principle, which does not arise from experience, and indispensable as a rule for scientific knowledge.* He says,^ that on the strength of this principle we hold to be false what contains a contradiction, and believe to be true what is opposed as its contradictory to what is false. The last case, however (though Leibniz did not recognise it) presupposed that judgments may be known to be false in another way than by an internal con- tradiction. Every contradiction must be represented in the form of two judgments which are opposed to each other as contradictories, the one or other of which is necessarily false. But we cannot know, merely by means of the axiom of Con- tradiction, which of the two is false. We only know, accord- ino- to this axiom, that it is false that both are true. But to this falsehood nothing is opposed as its contradictory save the axiom — The tw^o members w^hich a contradiction contains in itself are not both true. The axiom *is correct enough, but does not teach us how to find out which of the two members is the true one ; and this is the problem. It is only when we know in some other way the falsehood of a definite one of the two members, that the axiom, that the contradictory opposite of the false is true, satisfies the demands of our knowledge and comes to have a real value. Wolff, like Aristotle, considers the metaphysical axiom to be self-evident, — fieri non potest, ut idem praedicatum eidem subiecto sub eadem determinatione una conveniat et non con- veniat, immo repugnet,' or: si A est A, fieri non potest, ut simul A non sit A;^ and deduces from it, by means of the definition of Contrary and Contradictory Opposition, the logical axiom of truth and falsehood, — duae propositiones con- trariae non possunt esse simul \ er 2iQ \^ propositionum contra- * Nouv. Essais J iv. 2, § 1. ^ Monadol. § 31. * Ibid. § 271. . "^ Ibid. § 520. 3 Log, § 529. ii 256 \n- 'The Axiom of Contradiction. §77. The Axiom of Contradiction, 257 dictorlarum-«/^.m necessario falsa.^ WolfF also followed Aristotle in not considering the axiom of Contradiction to be the one principle of the whole of Locjic (although he bases his Ontology upon it), and in mentioning it only occasionally in Logic. Baumgarten savs, in his Metaphysic r^ nihil est A et non-A : haec propositio dicitur principium contradictionis et absolute primum. .... Eeimarns^ formularises the law of Contradiction (principium Contradictionis) thus —A thing cannot be, and at the same time not be. . . , Kant' considers the axiom of Contradiction to be the prmciple of Analytic judgments. It is sufficient to establish their truth, and it furnishes a universal, though negative, criterion of all truth ; for contradiction completely does away with and abolishes all knowledge. In Synthetic knowledge, according to Kant, it is inadmissible to act contrary to this inviolable principle ; but it 'is no test of the truth of a synthetic judgment. It is the conditio sine qua non, but not the ground of the determination of the truth of our synthetic knowledge ; for even if a cognition be not self-contradictory, it may yet be contradictory to its object. Kant defines the expression of the axiom therefore—' A pre- dicate does not belong to a thing which contradicts it.' He rejects the Aristotelian-Wolffian formula,— It is^ impossible that something is and is not— partly because apodictic certainty, which should be understood from the axiom itself, is super- fluously brought in (in the word impossible), partly, and more particularly, because the axiom is aifected by the condition of time. It is a merely logical axiom, and its expression must not be limited to the relation of time (or rather, the notion of con- tradictory opposite already includes identity of relation of time in the two members, so far as a reference to time exists in the case under consideration). Kant comprehends the axiom of Identity and the axiom of Contradiction under the common I Log. § 532. ^ Metaph. § 7. ^ Vernunßlehre, § 14. 4 Krit. der r. Vern. p. 190 if. ; cf. p. 83 ff. designation. Axiom of Contradiction and Identity. ^ Those who have worked at Formal Logic since Kant generally share his views about the axiom of Contradiction, but think differently of its relation to the axiom of Identity. Some seek to deduce the latter from the former, or the former from the latter ; while others consider each to be a separate and independent axiom. The question only amounts to how each of these axioms is to be taken. According to different ways of expression and comprehension they are to be considered either the positive and negative form of one and the same law, or two different laws. Fichte^ believes the axioms of Identity and Contradiction to be the basis of our knowledge of the primary activity of the Ego (positing itself and the Non-Ego) : and finds this action of the Ego to be the real basis of these axioms. HegeP expresses the axiom of Contradiction in this way — A cannot be A and at the same time not be a. He considers it to be the negative form of the axiom of Identity, according to which A = A, or everything is identical with itself. He therefore thinks that this axiom, instead of being a true law of thought, is only the law of the reflective or ' abstract ' understanding. The form of the proposition itself contradicts it. A proposition promises a distinction between subject and predicate, but this law does not perform what its form demands. It is, more- over, invalidated by the following so-called laws of thought (the axiom of Difference, the axiom of Opposition or of Ex- cluded Third, and the axiom of the Reason). The truth of these laws is the unity of the identity and the difference, which finds its expression in the Category of the Reason. Thought as understanding lets things stand in their strict deter- minateness and distinction from others : its next higher stage is the self-elevation of those finite determinations and their passing over into their opposites, wherein lies their Dialectic or negative-intellectual moment. Lastly, the highest stage is the ' Logik, ed. by Jäsche, p. 75. ^ Grundlage der Wissenschaftslehre, p. 1 7 ff. 3 J Logik, i. 2, p. 36 ff.; 57 ff.; Encycl. § 115; cf. 119 and §§ 79-82 : * A kann nicht zugleich a und nicht a sein.* S I 25^ § 77- ^^^ Axiom of Contradiction. §77. The Axiom of Contradiction, 259 unity of the determinations in their opposition, the speculative ov positively-intellectual moment, in which both the duahsm of the understanding and the one-sided monism of the negative power of the reason reach their right position as the mutually dependent elements of free speculative truth. These Hegelian doctrines are not without truth (cf. § 80) in reference to con- trary opposites ; but their transference to the relation of con- tradictory opposition is based, as Trendelenburg has proved in his ' Logische Untersuchungen,' so clearly that we need only refer to his work in this place, upon the substitution of real opposition for logical negation. Chalybäus, too, says,^ ' it must be granted that in the Hegelian system it would be more correct to say opposite instead of contradiction.' Cf. § 31 and § 83, on the dialectic method ; § 42, on the recognition of the gradation of things as the true mean between the two extremes, which lie in the dualistic or ' abstract-understanding ' separa- tion, and the monistic or ' negative-rational ' identification ; and also the deduction of the law of excluded middle in the next paragraph. As regards Hegel's charge, that the axiom of Contradiction does not pay attention to the difference of predi- cate from subject, this has to do only with the form of sentence selected by him to express it, which so far from being essential to it is rather an expression very unsuitable and deviating from the true meaning. The true expression pays attention to pre- dicate and subject, and to every relation of the judgment. Herharf reduces the axiom of Contradiction to the formula — ' What is opposed is not one and the same.' He not merely asserts the validity of the axiom, but exaggerates its signifi- cance. He makes it exclude not merely the possibility of unitincr contradictory opposites, or the affirmation and nega- tion of the same, but also the possibility of uniting contraries, and of uniting a mere plurality of predicates in the same sub- ject (unless it is an aggregate without true unity), and there- fore the impossibility of thinking a thing with several changing 1 Die hist. Entwickelung der speculativen Philosophie von Kant hs Hegel, 2nded. p. 321 ; English translation by Edersheim, p. 419. 2 Lehrbuch zur Einl. in die Philos. § 39. qualities. Both extremes, the Hegelian and the Herbartian, are only expressions, from different sides, of the same funda- mental error — the substitution of contradictory and contrary opposition. Hegel transfers what is true of the latter to the former : Herbart, what is true of the former to the latter. [^Hamilton^ thus states the axiom of Contradiction, or, as he calls it (after Krug), Xon-Contradiction —What is contradictory is unthinkable. The logical import of the law lies in this, that it is the principle of all logical negation and distinction, and that it, together with the law of identity, regulates the cate- gorical syllogism. He does not make it, as some other formal logicians do, the only primary law of Logic ; but makes the law of Identity and the law of Contradiction co-ordinate and reciprocally relative, and says that neither can be educed as second from the other as first. In every such attempt at deri- vation the supposed secondary is always necessarily presupposed. The two are, in fact, one and the same law, differing only by a positive and negative expression.^ Boole^ in his attempt to reduce all logical to mathematical relations, to explain every possible operation and combination of thoughts by mathematical principles, and express them in mathematical notation, asserts, as his Fourth Proposition — ' That the axiom of Metaphysicians which is termed the prin- ciple of contradiction, and which affirms that it is impossible for any being to possess a quality, and at the same time not to possess it, is a consequence of the fundamental law of thought, whose expression is, x^ — x,^ He proves his proposition very simply and elegantly from his mathematical premisses, but can- not be said either to have explained or derived the logical law. To prove his whole theory, as well as this particular part of it, Boole must show that the fundamental mathematical relations are (1) simpler, and also (2) of more extensive application than the logical. If this be shown, then he may go on to show that \} Lect. on Logic j i. 81-2 ; cf. Hansel's Proleg. Log. p. 195 ff. ^ For a list of authorities upon this law of Contradiction cf. ib. ii. 246. 3 Laws of Thought, p. 49. 8 2 26o § 78. The Axiom of Excluded Third or Middle between two Juägntents opposed as Contradictories. 261 \\m 1 f the less simple relations of Logic, which have a narrower sphere of application, may be reduced to those of mathematics, and Logic become part of the latter science. But in fact the mathematical relations which Boole assumes (e.g.) to prove the law of contradiction are neither more simple nor of more extensive application than the logical axiom proved by them.* J, S. Mili^ says that the law of Contradiction is a principle of reasoning in the sense that it is the generalization of a mental act which is of continual occurrence, and which cannot be dispensed with in reasoning. He would express the law thus — The affirmation of an assertion and the denial of its con- tradictory are logical equivalents, which it is allowable and indispensable to make use of as mutually controvertible. A, Bain^ makes the law of Contradiction, with those of Identity and Excluded Middle, take rank among the maxims by which we attain consistency in thinking. Consistency re- quires that when we affirm a definite fact, we do not at the same time deny it ; having made an assertion, we are to abide by that. As by the law of Relativity everything that may be thought of, and every affirmation that can be made, has an opposite notion or affirmation, thoroughgoing consistency re- quires that we must be prepared to deny the counter notion or affirmation. The maxim of consistency which provides for this is the law of Contradiction.] § 78. The Axiom of Excluded Third or Middle (principium exclusi tertii sive medii inter duo contra- dictoria) is thus stated : Judgments opposed as contra- dictories (such as A is b, and a is not b) can neither both be false nor can admit the truth of a third or middle judgment, but the one or other must be true, * Cf. the whole of Chapters II. (of signs and their laws) and III. (Derivation of the laws of the symbols of Logic from the laws of the human mind), pp. 26-51. ' Examin. of Sir W. Hamiltons Philos. 3rd ed. p. 471. 3 Deductive Logic, p. 16.] and the truth of the one follows from the falsehood of the other. Or,_The double answer, yes and no, can- not be given to one and the same question understood in the same sense. The validity of this law also follows from the definitions of truth (§ 3), judgment (§ G7), and affirmation and negation (§ 69). These definitions assert, that the falsehood of the affirmation is equivalent to the want of agreement between the combination of concep- tions and the reality it represents, and consequently to the truth of the negation; and that the falsehood of the negation is equivalent to the agreement of the combination of conceptions with the reality it represents, and consequently to the truth of the affirmation. The remarks made under the law of Contradiction upon the entrance of a determination of time into the notion of contra- dictory opposition, and the other references to the distinctness of the sense in the judgments, to the possibility of proving the axiom, to its presuppositions, and to the case of apparent exception, are all applicable to the law of Excluded Middle. They are, indeed, to be more carefully attended to because this law is even more liable to be misunderstood. Various objections, partly against the value, partly against the truth of the law, are founded upon false ideas of its°aim and meaning. The VALUE of the law has been denied. It has been said to be devoid of meaning and to be superfluous. (The attacks have been made from the mutually opposite stand-points of the purely Speculative and of the Empirical Philosophy.) Its legitimate existence in Logic has been denied. It does not distinguish, it is said, between cases where the denial is proper, and those where it is not proper. It does not distinguish between partial and total negation. It is, consequently, a meaningless and barren formula.' But the strength of » UegeVs Enc//cL § 119; Beneke's Zo///y[-, i. 104 ff. Üfi 202 § 78. The Axiom of Excluded Third or Middle these objections lies in this, that they demand from the axiom what does not belong'to it. The axiom, rightly understood, does not say that we may search after predicates of any given subject by a sort of ' mounting to the sky,' and then find it able to be defined either by the positive notion or its contra- dictory opposite. It does not say that in order to know the predicates of Spirit, e.g., we may and do bring forward the notions of the qualities green and not-green, wooden and not- wooden, &c., and then rejoice in the certainty that in every case the one predicate must be applicable if the other is not. This would be absurd. The axiom presupposes a suitable question. It does not show what question is suitable. That follows from the essence of affirmation and negation (§ 69). There must be a motive for the affirmation. And usually the genus-notion, to which the predicate is subordinate, already belongs to the sub- ject. If the question be unsuitable, the axiom of Excluded Third gives an unsuitable, but not a false, judgment. (It is not false that Spirit is not blue, nor that a table does not think, &c. ; indeed, while the craze of table-turning and spirit-rapping lasts, this latter judgment is not even unsuitable.) The axiom is valid, without exception, in every case in which the question is distinctly unequivocal ; and therefore is not to be limited by annexing any condition which will embody the demands made above. ^ The axiom itself has nothing to do with its unsuitable application. It must be admitted, however, that the misinter- pretation of the axiom has been apparently sanctioned by the name which some logicians have given to the axiom of Excluded Third, and by the formula in which it is expressed. It has been called the ' Axiom of the determinability of every object by every predicate ;' and has been expressed in the formula — The one of all possible pairs of contradictory predicates must belong to every object. The application of the axiom in indirect proof shows that it is not valueless. The scientific postulate of systematic complete- ness demands that it be placed as the essential complement of I As I. H. Fichte, De Princ. Contrad. j'C. p. 30, and Ulrici, Loijiky p. 125, demand. between two Judg^nents opposed as Contradictories. 263 the axiom of contradiction ; and would demand the same in cases where it could not be applied. The TRUTH of the law has been denied. Objections are directed not merely against the value and productiveness of the axiom of Excluded Third, but also against its truth. Some logicians have limited it by certain exceptions. Others would entirely abolish it. The former think that the axiom is not valid when the subject is a general notion. For example, the triangle in general is neither rectangular nor not-rectangular.* But it is only the indefiniteness of the sense which causes the appearance of invalidity. If the sense of the sentence be — Every triangle is rectangular, the negation, and it only, is true. If the sense be — There are right-angled triangles which are objects of mathematics, the affirmation, and it only, is true. Others refuse to acknowledge the validity of the axiom at all.* The mean between the contradictory predicates, they say, is often the true predicate. All development rests on the union of opposites. Between ^ guilty ' and ^ not-guilty ' there is ' not-proven.' Between full imputation and no im- putation there is partial imputation. It would be a dangerous error to exclude this third case. It would often give judges the painful alternative of unjust acquittal or unjust condemna- tion, and give effect to expressions of only half truth in spite of better knowledge and desire. Absolute recognition or rejection, the simple division of the character into good and evil, leaving out of consideration all the intermediate grades, the partition of systems into true and false without making allowance for the gradual advance of knowledge, the separation of statements into credible or incredible and forged without including the myth or poetic truth, — all denote a certain crudeness of thought. The cultivated man knows how to recognise the finer ramifications of truth and error, and to draw the elements of truth, scattered everywhere, from under the coverings of error, as gold is drawn from dross. * Krug, DeJiklehre, § 19, teaches this. 2 Ilegel and his school, and Fr. Fischer, Logik, p. 40 ff. i\ 264 § 7^- 1^^ Axiom of Excluded Third or Middle Hegel says,^ ^ a philosophy of history has to seek a moment of spiritual truth in the most languishing constitutions.' Aru- totW^ and, more distinctly, Leibniz^ speak of elements of truth lying hidden in systems the most different and contradictory to each other, which the careful glance of him who searches most deeply may everywhere recognise. Leibniz * remarks (in opposition to Bayle) that the reason, when it recognises two views opposed to each other to be both false, thereby promises a deeper insight. But neither Aristotle nor Leibniz have explained themselves more definitely upon the relation of that relativity to the absolute validity of the logical laws of Con- tradiction and Excluded Middle, which is recognised by both philosophers. The opposition is established by later philoso- phers. ' If the knowledge of truth is not comprehended in a development,' Erdmann says, in HegeVs sense,^ ^ everything is either wholly truth or wholly not -truth. Truth becoming, or developing itself, is both or neither the one nor the other.' 'The strict maintenance of the laws of Identity and Excluded Middle, principles of the ' heathen Aristotle,' is even explained, humorously, but with all earnestness, to be unchristian,^ because the reconciliation of opposites is the fundamental thought of Christianity (guilt removed, a ' felix culpa '), while the persistency in opposition is heathenish. These observa- tions, however correct in themselves, and worthy of atten- tion, so far as they are to be considered as warnings against a false apprehension and application of the axiom of Excluded Third, prove nothing against the validity of the axiom rightly understood. They can only be held to be exceptions to it by exchanging contradictory for contrary opposition. Whoever ' 1 Philos. der Geschichte, ed. of 1837, p. 202. ' Metaph, i. 10 ; cf. ii. 1. 3 In his third letter to Eemond de Montmort, p. 704 of Erdmann's edition. * De Conform, ßd. et rat. § 80. * Gesch. der neueren Philos. i. 2, 171. 6 Fichte's Zeitschrifl für Phil. &c. xxviii. pp. 8, 9, 1856. 7 Like Fr. Fischer, Loyikj p. 40 ff. between two J udgments opposed as Cont^^adictories. 265 first explains that by Non-A he means something else than other logicians do, viz. contrary, and not as they do, contra- dictory opposition, and then upbraids them with the incorrect- ness of their axiom because it does not hold good under his terminology, acts no way differently from the man who, first of all explaining that he deviates from Euclid's usage, and understands, or at least comprehends, under * triangle' the spherical triangle, then turns round and blames Euclid because he teaches that the sum of the angles of a triangle are always equal to two right angles. The stricture, however, is to a certain degree legitimate when opposed to the formula — A notion or its opposite is to be predicated of every object. But if one keeps strictly to the notion of contradictory opposi- tion, its opposing members denote only the presence or absence of a strict agreement of the combination of conceptions with the actual existence they represent. No one can really and at bottom doubt but that one of these two members must always be true, and that the axiom of Excluded Middle, which only asserts this universally, is true also. It is already implicitly given in the definitions of truth and falsehood, and aflSrmatiou and negation. According to these definitions, to explain the negation to be false, is equivalent to the denial of the want of agreement with what actually exists, and equivalent to the affirmation of the truth of the aflfirmation. To explain the affirmation to be false, is equivalent to denying the presence of agreement with what actually exists; and this is ao-ain equivalent to the recognition of the truth of the negation. The negation cannot be interchangeable with the aflSrma- tion of the predicate opposed as a contrary. Not guilty is not equivalent to guiltless or pure. Not mortal (which may be said of a stone) is not equivalent to immortal or eternal. Not good {^ no one is good but God ') is not equiva- lent to .bad or wicked (the new-born child is not morally good. It requires education and the growth of personality in order to become good. But this is not to say that it is mo- rally bad) ; and so in all like cases. The truth of the nega- tion, which excludes the agreement of the positive statement i . 266 § 78. TAe Axiom of Excluded Third or Middle with actual existence, does not exclude any degree whatever of approximation to this agreement. The question— Is this criminal guilty of this distinct crime?— must be denied if only partial blame can be attached to him; because in this case the presupposition of blame conformable to the actual state represented does not occur. But the denial of this question does not make further questions, whether there has been any, and if so, what degree of approximation to full guilt, superfluous. It rather makes them necessary. The con- tradictory disjunction, guilty or not guilty, is not to be charged with the error of denying the possibility of half guilt (»r partial insanity. The error lies in making reciprocal the negation of this definite guilt with the affirmation of perfect innocence. The denial of guilt, as the accusation puts it, leaves open the possibility of a certain degree of guilt. In the same way the negation of a full ability to manage one's own affairs is always true, when its affirmation is false ; but this 'ne. The Axiom of Excluded Third or Middle ■ between two Judgments opposed as Contradictories. 269 III being of age and being under age ; observation from the stand- point of natural science and instruction finds a gradual deve- lopment. Practical necessity first imposes strict limits, which are to be defined only according to laws imposed by jurists.) In the questions about . Homer, the adherence to extreme views marks the starting-point of investigation. A maturer scientific treatment seeks to investigate, not whether, but how far, the poems are to be referred to one or to more authors. A modern philologist says, ' People should at length cease to settle the Homeric question by a yes or no.'* The question — Was Thales a theist? cannot be affirmed; but neither can it be denied in the sense that he was an atheist. His stand-point lies without and is below the opposition of the clearly defined pure Theism or Atheism. The same is to be said to the question — Did he subscribe to the mechanical or dynamical theories of natural philosophy ? The statement that Socrates was an upholder of the old morality and ancient simple faith of his people, must be denied ; so must the asser- tion that he was a partaker in the philosophical movement to which the Sophists belonged. His stand-point was already above these two opposites. It was the higher point in which they became one. His old accusers made the legitimate denial of the first statement the ground for affirming the second ; and not a few ancient and modern defenders have made the legiti- mate denial of the second the ground for affirming the first. Both were led astray in different ways by the same misappre- hension — a misapprehension which finds easy entrance, and is inevitable, so long as the peculiarity of the higher stand-point is not recognised. In the naive sayings of children and of persons of kindly feeling, who are not accustomed to put things to the test of objective fact, there is often truth. They express their actual subjective feelings. But the concep- tions in which this truth is embodied do not strictly agree with the external actual fact. Now if the truth of these assertions be enquired after, and if the answer be limited to yes or no, the axiom of Excluded Third appears to justify this procedure ; * G. Curtiusin ihn Zeitschrift für die östr. Gymii. p. 115, 1854. and does indeed justify it in so far as the negation is understood in the purely logical sense that a complete correspondence with fact in every particular does not exist. But it does not justify the negation in so far as it means a complete divergence from fact. It very often happens in this reference, that it is more difficult to formulate the question than to give the answer. In criminal cases the^ answer, guilty or not guilty, is left to the jury, but the statement of the question is entrusted to well-trained judges. A philosophical system may be partly true, when it contains true judgments along with false, and also when every individual judgment may approach more or less nearly to truth. And if a similar character pervades the whole system in strict connection, the very kind and deoree of approximation to truth which exists in the principles of the system may be found in every individual proposition. The different systems which have appeared in the course of history may, in this sense, be looked upon as different stages in the development of human knowledge, and as degrees of approxi- mation to perfect knowledge. He who now-a-days, in presence of this historical development of scientific notions, can put questions such as the following—Is the human soul free or is it not? Is freedom a true good or is it not? Do the New Testament writings contain the whole of the Christian Revela- tion or do they not ? Has the idea of philosophy embodied Itself in Plato, or has it not? and the like; — he who puts such questions, and demands a simple yes or no as answer, only proves that he has never studied the problems in hand, at least fundamentally. If he had, he would have first asked— ^lliat is freedom? What is revelation? What is truth? &c. In what sense and measure does the affirmation hold good, and in what sense and measure the . negation ? The conceptions, which exist before the scientific investigation, can- not be here presupposed to be self-evident. It is not their objective validity only that must be put to proof. In the form which they have before investigation, they are not absolutely valid, nor are they absolutely invalid. The chief task consists in finding the truly valid notion. This task does not indeed \ » « / f i ,lll km 270 § 78. TAe Axiom of Excluded Third or Middle ■ between two Judgments opposed as Contradictories. 271 promise ease. Thinking must strain itself to the highest degree possible. That restless bustle of action, which, with a ready yes or no, will proceed to external action, to stablish or revolutionise, but never will shake itself free of the bonds oi' those hurtful opposites, is not attainable by it. The true freedom of the mind is the stipulated reward of a disinterested resio-nation to pure thinking. Every false repose on a super- ficial affirmation or negation must be decidedly opposed. Bui we must hold as decidedly by the persuasion that there may b( pure truth, in whose attainment the gradual succession of approximations find their end and aim, which finds its fulfilment in adequate science ; for then only the question rightly stated, which has already included the determinations which correspond to the facts, can be answered by yes or no. In its limited province, mathematics has almost thoroughly reached this end (and natural science has in great part). Its development re- quires only upbuilding, never or seldom rebuilding. It is fool- ish to explain this excellence to be a defect in mathematics ; saying that it is a subordinate science, in which the laws of the reflective understanding yet hold good. The attainment of pure truth was an easier task for mathematics, because of the simpler nature of its problems, than it is to philosophy and to several of the other sciences. All, however, each in its sphere, are destined to reach the same goal by a gradual advance.^ History of the Axiom. — As the logical consciousness of the axiom of Contradiction was developed by Parmenides, in his polemic against the common affirmation of contradictory opposites by Heraclitus, so the origin of the doctrine of the Excluded Third is apparent in Aristotle* s opposition to the Platonic assertion of a Third or mean between Being and Not- Being. Plato set on one side Ideas, as that which is, on the opposite side, matter, as that which is not (but nevertheless made it the > [This thought runs through the late Prof. Grote's Exploratio Philosophica. Professor Grote had, apparently, in a quite independert way, reached many of the conclusions of those modern German phi- losophers who are supporters of the Ideal-Realismus.] substratum of sensible things), and between the two as the Third, sensible things. They are, he said, an indefinite mani- fold, and are in continuous becoming and change. As such, they neither truly are, nor yet are not. Their true place must be considered to be the mean between Being and Not- Being:^ Kal yap ravra kjra^(\>0TSpifyiv, Kal ovt elvai cuts firj slvai ovBsv avTOJP BvvaTov Traytcos vorjaai ovt afida£cos ivBe^STaL slvai ovdiv,^ dvar/Kij TTJs dvTCaa'is Bs dvrldsa'is, ris ovk sari fisra^v Kad^ avTTJv. The assertion of a mean term, Aristotle thinks, would lead to the absurd consequence that Existence would be one-and-a-half-ply, made up of the Being and the half- Being which is between it and not-Being. Then between these two another mean must be taken, and so on ad infinitum.* sTi sis airsipov ßaBisirai Koi ov fiovov rjjJLioXia td ovra so'Tai dXKd TrXsiw, Wolff teaches, like Aristotle® — inter contradictoria non dari medium;^ propositionum contradictoriarum altera necessario vera.^ Baumgarten uses the formula^, — omne possibile aut est A aut non A, seu omni subiecto ex omnibus praedicatis contradic- toriis alterutrum convenit — a formula which is liable to the misapprehension stated above, that it authorises a universal comparison of any possible subject-notion with any possible predicate-notion. ^ Metaph. iv. 7, § 1. * Metaph. iv. 7, § 9. 3 Ibid. §§ 5-6. 6 Ontolog, § 52. 1 Rep. 479 c. * Analyt. post. i. 2. 7 Log. § 532. ® It is singular, since these words of Wolff are only a translation of the A^ristotelian, that some think, such as Bachmann, Log. p. 62, that the axiom of Excluded Third is first found as principle of science in modern times and in Wolflf. 9 Metaph. § 10. >llll i!i 272 § 78. The Axiom of Excluded Third or Middle Kant^ explains the axiom, which elsewhere he incorrectly calls the axiom of Excluding Third, to be the basis of the logical necessity in apodictic judgments ; but does not deter- mine the formula more closely. Kiesewetter, following Kant, says, — 'The one or other of two attributes, contradictory to each other, must necessarily belong to every logical object' (The necessity lies only in the choice which must not be refused. The axiom does not teach at all, still less with apodictic certainty, which of the two members of the contradictory opposition is to be chosen. Hence the apprehension of the axiom, as a principle of apodictic judgments, rests on a misunderstanding.) Krug^ who disputes the possibility of applying the axiom in its common form to genus-notions,^ chooses the formula, — ' Of opposed determinations of one thing you can only affirm one, and if you have affirmed this one you must deny the other ' . — which is rather a formula for the axiom of Contradiction ; and * Every possible attribute must either belong or must not to every object thought as thoroughly determined;' in which formula both axioms are comprehended. Krug calls this axiom the principle of reciprocal capacity for determination. Fries^ uses the formulae, — ' A notion or its opposite belongs to every object.' — ' Any notion belongs either affirmatively or negatively to any thing.' He chooses the name, — Axiom of the determinability of any object by any predicate. The mis- apprehension of the axiom, already contained in Baumgarten's formula, is still more provoked by this. HegeVs strictures^ are justifiable against such a false appre- hension of the axiom, but not against the axiom itself. He says, ' Difference in itself gives the axiom, — Everything is essentially different ; or as it is also expressed, — Of two con- tradictory attributes only the one belongs to anything, and there is no third.' (This is, however, not strict enough. The definition, only one predicate and not the two together belongs * Logik^ p. 75. ' Denklehre, § 19. Following Polz, Comment. MetapJi. p. 107 sqq. 3 Cf. p. 263. -* Log. § 41. » Ibid. i. 2, ^(j ff.; Encycl. § 119. between two Judgments opposed as Contradictories, 273 to the same object, has rather to do with the axiom of Contra- diction. The axiom of Excluded Third, on the other hand, says — in every case the one predicate, and not both of the two, belongs to the same object, and Hegel himself recognises this.^ He calls the axiom in that form — the axiom of the opposite, or of opposition, or the axiom of Excluded Third, He thinks that this axiom contradicts the axiom of Identity. He combats it more especially by the assertion, that there is always a third between + A and — a, viz. a in its absolute value; and o is a Third between + and — . But here Hegel identifies the logical relations with the mathematical, from which, in spite of some similarity, they are to be essentially distinguished. Con- trary not Contradictory opposition exists ^ between positive and negative size in the mathematical sense. The negative quan- tity - A is by no means identical with the logical denial of + a. A quantity need not be either = +a or = — a. It may be either = + A or not = + A, and also either = — a or not = — a. And looked at apart from the signs, according to its absolute value, it may be either = A or not = A. Herhart and his school rightly hold firmly by the validity of the axiom of Excluded Middle.^ {Hamilton^ ^\y^^ the formula — ' Of contradictory attributions we can only affirm the one of a thing ; and if one be explicitly affirmed the other is denied. A either is or is not J5.' This law differs from the Laws of Identity and Contradiction by warrant- ing the conclusion from the falsehood of one contradictory proposition to the truth of another. Its logical significance ' Logih, i. 2, p. 67. ^ Kant noticed this in his Versuch, den Begriff der negativen Grössen in die Weltweisheit einzuführen, 1763 ; Sämmtliche Werke, ed. by Hartenstein, ii. 69 ff. ^ Herbart, L. z. Einl. in die Phil. § 39 ; Commentatio de principio logico exclusi medii inter contradictoria non negligendo, Gotting. 1833 ; cf. Hartenstein, Diss, de methodo philosophica logicae legibus adstrin- gencla, finibus non terminanda, Lips. 1835 ; Drobisch, Logik, 2nd ed. § 57, 3rd ed. § 60. * \_Lectures on Logic, i. 83. I \ \ 1 2 74 § 7^- Axiom of Excluded Third or Middle, etc. I § 79. Contradiction and Excluded Third, etc. 275 lies in this, that it limits the sphere of the thinkable in rela- tion to affirmation. It determines that of the two forms given by the laws of Identity and Contradiction, and by these laws affirmed as those exclusively possible, ' the one or other must be affirmed as necessary.' Hamilton seems to have fallen into the error of supposing that the law of Excluded Middle is a principle of Apodicticity, and gives necessary results. It necessitates the affirmation of one or other of the opposed contradictories. It does not affirm the one or other to be necessary. Besides, the formula which Hamilton uses is really the formula for the joint axiom of Contradiction and Excluded Middle, and does not express the latter purely. Cf. § 79. J. S, MilV thinks that this law is one of the principles of all reasonings, being the generalisation of a process which is liable to be required in all of them. It empowers us to sub- stitute for the denial of two contradictory pppositions the ' assertion of the other two. He denies in his Logic * the necessity and universality of the law, and says that it is not even true without a large exception. A predicate must be either true or false, provided that the predicate be one which can in any intelligible sense be attributed to the sub- ject. Between the true and the false there is always a third possibility — the unmeaning. There are many valuable re- marks in the pages Mr. Mill has given to the discussion of these law», and had he not been hampered by his empirical theory of the origin of all knowledge, and his consequent theory of the supposititious nature of demonstrative science, he would have approached very nearly to the doctrine laid down in the text. Had he only pursued the theory laid down in discussing propositions — that they express real rela- tions, he would have arrived at it. But there always seems to be a double view of Logic before Mr. Mill, and he shifts from the one to the other. On the one view Logic is a theory of knowledge, on the other it is almost a theory of naming. 1 Examination of Sir W. Hamiltons Philos. 3rd ed. p. 473. 2 i. 309. The two views come out most clearly in the chapters on pro- positions. Propositions in general describe facts, but Defini- tions describe names. In what is said of the laws of thought in his Logic the former view predominates ; in what is said in I the Examination, &c., the latter. A, Bain ' confuses the opposition of predicates as contra- dictories, with the so-called contradictory opposition of judg- ments, to the extent that he makes the one grow out of the I other ; while they are in no way related. He thus makes the law of Excluded Middle an ^ incident of partial or incomplete contrariety;' and says: *It is too much honoured by the dignity of a primary law of thought.'] § 79. The axiom of Contradiction and the axiom of Excluded Middle may be comprehended in the formula: A is either b or is not b. Any predicate in question either belongs or does not belong to any subject; or — of judgments opposed as contradictories to each other, the one is true and the other false ; or — To every completely distinct question understood always in the same sense, which has to do with the possession of a definite attribute by a definite subject, yes or no must be answered. These formulae contain the axiom of Contradiction, for they posit two contradictory mem- hers^ and assert that the aflfinnation and denial of the same cannot both he true ; a is either b, or is not b. They also contain the axiom of Excluded Third, for they posit only two mutually exclusive members, and assert, that any third besides afiSrmation and negation is inadmissible, and that both are not false., but one of the two is true, — a is either b or is not b ; there is no third. The comprehension of the axioms of Contradic- * Deductive Logic, p. 17.] T 2 I \ IRf! 276 § 79. Contradiction and Excluded Third tion and Excluded Third in the foregoing formula may be called the Principle of Contradictory Disjunction (principium disiunctionis contradictoriae). A suitable statement of the question is again the natural presupposition of the application of this principle. The transference of the denial to the predicate ' A is either B or non-B,' — is not false, provided that, by non-B, only con- tradictory opposition be understood. It is a useless artifice, however, and easily gives rise to a false meaning in the con- trary opposite. The simplest metaphysical formula of the pnnciple of Con- tradictory Disjunction is found as early as in Parmenides^ sanv rj ovK saTLV. It is here used only in the sense of the axiom of Contradiction to reject the common truth of the assertion of Being and Not-Being. Being and Not-Being cannot exist together, the one excludes the other. Aristotle, on the other hand, uses the comprehensive for- mula mostly in the sense of the axiom of Excluded Thircl.^ aXKÄ fjLr)r ovBs fiSTa^v ai^Ti(f)d(T£(os svhs-)(£Tai elvai, ovOsv, ahX dvdy/cr) rj ^dvai rj aTTo^di/at tv Kaß* epos otlovv,^ ttclv rj (jyavai rj dirocpdvai avajKalov.^ sttI ttjs KaTadas(t)s a£i> — TO srspov earai ysvoos nai to srepov aX'quss, ro o airav diai rj d7rodiaL dvay/caiov. Both cannot be false and a Third or Middle true. No place is left for a Middle. For a Middle, if it be true, or even thinkable, and have the reference to truth and falsehood, which belongs essentially to every judgment, must itself be one of that combination of members, which it cannot be accord- ing to its very notion. For in the Middle neither what exists nor what does not exist is affirmed or denied. It is in this way that the incompletely expressed reasoning of Aristotle against the Middle or Third must be completed.* Leibniz * places the negative form — ' A proposition is either true or false,' by the side of the affirmative form of the pri- mitive, identical, rational truth — 'Everything is what it is.* He calls this axiom the principle of Contradiction, and divides it into the two axioms which he includes in it — ' That a pro- position cannot be true and false at the same time ; ' and— * That there is no mean between the true and the false,' or rather — It is not possible that a proposition can be neither true nor false. In the same way Leibniz ^ calls, ' Principe de la Contradiction,' the one ' which asserts that of two con- tradictory propositions the one is true and the other false.* Leibniz, therefore, understands by the Principle of Contradic- tion that axiom which includes both what is usually called the Axiom of Contradiction and the Axiom of Excluded Third. Wolff* enunciates the formulae 'quodlibetvel est, vel non est;' ' propositionum contradictoriarum altera necessario vera, altera necessario falsa,' and says, 'patet per se, eidem subiecto A idem praedicatum B vel convenire, vel non convenire.' Many, both of the earlier and of the later logicians, have wrongly believed the formula — a is either B or not B, which includes both the axiom of Contradiction and of Excluded Third, to be the proper and simple expression of the axiom of Excluded Thu:d.-^ * Metaph. iv. 7, §§ 2, 6. « Nouv. Ess. iv. 2, § 1. 3 The'od. i. § 44. < Ontol. § 52 ; Log. § 532. Cf. upon the whole question, Katzenberger, Grundfragen der \ Logik, Leipzig, 1858. I I ■li 278 § 8o. Relations between Judgments § 80. The foregoing Axioms are not to be applied to judgments whose predicates stand to each other in the relation of contrary opposites (like positive and nega- tive quantities). In this relation it is possible under certain presuppositions, that (a) both judgments be false ; and that (b) both judgments be true. Both may be false : — 1. When that notion which is superordinate to the two predicates opposed to each other as contraries as their common genus-notion does not belong to the subject as its predicate. (Kant called this relation Dialectical Opposition.) 2. When that genus-notion belongs to the subject, but comprehends under it, besides the two predicates opposed as contraries to each other, other species-notions. In this last case the axiom of the Third lying as a mean between two contrary opposites finds application (priii- cipium tertii intervenientis inter duo contraria). Both may be true : — When the subject denotes an object, which is neither absolutely simple nor yet a mere aggregate, but is a synthetic unity of manifold determinations. When some of these determinations or attributes stand in the relation of contrary opposites to each other, the axiom of Coincidence may be applied to them (principium coincidentiae oppositorum). All development by strife and union of opposites rests on this principle. Judo-ments, whose predicates are opposed to each other as contraries (§ 53) — e.g. Caius is happy, Caius is sad— are to be strictly distinguished from judgments which are contrarily opposed to each other as judgments (§ 72)— e.g. all men are zv/iose Predicates are opposed as Contraries, etc. 279 learned, no men are learned. The former may not only both be false, but in a certain sense may both be true. For example, both joy and sorrow are contained in the feeling of yearning. The latter cannot both be true, but both may be false (§97). From both of these relations we must distinguish the relation of Contradictory Opposition, whose members cannot both be true nor both false (§ 79) ; for example — Caius is happy, Caius is not happy ; all men are learned, some men are not learned. Plato teaches that one and the same thing may unite in itself qualities which are different and even opposed to each other, although the quality itself is never identical with its opposite.* In a similar way, Aristotle explains that the object may change because it may take properties which are opposed to each other, but that the property itself always remains the same in its notion.* Since Aristotle says distinctly, that ordy contradictory opposites exclude every mean, he makes a mean possible in contrary opposites^ {hii 'yap fiovcov tovtodv avayKalov asi TO fisv d\r)9ss, to Be yfrsvBos slvai). Later logicians have seldom thought the relations of judg- ments with predicates opposed as contraries worthy of more particular attention. Augustine says, in his short doctrinal epistle to Laurentius :* — Omnis natura etiamsi vitiosa est, in quantum natura est, bona est, in quantum vitiosa est, mala est. Quapropter in his central iis, quae mala et bona vocantur, ilia dialecticorum regula deficit qua dicunt nulli rei duo simul inesse contraria. NuUus enim aer simul est et tenebrosus et lucidus, nullus cibus aut potus simul dulcis et amarus, nullum corpus simul ubi album ibi et nigrum .... sed mala omnino sine bonis et nisi in bonis esse non possunt, quam vis bona sine malis possint. But he does not strictly distinguish Contrary from Contradictory opposition. Nicolaus Cusanus, and after him Giordano Bruno, were the ^ Phaedon. p. 103 b; cf. Soph. p. 257 b, where the Ivavriov is dis- tinguished from the erefjoy. 2 Metaph. iv. 5, § 40. ^ Ibid. iv. 7, § 1 ; cf. Categ. x. 13 b, 2. * De Fide Spe et Caritate, c. v. ji !! i! il 2 8o § 80. Relations between yudgments, etc. first to enunciate expressly the principium coincidentiae oppo- sitorum. Kant rigorously distinguishes the opposition of contrary predicates from contradiction. Judgments of the first kind can both be false. For example, it is equally incorrect to attribute the predicates of limited and unlimited to what has no existence in space ; beginning in time, and beginningless, endless dura- tion in time, to the timeless. The opposition here is only * dialectic,' or apparent.^ Hegel and Herbarty as has been shown above, make no dis- tinction between the oppositions, but do this in opposite ways. The insight that the form of all development in the life of nature and mind (Geist) is the development of (contrary) op- posites out of the indifferent or the germ, and their union in a higher unity, is to be recognized as an abiding result of the speculation of Schelling and Hegel. In the same sense, /. H, Fichte,^ while he condemns the exchange,^ says quite correctly,"* ' est enim ubertas rei quaedam, si opposita ad se referre et in se copulare possit ; ' and Trende- lenhurg^ who shows the dialectic method of Hegel to be an exchange of logical negation for real Opposition,** recognises that^ * solet quidem natura, quo maiora gignit, eo potentius, quae contraria sunt, complecti.'^ If contrary opposites could not unite in any way there could be no multiplicity or development. Everything would be as Parmenides believes, ' The One alone truly exists ; ' or as Her- bart, in a milder way, expresses it, ' Each one of the many is * Krit. der.r. Vern. 2nd ed. p. 531 ff. * De Frinc. Contrad. 1840; cf. Ofitol. p. 159, 1836, where he in- correctly makes * Unterschied ' (Difference) and * Gegensatz ' (Oppo- site) equivalent to * Contrary ' and * Contradictory,' p. 165 ff. 3 P. 25. * P. 28. * Log. Unters. 2nd ed. i. 43 ; 3rd ed. i. 43. ^ Elem. Log. Arist. ad § 9, p. 65, 3rd ed. ; cf. Log. Tint. 2nd ed. ii. 234; 3rded. ii. 257. ^ Cf. also the work mentioned above (§ 69), Gustav Knauer, Conträr und Contradictorischj Halle, 1868. 81. TÄe Axiom of Sufficient Reason, 281 simple and unchangeable, unalterable, persisting in its simple quality.' — If contrary opposites were not relatively indepen- dent (or if contradictory opposites even could be united), there could be no unity nor persistence. Everything would be as Heraclitus, and in a more logically definite way Hegel, be- lieves. — ' Everything fleets. Everything is like and also not like itself. Nothing is definable by a permanent notion.' In reality both unity and plurality, persistence and change, exist together. And the one not exclusive of the other, as Plato represents by Ideas and Sensible Things, or as Kant almost similarly represents by his 'Ding an Sich' and phenomena. They exist, as was partly taught in antiquity by Aristotle and the Stoics, and in our time has been taught by Schleier macher in a purer and deeper way, in, with, and through each other; so that the uniting essential form and force dwells in the multi- plicity of phenomena, and inviolable law rules the change of actions. § 81. The Axiom of the {determining or sufficient) Reason subjects the deduction of different cognitions from one another to the following rule : — A judgment can be derived from another judgment (materially dif- ferent from it), and finds in it its sufficient reason, only when the (logical) connection of thoughts corresponds to a (real) causal connection. The perfection of the knowledge lies in this, that the ground of knowledge is coincident with the real ground. The knowledge of a real interdependence of things conformable to law is reached, as (§§ 42-42 ; 46 ; 57 ; 73) the knowledge of the inner nature of things in general, and more espe- cially of the individual existence, of the essence, and of the fundamental relations are reached. The external invariable connection among sense -phenomena is with logical correctness explained by an inner conforma- '.? Ii !l 282 § 8 1. The Axiom of Sufficient Reason, bility to law, according to the analogy of the causal connection perceived in ourselves, between volition and its actual accomplishment (whose existence we learn for the most part by striving against what resists us). The real conformability to law reveals itself iu the simple regularity of external and especially inorganic nature in a way more evident and more fitted to arrest the attention, than in the manifoldly complicated psychic processes. Yet these are the only cases, in which the peculiar character of that con- formability to law as the realisation of the internal powers, is immediately accessible to observation. So long as the man has no presentiment of an internal conformability to law, what happens externally is also referred to the lawless caprice of imaginary agents. A genetic treatment finds a thoroughgoing causal conform- ability to law in the (objectively real) relations with which mathematics has to do. The objective interdependence between quantities and between forms exists in and for itself, when not recognised by the subject. On this objective interdependence the physical processes rest, which exist independently of the knowing subject, and condition the possibility of existence of knowing subjects. On the objective nature of quantity and of space that conformahility to law is established, which Kant re- ferred falsely to a subjective origin. The logical form of axiom given above only asserts that the combination of judgments, by which a new one is derived from given ones, must rest on an objective causal nexus. Whether and in what sense everyihm^ objective stands in causal relations is to be decided elsewhere (in Metaphysics and Psychology). Plato and Aristotle make the thoroughgoing agreement {ofio- Xoyia, ^vi^aSsiv, ^vfKfxopHif) of cognitions with each other and with their grounds, an essential condition of their truth. Plato teaches : * ttuv to yiyvofisvov utt' ahiov tivo9 if dvdytcrjs ylyifEcdaL' iravjl yap dBvvaTOP X(ji}pl5 air lav yspsaiif a^su^^ 1 Tim. p. 28 A. « Cf. Fhaedon, pp. 100 a, 101 d; De Rep. vi. 511. § 8i. The Axiom of Sufficient Reason. 283 Aristotle places the essence of science in the adequate know- led o-e of causes. The syllogism warrants this knowledge, since the middle notion corresponds to the real ground.* Aristotle distinguishes, in his Metaphysics, four principles or causes i/ipXP-i or avTiat) : Matter, Form, Cause, and End;^ but with reference to our knowledge he distinguishes the grounds of Being, Becoming, and Knoudng.^ iraaayv fisv ovv kouov twi/ apx^v TO TTpw-rov sliac 66eu rj ecmv rj yiyvsrai rj ytyvcoaKSTaf TovTwv Be at fisv evv'irdp')^ovaai stVtr, at hs ektos. The axiom, ' Nihil fit sine causa' was in use among the ancients as an axiom of Physics. Cicero quotes it against Epicurus,'* ' Nihil turpius physico, quam fieri sine causa quid quam dicere.' Suarez.^ ' Omnia alia, praeter ipsum (Deum), causam habent.' Jacob Thomasius^ distinguishes * Omne ens, quod fieri dicitur, habet causam eßcientem ; ' — * Christianis omnino statu- endum est, canoni praesenti locum esse quoque universaliter in causa ^Wfl/z.' Leibniz was the first who expressly placed the axiom of Dettrmining (or as he afterwards called it) of Sufficient Reasoji, side by side with the axiom of Contradiction, as a principle of inference. He says,^ — ' It is necessary to remember that there are two great principles of our reasoning ; the one is the principle of Contradiction ; the other, that of " la raison determinante," which is, that nothing can be concluded, with- out it has a determining cause, or at least reason.' ^ ' Our intellectual inferences rest on two great principles : the prin- ciple of Contradiction, and the principle of Suflficient Reason, in virtue of which we know that no fact can be found real, no proposition true, without a sufficient reason, why it is in this way rather than in another.' In his Second Letter to Clarke 1 Arist. Anal. pt. I. 32 ; Eth. Nicom. i. 8 ; Anal. Post. i. 2 ; ii. 2. 2 Metaph. i. 3, § 1 and elsewhere. ^ Ibid. v. 1, § 9. * Be Fin. i. 6, 19, and elsewhere. * Metaph. i. 235. « Dilucid. Stahlianae, § 127. ^ Theod. i. § 44. "^ Monadologie {Princip. Fhil.\ § 30 sqq. 284 § 8 1. The Axiom of Sufficient Reason. §81. The Axiom of Sufficient Reason, 285 Leibniz also calls this principle, ^Principium Convenientiae.' At the end of the fifth letter to Clarke he makes the same threefold distinction as Aristotle : ^ ' This principle is that of a sufficient reason, why a thing exists, an event happens, a truth has place.' The first and second references belong to Meta- physics, the third to Logic. Wolff '^ and Baumgarten ^ seek to deduce the axiom of the Reason from the axiom of Contradiction, because they believe that the latter is the only absolutely a priori principle (which is to be combined with Experience however). If the ground of a thing lies in nothing, then nothing is the ground or reason itself. But this contains the contradiction, that nothing, as an actual principle, is also something. The mistake in this de- duction (the misinterpretation of the expression 'nothing is the ground,' because of a false realisation of ' nothing ') was pointed out by contemporaries. Wolff,^ following Leibniz,^ explains the axiom of Contradiction to be the ground of necessary, and the axiom of Sufficient Reason, the source of accidental truth. Kant^ thus enunciates the ^ Law of Causality:' ^ All changes happen according to the law of the connection of cause and effect.' He considers this to be a synthetic axiom ä priori, and a ground of possible experience, or of the ob- jective knowledge of phenomena, in view of their relation in the course of succession in time. He does not allow that it is applicable to ' Things in-themselves.' In Logic, Kant ex- plains the ' axiom of sufficient reason ' to be the principle of assertory judgments.^ He gives it* the form— 'Every pro- position must have a reason.' He makes this logical principle not co-ordinate with, but subordinate to the axiom of Contra- diction. On the other hand, the transcendental or material 2 Ontol § 70 sqq. ; cf. Metaph. § 30 ff. * Annot. ad Met. p. 9 ff. ^ Metaph. v. 1, § 9. 8 Metaph. § 20. « Frinc. Phil. § 30 sqq.; Ejn'st. ii. ad Clare, ß Krit. der r. Vernunß, p. 232 ff. 7 Xo^. ed. by Jasche, p. 73. 8 In the treatise Ueher eine Entdeckung, &c. Works, ed. by Har- tenstein, vi. 1 ff. principle, ' every thing must have a cause,' is in no way derivable from the axiom of Contradiction. On the basis of the Kantian theory Arthur Schopenhauer^ asserts that the principium rationis sufficientis essendi, fi endi, agendi, and cognosceudi, are the four fundamental forms of synthesis ä priori. Hegel (following Fichte and the Neoplatonists) resolves the law of the Reason, — ' Every thing has a sufficient Reason,' into the law of the combination of opposites, — ' The reason is the unity of Identity and Difference.'* Herbart^ seeks to explain the real (causal) nexus by means of his theory of the self -conservation of simple essences, in oppo- sition to their disturbance by conflict with others ; and to solve the question of how antecedent and consequent may be con- nected, by his so-called 'method of references,' i.e. by the hypothetical completions of what is given, which prove them- selves necessary by the fact that the law of Contradiction re- mains unviolated only when they are accepted. According to Schleier macher,^ the (causal) necessity rests on the inter-dependence of the system of the co-existence of Being, or on ' Actions,' just as freedom does upon its existence in and for itself — as 'power.' The true view is contained in the definitions of Hegel, Herbart, and Schleiermacher. It is that the whole cause is made up of the inner ground and the outward conditions.^ A more exhaustive representation and proof of this doctrine would lead us away from the province of Logic into that of Metaphysics. Delboeuf agreeing with the views laid down in this para- graph, enunciates as the principle which makes legitimate all our inferences (raisonnements) the axiom, ' The logical concatena- tion of the ideas corresponds to the real concatenation of things.'^ [J, S, MiW says that the most valuable truths relating to phenomena are those which relate to the order of their succes- * Ueher die vierfache Wurzel des Satzes vom zureichenden Grunde. 2 Logik, i. 2, p. 72 ff.; Encycl. § 121. » Allg. Metaph. ii. 58 ff. * Dial p. 150 and elsewhere. 5 Cf. § 69. 6 Cf. § 75. \J Logic, i. SCO. 286 § 8 1. The Axiom of Sufficient Reason. sion. In order to know such truths we must endeavour to find some law of succession which has the same attributes, and is therefore fit to be made the foundation of processes for dis- covering, and of a test for verifying all other uniformities of succession. This fundamental law is the ' Law of Causation ' — ' every fact, which has a beginning, has a cause.' The notions which are combined in this formula, along with the law it expresses, are gained by experience. Invariability of succes- sion is found by observation to obtain between every fact in nature and some other fact which has preceded it. The suc- cession is not usually between one antecedent and its conse- quent. The processes of nature are complicated. ' The cause is the sum total of the conditions, positive and negative taken together ; the whole of the contingencies of every description, which being realised, the consequent invariably follows.' On this law every inductive truth rests, and to it every inductive process must be referred. A, ' Bain * believes that there must be some guarantee for every real inference, and that the sole guarantee is the Uni- formity of Nature. Now uniformities of Nature are either of co-existence or succession. The evidence for uniformities of co- existence is special observation of each separate uniformity. In uniformities of succession the labour has been shortened by the discovery of a law of uniformity— the law of Causation. It may be expressed thus:— ^ Every event is uniformly preceded by some other event.' The most important form of the law of Causation is what Mr. Bain calls the * law of the conserva- tion of force which encompasses and pervades all the natural sciences, each one of which is but a partial development of it.' Sir W, Hamilton, in his lectures,^ enounces a law of Reason and Consequent, which he says is the foundation of the Hypo- thetical Syllogism. He expresses it, ' Infer nothing without a ground or reason.' In the Appendix to his Lectures, however, and in his Discussions, he refuses to admit this law, saying that, (1) inasmuch as it is not material it is a derivation of the three formal laws of Identity, Contradiction, and Excluded Middle; * Deductive Logic, pp. 18-20. P. 85.] S 82. Forms of Immediate Inference in General. 287 and (2) inasmuch as it is material, it coincides with the prin- ciple of Causality and is extralogical] The Leibnizian principium identitatis indiscernibilium * can only be expounded in Metaphysics, not in Logic. § 82. The Forms of Immediate Inference are : partly The derivation of a judgment from a notion^ i.e. the analytical formation of notions ; and partly — The deriva- tion of a judgment from a judgment. There are seven kinds of this latter derivation, viz. : (1) Conversion; (2) Contraposition; (3) Change of Relation; (4) Subalternation ; (5) AequipoUence ; (6) Opposition; (7) Modal Consequence. Conversion has to do with the position of the elements of the judgment withm its Relation, and often indirectly with the Quantity. Contraposition has likewise to do with the position of the elements of the judgment in its Relation with the Quality, and often indirectly with the Quantity. Change of Belation has to do with the Relation itself. AequipoUence refers to Quality ; Opposition to Quality and indirectly to Quantity. Modal Consequence has to do with the Modality of the judgment. All these deductions rest on the axioms of Identity « and Contradictory Disjunction. Aristotle discusses Conversion {di/Ti(TTpE(j)Hv, dvTLscv, by which he understood Contraposition, and dvasiy, by which he meant Conversion, He applied both terms to categorical and also to hypothetical judgments. Appuleius seems to have been the first to use the Latin term aequipollens in his definition : ' Aequipollentes autem dicuntur (propositiones), quae alia enunciatione tantundem possunt et simul verae fiunt aut simul falsae, altera ob alteram scilicet.' ^oeYA/M^ calls equivalent judgments indicia convenientia or consentientia. He uses the phrase conversa per contra posi- tionem for Contraposition, and calls Conversion in the strict sense Conversio Simplex. Simple Conversion is accomplished either principaliter, i.e. without change of quantity, or per accidens, i.e. with change of quantity. In other respects, the terminology employed by Boethius is the same as that of the Scholastic and of modern formal loo-ic.^ PFolff does not call immediate inferences ratiocinatio (because he means by ratiocinatio the deduction of a third judgment from two given ones only). He calls them consequentias immediatas.3 He explains them to be abbreviated hypothetical syllogisms ;^ and accordingly discusses them after Sylloo-ism. Kant,^ and most modern logicians along with himt have reversed the brder. Kant founds the division of immediate inference on his table of Categories. Subalternation, accord- ing to^ his view, rests on Quantity/ ; Opposition on Quality (Aequipollence is only a change of the expression in words, and not a form of judgment) ; Conversion on Eelation ; and " De Interp. c. x. 20 a, 39. * Cf. PrantI, Gcsch. der Logik, i. 568 ff. ; 583, 692 ff. 3 Log. § 459. 4 ibid. § 460. s Log, § 41 ff § 83. Analytical Formation of the Judgment, etc. 289 Contraposition on ModaUty. The later logicians have mostly kent by the principle of the Kantian division, but have sought to remedy, with greater or less success, many insuffixiiencies which lie in the Kantian statement. ^ The Analytic Construction of Judgments should not be reckoned among immediate inferences (and was not in the first edition of this Logic) ; but belongs to this species of inference. § 83. The Analytic Formation of Judgments rests on the axiom (§ 76) that every attribute may be posited as a predicate. The distinction between Synthetic and Analytic Judging belongs to the genesis oi ]nAgm^r^t^. Every judgment is so far synthetic, that it, accordmg to the definition, is the consciousness of the real validity of a combination (synthesis) of conceptions. But the synthesis of the members of the judgment may origmate in diiferent ways, either immediately by the combination of the conceptions presented, or mediately by the ana^ lysis of a whole conception earlier formed, in which the members of the judgment are already contamed in an undeveloped form. In the former case the con- struction of the judgment is synthetic, in the latter it is analytic. The judgment derived analytically from the notion of the subject, is valid only on the pre- supposition of this subject-notion The validity of the subject-notion can never be inferred from it. In .i..ry judgment the subject is the conception otherwise definite, but in reference to the predicate still indefinite In the propositions-This accused man is guilty. This accused man is not cruilty-the subject is the conception of the accused per- son, so far as he is a distinct person who stands under an accusation ; while the connection of the conception of guilt with the conception of the subject still remains an open ques- U i ' i I - 290 § St,. The Analytical Formation of the yudgment, etc. 291 tion, 1 e. an indefiniteness, which may be made definite, and is made definite by the acceptation or rejection of the predicate notion. In the judgment-The earth is a planet-the case is the same. The subject, the earth is on other sides definite perhaps as 7^ ihpioTspvo,, -rrdmrnv ^Sof dc4,a\h aUi; but in reference to what the predicate asserts it is still indefinite. 1 he judgments-Iron is metal, every body is extended, the quadrate ,s a parallelogram-have sense and meaning only in so faras he who judges has left a place in his notion of the subject for the determmation given in the predicate, but does not yet know this determination. He conceives iron perhaps by imme- diate sense intuition. He understands by body the perceivable thmg, about which it is not quite determined whether it is always extended or not. He conceives the square as an equi- lateral rectangular four-sided figure, without being conscious that the opposite sides are parallel. The subject of a definition denotes the thing only as that to which the name belongs. The predicate brihgs the closer determination, which was left inde- hnitc in the conception of the subject. Thus all these judnments, according to their character, are synthetic. It is only the mode of making the synthesis of the parts of the judgment that is different. Kecourse to the definition of the subject-notion, in the anal^^fical construction of judgments, means to call into one s consciousness the moments which would not have been thougfit along with the name alone. In the s>,nthetie construc- tion of notions the synthesis may be accomplished either by perception or by an inference. The inference rests either on circumstances known otherMise (as in the proof by witnesses of the guilt of the person accused), or u,,on attributes thou-ht expressly in the notion of the subject itself. The necessary connection of the attributes thought in the predicate is reco/- msed from these because of a causal relation of dependence e.g. from the equality of sides, the equality of angles in a triangle) The last named way often exists where Kant speaks of a ' synthesis a priori.' Thomas of Aquino^ and others explain identical propositions ^ Summa Thtol i. 2, 1. to be absolutely certain, on the basis of the Aristotelian axiom of Contradiction.^ Locke's remarks on * frivolous propositions/ whose predicate only repeats the notion of the subject or single parts of it,'^ and Hume's distinction' between ' relations of ideas ' and ' matters offact,^ paved the way for the Kantian distinction. Leibniz* held that all the primitive intellectual truths are identical propositions. Wolff's^ notion of the Axiom — propositi© theoretica inde- monstrabilis — embraced, besides the identical propositions, those also which were derived from identical propositions by analysis and combination.^ The difficulty, which Kant after- wards indicated by the distinction between analytic and syn- thetic judgments, is concealed behind the indefiniteness of his expression, in those places in his Logic ^ where Wolff mentions the relation in question. He says,® ' propositi© ilia inde- monstrabilis dicitur, cuius subjecto convenire vel non convenire praedicatum terminis intellectis patet.' He tries to make the phrase ' terminis intellectis patet ' evident by examples. He explains it partly in this way, that we are to understand by it the warrant that those predicative determinations which do not belong to the notion of the subject, as it is exhibited in the definition, are yet inseparably connected with it : ' ea, quae praedicato respondent, ab iis, quae ad subiecti notioncm referi- mus sive quae ad definitionem eius pertinent, separari non posse animadvertimus.' Wolff does not state the reason of this inseparability. Hence he is not conscious of the difficulty that if the predicate be found by merely going back to the definition of the subject, and to the definitions of single notions which are found in the definition of the subject, the judgment is then merely an analytical judgment, which has indeed apodictic cer- tainty, but does not extend our knowledge. (His examples are • Cf. Arist. De Tnterp. c. xi. ^ Essay iv. 8 ; cf. 3, 7 ^ Evqniry iv. ; cf. Locke, Ess. iv. 4, 6. ^ Nouv. Ess. iv. 2; MonadoL § 35. ß Ibid. §§ 268, 270, 273 ; cf. 264. •^ Ibid. § 262. Ü 2 ^ Lofjik, § 267. 7 Ibid. § 261 ff. 292 §83. The Analytical Formation of the yudgment, etc. 293 specimens: The whole is greater than a part; Radii of the same circle are equal to each other, &c. ; and the case appears to be universally the same, according to the Leibnizo- Wolffian axiom that all primitive intellectual truths are identical propo- sitions.) Nor does he see that if to go back to the definition of the subject is not sufficient, and if the predicate constitutes an essentially new determination, which is not contained in the content of the subject-notion given in the definition, as far as analysis leads us, our knowledge may be enlarged, but we want a ground of certainty for this enlargement. This is the point where Kant, who got his impulse from other sides also (viz. from the investigations of Locke and Hume), finds the first motive to an advance beyond the stand-point of Leibniz and Wolff. KaiiO rightly distinguishes the analytical and synthetical formation of judgments, however wrongly he may transfer the distinction to the judgments themselves. He calls Anali/ticalJudgmentsiho^Q in which the connection of the predicate with the subject rests on the relation of identity (e.g. « = «, or. All bodies are extended ; which depend on the definitions : equality is identity of size ; body is extended sub- stance). These do not assert in the predicate anything beyond what is already thought in the notion of the subject, although not with the same clearness or strength of consciousness. They are merely explanatory judgments. He calls Synthetic Judgments those in which the connection of the predicate with the subject does not rest upon the relation of Identity (e.g. the straight line is the shortest between two points ; or, every body is heavy. These examples proceed on the presupposition that shortness does not enter into the defini- tion of the straight line, nor weight into the definition of body. If the notion of the subject were already so defined and limited the judgments would be analytic). In these judgments there may be a necessity, belonging to the subject, to think the pre- dicate along with it ; but the predicate is not actually, nor in a » Krit.der r.Vern.,EinLiy.\ Prolecj. zu einer jeden künjtigtn Mdaph. § 2 ; Log, § 30. covert way, thought in the subject. Synthetical judgments are am pliative judgments. Hegel, by his dialectic method, seeks to do away with the distinction of analytic and synthetic judgments by means of the notion of development. He says,^ ' Dialectic progression is the established judgment of the Idea ; — this progression is both ana- lytic, because by the " immanent " Dialectic that only is posited which is contained in the immediate notion, and synthetic, because the distinction has not yet been posited in this notion.' This method is itself untenable. A smaller content has no l)ower in any way to make itself increase to a larger content. The genuinely scientific formation of notions demands that the subject should be regarded as the germ out of which the dif- ferent predicates grow. For example, the notions of circle, of gravitation, &c., may be looked upon as the germ, the capacity, the dynamis, in which lie unfolded the rich manifoldness of geometrical propositions or judgments in the doctrine of the circle, in astronomical knowledge, &c. But the germ, the dynamis, that which Hegel calls the In-itself-ness ( Ansichsein), is only the inner ground of the development. The external conditions must be added if the development is to be more than a mere analysis, and is to lead not only to the bringing into stronger consciousness the content already present, but to an enlargement of content. In the above examples, straight lines, such as sines, tangents, secants, &c., must come into relation with the circle ; the masses and distances of the heavenly bodies into relation with the principle of gravitation. In short, elements must enter which, in relation to this subject at least, are separately acquired, and are not to be obtained or (to use Kant's word) ' picked out ' (heraus- klauben) of it. Without this external element the methodic procedure would be analytic (the mere assertion of what already lies in the subject), not synthetic (no enriching the content, no advance to new predicates). With this external element it is synthetic, but no longer analytic. The point of view of development in the construction of the judgment, » Encycl. § 239. 294 § 84. Conversion in General, and in all provinces of philosophical thinking, is essential ; but the dialectic method has not been able to do away with the necessity of the Kantian distinction. Schleiermacher * explains the distinction between the analy- tic and synthetic judgments to be a fleeting and relative one. The same judgment can be analytic and synthetic, according as what is said in the predicate has or has not yet been included in the notion of the subject. But the distinc- tion holds in reference to any single subject standing by itself. The incomplete judgment (which contains only the subject and predicate) is more analytic, the complete (which contains the object also) is more synthetic, the absolute judgment (whose predicate is the world) is again analytic. It must be urged, however, against Schleiermacher that the distinction of the analytic and synthetic character of the judgment is not connected with its completeness or incompleteness. Delboeufssiys'^ the advance of science consists in this, that synthetical judgments change to analytic, i.e. predicates sub- joined empirically into those which exhibit necessity. This thought, in itself quite correct, is not so in relation to Kant's distinction. The meaning which Delboeuf gives to the ex- pression is essentially different from the Kantian terminology, according to which an apodictic connection, which rests on a known causal relation, is synthetic. [_J. S. MilVs distinction of propositions into verbal and real\ those which ' assert of a thing under a particular name, only what is asserted in the fact of calling it by that name,' and those which predicate ' some attribute not connoted by that name ; ' corresponds very nearly to Kant's distinction between analytic and synthetic propositions.^] § 84. Conversion is that change of form, by means of which the parts of a judgment change their place in reference to its relation. » Dial. §§ 155, 308-9; Beilage, E. Ixxviii. 5. ^ Proleg. philos. de la Geom. p. 46 fF. and Log. p. 103. 3 Cf. Logic, i. 119ff. lis Inner Aulhorisalion. 295 In the categorical judgment the subject becomes pre- dicate and the predicate subject ; and in the hypothetical judgment, the conditioning proposition becomes the con- ditioned, and the conditioned the conditioning. The conversion of the categorical judgment is in- ternally correct^ only when the notion of the predicate can itself become substantive, i.e. when the sum total of the objects, to which what is designated by the predicate-notion belongs, are all of the same kind, or are a class or genus (in the sense of § 58). For in this case, these objects only can be comprehended under a substantive notion, which can become a subject-notion (according to § 68), while the earlier subject-notion, from its connection with the auxiliary notion of exist- ence, may refer to a relation of inherence, and so take the predicative form (cf. § 68). The internal correctness of the hypothetical judgment, generally, lies under no limitation, because it denotes only a causal nexus, whether in the direction of from cause to effect, from effect to cause, or from effect to effect. When relations of time come into consideration, the first presupposition is the most natural, and there- fore the consequent, because the antecedent in Conver- sion is frequently to be expressed in the form of a final judgment (If it be — then must, &c.). The question of the internal correctness of Conversion was not discussed by Aristotle, The Aristotelian principle, that the elements of thought generally correspond to actual exist- ence, and that the subject and predicate especially, which find expression in the 61/ofia and prj/jia, must correspond to the thing, and to the action or quality, forms the basis for such a discussion ; but Aristotle did not apply it to Conversion. 296 § 84. Conversion in General, etc. ^85. The Universal Affirmative judgment. 297 The possibility of making the predicate substantive ^ is a tacit presupposition, but is not further discussed. The post-Aris- totelian and the modern formal Logic have still more neglected metaphysical relations referred to. Schleiermacher * has hinted at it, and Trendelenburg^ has remarked that in Conversion ' The Accident is raised to be Substance,' (or rather) that the substance in which it inheres becomes the object thought of instead of the attribute inhering ; but it does not follow from this, that Conversion, if we except the case of the univer- sal negative judgment, is * a mere artifice of formal Logic,' and can lead to no sure result. Logic, as a doctrine of knowledge, can and ought to investigate what and how much follows by conversion* from a single given judgment, presupposed to be » Anal Prior, i. 2. ^ j^fi^l § 325. 3 Log. Unters. 2nd ed. ii. 303 ; 3rd ed. ii. 336. * The stand-point of logical treatment is completely mistaken, and numerous mistakes are inevitable in particular cases, when this investi- gation is supposed to be undertaken in order to ' teach and make possible an arbitrary thinking, according to artificial rules and for- mulae,' or to ' reduce thinking to a mechanical schema, in order to proceed arbitrarily according to this schema, so that we require to think according to the schema only, and not according to the notions.' * One might as well reproach the mathematico-mechanical procedure with being one-sided and arbitrary, if it investigates what follows simply from certain simple presuppositions, and looks at these apart from other data, from which they can never be actually separated. If, for example, the path and position of a projectile be computed solely on the ground of gravitation and inertia, without taking into consideration the influence of the resistance of the air, the concrete intuition will apjmrently determine the result more strictly and more accurately than the computation. But if mathematical mechanics did not use this abstract procedure the laws of motion could not be known, and the science would be ruined. It is true that there is commonly more than merely one judgment given to us, and that we ought to know more about the relation of the spheres of its subject and pre- dicate fro'in other sides than that only which the judgment, con- sidered purely in itself, shows. If the given judgment be: All men are ♦ J. Hopj>e, Die gesammte Logik, Paderborn, 1868. internally correct. It must also show on what this internal correctness depends. The conversion of the disjunctive judgment, whether cate- oforical or hypothetical, does not require special rules any more than the conversion of the copulative or any other co-ordinated judgment. Its rules come directly from the laws of the Con- version of simple judgments. The hypothetical '^xxi^Lgm^nt is also the type for the cognate kinds of judgments. § 85. By Conversion there follows — I. From the Universal affirmative categorical judg- ment (of the form a) : Every S is P, The particular affirmative judgment (of the form i ) : At least one or some P are S (at least a part of the sphere of P is S). From the Universal affirmative hypothetical judgment : whenever a is, b is, The particular affirmative : At least once or sometimes, when b is, a is (at least in part of the cases, where b is, a is). The proof lies in the comparison of the spheres. mortal, or : All men are sensible-intellectual dwellers on earth, we know in other ways that there are also other mortal beings, but that there are no other sensible-intellectual inhabitants of earth. Ke who keeps to the example, and adds the other knowledge got in another way, can, without the trouble of abstraction, attain a completer result than the judgment which results according to the rules of Logic from a single given judgment, and so can very easily, on the ground of supposed * notional ' procedure, triumph over the logician, who troubles himself and others with his abstract schemata. But this procedure does not abolish a false logic for the sake of a better ; it destroys the possibility of a methodically progressive logical knowledge of the laws of thought. It is only after the investigation. What follows from one datum? is finished — that the scientific theory of thinking requires to subjoin the consideration of other data. 298 85. Conversion of the Universal Affirmative Judgment. 299 The given Categorical judgment : All S are P, pre- supposes (§ 71) the relations of the two spheres, which are signified by the Schema — a, 1. CV) ^> i.e. the action or quality, which the predicate-notion P denotes, is (a, 2) found in all the objects which the subject-notion S denotes, while it remains uncertain whether it is also found in others (a, 1) or is not so found (a, 2). Under the first present position it may only be said of part of the objects to which the action or quality denoted by the former predicate -notion P belongs, that they are S, under the second it may be said of all of them. It cannot be decided, from the given judgment alone : All S are P, when other data are excluded, which of the two presuppositions holds good in any case. But this decision is not required. The hiference : At least some P are S, is true on both presuppositions. And this is what was to be proved. In the same way the Aj(pö#Ae^/ca/ judgment: When- ever Ais, B is, presupposes two relations of spheres, whose Schema is — 1. 2. i.e. the relation denoted by b is found everywhere where A is ; while it remains uncertain whether it is found lu other cases (1), or is not so found (2). But under both presuppositions the inference : At least in a part of the cases where b is, a is, is equally true. And this is what was to be proved. There are cases, therefore, where the Converse : All P are S, or: Whenever b is, a is, holds good in the universal judgment. But at each time a special proof is necessary to show that the case before us is such a case, and this proof can only be given when other data besides the judgment to be converted are present. [Cf. Appendix B.] Conversion without change of Quantity is called by modern logicians Simple Conversion (Conversio Sim- ple j^)^ Conversion which is accompanied by change of Quantity is called Conversion per accidens. These uni- versal affirmative judgments, which admit simple or pure Conversion, are called reciprocal. If the judgment given is only problematically valid, or if it is apodictically certain, the same modality be- longs to the judgment reached by Conversion. For the degree and the kind of the probability or certainty, which the given judgment has, must pass over to the judg- ment which follows from it. The validity of the second is entirely dependent upon the validity of the first. Examples, — If the proposition is true : Every true duty must harmonise (not only with objective laws but also) with one's own moral consciousness, — the other must also be true : Something which harmonises with one's own moral conscious- ness is a true duty, but it does not follow that : Whatever harmonises with one's own moral consciousness is a duty. If the proposition is true : Whenever an action is evil in the full sense, it must contradict one's own moral consciousness (or. 300 §85. Conversion of the If it is evil, it contradicts, &c.)'; the axiom is also true: In some cases (at least), if an action contradicts one's own moral consciousness, it is evil. But the converse does not follow for all cases. From the proposition : Whenever the predicate in Greek has the article, the spheres of the subject and of the predicate-notions coincide with each other, the proposition follows: In some cases, at least, where the spheres of the subject and predicate-notions coincide with each other, the predicate in Greek has the article (in those cases, namely, where this coincidence not only exists, but is expressly denoted. But it must be known from other data that the converse pro- position holds good with this limitation). The validity of the converse follows from the given proposition only, *in some cases, at least.' We cannot learn from the given proposition whether the converse holds good only in some or in all, and if true in some only, in what cases. Simple convertibility is one condition of the correctness of Definitions.' The definition is adequate only when the de- finiendum (S) and the definiens (P) are reciprocal notions, and have the same extent ; and in this case P can be as universally predicated of S, as S of P. But definitions are not the only cases in which universal affirmative judgments admit of simple conversion. Almost all geometrical propositions are universally true in the converse form ; but this must be shown in every case by special mathematical proof. It does not follow from the logical laws of Conversion. The proposition : All coinci- dent triangles have an equal content, can only be converted •per accidens : Some triangles of equal content are coincident. In the same way, the proposition : All parallelograms having equal base and height are parallelograms of equal content, is to be converted : Some parallelograms of equal content have equal bases and height. It must be observed with reference to alo"ebraical propositions, that the mathematical notion of equality is not identical with the logical copula. The simple converse of : All a = b, is not : All b = a, but : Whatever is equal to B is A. But Logic does not wan ant this simple cou- * As has already been noticed, § 62. Ufiiversal Affirmative Jtidgment. 301 version, and mathematical considerations lead only either to the proposition : All b = a, or to the proposition : Whatever is equal to b, is equal to a. Equal quantities are, with reference to quantity, identical ; but we cannot make them absolutely identical, while the different relations which lie in the diflPerent expressions, have meaning. These rules for Conversion would be false if Herbarfs opinion,* shared by Drobisch ^ and Beneke? were correct. He believes that the truth of the affirmative categorical judo-ment is not conditioned by the actual existence of the object, thouo-ht in the notion of the subject, but that every kind of judgment is valid only hypothetically, on the hypothesis of the affirma- tion of the subject. Herbart himself feels the difficulty arising from this, but knows better how to state it than to overcome it.^ His example is: The wrath of the Homeric gods if there are any— is terrible. But they are merely poetic, and have no real existence, and hence, though many a terrible thing actually exists, the truth of the converse does not follow : Some terrible thing — if there be any— is the wrath of the Homeric gods. But, in fact, the truth of the affirmative categorical judgment always includes the truth of the hypo- thesis, that the object designated by the subject exists. If we refer that assertion about the wrath of the Homeric gods to external actual existence, then, because that wrath does not exist, it is as false as the converse. But if we allow to the world of the Homeric gods an ideal actual existence, both the proposition and its converse are equally true in this sense ; and the rules of conversion are warranted to be correct in this application also. The rules for the Conversion of the Hypothetical judgment and their proof enunciated in this and the following para- graphs, are correct, only on the hypothesis that the condition- ing proposition denotes cases which actually exist. The hypothetical proposition expressed by ' Whenever,' involves this hypothesis, just as the categorical judgment involves the ' Lehrbuch zur Eint, in die Phil. § 53. ' Log. 3rd ed. p. 59 ff. » 11,^^ i. 165. * Lehrb. § 59, Anni, 302 §85. Conversion of the presupposition of the existence of the subject, provided that the nexus does not refer to a merely hypothetical actual exist- ence, and the clause ' if this at all happens ' is not to be added in thought. Cf. §§ 68, 94. As to Modality, the judgment : All S are P, may be un- certain, and yet the judgment: Some P are S, be certain. This happens, when it is certain that some S are P, and when the uncertainty of the universal judgment refers only to the other S. The certainty of the converse follows not from the uncertainty of the universal affirmative, but from the certainty of the particular affirmative judgment (§ 86), and therefore from a datum reached in another way. If we only know that it is uncertain whether all S are P, we are uncertain whether some or perhaps none S are P ; and it also remains uncertain whether some P are S. The use of circles as an aid in the demonstration of the doctrine of Syllogism, especially in Syllogistic proper, has been referred by modern logicians (e.g. by Maass, J. D. Gergonne, Bachmann, and Bolzano) to Euler} But Drobisch ^ [and Hamilton ^] have rightly remarked that, according to the testimony of Lambert,^ Joh. Chr, Lange, in his ' Nucleus Logicae Weisianae,' 1712, uses circles, and that Christ Weise, rector of the Gymnasium at Zittau (d. 1 708 ), (on whose doctrines many of the thoughts in this compend are based,) was probably the inventor. [According to Hamilton, Lambert's method of ' sensualising the abstractions of Logic ' by parallel lines of the different lengths, is to be found in the ' Logicae Systema Harmonicum,'* of Alstedinos, published in 1614.] Demon- stration by means of direct comparison of spheres could only come into use after that the authority of the Aristotelian methods of reduction had been impugned (more particularly by Cartesianism).^ These methods prevailed unconditionally, * Lettres ä une princesse (TAUemagne sur quelques sujets de phi/siqiiß et de philosophies 1768-72, ii. 100. 2 Log, 3rd ed. p. 96. ^ [j^ect. on Log. i. 256.] 4 Architectonic, i. 128. ^ [P. 395.] ''' Cf bolow, §§ 105, 113 ff. Universal Affirmative Judgme^it. 303 if we except some attempts at independent proofs among the Earlier Peripatetics and by the Neoplatonist Maximus,' in the latter period of Ancient Philosophy, and during the Middle Ages. The ' Logique, ou Tart de penser,' "^ belonging to the Cartesian School, teaches certain reductions, but enunciates along with them a general principle,^ according to which the validity of any syllogism may be immediately determined. The principle is, that the conclusion must be contained {contenu) in one of the premises, and that the other premise must show that it is contained, cf. § 120. This thought is not far removed from an attempt at a sensible representation by means of circles. Among the German logicians Thomasius rejected the reductions. The tendency of that age to treat Logic mathematically, which I^eibniz was partially influenced by, and tlie didactic requirement of clear and sensible representation, may have led to the use of these schemata. Frantl* derides, not quite correctly, this sensible represen- tation, as serving only to * train stupid heads.' It is, however, no more necessarily antagonistic to the consideration of the distinctive logical and metaphysical references, and to the scientific character of Logic, than the sensible representation of geometrical proofs in the figures denoting them need be l>rejudicial to mathematical accuracy. Figures of another kind, which represented sensibly only the three different positions or fundamental relations of the middle notion to the two other notions, in the three Aristotelian figures of the Syllogism, were used in Logic in antiquity.*^ Lamherfs symbolical notation of the relations of extent between the subject and predicate by means of the relations of the extent of lines partly continuous partly dotted,^ may be justified against the accusations of Maass ^ and Bachmann.* ' Cf. Prantl, Gesch. der Log. i. 362, 639. ^ Which appeared in 1662. ^ Logique, ou VArt de Penser^ iii. 10. * Gesch. der Log. i. 362. ■^ Cf. Barthelemy Saint- Hi laire in the Appendix to his work, De la Logique (V Arist. 1838. •^ Neues Organ. Dian. § 174 ff. 7 j^ogik, Vorrede, p. 11. ' Log. p 142 ff. 1 ^ ^ 1 304 86. Conversion of tlu Particular Affirmative jfudgme^it. 305 They wrongly believe that the mere subordinate reference of the upper or under position of the lines is the principal point of view. But Lambert's notation is neither a very easy nor a sure way of representation. The notation by triangles adopted by Maaas is not so convenient as that by circles. Gergonne^ symbolises the relations of circles by simpLi signs— the identity of two spheres by i, the complete separation by H, the crossing by x, the comprehension of the sphere of the subject in that of the predicate by C, and, lastly, the com- prehension of the sphere of the predicate in that of the subject by 0. By the use of these signs the representation attains brevitv and elegance, but loses immediate intuitiveness. [Mansel objects to the use of any sensible representations whatsoever. He thinks that to represent the relation of terms in a syllogism by that of figures in a diagram is to lose sight of the distinctive mark of a concept,— that it cannot be presented. The diagrams of Geometry, he says, furnish no precedent, for they illustrate the matter, not the form, of thought. This last statement is scarcely correct. Hamilton employs, in his Lectures on Logic, the circlo notation of Euler, and also a modification of Lambert's linear method. The notation (linear) which he afterwards adopted is very intricate, and while free from the objection that it con- founds logical with mathematical extension, does not intuitively represent the logical relations. ^ For a history and criticism of various methods of logicnl notation, cf. Hamilton's Lectures on Logic, i. 256 andii. 460 ff.] § 86. By Conversion follows — I. From the particular affirmative categorical judgment (of the form i) : Some S are P, The particular affirmative judgment (also of the form i) : At least some P are S. » Essiii de Dialectique rationnellem the Annates des Matheinatiqiie^, tom. vii. 189-228, 1816-17. [2 Cf. Lecf. on Loijic, ii. Appendix, p. 409 ff., and Discussions, pp. 657-661.] And from the particular conditional judgment : If A is, B sometimes is, The particular conditional follows : Sometimes at least if b is, a is. The proof results from the comparison of the spheres. The given categorical judgment : Some S are P, when the predicate P belongs only to some S, presupposes two relations of spheres, which are denoted by the Schema : — i,l. i, 2. But since the possibility is not excluded, that the same predicate P belongs also to other S, the two fol- lowing relations of the spheres also exist : — 1,3. i,4. These Schemata are to be taken in the same sense as in § 85. Now in i, 1 and i, 3 some P only are S ; and in i, 2 and i, 4 all, and therefore at least some P are S. But this is what was to be proved. In the corresponding hypothetical judgments the rela- tions of the spheres are the same and the result equiva- lent. The Conversion of the particular affirmative and of the particular conditional judgment is therefore a Con^ versio simplex. For both the given judgment, and the I 3o6 587. Conversion of the Universal Negative yudgment. 307 judgment arising from the conversion, take the form of the particular affirmative (i). The Modality of the given judgment and of its con- verse is the same. Examples of i, 1 are: Some parallelograms are regular figures ;— of i, 2 : Some parallelograms are squares ; — of i, 3 : Some parallelograms are divided by a diagonal into two coinci- dent triangles ;— and of i, 4 : Some parallelograms are divided by both diagonals into two coincident triangles. The relation of spheres i, 1 admits of many other modifications. If two spheres are of unequal size, it can happen that most S are P, and relatively very few P are S, or a few S are P, and most P are S. Although the number of S which are P, and of P which are S, is in itself necessarily the same, yet the relation of the sum total of individuals is a different one in each of the two spheres. For example, some, and relatively not a few, planets belonging to our system are heavenly bodies which may be seen by us with the naked eye ; but only a very few of the heavenly bodies visible to the naked eye are planets of our system. This con- version is not, therefore, conversio simplex, in the stricter sense that the quantity remains the same in each reference. It is so only in the more general sense, that the judgment remains a particular one, and does not pass over to any other of the four classes of judgments designated by a, e, i, O. § 87. By Conversion follows — III. From the universal negative categorical judg- ment (of the form e) : No S is P, The universal negative judgment (also of the form e) : No P is S. And from the universal negative hypothetical judgment : If A is, B never is, Tlie similarly universal negative hypothetical judgment : If b is, a i;iever is. The validity of these rules may be directly proved by the comparison of spheres. Th6 Schema of the uni- versal negative categorical judgment is the complete separation of the spheres : — i.e. The action or quality which the notion of the pre- dicate P denotes, is to be found in no object which the subject-notion S denotes, and, if it really exists, only ill other notions. Hence the judgment: No objects in uliich the predicate P is found, and which may there- fore be denoted by the notion P made substantive, are S. And this is what was to be proved. The same may be proved indirectly. For if any one P were S, then (according to § 86) some one S would be P ; but this is false according to the axiom of Con- tradiction (§ 77), for it is opposed contradictorily {^j 72) to the given judgment : no S is P. Hence the assertion is false, that any one P is S, and it is true that no P is S ; which was to be proved. The corresponding hypothetical judgment presupposes the analogous relation of spheres : — i.e. The case denoted by b is never found where A is present. Whenever b happens, it takes place under other conditions. The case b does not occur together z i '1 5 3o8 §87. Conversion of the with the case a ; and the case a does not occur with the case b. If b is, a never is; which was to be proved. The indirect proof may be led here as well as in the universal negative categorical judgment. For if it once happened that when b is, a is also, then (according to § 86) the converse would be true that, once, when a is, B is; this would contradict the given presupposition, that when a is, b never is, and is therefore false. Hence it is false, that when b is, a is once ; and the proposi- tion is true ; when b is, A never is ; which was to be proved. The converse of the universal negative judgment is therefore tiot accompanied with any change of quantity, and is throughout simple conversion. The rule also holds good without exception that Modality remains unchanged in the conversion. If it is apodictically certain that no S is P, the same kind of certainty passes over to the judgment, that no P is S. If that is only probable, or is true only perhaps, and the assertion remains possible, that, perhaps at least some one S is P, then (according to § 86) there is the same possibility for the assertion that, perhaps at least, some one P is S. It does not follow : no P is S ; but only : Probably or perhaps, no P is S. The following are examples of the conversion of the univer- sal affirmative categorical judgment. If the judgment be given as true : No innocent person is unhappy, it follows with equal truth: No unhappy person is innocent. If the proposi- tlsi' cf. c. xiii.; c. xvii.: otl ovtc avTiarpecfyst TO sv Tw evlsxeaOaL arsprjriKov, If the judgment is given : to A h'hexsTai fjLTfBsvl t« b, it does not necessarily follow that to B hhs)^sa6ai firjBsil tw A. Aristotle understands the first pro- position in this sense : Every B, each by itself, is in the state of possibility to have or not to have a for a predicate. He understands the second proposition similarly, in this sense : 310 § 87. The Uftiversal Negative Judgment, \ "^Z, T/ie Particular Negative Jtidgnient. 311 Every a, each by itself, is in the state of possibility to have or not to have b for a predicate (cf. § 98). Now the case may occur, as Aristotle rightly remarks, where all b are in that double state of possibility, while some A are in the state of necessity, not to have b for a predicate. Hence the Schema 18:- In cases of this kind the first judgment (to a IvUx^-rai iivlivX iw B) is true, and the second (to b ivhixsrai firiBspl rw a) is false. Hence the second is not the necessary consequence of the first. In this sense Aristotle's doctrine is well founded. But it does not contradict our proposition (which Theophrastus ^x\^ Eude- mus had recognised^), that universal negative propositions of any modality, and consequently the problematical, are con- verted with Quantity, Quality, and Modality unchanged.- The contradiction is not overcori.3 by the circumstance that the Aristotelian ivBex^aOai does not denote subjective uncertainty like the perhaps of the problematic judgment, but the objective possibility of Being and Not Being, more especially (in dis- tinction from ^vvaaOai) in the sense of there being nothing t^' hinder it. For the argument of Aristotle remains correct, il subjective uncertainty be substituted for the objective pos- sibility. If it is uncertain of all B, whether they are or are not A, it does not follow that it must be uncertain of all A, whetliei they are or are not B. The certainty that they are not B mu} exist of some A. But this does not prejudice the above demon- stration that from the proposition : Perhaps no B is a, the proposition follows : Perhaps no A is B, For this last propo- sition is not equivalent to tha:, which can not be deduced : It is uncertain of all A, and of each one by itself, whether they are or are not B. It is equivalent to the following : It is un- certain whether all A are not B, or whether there be at least 1 Cf. Prantl, Gesch. der Log. i. 364. any one A which is B. And this proposition can very well exist alono" with the certainty that some A are not b. Similarly, from the proposition : It is (objectively) possible that no B is A, the proposition follows necessarily : It is (objectively) possible that 710 A is B (while it is also possible that at least some one x is b). Conversion in the Aristotelian way, according to which the possibility not to he B is adjudged to every individual A, holds good (as Aristotle himself shows ' ) in two cases - ( 1 ) when by ii^Sexecr^at is understood what might be expressed by it o/ao;- vvfJMS : tx)he at least in the state of possibility, without exclusion of the necessity; and (2) where all necessity whatever is ex- cluded, and with it necessity in the direction from A to B, so that no A are present which are in the state of necessity not to he B. The apparent contradiction between the doctrine enun- ciated in the text of this paragraph and the Aristotelian is solved in this way.^ § 88. Nothing follows from the conversion of the particular negative judgment. The particular negative categorical judgment asserts, that some S have not the predicate P, without saying anything definite about the rest of S. Its Schema is accordingly the combination in the three figures : — 1. (10 2. 3. or in the one figure, which, comprehending the three > Anal. Pr. i. c. iii. » Cf. Prantl, Gesch. der Log. i. 267, 364. ii\ 312 § 88. The Particular Negative Judgment, possible cases, denotes the definite by the continuous, and the indefinite by the dotted lines : — §89. Co7itraposition in general, etc. 313 According to this, it can happen that when some S are not P: (1) Some P are not S, and other P are S ; — (2) All P are S ; and (3) No P are S. Nothing can be said universally of the relation of P to S in a judgmont whose subject is P. Similarly, the Schema of the particular negative hypothetical judgment : Sometimes when A is, b is not, is the following: — It may happen that when B is, (1) A sometimes is and sometimes is not; (2) a always is, and (3) a never is. Hence the general relation of b to a is quite in- definite. Examples of these different possible cases are the following : — Of the particular negative categorical judgments of the form 1 : Some parallelograms are not regular figures. Of the form 2 : Some parallelograms are not squares ; or : Some rectilineal plane figures, which are divided by a diagonal into two coinci- dent triangles, are not parallelograms. Of the form 3 : (At least) some parallelograms are not trapezoids ; or : (At least) some rectilineal plane figures, which are divided by a diagonal into two triangles not coincident, are not parallelograms. Of the particular negative hypothetical judgment of the form 1 : Sometimes, when the accused has confessed himself to be guilty, the accusation is not established. Of the form 2 : Sometimes, when unestablished accusations are raised, there is not calumny (only error). Of the form 3 : At least sometimes, when the advocate of a higher ideal principle is condemned to death by the advocates of a principle which is less in accordance with reason, but has become an historical power, the right and wrong have not been shared equally by both parties. § 89. Contraposition is that change of form, accord- ing to which the parts of the judgment change places with reference to its relation, but at the same time one of them receives the negation, and the quality of the judgment changes. Contraposition in categorical judg- ment consists in this, that the contradictory opposite of the predicate notion becomes the subject, and in this transference the quality of the judgment passes over to its opposite. In the hypothetical judgment, it con- sists in this, that the contradictory opposite of the conditioned becomes the conditioning proposition, and there is, instead of an afiirmative nexus between the two parts of the judgment, a negative one, and instead of a negative an afiirmative one. The internal correctness of Contraposition is to be decided by the same axioms as that of Conversion (cf.§84). The term ^ conversio per contrapositionem,^ used by Boethius (§ 82), where ' contrapositio ' means the change of one member into its contradictory opposite, is in itself unobjectionable, if the notion of conversion is sufiiciently widely understood and defined. But then a term would be needed to designate the first kind of Conversion in the wider sense, or Conversion in the stricter sense. Boethius (cf. §82) calls it * conversio 3H 5 QO- Contrapositmi of the Universal Affirmative Jiidgnient. 315 simplex.' But modern Logic cannot well adopt this term, since it denotes by this expression Conversion without change of quantity. Hence it is more convenient for us to use the notion * conversio ' in the narrower sense only. Schleiermacher^ adduces the following example of a contra- position (' Umwendung '): ^ All birds fly; not everything that flies is a bird ' (instead of: What does not fly is not a bird). This, however, rests on a mistake, and not on a peculiar though admissible terminology. For the Contraposition, however diiferently in other respects its notion may be defined, must in every case fall under the higher notion of immediate conse- quence. If the judgment is given : All S are P, the judgment: Not all P are S, or : Some P are not S, cannot be derived from it by any kind of consequentia immediata. Now Schleiermacher himself, in his example, asserts as a new presuppositim, the perception that other animals fly, and makes this the basis of the judgment to be derived. § 90. By Contraposition follows — I. From the universal affirmative categorical judg- ment (of the form a) : Every S is P, The universal negative judgment (of the form e): No not-P is S (Everything that is not P is not S). And from the universal affirmative hypothetical judgment: Whenever A is, b is, there fol- lows, The universal negative: When b is not, a never is (It always happens that when b is not, A is not also). Proof may be given directly by comparison of spheres. The sphere of P in the categorical^ and the sphere of b in the hypothetical, judgment, either includes the sphere » Dial p. 286. of S, and that of A, or is exactly coincident with it. These relations are to be explained in the same way as § 85. In both cases, whatever lies outside of the spheres of P and of b, must also lie outside of the spheres of S and of a; i.e. whatever is not P, is also not S, and it always happens, when B is not, that a is not ; which was to be proved. The Modality remains unchanged in Contraposition in this and in the other forms (§§91 and 92), for the same reasons as in Conversion. The expressions, ' contrapositio simplex * and ' con- trapositio per accidens,' are used as in Conversion with reference to Quantity, Examples, — Every regular figure may be inscribed in a circle (so that all its sides become chords) : Every figure, therefore, which cannot be inscribed in a circle is not regular. Every rectangular triangle may be inscribed in a semicircle (so that its one side becomes the diameter, and the other two chords) : Every triangle, therefore, which cannot in this way be inscribed in a semicircle is not rectangular. Wherever there is a good conscience, there will be correct conduct : Wherever, therefore, there is not correct conduct, there is not a good conscience. Wherever there is perfect virtue, there is also complete internal satisfaction : Wherever, therefore, there is not complete Internal satisfaction, there is not perfect virtue. Every sin contradicts the moral consciousness : What does not contradict the moral consciousness, is not sin. Whenever the predicate in Greek has the article, the spheres of the subject and predicate notions coincide : When the spheres of the subject and predicate notions do not coincide, the predicate in Greek has never the article. The universality with which Contraposition holds good of a general affirmative judgment is worth noticing, in opposition to the merely particular validity of the judgment reached by con- version. Four universal judgments (of the forms a and e) \ 316 § 90, T/ie Universal Affirmative Juclgment, may always be enunciated, two of which are valid or invalid of each other. The first pair may be valid without the second, and the second without the first. If the judgment is true: Every S is P, it follows that : What is not P is not S. But it does not follow : Every P is S, nor, what is equivalent to this : What is not S is not P. If the judgment is valid : If A is, B is, it follows : If B is not, A is not ; but it does not follow : If b is, A is, nor, what is equivalent to this ; If A is not, B is not. For example, if the judgment is recognised to be valid : That in which consists the essence of an object is, in its fluctuations, the measure of the completeness of the object, the judgment of equal universality follows by Contraposition : Whatever in its fluctuations is not the measure of the completeness of an object does not contain the essence. But it does not follow ; What- ever (only some at least) is, in its fluctuations, the measure of the perfection of an object contains its essence. Nor does the equivalent proposition follow : Whatever does not contain the essence of an object, is not in its fluctuations the mea- sure of its completeness. (Certain external marks may very well fluctuate in strict proportion with the essence.) If the proposition is true : Every good thing is beautiful, it follows : What is not beautiful is not good. But it does not follow : Every beautiful thing is good, nor : What is not good is not beautiful. The propositions : Where there is not a very com- prehensive memory, there is not a very comprehensive under- standing, and : Where there is a very comprehensive under- standing, there is a very comprehensive memory, are equivalent. But the propositions: Where there is not a comprehensive understanding, there not a comprehensive memory, and: Where there is a com] irehensive memory, there is a compre- hensive understanding, are essentially different from these, although equivalent to each other. The two first propositions are both true, the two latter are both false. The propositions : Whoever does not recognise a state to be independent, does not recognise its rights of embassy, and : Whoever recognises the right of embassy of a state, recognises also its independence, are equivalent. The two following propositions, which are equiva- 91. The Universal Negative Juägment, 317 lent to each other, may be false without detriment to the truth of the former : Whoever recognises a state to be independent, recognises also its rights of embassy, and : Whoever does not recognise the rights of embassy of a state, does not recognise it to be independent. (England in 1793 recognised the French Republic to be independent, but it did not admit its rights of embassy.) In like manner the proposition: Whenever desire has gained its utmost height, all pain is removed, admits of simple Contraposition, but only of Conversion accompanied by change of Quantity. On the other hand a proposition which is a definition or corresponds to a definition in this, that the spheres of the subject and predicate notions coincide, admits both of simple Conversion and of simple Contraposition. For example : Every calumny is an untruthful statement of deeds which are false and defamatory : Every such statement is a calumny; and: What is not such a statement about such deeds (e.g. a false and defamatory account of actions which are true) does not fall under the notion of a calumny. § 91. By Contraposition follows — II. From the universal negative categorical judg- ment (of the form e) : No S is P, The particular affirmative judgment (of the form i): At least some not-P are S (At least something, which is not-P, is S). And from the universal negative hypothetical judgment: if a is, b never is, The particular affirmative: (At least) in some cases, if b is not, A is not. For the universal negation both in the categorical and m the hypothetical judgment presupposes a complete separation of the spheres, and S and a must be found outside of the spheres of P and b ; i.e. S belongs to what 18 not-P, and a exists in those cases where b is nqt. f I 31 8 § 92. The Particular Negative Judgment, And so some not-P is S, and in some cases where b is not, A is. The possibility that every not-P is S, or that if B is not, A always is, is not excluded ; but happens only when S and P, or A and b, taken in their whole extent, include everything existing. Examples. — Nothing good is ugly : Something not-ugly is good. Nothing ugly is good: Something not-good is ugly. No animate essence is lifeless : Something not-lifeless is ani- mate. No animate essence is inanimate : (At least) some not- inanimate is animate. The divine is not finite: (At least) something not-finite is divine. The finite is not divine: (At least) something not-divine is finite. § 92. By Contraposition follows: — III. From the particular^ negative categorical judg- ment (of the form o) : (At least) some S are not P, The particular affirmative judgment (of the form i) : (At least) some not-P are S (At least, something which is not P is S) ; And in the same way from the particular negative hypothetical judgment: (At least) sometimes, if A is, b is not, The particular affirmative : (At least) in some cases, if b is not, A is. For particular negation presupposes, that (at least) part of the spheres of S or A lies without the spheres of P or b, without making any definite statement about the other part ; and so that some of what lies outside of the spheres of P or of b, are S or a ; i.e. some not-P are S ; sometimes, if b is not, a is. The case : All not-P are S : If b is not, A always is, may exist, not only when no S § 93. The Particular Affirmative Judgment. 319 is P, and when if A is, b never is (as is possible accord- uig to the given judgment) (cf. § 91); it may also occur when only some S are not P, and when it only sometimes happens that if A is, b is not. The latter case occurs more especially when S or a refer to the sum total of all existence, and P or b to a part of it. But, whichever of these different possible cases exists, anyhow the pro- position is true : At least some not-P are S, and : At least in some cases, if b is not, A is. Examples, — Some parallelograms are not regular figures : Something which is not a regular figure is a parallelogram. Some parallelograms are not squares: Some not-squares are parallelograms. (At least) some parallelograms are not trape- z(ids: Something, which is not a trapezoid, is a parallelogram. Some living thing is not animate: Something not-animate is living. Some real essences are not animate : (At least) some- thing, which is not animate, is a real essence. § 93. No conclusion follows by Contraposition from tlie particular affirmative judgment. The particular affirmative categorical judgment has, in general, two forms (i, 1 and i, 2), which correspond to the presup- position : only some S are P, and two forms (i, 3 and i, 4), which correspond to the presupposition : at least some, but in fact the other S also, are P. If the first two forms were the only ones, it might follow (§ 92) : Some not-P are S. But this consequent has no universal validity, because it is not suitable to the last two forms. The consequent : (At least) Some not-P are not S, which contains the proper contraposition, is true on the hypothesis of the last two forms, where all not-P are also not S (§ 90). It may be applied fre* •I» 320 § 93- Impossibility of the Contraposition of quently and almost in the greater number of examples to the first two forms also. But in case of the first two forms, it can happen that it is false. The form i, 2 is represented by the figure : — It is usually the case that besides the Not-P which are S, there are some Not-P which are not S ; but it may happen that S comprehends the sum-total of existence, and then all not-P will be S. It will not then happen that there are some not-P which are not S, and that consequent will be invalid. The schematic represen- tation of the form i, 1 is given in the figure : — There are commonly some Not-P which are not S, be- sides the Not-P which are S, but the opposite case can also occur. The form i, 1 (which is distinguished from i, 3 and i, 4 by the fact that some S are P, and others are not, and form i, 2, by the fact that some P are not S) exists, when the case represented by the following figure occurs : — tAe Particular Affirmative Judgment, 321 Where P extends from the centre to the periphery of the second circle, and S from the periphery of the first to the periphery of the third circle. If the sphere of S is a limited one, there will be many not-P which are also not S; but if its sphere is unlimited outwards, i.e. if S comprehends all existence with the exception of that part of P which is denoted by the smallest circle, there are no longer some not-P which are not S, but all not-P are S. This relation frequently occurs where S is a notion designated by a negation (S=Not-I, where I stands for the innermost circle) ; and it can also occur Avith an S positively designated. Hence the consequence : Some not-P are not S would be false. (The like holds good, if in ik^ above figure S and P change places, when the sphere of P is unlimited towards the outside.) There are cases when the judgment : Some S are P, is true, where (at least) some Not-P are S, and there are also cases, where No Not-P is S. There are cases where (at least) some Not-P are not S, and also cases, where all not-P are S. Hence where that one judg- ment only is given, nothing can be universally asserted of the relation of the Not-P to S in a judgment whqge subject is Not-P. The corresponding hypothetical ]\\^gm.^wt^ since all its relations of spheres are similar, just as little admits any universal inversion. It is enough to give examples of the two cases where all ^ot-P are S, and where therefore the judgment proves false, which would correspond to the universal form of Contraposi- tion : Some Not-P are not-S. 1. Some reality is material (inanimate). It does not follow from this that ; Some thing not- \ 322 §93. Impossibility of the Contraposition, etc. \ 94. Change of Relation, 23 material (psychic) is not real; for every not-material (psychic) is real. 2. Some living essences are inanimate. It does not follow from this that: Something not-inanimate (animate) is not a living essence ; for everything which is animate is living. The first "example corresponds to the form i, 2, where the sphere of S extends to the infinite. The second example corresponds to that case of i, 1, which is sensibly represented by means of the three concentric circles. The inmost circle (i) is, in this example, formed by the inorganic or elementary essences ; the first enclosing ring (a^) embraces plants, and the outer ring (a^) animated essences; P = i + A^ = inanimate essences ; and S = Not-i = a^ + A2 = animate essences. The -proof for the inapplicability of Contraposition to the particular affirmative judgment is commonly given in another way. The judgment: Some S are P, is reduced to the par- ticular negative to which it is equivalent : Some S are Not-P. And since the latter cannot be converted (according to the laws of Conversion), so the former cannot be transposed.^ But this demonstration is beside the mark, unless it is shown that the proof of the impossibility of converting the particular negative judgment, which is constructed for the case where P is\ positive notion, holds good for a negative predicate Not-P. If this is not specially proved, then that proof may, without anything further, be transferred to the case of a nega- tive predicate-notion, just as little as in mathematics, e.g., a proof, which has been given of a positive whole exponent, holds good directly for a negative fractional exponent. The transference must obpously submit to a strict test, for the whole power of the proof, that P O S does not follow from S O P, rests on the possibility that in S O P the sphere of S wholly comprehends that of P, and that all P are S. But it this relation is found naturally with a positive predicate, its possibility is not at all directly evident if the predicate i^^ a negative notion and consequently of unlimited extent. The doubt rather demands attention, whether this unlimited sphere may be completely included by the sphere of S, which, when I Cf. e.g. Drohisch, J.orj. 2nd. ed. § 77, p. 8G. S is a positive notion, appears to be limited. If it cannot, the proof loses its validity for this case, and with it is lost the validity of the proof by Reduction of the impossibility of Con- traposition in S i P.* Ticesten says,' 'Particular affirmative judgments cannot submit to contrapoj?ition. If some a are h, it remains un- decided whether a is partly or not at all without the sphere of />, and partly or not at all within the sphere of not-i.' This is no proof. At the most, it is an introduction to a proof. For, from what is given, it follows at once that it is uncertain whether some a are not-b, and whether some noUh are a ; it does not follow so immediately, that it is also uncertain whether some not-h are not-a. And the inadmissibility of the consequence : (At least) Some noi-h are not-a, is what was to be shown. It should have been said ; If some a are A, it remains undecided whether not-A lies wholly or at least partly without the sphere of a (or, wholly or at least partly within the sphere of not-a). § 94. If in Conversion and Contraposition the posi- tion of the individual members of the judgment can be ^ Drohisch, in the 3rd ed. of his Logic, § 82, p. 88, has sought to show that the proof for the inconvertibility of the particular negative judgment holds good for a negative (Not-P) as well as for a positive predicate (P) ; but his proof is not sufficient. He only proves that the proposition : Some Not-P are S. cannot be inferred, because the case exists in which the contradictory opposite judgment : No Not-P is S, is true. What was to l^ proved, that it cannot be con- cluded that: Some Not-P are not S, does not in the least degree follow ; for this judgment may be recognised to be true when some Not-P are S, as easily as it is true when no Not-P are S. When, accord- ing to circumstances, the one or other of two judgments contradictorily opposed to each other may be true, it is only implied that neither the one nor the other of these two judp^ments is true in every case. Another judgment which coexists with both may be true in evenj case. Judg- ments contradicting each other (No Not-P is S, and Some Not-P are S) may both be vncertain, and a third judgment (Some Not-P are not S) may be certain. Drobisch's reasoning is not sxifficient. ' Log, p. 79. t2 I I 24 94. Change of Relation, §95. Sub alternation. 325 exchanged while then- relation remains unaltered, there may also be a change in the Relation itself. This occurs when an hypothetical is formed from a simple categorical judgment (which is always possible), or when several hjT)othetical are formed from a disjunctive categorical judgment, or when the converse of both cases happens. The possibility of this change of form rests on this :— 1. The relation of inherence always includes a certain dependence of the predicate upon the subject, which may always be made conspicuous when it is treated by itself, and is expressed in an hypothetical judgment. 2. The disjunctive judgment is the comprehensive expression of several hypothetical judgments, and may be resolvöd into them as easily as these mutually-related hypothetical judgments may be reduced to a disjunctive judgment. From the judgment: A is B, the judgment: If A is, B Is, may be deduced. But the categorical judgment is not always correct, when the hypothetical is ; for the latter does not pro- ceed upon the hypothesis of the existence of a, but only on the fact that B stands in a relation of inherence together with a. From the judgment: Every A, which is B, is C, follows the judgment: If A is B, a is c ; and the latter, which pre- supposes the existence of such A which are B, may be reduced to the former. The- judgment: a is either b or C, divides into the mutually connected hypothetical judgments: If A is b, it is not C, and If a is c, it is not B ; If A is not B, it is c, and If A is not c, it is B. And the latter may be again reduced to the former. The possibility of this Change of Relation does not prove ' that difference of Relation is only verbal, and has no logical or 1 As several modern logicians believe — viz. Herbart, Einleit. §§ 00, 60 Rem.; Beneke, Log. i. 103 ff. ; Dressier, Denkkhre, 199 fF. metaphysical significance. If this view were correct, the change of form could be accomplished, without alteration of the material constituent parts of the judgment, equally well by changing the hypothetical judgment into a categorical as by changing the categorical into an hypothetical. But this is not the case. The transformation of the hypothetical jud«*- ment into a categorical is only admissible, in so far as a re- lation of inherence is connected with the relation of depen- dence, and the existence of the subject is ensured, as it is in the cases adduced above. It is not possible whenever the hypothetical judgment is given : If A is B, c is D ; for the fact that A is B does not stand in the same relation to the fact that c is D, that A does to B or c does to D. The former is not the latter, nor can it be considered to be a kind of the latter. But the A is a B, and can be held to be a kind of B. There is not only a verbal, but a logico-metaphyslcal dif- ference, w^hich reveals itself indeed in language, the flexible jrarment or rather the organic body of thought, but belongs originally to thought itself. One fundamental . relation exists hetween the parts of the hypothetical judgment, and another between those of the categorical. The two are essentially related and connected with each other,^ but they are not to be thought identical. Cf. §§ QS, 85. § 95. Suhalternation (Subaltematio) is tbe passing over from the whole sphere of the subject-notion to a part of it, and conversely from a part to tbe wliole. By Subalternation follows : — 1. From the truth of the universal categorical judgment (S a P or S e P) the truth of the corresponding par- ticular (S i P or S o P), but not conversely the former Ifrom the latter. ' Cf. Trendelenburg, Log. Unters. 2nd ed. i. 343; 3rd ed. 351: r The settled product of causality is substance ; ' 2nd ed. i. 355 ; ii. 2i6 j 3rd ed. i. 363 ; ii. 270. i ? i if I s 326 § 96. (Qualitative) Aeqtiipollence. \ 96. (Qualitative) Aequipollcnce. 327 2. From the falsehood of the particular the falsehood of the universal judgment, but not conversely the former from the latter. The proof for the correctness of the first consequence lies in this, that the subalternate judgment repeats an assertion lying in the subalternant, and only asserts as true what is already recognised to be true. The second consequence is founded on this, that, if the universal judgment be true, then (according to 1) the par- ticular is true, which contradicts the hypothesis. The converse consequences, however, are not universally valid, because the truth of the particular judgment may co-exist along with the falsehood of the universal, be- cause it may happen that Some S are and others are not P. The same laws hold good of hypothetical judgments (If A is, B always is— At least in some cases, if a is, b is also). The consequence from the universal to the particular is called consequentia or conclusio ad subaliernatam pro- positionem, that from the particular to the universal con- clusio ad subalternantem. The older logicians were accustomed to express the law of consequence, ad subaltern atam propositionem, in the dictum de omni et uuUo, in the following way : ' quidquid de omnibus valet, valet etiam de quibusdam et singulis ; quidquid de nuUo valet, nee de quibusdam vel singuHs valet.' § 96. By (qualitative) Aequipollence (aequipoUentia) modern Logic means the agreement in sense of two judgments of dififerent Quality. This agreement becomes possible by the fact that the predicate notions stand m the relation of contradictory opposition to each other. Consequence per aequipoUentiam proceeds from the judgment : All S are P, to the judgment : No S is not-P, and vice versa; from the judgment; No S is P, to the judgment : Every S is a Not-P, and vice versa ; from the judgment: Some S are P, to the judgment; Some S are not Not-P, and vice versa ; and lastly from the judgment ; Some S are not P, to the judgment ; Some S are Not-P, and vice versa. The proof for the correctness of these consequences lies in the relation of the spheres, according to which every S, which does not fall within the sphere of P, is outside it, and must lie in the sphere of Not-P ; and whatever falls within this cannot lie within the sphere of P. • Every sin contradicts the conscience ; there is no sin which does not contradict the conscience. Nothing sinful is in harmony with the ethical consciousness ; whatever is sinful is not in harmony with the ethical consciousness. The earlier logicians * understand by Itrohvva^ovaai irpo- rdjsis, iudicia aequipoUentia sive convenientia, every kind of equivalent judgments, i.e. those which with material identity are necessarily true or false together because of their form. (Cf. the expression avTiaTps(j)£iv found in Aristotle.^) Kant * and some modern logicians with him will not allow the inferences of Aequipollency to be inferences proper, because there is no consequence, and the judgments remain unchanged even according to form. They are to be looked at only as substitutions of words which denote one and the same notion. But since in Aequipollency the Quality of the judg- * Cf. § 82. * De Interpret, c. xiii. p. 22 A, Iß. ^ Log. ei Jiische, § 47, Rem. M I 328 § 97>.«^ Opposition, §97. Opposition. 29 ment passes over to its opposite, however trivial the change may be which here exists, it evidently concerns the fonn of the judgment itself, and not its mere verbal expression. § 97. Opposition (oppositio) exists between two judg- ments of different Quality and different sense with the same content. By Opposition follows (cf. §§ 71 and 72) :— 1. From the truth of one judgment the falsehood of its contradictory opposite, since according to the axiom of contradiction (§77) judgments opposed contradic- torily cannot both be true ; 2. From the falsehood of a judgment the truth of its contradictory opposite, since according to the axiom of Excluded Third (§78) judgments opposed as contra- dictories cannot both be false ; 3. From the iruth of one judgment the falsehood of the contrary opposite (but not conversely from the false- hood of the one the truth of the other), according to the axiom that judgments opposed as contraries cannot both be true (though both may be false). Otherwise the assertions opposed as contradictories, which (according to § 95) are contained in them and may be deduced by Subalternation, must both be true, and the axiom of Contradiction does not admit this (but their common falsehood includes neither the truth nor the falsehood of assertions which are opposed to each other as contra- dictories) ; 4. From the falsehood of a judgment the truth of its suhcontrary (but not conversely from the truth of the one to the falsehood of the other), according to the axiom, that suhcontrary judgments cannot be both false (but may both be true), because otherwise (according to 2) their contradictory opposites, which stand to each other in the relation of contrary opposition, must both be true, and also (according to 3) cannot both be true. According to 1, there follows by an inference ad contradic- toriam propositionem. From the truth of S a P, the falsehood of S O P From the truth of S e P, the falsehood of S i P From the truth of S i P, the falsehood of S e P From the truth of S O P, the falsehood of S a P. According to 2, there follows by an inference ad contradic- toriam propositionem : — From the falsehood of S a P, the truth of S O P From the falsehood of S e P, the truth of S i P From the falsehood of S i P, the truth of S e P From the falsehood of S O P, the truth of S a P. According to 3, there follows by an inference ad contrariam propositionem : — From the truth of S a P, the falsehood 6f S e P ; From the truth of S P, the falsehood of S a P. Accordino" to 4, there follows by an inference ad subcon* trariam propositionem : — From the falsehood of S i P, the truth of S O P ; From the falsehood of S O P, the truth of S i P. The like consequences hold good in the corresponding hypo- thetical judgments. Although the transformations given in this paragraph are so simple that they seem to need no examples or illustration, yet one may be given to show that attention should be paid to these relations not merely for the sake of logical theory, but also for their practical application, which is not unimportant. The truth of the affirmation is equivalent to the falsehood of I i '1 330 ^97- Opposition, \ 98. Modal Consequence. 331 the negation, and the truth of the negation to the falsehood of the affirmation. Affirmation is opposed to ignorance, inat- tention, or negation. Negation is (according to § 69) only suitable where a motive for affirmation can at least be thought, and more especially where an affirmation has actually been made by others. Hence in the interpretation of an affirmation the sense of the negation must be kept in mind, and in the interpretation of a negation the content and form of its cor- responding affirmation. According to this rule, if Heinrich Düntzer's conjecture^ in Hor. Epod. v. 87, * venena magna,' be accepted, an explanation different from Düntzer's must be given. Düntzer translates: ' Strong . charms may perpetrate intentional transgression ; they cannot change a man's condi- tion.' But the first part of this sentence (if we suppose that Horace expressed these thoughts by these words) is languidly directed against the witches. The negation which in the natural construction refers to the whole of the sentence is opposed to an affirmation made by the witches. They believe that a change in human nature (convertere humanam vicem, the change from hate or indifference to love), unattainable by weaker charms, may be brought about by stronger (venena magna) ; and they believe those charms to be strong (as Dun- tzer remarks) for whose preparation crimes are necessary. But they have not avowed to themselves nor to others the whole nefas ; the fear of the knowledge of the crime still remains to some 'extent, even when the fear of the crime itself has departed ; and so the perpetrators assure themselves and others that the scrupulous distinction between fas and nefas vanishes only in ' more potent ' means, and that in means of that kind fas and nefas are equivalent. They declare : venena magna (ac?) fas nefasque (i.e. venena magna per fas nefasque adhibita) valent convertere humanam vicem ; and the boy whom they threaten denies this assertion. The truth of the negation which he asserts is equivalent to the falsehood of what the witches affirm. 1 rUlol. xxvii. 184. § 98. Modal consequence (consequentia modalis) is change of modality. By modal consequence follows (cf. §^69):— 1. From the validity of the apodictic judgment the validity of the assertorical and of the problematic, and from the validity of the assertorical, that of the pro- blematic judgment; but from the validity of the pro- blematic that of the assertorical and apodictic does not conversely follow, nor from the validity of the asser- torical that of the apodictic ; 2. From the inadmissibility of the problematic judg- ment follows that of the assertorical and apodictic, and from the inadmissibility of the assertorical that of the apodictic judgment; but from the inadmissibility of the apodictic judgment does not follow conversely that of the assertorical and problematic, nor from the inad- missibility of the assertorical that of the problematic judgment. The first consequence depends (in the same way as Subalternation) on the fact that the judgment de- duced only repeats a moment which is contained in the given judgment. Apodictic certainty, when we abstract the reason of the certamty, justifies us in stating the judgment in its assertorical form, as simply true, and therefore still more in attributing to it at least probability. In the same way the immediate cer- tainty which the assertorical judgment expresses, in- cludes probabUity as a moment. On the other hand, the certainty of the higher degree is not conversely con- tained in that of the lower degree. The second consequence rests on this, that where the ■ I I 332 § 9^. Modal Consequence. lower degree of certainty is wanting, the higher must also be absent. On the other hand, it is not to be concluded conversely, that, where the higher degree is not present, the lower must also be absent. Since Modahty treats of the degree of (subjective ) certainty, the terms: validity or admissibility^ and invalidity or inad- missihility, must be used, and the notion of truth or falsehood must not be unconditionally substituted for them. For example, if the assertorical judgment : A is B, is inadmissible, the reason may consist in this, that we have not the (subjective) con- viction of its truth, while the judgment in itself may be true. In this case the problematic judgment : A is perhaps B, may remain thoroughly admissible or valid. But if the assertorical judgment : A is B, is false, then according to the axiom of Ex-cluded Third (§ 78) its contradictory opposite : A is not B, is true ; and if this is once established, the problematic judgment : a is perhaps B, is no longer correct. The same postulate holds good in this relation which is true of the particular judgment, that the assertion of the less (there of some, here o^ perhaps, &c.) is to be understood not in the exclusive sense {only some, only perhaps, &c.), but in the sense of containing the possibility of the greater {at least some, at least perhaps). Analoo-ous laws are valid with reference to objective possi- bility, actuality, and necessity, but their explanation belongs rather to Metaphysics than to Logic. Aristotle has treated of them in his logical writings, especially in De Interp. c. xiii. He finds a difficulty in the question, whether possibility follows from necessity. On the one hand, it appears to do so. For if it were false that what is necessary is possible, it must be true that what is necessary is impossible, which is absurd. But on the other hand, it appears that the proposition must also be valid : "What has the possibility to be has also the possibility not to be, and so what is necessary, if it were something pos- sible, would have a possibility both to be and not to be, which is false. Aristotle solves this difficulty by the distinction, that %()(). Mediate Inference, Syllogism and Induction, 333 the notion of the possible is used partly in a sense in which necessity is not excluded {at least possible), in which sense it may be applied to those energies which include the dynamis, partly in a sense which excludes necessity {only possible), in which sense it may be applied to the dynamis which are not energies. In the former sense the necessary is a possible, in the latter it is not. (In reference to possibility in the nar- rower sense, which excludes necessity, Aristotle says ^ that the fii] spEex^crOai, since it denies possibility on both sides equally, finds application not merely where the thing is impossible, but also where it is necessary.) Later logicians, since they appre- hend the judgment of possibility according to the analogy of the particular, and accordingly presuppose the meaning : at least possible, enunciate the rule : ' ab oportere ad esse, ab esse ad posse valet consequentia : a posse ad esse, ab esse ad oportere non valet consequentia.' § 99. Mediate Inference divides into two chief classes : Syllogism in the stricter sense (ratiocinatio, dis- ciirsus, o-uXXoy/o-jOLoV), and Induction (inductio, eTraywyrj), Syllogism in the stricter sense, in its chief forms, is in- ference from the general to the particular or individual, and in all its forms inference proceeding from the general. Induction is inference proceeding from the individual or particular to the general. Inference by Analogy, which proceeds from the individual or parti- cular to a coordinate individual or particular, is a third form distinct from both, though able to be reduced to a combination of the other two. If it is proved universally that only two tangents can be drawn to any conic section from one and the same point, and it is then inferred: The Hyperbola is a conic section, for this proposition holds true of it, the reasoning is a Syllogism. But if, on the contrary, it is first shown of the circle, that from one * Ancdyt. Fv. i. 17. I i 334 \<^^. Mediate Inference. Syllogism and Indue Hon, and the same point only two tangents can be drawn to its cir- cumference, and then the like is inferred of the ellipse, para- bola, hyperbola, and it is concluded : this proposition holds good of all conic sections whatever, the reasoning is an Induction, Kepler and his followers proceeded inductively in the esta- blishment of the laws named after him, for they generalised the truth of the results proved of Mars, and extended them to the other planets. But the converse procedure accomplished by Newton is syllogistic, for he proved, on the ground of the principle of gravitation, that every planet must move round its central body, or rather round the common centre of gravity, in a path which is a conic section, and such that the radius vector sweeps over equal areas of the plane of the orbit in equal times, and that when several bodies move around the same centre of gravity, the squares of their periods must be pro- portional to the cubes of their mean distances ; and he applied these axioms to planets, moons, and comets. The molten con- dition of the interior of the earth is proved inductively from the connection of volcanic phenomena, deductively or syllogis- tically from the process of the earth's formation (probable on astronomical grounds). The Syllogism in reference to its most important and, for positive knowledge, most productive forms, may be called « the inference of subordination'' (with J. Hoppe,' who also calls it * inference by analysis of notions'); Induction (with Hoppe), the ' inference of superordination ;' and inference by Analogy (Hoppe does not recognise Analogy as a special form), ' in- ference of coordination.' ^ ^ Die gesammte Logik, i. Paderborn, 18G8. 2 The remarks made above (§ 84) upon Hoppe's charge of schema- tism in the logical treatment of immediate inferences may be repeated of what he calls the ' schematic and mechanic procedure ' of Syllogistic. If it is supposed that over and above the given judgment we know the particular kind of knowledge involved, the particular kind of union of predicate with subject, and which of the different relations of the pre- dicate with the subject actually exists in the individual case, then of course more may be concluded than is admissible according to the * schematic procedure ; ' but the number of the legitimately presupposed data has been exceeded. § loo. Simple afid Complex Syllogism, etc. 335 The Syllogism has ever experienced much childish trifling at the hands of its advocates, and much perversity from its opponents. But he who fairly compares both, will find the greater misunderstanding on the side of the opponents. Its advocates possess at least a certain degree of acquaintance with the matter, while many of its opponents, with equal ignorance and arrogance, abuse what they do not under- stand. § 100. The syllogism is simple (simplex), when from two judgments, which are different and have a common element, a third judgment is derived. It is composite (compositus), when more than three elements of judg- ments, or more than two judgments, serve to establish the conclusion. The common element mediates the inference, and is accordingly called the middle (medi- ating) notion or middle term (medium, terminus medius, nota intermedia, to jtteVoy, 2^©^ /jtsVo^). It comes, as the name tells, into each of the premises, but not into the conclusion. The given judgments, from which the new one is derived, are called premises (propositiones prae- missae, indicia praemissa, posita, Tr^orda-sic^ roc Trporsivo- [xsvoLf TOL reSsvTOL^ TO, xslfjLsvoL^ also sumptiones, accepti- ones, X75aju,aTa), and the judgment deduced, the conclu- sion (conclusio, indicium conclusum, illatio, (ru[jL7rifia(rixa^ eTTi^opd), The one premise, which contains the sub- ject, or the subordinate propositional member (e.g. the hypothesis) of the conclusion, is called the Miiior Pre- mise (propositio minor, assumptio, tt^oVxtjv}//^) ; the other, which contains the predicate or the superordinate propositional member (the axiom or principal sentence), is called the Major Premise (propositio major, 7v^/x^aa). J. I I I 336 § loo. Simple and Complex Syllogism, etc. The component parts of the syllogism or the members of the judgments contained in it, are comprehended under the name, Elements of the Syllogism (Syllogismi Ele- menta, ra row «TuXXoy/o-jotou (rroip^sTa). The Relation of the syllogism is determined by that of its premises, i.e. the syllogism is copulative, disjunctive, hypothetical, &c., or mixed, according to the form of the premises. If the premises are of different forms, the Relation of the Syllogism should, by preference, be that of the Major Premise. From two judgments, which have nothing in common, no new relation can be established, and no conclusion deduced. If a third follows from two judgments, they must either have a common element, or can receive it by a mere change of form. The latter case exists, when one element of the one judgment is the contradictory opposite of an element of the other. This case can be enumerated among simple syllogisms only if the notion of such syllogism be defined in this way, that every syllogism which is founded on two given judgments inde- pendent of each other, without a third not produced by a mere change of form being brought in, is to be called simple ; and that that only is compound which presupposes more than two judgments given. But in the course of exposition this defini- tion would lead to many mistakes. Several of the rules which svlloffistic must enunciate (e.g. the axiom: ex mere negativis nihil sequitur, cf. § 106.; the statements about the number and form of the valid moods, &c.) would not hold good, and would require to be superseded by others less simple and evident. In internal correctness also this terminology would be inferior to that enunciated in the text of this paragraph. For in the case, when two elements of the two premises stand to each other in the relation of contradictory opposition, the conclusion cannot be reached unless a judgment which follows by aequipollence from one of the given judgments is added in thought. Hence the inference is actually compound, — com- § loi. Syllogism as a Form of Knowledge, etc. 337 pounded, viz. of an immediate consequence and a simple syl- logism. The expressions opo^ and nrpoTaai^ are explained by Aristotle} He also defines the middle notion (to fiiaovy^ The name (TVfnrspaa-fia is often found.» The terms XyjfifjiaTa and i'Tn(f>opd belong to the Stoics. § 101. The possibility of the syllogism as a form of knowledge rests on the hypothesis, that a real conforma- hility to law exists, and can be known, according to the axiom of Sufficient Reason (§81). Perfect knowledge rests on the coincidence of the c:round of knowledo-e with the real cause. Hence that syllogism is most valuable^ in which the mediating part (the middle notion, the middle term), which is the ground of the knowledge of the truth of the conclusion^ also denotes the real cause of its truth. The doctrine stated in this paragraph is the most important in the whole of syllogistic. The decision of its most important question of debate depends on the reference in the syllogism to a real conformability to law. Is the syllogism a mean to knowledge, and is it to be set side by side with the notion and judgment as a form equally correct in this sense, or is syllo- gistic procedure to be reckoned a mere combination of notions, which may perhaps serve to give greater clearness to the knowledge we already possess in an undeveloped way, and j may have some worth for the purpose of communicating our knowledge to others ? If the conviction of the universally valid truth of the premises is not founded on the presupposition of a real conformability to law, but is first reached by com- parison of all individual cases, — then it is evident that those cases which are asserted in the conclusion must also be included in the cases compared, that the truth of the conclusion must aheady be established ere the truth of the premises can be ' Anal. Pri. i. 1. 2 n^jj j ^ 3 Jbid. i. 9. Z I J 338 § loi. Syllogism as a Form of Knowledge, Its Relation to the Real Reign of Law. 339 recognised, and that we really fall into the fallacy of the Circle when we attempt again to deduce the conclusion from the premises. This last deduction can, at most, have the value of a ^deciphering of our notes' (Mill), and can serve only to recall to our recollection, to make clear, or to communicate to others. And in fact, syllogistic does no more in many cases. For example, if the syllogism is enunciated: Every body describing an elliptical orbit round our Sun is of itself a dark body ; Vesta is a body describing an elliptical orbit round our Sun ; therefore Vesta is in itself a dark body,— it is evident that I can recognise the universal validity of the premises only when I know that Vesta belongs to the bodies describing an elliptical orbit round our Sun, and that it possesses no light of its own. So little can I know the truth of the conclusion from the truth of the premises, that, on the contrary, the conviction of the truth of the first premise must be founded on the pre- viously established conviction of the truth of the conclusion, and that if the conclusion is shown to be uncertain or false, the first premise shares the same fate. The proposition, that all planets are always seen within the zodiac (which is true of all the planets known to the ancients) loses its apparently universal validity, so soon as any one is found (among the asteroids) which passes beyond the zodiac. It cannot be inferred from the general proposition, as if this proposition were established jneviously to and independent of a complete enumeration ot the particulars, that there can be no planet which passes beyond these limits. The planet Fallas actually passes beyond them. But all cases are not of the same kind. So far as a definite conformability to law can be established with reference to any relation to be explained, the universal may be recognised to be true before a thorough investigation of the sum total ot all the individuals, and therefore the truth of the individual> can be arrived at from its truth by syllogistic deduction. Foi example, since Newton's time we can know that the laws ol Kepler have universal validity, without first testing then application to all planets and satellites, and Avhenever a ne^v body of this kind is discovered, those laws may be syllogis- tically applied to it with perfect assurance. The certainty oi the laws derived from the principle of gravitation is so firmly established, that when the observed orbit of Uranus appeared to contradict them, this observation did not raise an objection to their certainty; it rather justified the inference of the presence of some planet hitherto unobserved, and afiecting this orbit, — an inference which led to the discovery of Neptune. In this way, in all cases in which our thinking rests on the foundation of a definitely known real conformability to law, the syllogism is a completely correct form of knowledge, to which we owe valuable extensions of science. If the middle term in a syllogism which makes a real addition to our knowledge is the expression of the real cause, it must not be forgotten that the real cause can only accomplish the effect in combination Avith the corresponding external conditions. For example, in the inference ; What lengthens the pendulum increases the times of its swing ; Heat lengthens the pendulum, and so increases the times of its swing, — the lengthening of the pendulum by heat is the real cause of the increase of the time of its swing, but is so only because of the attraction of the earth and the motion of its parts according to the laws of the case. Cf. § 69, and § 81, upon the combi- nation in every cause of the (internal) ground and (external) conditions. Aristotle expresses the doctnne stated in this paragraph with perfect distinctness when he demands that the middle term must express the real cause :^ to fjusp yap aXnov to fjuso-op. Aristotle does not here ' trace the real back to the formal,' as Drobisch says,'^ but conversely gives depth to the formal by showing its reference to the real. For although the exi)ression quoted admits of two meanings, because both subject and l)redicate have the definite article, and the sentence is re- ciprocal, only one meaning corresponds to the context. In order to be sure of existence, says Aristotle, and in order to recognise essence, we must have a middle term. If we have this, we know the cause, and have found Avith it what was * Anal. Post ii. 2, 90 a, 6. ^ Loj. Pref. 2nd ed. p. xi. z 2 i'l M i 340 10 1. Syllogism as a Form of Kfiow ledge. especially sought, and what we must seek ; for the certainty of the (real) cause evidently ensures the certainty of the existence. And the meaning of our proposition is : The signi- ficance of the middle term lies in this, that it corresponds to the cause.^ The opposite thought: The essence of the ahiov lies in this, that it is the middle term of an inference, would not correspond to the context. For from the propositions : the alriov ensures the existence, and : the essence of the ahiov lies in this, that it is the middle term of an inference, what Aristotle wishes to prove, that whenever we have the middle term the existence is ensured, would not follow. It would be a fallacious universal affirmative syllogism in the thinl figure. Waitz says in his Commentary i^ ' Quum omnis quaestio iam in eo versetur, ut rei subiectae naturam sivc causam, per quam res ipsa existat vel ob quam aliud quid de ea praedicetur, exploremus, quam quidem causam terminus medius exprhnere debet: The examples, which Aristotle adduces here and in other passages, show that he does not mean to resolve the real into the formal, but to comprehend the form in its relation to the content. The real dvr^^pa^is of the earth between the sun and the moon is the ainov of the eclipse of the moon. Now it is evident that the essence of that real position of heavenly bodies with regard to each other docs not lie in this, that it is the middle term of a syllogism, but on the contrary, the essence of the middle term lies in this, that it denotes the real cause. (An opaque body which comes between a luminary and a body, which, dark in itself, is light by means of the other, causes an eclipse of the latter. The earth is an opaque body, which at certain times comes between the luminary, the sun, and the moon which is dark in itself and made luminous by the sun. Hence at certain times the earth causes an eclipse of the moon.) In the same sense Aristotle teaches^ that the four 1 This does not conflict with what Aristotle says {Ancd. Post. ii. 12, init.): to yap ^iinov u'trior. Becoming and having become, &c., luivc the same mean ; but the mean is the cause, — therefore they have the Bjune cause. /^s Relation to the Real Reign of Law. 341 2 Ad Anal. Post. ii. 2, 380. C. XI. metaphysical alrlai : Essence, Condition, Moving Cause, and Final Cause, are all denoted by the middle term, and are to be so denoted, not because they are all reduced to a single formal reference, and their real metaphysical character de- stroyed, but, on the contrary, because the real reference of the metaphysical alriaL is represented in the middle term. Aristotle remarks,^ that in what actually happens, there is partly a strong causal necessity and universality, but partly only an cos eirl TO TToXVf and adds : tow Br) tolgvtcou avdycrj kol to fjbscrov 6>s sirl 70 TToXv eliai. The nature of the middle term is evidently determined by the nature of the case, the ' formal' by the 'real,' and not conversely. The Aristotelian postulate, that (human) thinking must conform to existence, proceeds also upon this. It was reserved for a modern philosopher, Kant, despairing, in consequence of so many failures made by dog- matic philosophers, of establishing a knowledge of ' things-in- themselves,' to grasp the converse principle, that the real (the world of phenomena) must adapt itself to the forms of our human capacities of knowledge, and accordingly to attempt to * trace the real back to the formal.' Aristotle admits that there are also syllogisms, in which the actual cause is not appre- hended, and that the effect, because it falls within sense-per- ception and is therefore able to be known by us, serves for the middle term, and that we infer back from this to what causes. Wc may do this when the effect can have one cause only, and the judgment, in which the causal-nexus is thought, is there- fore to be converted simply — avria-Tpecpov.^ He refers the fol- lowing example to this last case : What does not twinkle is near ; the planets do not twinkle, therefore they are near. But syllo- gisms of this kind are of less value and are not valid in the most strictly scientific manner. The scientific or apodictic syllogism must derive the conclusion from the true and proper cause.'^ ^ c. xii. pr. fin. ^ Anal. Pr, i. 13. ^ Anal. Post. i. 2, 6, and passim. Drobisch says in the third edition of his Logic J p. 170, that the Aristotelian axiom, ro aiTLov to fiiaov, nppears to have the meaning, that when the syllogism is applied to real f'hjects, the middle notion has the meaning of cause, or the cause is 342 § loi. Syllogism as a Form of Knowledge. lis Relalion lo Ike Real Reign of Law. 343 In so far as the true and proper ground of a thing lies in its essence {ovaia or rt 'sari), to this extent the syllogism rests upon the essence,^ and since the definition gives the essence, syllo- gistic knowledge stands in the most intimate reciprocal relation to knowledge by definitions, in spite of their undeniable dif- ference. The definition is the principle of the syllogism in so far as it supplies the major premise, and the syllogism leads to definition in so far as its middle notion reveals the essence in the cause. ^ Later logicians, and among them the Stoics, neglected to refer the middle term to the real cause, and syllogistic thinking generally to the real conformability to law, and confined their attention too exclusively to the easier technical parts of the Aristotelian syllogistic. Hence we need not wonder that the Sceptics of antiquity combated the syllogistic procedure hi general by the assertion, which has often been repeated in modern times, that the premises so far from being able to establish the truth of the conclusion, presuppose it. Sextus Empiricus^ says that the major premise can only be made certain by induction, and that induction presupposes a com- plete testing of every individual case; for a single negative instance (the crocodile moves not the under, but the upper iaw) can destroy the truth of the universal proposition (all animals move the under jaw). On the other hand, if the test- infr has completely included every individual member, we known by it, hut not that it is the cause. It seems to me that, ac- cording to Aristotlo, the middle notion (is not, but) expresses the real cause and corresponds to -it, tliat the cause is recognised by it. But I cannot appropriate the expression that the middle term, in its application to the real, receives the meaning of cause. Since the middle term brings the real cause (independent of it and existing before it), or as Drobisch says, the ' chief cause,' within our knowledge, it follows that in a syllogism of this kind the * formal,' or the manner of knowing, is conditioned by the ' real,' or the objective causal relation. This holds good also in mathematical inferences. 1 Metaph. vii. 9, § 7, ed. Schw. 2 Anal. Post. i. 8; ii. 3, sqq. ; De Anima, ii. 2, § 1. 3 Pyrrlwii. Hypoiifp. ii. 194 if. , . ar